Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
PLENARY INVITED PAPER
ON A VERY HIGH RATE SENSITIVITY OF CONCRETE FAILURE AT HIGH LOADING RATES AND IMPACT Janusz R. KLEPACZKO Laboratory of Physics and Mechanics of Materials Metz University, Ile du Saulcy, F-57045 Metz, France, e-mail:
[email protected] ABSTRACT During last decades, there has been increasing interest in the effect of high strain rates on mechanical behavior of materials including fracturing of rocks and rock-like materials such as different concretes. The subject of this contribution is on recent results of concrete testing at high strain rates in tension, compression and shear. The so-called pseudo-viscosity of compression failure discovered recently at high strain rates is analyzed. Special attention will be given to the recent results obtained in France, and in particular at Metz University, for dry and wet concrete loaded at different rates in tension. Experimental technique applying wave mechanics will be discussed anew to test brittle materials at high strain rates in tension. This technique is based on the phenomenon of spalling combined with the Hopkinson measuring bar. The results obtained in LPMM-Metz for the tension mode of failure will be compared with the recent results obtained in tension and shear modes at the University of Florida. It has been found that a high "anisotropy" of failure occurs for different modes of failure at high strain rates. The highest rate sensitivity is found in tension and the smallest in compression. The rate sensitivity in the shear mode is closer to the tension case. Clearly, the hydrostatic component of stress affects strongly the failure mechanisms of brittle materials. Finally, a model of failure applicable to short-time loading, which is based on the statistics of Weibul, will be mentioned.
Keywords Concrete, rate sensitivity, failure criteria, dynamic tension, spalling, dynamic compression. PRELIMINARIES Many concrete structures of special application like covers of nuclear reactors, off-shore units, shelters of strategic destination for personnel and equipment, are constructed with a thick reinforced concrete elements, for example slabs, shells, shear walls. Such constructions are susceptible to be subjected to accidents including earthquakes, collisions, impacts or explosions. It is clear that design and optimization of such structures, which are at high risk of being loaded by short time forces, must be accompanied by a precise data bank on dynamic behavior of concrete. During recent decades behavior of concrete in uniaxial compression has been studied at relatively wide range of strain rates, typically from quasi-static rate -lo4 I/s to high strain
2
Janusz R. KLEPACZKO
rate -lo3 11s. However, this is not the case when compared to dynamic behavior of concrete in tension where experimental data are very limited because existing experimental techniques will not allow for reaching in most cases the maximum strain rate of 30 Us. Indeed, very few experimental methods permitted to exceed the strain rate limit of 10 Us. Among those few experiments, the early one based on wave effects causing a spall failure, that can be also called the "Stress-Wave Technique", [l-31, can be mentioned. In those methods a compression longitudinal elastic wave generated on one side of relatively long bar is reflected at the free end as a tension one causing failure by spalling. The first publication on concrete spalling was reported in [2]. A compression incident wave is usually generated by explosives or by mechanical impact on to the incident side of the bar. This technique permits to attain a strain rate of about 20 Us, [4,5]. The range of strain rates of the same order as in the "Stress-Wave Techniques" can be obtained by different adaptations into tension the Kolsky apparatus more commonly called the Split Hopkinson Pressure Bar (SHPB), [ 6 ] .One of a more recent arrangement of the Kolsky apparatus to test concrete in tension is loading of the incident bar by impact tension using a falling mass, such setup has been constructed by the Delft University of Technology, [7]. Another direct adaptation of SHPB to tension is application of the Brasilian specimen placed between the incident and transmitter bars. Experimental programs on concrete by means of this technique, [8], were conducted recently at strain rate in tension of about 20 Us, [9]. Those low and high strain rate tests in tension on variety of concretes indicate true rate effects on failure for this material with two ranges of strain rate. The first one is characterized by a moderate increase of the failure stress from quasi static rates up to 1.O lls, for example the review published in [lo]. In the second one, the dynamic strength may increase even up to six times of the quasi-static value at strain rate of 20 l/s, [4,11]. For strain rates lower than about 1.O Us, several investigators attribute the rate effects observed to the presence of excess moisture in concrete, [12,13]. The higher strengths in the second region may be due to viscous-type and inertia forces acting on micro-cracks at the macro level or due to dynamic superposition of micro-cracks, [ 151. Nevertheless, the substantial increase of the rate sensitivity of failure in the second region, that is at strain rates higher than 1.O l/s still poses an open question as to physical reasons of this phenomenon. One of many reasons may be related to the inertia of micro-cracking, [ 141, or in parallel a multiple dynamic interaction of many micro-cracks, [ 151. More recently, a set of results has been presented in [ 161 on "mini concrete" failure (small size of aggregate) in tension and compression. Later new results for the same material tested at high strain rates in shear were published in [17]. In order to obtain the shear mode of loading a large diameter SHPB was applied with a special specimen configuration to convert compression into shear. Again, a high rate sensitivity of failure stress was found above strain rate approximately 10.0 Us. Experimental techniques, which are briefly mentioned in the previous part of this paper, have some limitations, specially in case of tension, as to measurements and precision of experimental conditions. Thus a new experimental technique to test dynamic tensile strength of brittle materials has been developed in the Laboratory of Physics and Mechanics of Materials at Metz University, [18]. This experimental technique combines in an efficient way all advantages of Hopkinson bar used as measuring instrument and as device to impose a wave loading onto specimen being in touch with the transmitted side of the bar. The arrangement is discussed briefly in the next part of this paper. The LPMM setup has permitted to conduct a series of spall tests on so called "mini-concrete" MB 50 due to small size of aggregate (maximum diameter 2.0 mm). Experiments were conducted on this concrete in dry (0 % of humidity) and wet conditions (100% humidity) at the range of strain rates very difficult to reach in tension by other experimental techniques, that is from 20 I/s to 120 Us.
-
3
On a v e y high rate sensitiviv of concrete failure at high loading rates and impact
The overall scope of this study is the characterization of mortar or concrete behavior at high strain rates in tension, shear and compression. Experimental results reported in the literature and discussed below indicate for a strong increase of the strength observed at high strain rates in tension shear and compression. The analysis of the relation between the failure stress and the loading time indicates for a delayed fracture. TENSION TEST - EXPERIMENTAL TECHNIQUE
An important limitation for experimental methods of dynamic tension for brittle or quasibrittle materials, which are also heterogeneous, is the effect of wave propagation and wave dispersion in specimens. As to problems related to measurements, a direct determination of small strains on a concrete specimen surface is not so precise. In both cases, like application of strain resistance gages and displacements gages to measure the mean deformation over all specimen length at the instant of failure is also difficult. For example, use of the linear voltage differential transducers (LVDTs), in order to measure the net specimen displacement, shows in addition to inertia effects, some difficulties associated with a band pass of signal conditioners, [7]. Concerning the experimental techniques of dynamic tension test of brittle materials, which are based on the split Hopkinson pressure bar (SHPB) arrangement, it is difficult to find a compromise between the diameter of Hopkinson bars and the specimen size. Both sizes are important because phenomenon of the wave dispersion in bars and specimen limits the maximum strain rate defined as the difference of the two velocities of two specimen faces, [6].A more detailed discussion of those problems obscuring measurements in tension SHB, including wave dispersion, is given in references [ 18,21-271. The principles of the arrangement based on only one Hopkinson bar, which are shown in Fig.1, are as follows: a striker bar which is accelerated by a gas launcher impacts coaxially an instrumented Hopkinson bar in tight contact with a concrete cylindrical specimen. The striker, the bar and the specimen are of the same diameter 40 mm. The lengths are respectively: 120 mm, 1000 mm and 120 mm. The striker and the measuring bar are made of the same hard aluminum alloy 6060-T5 having very close mechanical impedance in comparison to concrete.
ur VO
e
CT5 t.
3 2
y>ccitricii
Mcdwriiig bdr
plolcclllc
Fig. 1 Arrangement for dynamic tensile test by spalling, 51,52 and 53 are SR stations. After impact of the striker on the measuring bar an incident compression wave 01 (t) is generated, this wave propagates along this bar up to the interface bar/specimen. Because a slight difference in the mechanical impedances of the measuring bar and the specimen, the incident wave is partly reflected back as tension wave OR (t) and partly transmitted into the specimen as compressive wave OT (t). This transmitted compressive wave is refldcted from the free end of the specimen as a tension wave. A superposition of the transmitted
4
Janusz R. KLEPACZKO
compression wave into specimen with the reflected tension wave, which propagates in the opposite direction, generates a fast increasing tension stress causing fracture at the specific distance from the specimen free end. Possibility to use different striker lengths (80 mm, 120 mm, 160 mm) and to apply different impact velocities enables to achieve relatively high local loading rates of spalling. However, application of high amplitudes of the incident wave leads to a consecutive multiple spalling, for example Landon and Quiney [2]. In such situation the chronology of spalling is very important. When a multiple spalling occurs only the first one was analyzed (only the first spalling is recorded by the measuring bar). In order to find the chronology of spalling, as well as to observe development of failure, a coupled arrangement of six fast CCD cameras has been applied [ 191. It is important to note that the specimen wave history of loading can be exclusively controlled by the Hopkinson bar data. In order to determine the whole wave history the Hopkinson bar called also the measuring bar has been instrumented with three SR gage stations, Fig.1, with adequate potentiometric circuits and three wide band amplifiers. More details on measurements are given elsewhere [ 181. In order to analyze the experiment the principal objective is reconstitution, with maximum possible precision, the stress impulse CJT (t) transmitted into a concrete specimen. The reconstitution of the transmitted wave OT (t) is based on precise measurements of the incident q(t) and reflected oR(t) waves. The time of the specimen loading is determined by taking into account the geometrical wave dispersion analyzed theoretically elsewhere, [ 18,2 1-27]. On the other hand, it was assumed, because of the small length of the specimen (120 mm), that the theory of one-dimensional wave propagation is sufficiently exact for this case. Starting from the computer files of the compression wave transmitted into specimen in the form GT(t), all process of wave superposition up to failure, which is assumed instantaneous over entire specimen cross section, is simulated numerically by a special program written in the MappIeR framework. The numerical analysis permits for determination of the loading history aF(t) in the specimen cross-section where spalling occurred, the critical time to failure L,and also the local strain rate B =
4 where , ZC is the distance of the failure from the specimen free 4
end. The distance of the cross-section & from the specimen free end where spalling occurred was carefully measured after each experiment. TENSION TEST - EXPERIMENTAL RESULTS A review of experimental techniques applied in tensile testing of concrete and comparison of some results was published in [lo]. The experimental results of the last three decades of the XX Century were collected in the form of the DIF as a function of the logarithm of strain rate in one of the figures in that paper, where the DIF means the Dynamic Intensification factor, defined as the ratio of the current failure stress at specific strain rate to the quasi static failure stress at strain rate Us. It was shown that the rate sensitivity of the failure stress substantially increases as a function of strain rate. The rate effect intensifies at strain rates above approximately 0.1 Us. This review also shown that it is very difficult to test brittle materials, including concrete, at strain rates above -jO Us. Since that time no experimental data were available at strain rates above -10 11s. Strain rate effects in tension on various cementitious materials have been reported in several publications, [8,9,16,17,20,29]. Here, only two sources will be analyzed, that is the results reported in [17] and the data of LPMM-Metz, [18]. In general, it is of interest what kind of law governs the rate-sensitive failure at strain rates above -10 lls. Two
On a very high rate sensitivity of concrete failure at high loading rates and impact
5
approximations given below will be analyzed, the standard definition of the rate sensitivity p and the pseudo-viscosity q. Those two parameters are defined by the equations given below. The standard rate sensitivity p
OF
+ p log
= OFO
(
fo)
and
p=(*)
ai0g.i
when the DIF is introduced equation ( I ) is transformed into the form
)-!
D = 1 + pDlog( where D = a , / a , , and The pseudo-viscosity q
pD=p/O,,,,
and
pD= ( alog8 E)
&=1.0 11s.
when the DIF is introduced equation (3) is transformed into the form
D=1+qD8
and
r].=(%)
a0
(4)
where qD = r ] / a,, . Values of the rate sensitivity p and the pseudo-viscosity q has been analyzed for experimental data given for tension in [8,17]. The standard SHPB arrangement was used together with the specimen splitting technique. The large diameter SHPB loads a disk specimen rotated go", so the load is applied along the specimen diameter. This is so-called "Brasilian Test" applied in dynamics. However, in order to determine the failure stress in tension a hybrid approach must be used by applying numerical analysis along the specimen. It has been confirmed numerically that the stress distribution in the central part of specimen at failure is similar for both the dynamic and quasi-static loading [8]. But because of dense distribution of experimental points obscuring the trend of data the experimental points were reanalyzed by approximation of clusters of two to three points by one mean point. Such procedure resulted in more clear trends to be shown. The reanalyzed results are shown in Fig.2; a - in the form of D(log 8 ) and b - in the form of D( i ). After Fig. 2b the rate sensitivity can be determined only at strain rates higher than -5.0 11s. The same is for determination of the pseudo-viscosity qo after points of Fig.2b. Simply, the transition strain rate from the low strain rate behavior to the high strain rate behavior is estimated for those experiments as 8, =4.6 11s. Estimated values for both rate sensitivities are p0=2.15 and q~=3.28*10-~ s.
6
Janusz R. KLEPACZKO
FAILURE IN COMPRESSION FOR MORTAR
“ 1 6 0.5
o ! 1 2 3 Log (STRAIN RATE) [lk]
0
Fig.2a
4
FAILURE IN COMPRESSION FOR MORTAR
3 ,
o ! 0
200
400
600
800
1000
STRAIN RATE [lls]
Fig.2b Fig.2 Rate sensitivity of mortar in tension, [8,17], a- logarithmic scale, b- linear scale. The LPMM experimental data obtained up to much higher strain rates intension, -120 Us, for wet mini-concrete MB 50, [18], are shown in Fig.3 together with the data of Fig 2 for mortar, Fig.3a in the logarithmic scale of strain rate and Fig.3b in the linear scale of strain rate, The concrete that has been tested in LPMM (MB 50) had the maximum aggregate size 2.0 mm, relatively high cement dose CPA HP and the ratio of the watedcement was 0.5. The technology in preparation of the concrete was optimized to assure a high level of homogeneity of all components. All doses and mechanical characteristics of the concrete are given in [18]. The stress rates determined by the numerical analyses of the records vary between 800 GPa l/s up to 5000 GPa l/s, corresponding to strain rates varying from -20 l/s to -120 Us.
7
On a very high rate sensitivity of concrete failure at high loading rates and imact
FAILURE IN TENSION FOR MORTAR AND WET CONCRETE 14 m=
12
0
1
0.5
1.5
2
2.5
Log (STRAIN RRATE) [ l l s ]
Fig. 3a FAILURE IN TENSION FOR MORTAR AND WET CONCRETE 14
--
12
r
z
10
$ 8
z
F 6
z
! k 4 0
2
01
0
Fig.3b
100 STRAIN RATE (I/$] 50
150
Fig.3 Rate sensitivity in tension of mortar (shown in Fig.2) and wet concrete MB 50, a- logarithmic scale of strain rate, b- linear scale of strain rate. As shown in Fig. 3 a substantial increase of strength is observed as a function of strain rate. Remembering the quasi-static strength of the wet concrete as CTF = 4.0 MPa the relative increase of strength at high loading rates (DIF) is of the order from 4 to 10 times within that range of strain rates. Another conclusion obtained aAer experimental results reported in the literature, as well as the results reported in this paper, is that above strain rate 1.0 l/s the same trend of steep increase of the tensile strength is found without any sign of saturation at
-
8
Janusz R. KLEPACZKO
-
120 Us. In general, the results for the mortar obtained at much lower rates are fitting very well with the results for the MB 50 wet concrete. However the rate sensitivities PO and T ~ for MB 50 are higher than for the mortar, PD = 9.85 and T ~ = D 8.94*102 s . The same analysis of the test data has been applied for the MB 50 dry concrete. The results for dry MB 50 along with the mortar data are shown in Fig.4, Fig.4a as the logarithmic scale of strain rate and Fig.4b in the linear scale. FAILURE IN TENSION FOR MORTAR AND DRY CONCRETE
-7 -6-
gz 5 -
Pz 43 -LL
E 2 -
0
0.5
1
1.5
2
Log (STRAIN RRATE) [ U s ]
Fig.4a
FAILURE IN TENSION FOR MORTAR AND DRY CONCRETE 8
-7
C 6 2
Q 5 v)
Ez 34
k 2 1
0 0
Fig.4b
20
40
60
80
100
STRAIN RATE [l/s]
Fig.4 Rate sensitivity of mortar in tension (shown in Fig.2) and dry concrete MB 50, a- logarithmic scale of strain rate, b- linear scale of strain rate. As shown in Fig.4 a substantial increase of DIF in observed for the dry concrete. Since the quasi static failure stress is estimated as OF = 5.0 MPa at high strain rate 2 80 U s the DIF increases up to -7.5. Again, above the critical strain rate estimated for tension as 4.6 l/s the
D
9
On a very high rate sensitivity of concrete failure at high loading rates and irnact
rate sensitivities of the dry MB 50 are high, but slightly lower in comparison to the wet concrete, PD = 4.91 and V D = 8.31*10-2 s. Of course, in both cases, that is wet and dry concrete estimation of the rate sensitivities in tension is preliminary. No statistical methods were applied indicating which fit is better, logarithmic or linear. More detailed statistical analyses with higher number of tests should be performed in the future. SHEAR TEST - EXPERIMENTAL RESULTS The only shear tests reported relatively recently are those in [ 171. The same mortar was tested as in tension using the Brasilian specimen, Fig.2. This time the shear strength data were obtained by using a special geometry sp.ecimen loaded in compression by SHPB, [ 171. Those results have been reanalyzed using real experimental points provided by Dr. Ross [29]. The failure stress as a function of strain rate is shown in Fig.5. In FigSa is shown the shear strength as a function of the logarithm of strain rate, and in Fig 5b in the linear scale of strain rate. The rate effects in shear are equally strong as in tension. The transition point from the low rate sensitivity to the high rate sensitivity region is estimated as .kc = 10 l/s, see FigSa. Because of the limited number of tests performed in shear it is difficult to estimate the rate sensitivities. A rough estimation leads to the following values: PD =3.29 and T D =1.39*10-2 s. At strain rate -lo2 l / s the level of DIF is lower, DIF = 4.5 as compared to the tension data for the wet concrete MB 50 (Fig.3), at strain rate -lo2 l/s the DIF is approximately -10. Value of DIF at -lo2 l/s estimated by extrapolation (Fig.4a) for dry MB 50 is -7.5, still higher than for strength of mortar in shear.
FAILURE IN SHEAR FOR MORTAR
4.5 -
- 3.5 -
f
4-
L
0.5
transition point
0
0
FigSa
0.5
1
1.5
Log (STRAIN RATE) [l/s]
2
2.5
10
Janusz R.UEPACZKO
FAILURE IN SHEAR FOR MORTAR
I
o ! 0
Fig.Sb
50
100
150
STRAIN RATE [Ils]
Fig.5 DIF strength of mortar in shear, [ 17,291, a- logarithmic scale of strain rate, b- linear scale. Because of limited number of points, values of the rate sensitivities in shear are approximate. Similarly as for tension, more tests should be performed in shear to apply statistical approach to find which approximation is the most exact. It seems that for higher strain rates the pseudo-viscosity approach (linear approximation) to the rate sensitivity is slightly better. It is interesting to note that transition from low to high strain rate sensitivity occurs for shear at strain rate -10 l/s. This is higher value than for tension -4.6 Us.
COMPRESSION TEST - REVIEW OF EXPERIMENTAL RESULTS Compression test of concrete has been applied probably at the same time when this construction material has been put on the market. In spite of early applications, for very long time compression tests were carried out only in quasi-static conditions. Development of new experimental techniques like fast hydraulic machines and SHPB, with specimen confined or not, make it possible to advance compression testing to high strain rates. Availability of those new devices caused more research and publications in compression testing of mortar, variety of concrete and geologic materials. Typical range of strain rates applied in compression l/s to -lo3 Us, that is nine decimal orders. testing is from In this paper only the high strain rate region will be discussed. The main task is to demonstrate variations in the rate sensitivity of concrete when the loading path (hydrostatic component of stress tensor) changes fi-om tension via shear to compression. Only one paper reports those three paths of loading for the same concrete, [17], so the results reported for compression have been reanalyzed in the same way as for tension and the final result is shown in Fig.6, in Fig.6a in the logarithmic scale of strain rate and in Fig.6b the linear scale is used.
11
C,, .v e y high rate sensitivity of concrete failure at high loading rates and impact FAILURE IN COMPRESSION FOR MORTAR
0
1
2
4
3
Log (STRAIN RATE) [l/s]
Fig.6a FAILURE IN COMPRESSION FOR MORTAR
-=
32.5 -
A
1
I 0.5 - transition point
'
I
0 0
200
400
600
800
1000
STRAIN RATE [Ws]
Fig.6b Fig.6 Rate sensitivity of mortar, reanalyzed after [ 171, a- logarithmic scale, b- linear scale of strain rate. Although the scatter of data is substantial it can be concluded that linear approximations in both cases is acceptable. However, in order to show which fit is the best more tests should be needed to apply statistical analyses. Here a preliminary estimations of the rate sensitivities D 3.28*102 s. It is interesting to note that both yield the following numbers: PO = 2.15 and T ~ = rate sensitivities are much lower than those obtained in tension and shear. On the other hand the transition strain rate to the high rate sensitivity regime is much higher, i.c = 49 l/s. Also the MB 50 wet and dry concrete was tested in compression in LPMM-Metz (fast hydraulic machine) and in Ecole Polytechnique-Palaiseau (SHPB and direct impact). The results for the complete spectrum of strain rate from lo4 11s to -lo3 l/s are published elsewhere [30], here the results has been transformed into DIF and limited only to the high strain rate region. Such transformed data for MB 50 are shown in Fig.7 for the wet state and
12
Janusz R. KLEPACZKO
in Fig.8 for the dry. For the wet and dry MB 50 the quasi-static failure stress was respectively OF = 42 MPa and (TF = 52 MPa. FAILURE IN COMPRESSION WET CONCRETE MB 50
-
- 3.5 = . 3
z
9 2.5
v) v)
$
a
2
2 1.5
8
z 1 U
5 0.5
1
1.5
2
2.5
,
3
Log (STRAIN RATE) [lk]
Fig.7a FAILURE IN COMPRESSION WET CONCRETE MB 50
-
3.5 2 3 G5 2.5 v) 0
E
2
8
1.5
E
l
z
LL
0.5 0
0
Fig.7b
200 400 STRAIN RATE [l/s]
600
Fig.7 Rate sensitivity of wet MB 50 concrete in compression, a- logarithmic scale, b- linear scale of strain rate, the lowest three points - hydraulic machine, squares - direct impact, diamonds - SHPB . In this case the linear fit to the data seem to be slightly better for the logarithmic scale of strain rate, but the limited number of points eliminates statistical approach to show the best fit. The rate sensitivities obtained for this wet MB 50 are as follows: PD = 2.74 and q D = 6.46*10” s. Again those rate sensitivities are much lower than obtained for the same material in tension, see Figs.3 and 4.The transition strain rate is estimated for MB 50 as -90 Us. The same analysis has been performed for the dry MB 5 and the results are shown in Fig.8, in both logarithmic and linear scales of strain rate.
13
On a very high rate sensitivity of concretefailure at high loading rates arid impact FAILURE IN COMPRESSION DRY CONCRETE MB 50
-
2.5
Y
z
2-
2
1.5 -
=8
1-
Q rn
. . =. ... . #
E
8
4
.=e
z
I.0.5 0
01 I
1.5
2
2.5
3
Log (STRAIN RATE) [lls]
Fig.8a
FAILURE IN COMPRESSION DRY CONCRETE MB 50
-- 2.5 :2
E! rn
8
1.5
f8 l
t
z
5 0.5
[transition]
0
0 0
Fig.8b
200
400
600
800
STRAIN RATE [ l l s ]
Fig.8 Rate sensitivity of dry MB 50 in compression, a - logarithmic scale, b - linear scale od strain rate, the lowest points (diamonds) - direct impact, squares - SHPB. The results for the dry MB 50 are very similar as for the wet concrete. The linear approximations are equally possible for both cases. The rate sensitivities for the dry MB 5 are: PO = 1.63 and T ~ =D 2.4*10-3s. As expected those values are lower than obtained for the wet concrete. An enhanced rate sensitivity of failure by the water content in concrete is relatively well documented in the low strain rate range. The result reported here is relatively new. The effect of the water content can be measured by the ratio of the rate sensitivities for wet and dry concretes, Rp = POW/ POD and R,= ~ D /W~ D ,D in the case of MB 50 those ratios are: Rp = 1.68 and R, = 2.69. The effect of the water content is quite substantial in compression. On the other hand the same ratios can be obtained for MB 50 tested in tension. After values of the rate sensitivities given for tension failure by spalling in the previous part of this paper the
14
Janusz R.KLEPACZKO
ratios of the rate sensitivities are: Rp = 2.01 and R,,= 1.08. The effect of the water content is also present in tension failure. Because availability of experimental data for mortars and concrete from different sources some of those results are shown and discussed in the next part of this paper. The main reason is to gather more results in order to find a range of rate sensitivities for different materials from different sources. The absolute values of the pseudo-viscosity q will be only analyzed here. The first example is estimation of the pseudo-viscosity for mortar of different maturity, 28 days and 6 months [14]. The failure stress of mortar versus strain rate in the linear scale of strain rate is shown in
Fig.9 Rate effects and pseudo-viscosity for mortar of two maturity periods, [14]. Another example is shown in Fig.10 in the form of reanalyzed data obtained in compression (SHPB) and reported in [31]. The chart shown in Fig.10 is in the form GF (i). MAXIMUM STRESS VS STRAIN RATE
180
z
I6O 140 -
::120 Y
5
3
9
-
-
100-
806040-
20
Mortar (Giorgia Tech.)
0
200
400
600
800
1000
1200
1400
1600
STRAIN RATE [lh]
Fig.10 Reanalyzed data for mortar reported in [3 11.
1800
On a very high rate sensitivity of concretefailure at high loading rates and impact
15
For both cases shown in Figs.9 and 10 relatively good fit to the points is obtained in the linear scales of failure stress and strain rate, indicating that for this wide range of strain rates the absolute value of the pseudo-viscosity q is a reliable measure of the rate sensitivity of mortars and concrete in compression. These data, and also other sources, were used to compare the pseudo-viscosity for different materials (coal, mortar and concrete), this comparison is given in Table 1 .
Coal Coal
3.03 4/29
ofo- z***
Mortar Mortar Mortar
4.52 4.39 3.35
ofm- 28 days
Mortar Mortar
4.27 5.95
of,,,- 28 days of,,,- 6 months
Mortar
8.63
of,,,- no maturity
Concrete (dry) 12.48 Concrete (wet) 21.14
ofm
Klepaczko (1982)
-Z Tianxi et al. (1983)
of,,,- 2 months of,,,- 3 months Klepaczko ( 1990)
Zhou (1 999)
ofm- more than 28 days Gary and of,,,- more than 28 days, Klepaczko (1996)
of,,,- more than 28 days Brara and Concrete (wet) 87.1 (spa11 tension) Klepaczko (1999) * Note qo = 3 q a . ** I direction parallel to the bedding plane. 45' direction inclined 45' to the bedding plane. *** Z - direction is perpendicular to the bedding plane.
I
Table 1 shows that the order'of the pseudo-viscosity q is comparable for di ferent rock-like .values l of q. materials, including coal. In general the MB 50 concrete shows relatively hi $ Also a substantial increase of q for tension in comparison to compression is obvious. An interesting effect of aggregate on the rate sensitivity in compression has been reported in [Malvern]. The compression test data reported in [Malvern] (SHPB) has been reannlyzed
16
Janusz R. KLEPACZKO
for four different concretes and the results are shown in Figs.11 and 12. Although number of points was limited the statistical analyses by linear regression were performed in order to more precisely compare the differences of the rate sensitivity q for those concretes. The regression coefficients are given in figures as well as in Table 2. It is clear that the rate sensitivity to failure may vary when the strength parameters of aggregate change. The correlation coefficient is found to be around 0.9. This is not the value indicating for a perfect MAXIMUM STRESS VS STRAIN RATE
-0.95031 Andesite aggregate
E
Seattle gravel aggregate
04 0
20
60
40
80
120
100
140
STRAIN RATE [ l l s ]
Fig. 1 1 Rate sensitivity of two concretes with different aggregates, reanalyzed data after [ 111, triangles represent the best fit. MAXIMUM STRESS VS STRAIN RATE 300
-P
250
)-l
Limestone aggregate
200 v) v)
Lu
g
150
5
9
E
lcon.0.90161 Solite Lightweight aggregate
loo
50
04 0
20
40
60
80
loo
120
STRAIN RATE [lls]
Fig. 12 Rate sensitivity of two concretes with different aggregates, reanalyzed after [ 1 I], extreme triangles represent the best fit. fit when the correlation coefficient should be close to 1.0. However, for relatively small range
On a very high rate sensitivity of concretefailure at high loading rates and impact
17
of strain rates applied, maximum strain rate -120 l/s, the correlations indicate that the linear approximation is acceptable for the purpose of comparison. The figures as well as Table 2 indicate that different kinds of aggregates may change not only the stress level of failure but also the rate sensitivity. It is interesting to note that a stronger aggregate increases the rate sensitivity. Since it is believed that the main source of the rate sensitivity in concrete, rocks and ceramics are processes related to micro-cracking inertia and its mutual interaction a stronger aggregate will slower those processes. The rate sensitivities found for those concretes are much higher, 35.0 [Pa*s]*104 < q < 116 [Pa*s]*104 that those obtained for mortars, 3.4 [Pa*s]*104 < q < 6.0 [Pa*s]*IO4 . Mortars have larger contact surface per unit volume between quartz grains and matrix so the probability of cracking on the meso-level is higher. TABLE 2 VALUES OF PSEUDO-VISCOSITY q DETERMINED FROM EXPERIMENTAL RESULTS, DATA AFTER [ 111
7 = (--)aT U f m
as
Material
Pseudo-Viscosity
[MPU * s]
T - constant temperature
Conditions
Correlation
Seattle Gravel
44.46
13.0
0.9291
Limestone
115.50
13.0
0.9203
34.3 1
9.5
0.9016
Solite Lightweight
The review of the concrete behavior at high strain rates in tension, compression and shear confirmed occurrence of very high rate sensitivities for all types of loading. Although transition from the region of low rate sensitivity to the high rate sensitivity is not abrupt, in general the transition strain rate can be specified practically for all experimental data. It is interesting to note that this transition increases at least one decimal order for compression. GENERAL DISCUSSION AND REMARKS ON MODELING
It is well known that concrete is a multiphase complex material consisting aggregate of various sizes and irregular shape. The aggregate is dispersed and embedded in hardened cement paste. Different imperfections like small voids, interfacial cracks between aggregates and cement matrix, micro-cracks inside the cement paste and small water bubbles are usually
18
Janusz R. KLEPACZKO
found due to manufacturing procedures. In addition, during the hardening period variety of physical and chemical processes occur. This is the main reason why mechanical behavior of concrete is so complex. The multiplicity of factors affecting the mechanical behavior in general, and at high loading rates in particular, may explain many difficulties encountered in attempts to formulate general constitutive models for this material. Variety approaches may be already found in the open literature. It is out of scope of this paper to review all formulations, the most common is application of the framework of rate-dependent plasticity theories with account for compressibility. A promising direction in modelirig of failure end fragmentation of brittle solids is a multiscale approach, [15]. Such models have been developed for ceramics, however, there is no limitation in application of the multi-scale approach to concrete. Here, one model that seems to be applicable to concrete failure in dynamic conditions of loading will be briefly discussed. Since the population of flaws that lead to crack nucleation may be different in tension and in compression the model discussed is limited to damage in tension. The main factor leading to structural failure is assumed to be crack nucleation and growth. Cracks are supposed to emanate from defects and relax the local stress of their surroundings and next to propagate. This process leads finally to formulation of damage in larger volumes and kinetics law. The model predicts transition between single and multiple fragmentation. The nucleation of a crack in brittle materials subjected to quasi-static tension is assumed to be due to existing micro-defects defined by the local failure strength a, (n,). When the equivalent stress a(x,), that is the maximum principal stress, is greater than a,(x,) a crack emanating from the defect leads to the failure of entire structure. The local failure strength is a random function related to the defect spatial distribution within the material. Therefore, the ultimate strength in the model is not deterministic and the failure probability PF can be defined by the Weibull distribution, [32], leading to the "weakest link model". The distribution PF can be represented by the following relations
where ht is the defect density, m is the Weibull modulus, QO and ho are respectively the reference stress and the reference defect density, (SF is the failure stress, that is the maximum equivalent stress in the considered domain, Z,r is the effective volume, surface or length. The microstructure of the undamaged material is approximated in the model by the defect density ht with random spacing. The mean failure stress ow and corresponding standard deviation q d are given by
Note that in the present discussion all relations are given in general form the explicit relations are given in the original publication [ 15). In order to take into account crack nucleation the interaction of nucleated defects and other defects that would nucleate must be analyzed. When a crack nucleates it creates obscuration zone with time where the local stress normal to the crack is decreasing. The defects inside this zone are shielded and do not nucleate. Thus, the total density ht can be split into two parts: the density of broken ht, flaws and the .density of shielded (obscured) flaws h, . The distribution of total flaws within the zone of measure Z is assumed to be modeled by i Poisson point process of intensity ht [o(t)]. New cracks will initiate only if the defect exists inside the considered zone and if does not belonging to the relaxed zone. The time evolutiori
On a very high rate sensitivity of concretefailure at high loading rates and impact
19
of the broken flaws is given by
with hb(0)= h,(O)= 0. For a very high stress or strain rate most of the initial defects nucleate before any significant development of the shield zones, that is
On the contrary, when a very low stress or strain rate is applied, the shielded zone occupies the whole volume and then
z,(t)=, Z
(9)
where n is the space dimension (n = 1 for a line, n = 2 for a surface and n = 3 for a volume). It means that after the first crack nucleation (weakest defect) the further nucleation is stopped due to shielding and the shield zone &(t) occupies the whole volume Z. The initial defect population hl defines both the quasi-static and dynamic failure. The fraction of relaxed zone (9) defines also the rate-dependent damage D(t). Because of those two extreme cases a transition must be assumed between those two processes of failure: the low rate failure and the high rate failure. When the dynamic proportional loading is considered with a constant stress rate d- = d D~i d t the characteristic stress CT,= d-tc can be defined by the characteristic zone of measure Z, containing one flaw that may break at the characteristic time . Consequently, two failure criteria were derived in [15], one in the form of Eq.(6) , for quasi-static cases (one defect triggers failure) and the second given below for dynamic loadings where the ultimate applied stress Ci is related to the local critical stress ccand the Weibull statistics P
The ultimate stress in tension id defined by standard relation
Those closed form solutions were analyzed numerically in [ 15,331 using Monte-Carlo simulations. The result of the simulation for a ceramic is shown in Fig.13. It is interesting to note that the closed form solutions for quasi-static or dynamic regimes, as it is observed in the experiments discussed in this paper, permit to find the point of transition kc = E i., . The transition between single and multiple failures can be estimated as the intersection between the weakest link and the multiple fragmentations, the condition is given by, [ 151
20
Janusz R. KLEPACZKO
---- Weibull law
Multi-scale
Dimensionless volume, Z/Z, 10-5 10-4 10-3 10-2 10-1 1
10’
102
1o3
10
1o4
102
103
1o5
Stress rate (MPdps) Fig.13 Ultimate macroscopic failure stress vs. stress rate predicted by the multi-scale model [15] and Monte-Carlo simulation [33] for a ceramic. The transition does not only depend upon Weibull parameters characteristic of a material but also involves the size of the considered element Z and the applied stress rate & , [15]. It can be concluded after analysis of the multi-sale model that the fragmentation of brittle materials at different rates is a combination of material parameters, size and rate or strain rate. Fig.13 shows that when Z / Z , 2 1 the scatter of the ultimate strength becomes very small. In other words, when the loading rate increases the characteristic scale of fragmentation decreases. In extreme conditions, for example loading by high explosives, high loading rates lead to fragmentation in the form of powder. The model discussed here has not yet been applied for a concrete loaded at different rates but it seems to cover all features observed in experiment. At present stage of development the multi-scale model is derived for tension. It is clear that the hydrostatic component of the stress tensor will change the model variables. HYDROSTATIC COMPONENT AND RATE SENSITIVITY
It is well known that hydrostatic pressure changes mechanical responses of rocks and concrete to different paths of loading. However, it is reported here for the first time that pressure component of the stress tensor changes strain rate sensitivity. This is clearly demonstrated by comparison of figures with experimental data for tension and compression and as well as the values of the rate sensitivities. It is clear that hydrostatic pressure suppress the rate sensitivity. This is shown in Fig.14 where the current levels of failure strength estimated for a hypothetical concrete in the form of points at increasing strain rates is shown versus the stress triaxiality defined as
3ffF
21
On a very high rate sensitivity of concrete failure at high loading rates and impact
Of course, for shear the triaxiality is zero, for tension -1/3 and for compression +1/3 (tension stress here is assumed as negative). The distances on each path represent failure stress OF at increasing rate sensitivities: 1.0; 10; 50 and 100 I/s. For example, the maximum distances for strain rate -lo2 l/s when connected by an iso-line produce a highly anisotropic effect of rate sensitivity for concrete. The rate sensitivity for shear is slightly lower than for tension. This may be caused by the fact that the material separation occurs partly by tension in cement paste because presence of aggregates, but also in some areas a hydrostatic component mainly due to the local inertia may be present. In compression a substantial decrease of the rate sensitivity is found. Within the framework of the multi-scale approach the hydrostatic pressure will not only suppress the micro-cracking but also will move the critical point into higher strain rates. Of course further experimental studies specially in tension and shear and with relatively large number of experiments must be performed in order to find meaningful differences between failure stresses for different paths.
STRAIN RATE EFFECTS ON CONCRETE 1.2
-
SHEAR
TENSION
1 -
0.8 -
0.6 I’ 0.4
points represent increasing strain rate
-0.4
-0.3
-0.2
o.2 -0.1
11
COMPRESSION
0
** 0.1
HYDROSTATIC COMPONENT
Fig. 14 Effect of pressure component on rate sensitivity of hypothetical concrete, increasing distances from 0 represent approximate failure stress at strain rates 1.0, 10, 50 and 100 l/s. Values of the rate sensitivities as well as transition points from single to multiple fragmentation for all three paths can be found from experimental data shown in the schematic form in Fig.15 where the failure stress is drawn versus logarithm of strain rate. The only known experimental results obtained for the same mortar, and presented in the form of Fig. 15, are those reported in [17]. The slopes of approximations by straight lines shown in Fig.15 determine the rate sensitivity PO for tension, shear and compression. Both rate sensitivities, that is values of PO and T ~ D, are presenter for mortar versus the level of triaxiality in Fig.16. This figure is clearly indicating, as already mentioned, a significant effect of stress triaxiality on rate sensitivity. Suppression of both rate sensitivities at increasing pressure is obvious. Because of scatter in original data the rate sensitivity for shear is slightly higher than for tension. A correct trend is observed for the pseudo-viscosity T ~ D. Both rate sensitivities PD and V D , but only for tension and compression, are shown versus triaxiality in Fig.17.
22
Janusz R.KLEPACZKO
TRANSITION OF FAILURE MODES
-6
-4
0
-2
2
4
Log (STRAIN RATE) [ V s ]
Fig.15 Schematic behavior of concrete in tension, shear and compression vs. logarithm of strain rate.
EFFECT OF STRESS TRlXlALlTY ON RATE SENSITIVITY OF MORTAR
'I
0.5 rl "
-0.4
-0.2
I
0
0.2
0.4
STRESS TRlAXlALllY
Fig. 16 Rate sensitivities PD and Y D for mortar vs. stress triaxiality. Figures 16 and 17 confirm existence of the "anisotropy" of rate sensitivity due to the effect of stress triaxiality. A simple explanation lies in the fact that hydrostatic stress component closes micro-cracks and the available density of the micro-cracks to be activated is reduced.
On a very high rate sensitivity of concretefailure at high loading rates and impact
23
EFFECT OF STRESS TRlAXlALlTY ON RATE SENSITIVITY OF MB 50
Y
10 -
I -0.4
n l "
-0.2
I
0
0.2
0.4
STRESS TRlAXlALlTY
Fig.17 Rate sensitivities OD and V D for concrete MB 50 vs. stress triaxiality.
DISCUSSION AND CONCLUSIONS Although it has been shown that rate sensitivity of mortars and concrete substantially increases at strain rates higher than -10 Us it is not clear what is the best approximation. Two rate sensitivities were analyzed, that is the rate sensitivity p and the pseudo-viscosity q. Another definition, related to the rate sensitivity 0, is the logarithmic rate sensitivity m, [30]
Every definition of the rate sensitivity is given in partial differentials so after integration a specific constitutive relation is obtained. Presently it is not possible to suggest the most exact approach because limited sets of experimental data that could be analyzed by statistical means. For example, the multi-scale model based on the Weibull statistics leads to the rate sensitivity p as the best and physically meaningful constant. The other approach based on the cumulative criterion derived in [34] based on the time accumulation of rate-dependent defects leads to the logarithmic rate sensitivity m as the meaningful constant. This criterion is based on some physical considerations, it is assumed that the thermal energy of atoms accompany the failure process, thus the criterion is formulated in the following integral form
24
Janusz R. KLEPACZKO
where ob , t,, and a(t) are the material constants at constant temperature. The constant t,, is the longest time of loading when the failure stress failure stressab , that
OF = (TFO
for & > t,,
OF( t,,
) approaches the quasi-static
. Thus the transition point from low to the high
rate sensitivity is defined. The exponential a depends on the absolute temperature T and is directly related to the activation energy of the material separation AGO with k being the Boltzman constant. When a proportional loading is assumed, that is 0, = E l t ,
the criterion can be written in a simplified and explicit form
where E is the Young’s modulus of the material and i is the local strain rate. The material constants obtained after experiments of spalling for MB 50 concrete are ko = 50 ps, a = 0.912 at ambient temperature T = 300 K and ob =4.2 MPa, [35,37]. For constant strain rate the cumulative criterion (16) predicts the logarithmic rate sensitivity as
m=- 1 l+a With a = 0.912 value of m is close to 1/2 so the spa11 strength increases in proportion to the square root of strain rate, Q, = l”*. The cumulative damagelfailure criterion proposed in [34] has been adopted for concrete in the FE and Discrete Element (DE) simulations with very good results [35]. The logarithmic rate sensitivity can be related to both the rate sensitivity p and the pseudo-viscosity q , the relations are given by
p = -*mF
and
v=-
1 &-(l/(Itlk7)) l+a
Since a + 1 = 2 the pseudo-viscosity can be approximated by
Thus the pseudo-viscosity should decrease with strain rate if the logarithmic rate sensitivity is a true material constant. An exponential proportion of the failure stress to the strain rate, but with the exponent 1/3, was found in the criterion of fragmentation discussed in [36]. This last criterion based on the linear fracture mechanics (with exponent 1/3) underestimates an abrupt increase of tensile failure for MB 50 concrete with strain rate. On the contrary, the cumulative criterion, Eq.( 16), based on the cumulative delay of damage reproduces better the mean value of the slope p = ’OF from Figs. 3a and 4 a . aiogi Main conclusions aRer this study are:
On a very high rate sensitivity of concrete failure at high loading rates and impact i. ii. iii. iv. v.
25
The rate sensitivity of mortars and concretes are very high in tension, shear and compression above strain rate -10 Us; Those rate sensitivities failure stress are not equal and they diminish as a function of increasing triaxiality of stress; The rate sensitivity of wet mortar or concrete is usually higher at high strain rates than for the dry materials; The modeling of quasi-static and dynamic failure based on the Weibull statistics is a promising direction in future application to concrete. Further statistical analyses of experimental data are of great importance in order to establish more exactly the rate sensitivities in tension, shear and compression for one material and to determine effects of the stress triaxiality on the failure stress.
ACKNOWLEDGEMENTS Part of this paper was presented as a seminar at the University of Florida Graduate Engineering & Research Center in Shalimar, FL (May 2002). This work was sponsored (in part) by the Air Force Office of Scientific Research, USAF, under grantkontract number F49620-00-1-0288. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsement, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. REFERENCES 1. Abbott, B. W., and Cornish, R. H., A stress-wave technique for determining the tensile strength of brittle materials, Experimental Mechanics, 1965, pp. 148-153. 2. Landon, J. W. and Quinney, H., Experiment with the pressure Hopkinson bar, Proceedings Royal Society of London, series A : Math. Phys. Sci., A103, 1923, pp. 622-643. 3. Goldsmith, W., Polivka, M. and Yang, T., Dynamic behaviour of concrete, Experimental Mechanics, 6, 1966, pp. 65-79. 4. Mellinger, F. M., Birkimer, D. L., Measurement of Stress and Strain on Cylindrical Test Specimens of Rocks and Concrete Under Impact Loading, Technical report 4-46, U.S. Army Corps of Engineers, Ohio River Division Laboratories, Cincinati, Ohio, 1966. 5. Birkimer, D. L., Critical Normal Fracture Strain of Cement Portland Concrete, Ph.D. Thesis, University of Cincinati, Ohio, 1968. 6. Kolsky, H., An investigation of the mechanical properties of materials at very high rates of loading, Proceedings Physical Society of London, Section B, 62, 1949, pp. 676-704. 7. Rheinhardt, H. W, Kormeling, H. A., Zielinski, A. J., The SHP bar, a versatile tool for impact testing of concrete, Materials and Structures, 19, 1986, pp. 55-63. 8. Ross, C. A., Thomson, P.Y. and Tedesco, J. W., Split Hopkinson pressure bar tests on concrete and mortar in tension and compression, ACI Material Journal, 86, 1989, pp. 475-48 1. 9. Ross, C. A., Tedesco, J. W., and Kuenen, S. T., Effects of strain rate on concrete strength, ACI Materials Journal, 92, 1995, pp. 37-47. 10. Brara, A., Klepaczko, J.R., and Kruszka, L., Tensile testing and modeling of concrete under high loading rates, Proceedings, Brittle Matrix Composites 5 (BMC 5) A.M. Brandt V.C.Li and I.H.Marshall, Eds, Warsaw, Poland, 1997, pp. 281-290.
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Janusz R. kXEPACZK0
11. Malvar, L. J., and Ross C. A., Review of strain rate effects for concrete in tension, ACI Material Journal, 95, 1998, pp. 735-739. 12. Toutlemonde, F., and Rossi, P., Major Parameters governing concrete dynamic behaviour and dynamic failure of concrete structures, DYMAT Journal, 2, 1995, pp. 69-77. 13. Ross, C. A., Jerome, D. M., Tedesco, J. W., and Hughes, M. L., Moisture and strain rate effects on concrete strength, ACI Materials Journal, 93, 1996, pp.293-300 14. Klepaczko, J. R., Behavior of rock-like materials at high strain rates in compression, International Journal of Plasticity, 6, 1990, pp.415-432. 15. Denoual, C., and Hild, F., Dynamic fragmentation of brittle solids: a multi-scale model, European Journal of Mechanics, Nsolids, 21,2002, pp. 105-120. 16. Rheinhardt, W., Strain rate effects on the tensile strength of concrete as predicted by thermodynamic and fracture mechanics models, Proceedings, Cement-based Composites: Strain Rate Effects on Fracture, S.Mindess and S.P.Shah eds, Pittsburgh, Pennsylvania, 64, 1985, pp. 1-12. 17. Schmidt, M. J., Shear strength of concrete under dynamic loads, ASME Pressure Vessel and Piping Conf., Boston MA, 1999, pp.250-258. 18. Klepaczko, J. R., and Brara, A., An experimental method for dynamic tensile testing of concrete by spalling, International Journal of Impact Engineering, 25,2001, pp. 387-409. 19. Faure, L., and Klepaczko, J. R., A Fast Video Setup with CCD Cameras, Technical Report, ISGMP-LPMM, Project GDR 972 “Impact on Materials”, Metz University, France, 1996. 20. Zielinski, A. J., Fracture of Concrete and Mortar Under Uniaxial Impact Tensile Loading, Ph.D. Thesis, Delft University of Technology, Delft University Press, 1982. 21. Franz, C., and Follansbee, P. S., Wave propagation in the split Hopkinson pressure bar, Journal of Engineering Material Technology, 105, 1983, pp. 61-66. 22. Pochhammer, L., On the propagation velocities of small oscillations in an unlimited isotropic circular cylinder, Journal fdr die Reine und Angewandte Mathematik, 81,1876, pp. 324-326 (in German). 23. Chree, C., The equation of an isotopic solid in polar and cylindrical coordinates, their solutions and applications, Cambridge Philosophical Society Transactions, 14, 1889, pp. 250369. 24. Gong, J. C., Malvern, L. E., and Jenkins, D. A., Dispersion investigations in the SHPB, Journal of Engineering Material Technology, 112, 1990, pp. 309-314. 25. Lifhitz, J. M., and Leber, H., Data processing in the SHPB tests, International Journal of Impact Engineering, 15, 1994, pp. 723-733. 26. Zhao, H., and Gary, G., On the use of the SHPB techniques to determine the dynamic behaviour of materials in the range of small strains, International Journal of Solids and Structures, 28, 1996, pp. 1-7. 27. Bacon, C., Separation of waves propagating in elastic or visco-elastic Hopkinson pressure bar with three-dimensional effects, International Journal of Impact Engineering, 22, 1999, pp. 55-69. 28. Weerheijm, J., Concrete Under Impact Tensile Loading and Lateral Compression, Ph. D. Thesis, Delf? University of Technology, Delft University Press, 1996. 29. Ross, C.A., Private communication, June 2002. 30. Klepaczko, J. R., Study of concrete a t high strain rates in tension and compression, fracture criteria and modelling, Proc. Int. Symp. Brittle Matrix Composites 6, Warsaw, 2000, pp 189- 205. 31. Grote, D.L., Park, S.W. and Zhou, M., Experimental characterization of the dynamic failure behavuior of mortar under impact loading, Journal of Applied Physics, 89, 2001, pp.2115-2123.
On a very high rate sensitivity of concrete failure at high loading rates and impact
27
32. Weibull, W., A statistical theory of the strength of materials, Roy. Swedish Inst. Eng. Res., 1939, p. 151. 33. Denoual, C. and Hild, F., A damage model for dynamic fragmentation of brittle solids, Comp. Methods Appl. Mech. Eng. 183,2000, pp. 247-258. 34. Klepaczko, J.R., 1990, Dynamic crack initiation, some experimental methods and modeling, in: Crack Dynamics in Metallic Materials, J.R. Klepaczko. Ed., Springer-Verlag, Vienna-New-York, pp. 428-450. 35. Brara, A., Camborde, F., Klepaczko, J.R. and Mariotti, C., Experimental and numerical study of concrete at high rates in tension, Mech. of Materials, 33, 2001, pp. 33-45. 36. Kipp, M. E., Grady, D. E. and Chen, E. P., Strain rate dependent fracture initiation, International Journal of Fracture, 16, 1980, pp. 471-478. 37. Brara, A., Experimental Study of Dynamic Tension of Concrete via Spalling, Ph.D. Thesis, Laboratory of Physics and Mechanics of Materials, Metz University, France, 1999, (in French).
Proc. Int. Symp. .,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
DESIGN OF ENGINEERED CEMENTITIOUS COMPOSITES (ECC) FOR PROCESSING AND WORKABILITY REQUIREMENTS Gregor FISCHER* Shuxin WANG** Victor C. LI**
* Department of Civil and Environmental Engineering, University of Hawaii 2540 Dole St, Holmes Hall 383, Honolulu, HI 96822, USA email:
[email protected]
** Department of Civil and Environmental Engineering, University of Michigan 2340 Hayward Ave., Ann Arbor, MI 48109, USA email:
[email protected], vcli@,umich.edu
ABSTRACT The design of fiber reinforced cementitious composites (FRCC) is typically governed by their mechanical properties in the hardened state, such as the tensile and compressive strength and strain capacity. The intricacies of processing and workability of FRCC, with fiber volume fractions ranging from 1.5 to 20% depending on the particular composition, are often of secondary importance in small-scale laboratory production. However, the fresh composite properties significantly influence the performance of the composite in the hardened state, often leading to substandard mechanical properties due to non-uniform fiber dispersion or inconsistent compaction. More importantly, the large-scale application of FRCC in practice is often not feasible since special mixing equipment or processing techniques are required to overcome the difficulties associated with processing and workability. In particular, the uniform dispersion of short, randomly oriented fibers in the cementitious matrix at fiber volume fractions of more than 1.5% typically requires forcebased mixing equipment, such as high speed pan mixers, planetary mixers, or so-called omni mixers, which are commercially available at the laboratory scale (5dm3 to 200dm3). These specialized mixers are relatively expensive for large capacities and are rarely on hand in most concrete mixing plants and at construction sites. This paper focuses on the fresh mix design of Engineered Cementitious Composites (ECC), which represent one type of high performance FRCC with strain hardening and multiple cracking behavior. The particular version of ECC described in this study utilizes PVA fibers (dt=39pm, lt=12mm) at a volume fraction of 2%. The presented approach is guided by consideration of the practical requirements of producing cementitious composites at large scale under field conditions. The goal of this study is to design the composite such that mixing can be conducted in a conventional, gravity-based drum mixer while retaining
30
Gregor FISCHER, Shuxin WANG and Victor C. LI
the required workability and mechanical properties observed when mixing in a specialized, small-scale laboratory mixer. A case study is presented for the development of a flowable ECC with selfconsolidating consistency. This paper will present possible approaches to meeting these requirements, including control of the particle size distribution and chemical composition of the cementitious matrix, adjusting the mixing sequence and intervals, and proper utilization of cement types and common chemical admixtures.
Keywords ECC, processing, liquefaction, workability, self-consolidating INTRODUCTION The fresh properties of concrete in general and fiber reinforced concrete in particular are of vital importance for workability in the fresh (plastic) state as well as for the material properties in the hardened state with respect to the stress-strain behavior and durability. Fresh concrete should satisfy requirements pertaining to mixing and transporting, uniformity within and between batches, flow properties, compactability, avoiding segregation during placing and consolidation, and surface finish [I]. In case of fiber reinforced concrete (FRC), the requirements on mixing equipment and mix processing as well as uniformity of the material in particular with respect to fiber dispersion are essential to the application of FRC and its reliable performance in the hardened state. Successful production of FRC hinges on proper fiber dispersion as well as workability and can be carried out by three general methods: 1) The addition of fibers to the cementitious matrix during the mixing process in a conventional, gravity-based drum mixer, which is typically limited to small fiber volume fractions below 1% and is viable for common construction purposes due to the wide availability of the required mixing equipment. However, for most FRC composites, a fiber volume fraction below 1% does not significantly alter the mechanical properties with respect to tensile strength and strain capacity. In method 2), the addition of fibers during the mixing process at moderate fiber volume fraction up to 3% in customized, force-based mixers, such as pan mixers, planetary mixers, or so-called omni-mixers is not practical for large-scale construction purposes and limited to laboratory applications due to the limited availability of large-scale mixing equipment. Similarly, method 3) placing of fibers at large volume fraction up to 20% in the formwork prior to infiltration with cementitious slurry (SIFCON) is not practical since it requires a specialized construction process. Beyond the mixing process, the flowability, compactability, segregation resistance, and surface finish of the FRC,are interrelated parameters as in conventional concrete but are additionally affected by the presence and volume fraction of fibers. While the workability is similar to that of conventional concrete, of FRC with low fiber volume fractions (4%) High Performance FRC composites (HPFRCC) with enhanced mechanical properties in terms of tensile strength and strain capacity typically entail moderate or high fiber volume fractions (>1%), which consequently requires design of the composite fresh properties for adequate workability and reliable performance in the hardened state. In particular for applications of flowable HPFRCC with self-consolidating capabilities, the adjustment of the composite fresh properties is necessary. Previous research on the fresh properties of self-consolidating Engineered Cementitious Composites (ECC), with poly vinyl alcohol (PVA, Vf=2%) [2] and polyethylene (PE, V r l % ) fibers [3] focused on the rheological design by adopting a complementary
Design of Engineered Cementitious Composites (ECC)for processing and ...
31
electrosteric dispersion and stabilization technique to obtain cement pastes with desirable flow properties at constant particle concentrations. This technique involved the optimal combination of superplasticizer (melamine formaldehyde sulfonate, MFS), which acts as an electrostatic dispersant,. with a water-soluble polymer (hydroxypropylmethylcellulose, HPMC), which acts buth as a steric stabilizer and viscosity-enhancing agent [2]. This approach lead to a fresh composite mix (Table 1) with desirable deformability, cohesiveness, and high consistency and is used as a benchmark reference (M-ref) for the work described in this paper. In essence, the combination of polymeric admixtures (MFS and HPMC) is used to limit the flocculation between cement particles with appropriate dispersion (MFS) while achieving stabilization of the cement particles (HPMC), which consequently reduces the shear viscosity of the fresh cement paste and leads to a high deformability (flowability) of the fresh cementitious matrix without gravitational sedimentation (segregation) [2]. Mixing of the cementitious composite was conducted in a high-speed mixer with planetary rotating blade. The deformability of the resulting ECC was determined utilizing a conventional slump test cone and deriving a flowability index r. While the use of HPMC was found beneficial in achieving a flowable ECC mix, it also introduces a relatively large air content in the mix (-20%). This air content consists of small pores (
32
Gregor FISCHER, Sliuxin WANG and Victor C. LI
cement ratio in the previous study was kept constant at ~ 1 ~ 0 . to 4 5achieve a satisfactory first cracking strength as well as fiberlmatrix interfacial bond strength [2], in this study the w/c ratio is in a similar range (0.36-0.45) but is primarily determined and optimized by the targeted liquefaction mechanism. The tensile stress-strain behavior of the composite is consequently verified for a selected candidate mix proportion with optimal workability. In a first step, the dense microstructure of the particle system is achieved in this study by optimizing the particle size distribution of the composite using well-known guidelines for the aggregate gradation of conventional concrete [I]. Due to the small size of the particles governing the workability of the composite in the case of ECC, the particles considered for this ideal particle distribution include cement, mineral admixtures (fly ash), and sand. The particle size distributions of the individual solids used in this study are given in Fig.1. The ideal gradation of particles to produce dense packing and good workability was determined by Fuller and Thompson [4] and can be expressed by
where fd d d,,
= fraction
of particles smaller than d size smaller than D [mm] = maximum particle size [mm].
= particle
A particle gradation close to this ideal distribution provides a dense and stable particle microstructure in the fresh state without the necessity for a viscous, HPMC-enhanced water suspension between the particles. The flocculation (aggregation) of cement particles is intercepted by a strong polyelectrolyte, known as a superplasticizer [ 2 ] . After the optimal combination of solid particles according to the above expression is determined, the necessary amount of water to achieve the transition between solid and fluid state (liquefaction) will be experimentally determined.
1
0.1
10
100
Particle diameter [pm]
Figure 1
Particle size distributions of solids
1000
33
Design of Engineered Cernentitioics Cornposites (ECC)for processing and .. .
Additionally, the cementitious mortar itself must autonomously provide the dispersion of fibers in a gravity-based drum mixer, due to the absence of a mixing blade rotating at high speed. This requires careful fine-tuning of the viscosity of the fresh mortar via the water to solids ratio.
MATRIX COMPOSITION The materials used in this study were Type I cement, Class F fly ash, Class C fly ash, silica sand, water, superplasticizer (MFS), and PVA fibers. The composition of the solid particle system (except fibers) at the given individual distributions (Fig. 1) was determined by fitting the composite particle size distribution to the ideal curve and reducing the deviation (Fig.2) using a conventional spreadsheet program.
K
0 .c
0 ~; -
-
-
_ _ - - ' -
-
-
-
-
-
-
0.1
-
I
1 ___
Figure 2
10
Particle diameter [pm] -
1001
100 ~~
.
Composite particle size distribution
Using this procedure, the mass proportions between the solid ingredients were determined as follows: cement: 1, sand: 0.8, fly ash (F): 0.5, fly ash (C): 0.3. These solids proportions along with the weight ratio of superplasticizer to cement (MFS/C=0.03) were kept constant throughout this study.
MIXING PROCESS AND FIBER DISPERSION The essential part to successfully mix ECC in a regular drum mixer is to maintain a fluid consistency of the cementitious mortar throughout the mixing process. Due to the lack of coarse aggregates, the grinding force and blending effect when the aggregates drop from the top of the drum do not exist in ECC mixing, and the only blending effect is due to internal shear friction within the ECC mortar driven by gravity and rotation of the drum mixer. Therefore, the raw materials feeding rate has to be carefully tuned such that the dry materials can be blended into the mix and be simultaneously dispersed and stabilized by the superplasticizer before flocculating. Meanwhile, excessive water should be prevented during the mixing process, as a flowable but viscous mixture is preferred to convey the dry powders.
34
Gregor FISCHER, Shuxin WANG and Victor C. LI
In practice, the following mixing procedure is adopted. First, sand, fly ash and about one third of the cement are dry mixed for one minute. About eighty percent of the total water is then added. At this point, a fluid consistency and flowable mixture is easy to obtain due to the low content of cement in the mixture. Subsequently, cement.and the remaining water additionally containing the superplasticizer are fed into the drum alternately at a rate not to cause the accumulation of large lumps of cement. In a mortar batch of 250dm3, this process takes 8-10 minutes. Finally, PVA fibers are added. To facilitate fiber dispersion, the fibers are supplied in a bundled form by the manufacturer, such that the fiber bundles can be quickly conveyed by the mortar flow to reach a uniform distribution before the glue that bonds the fiber dissolves to hrther disperse the fiber. Typically, a uniform fiber dispersion can be achieved after 3 minutes mixing time given a proper consistency of the cementitious mortar. CASE STUDY PLOWABLE ECC
The fresh mix characteristics of previous versions of ECC required special mixing equipment, such as a high-speed planetary mixer and were suitable for conventional casting with subsequent vibration to achieve compaction. The initial development of flowable ECC with self-consolidating capabilities was based on optimizing the combination of polymer admixtures. This approach was successful in improving the flow properties of ECC, as determined by a slump test and quantified by the flowability index T=(D:-D:)/D:, where DF is the diameter of the ECC cake after flowing and Do is the diameter of the bottom of the slump cone (20cm). The benchmark reference mix (M-ref) had a flowability index r=12.3 at a relatively high water to cement ratio w/c=0.45 and water to solids ratio w/solids=0.26 (Table 1). Due to the relatively large volume of material required for the slump test, the development of flowable ECC in this study was initially conducted using a small-scale planetary mixer (V=2dm3) and a small flow cone (do=lOcm) commonly used for the preparation and quantification of the flow properties of cementitious mortar. Table 1
Summary of selected mix proportions and fresh mix properties
Design of Engineered Cmentitious Composites (ECC)for processing and ...
35
Using the solids proportions determined based on the ideal particle size distribution (Fig.2), a mix M-1 with w b O . 3 6 and w/solids=0.134 showed a relatively stiff consistency similar to that of conventional cast ECC with a cake diameter after lifting of the small cone of d=l3.5cm. Therefore, the water content for consecutive mixes was incrementally increased to wlc=0.40 in M-4 where the intended liquefaction mechanism was observed. The mix proportions used in M-4 resulted in a stable fresh mix with excellent fiber dispersion and flowability (d=25cm) showing no sign of segregation. The air content of mix M-4 was 5.19'0, which is a substantial reduction from the air content of the reference mix (-20%) and due to the targeted dense particle microstructure and the absence of HPMC. The transition of mix M-4 from the small-scale planetary mixer to the laboratory drum mixer (V=20dm3), however, did not show the desired results. In the drum mixer, the mortar was found too dry, stiff, and not capable of properly dispersing the fibers. This discrepancy may be caused by a lower degree of particle dispersion in the drum mixer as compared to the planetary mixer. Due to the substandard fiber dispersion of M-4 in the drum mixer, a slump test was not carried out. The water content was then increased in mix M-5 to w/c=O.42 and initially mixed at small volume in the planetary mixer. Flow properties of M-5 (d=25cm) were similar to those in M-4 (d=25cm), however, the air content in M-5 was 4.3% and further reduced compared to 5.1YOin M-4. Mix M-5 was then mixed in the laboratory drum mixer and all requirements with respect to workability were met. The particle and fiber dispersion were excellent due to a suitable consistency of the mortar. The slump test resulted in a flowability index P19.25, which is a substantial improvement compared to the benchmark reference (r=12.30). The air content of mix M-5 processed in the drum mixer was confirmed at 4.3%. It is noted that despite a significantly lower water content in M-5 (w/solids=O.158) as compared to that in the benchmark reference mix M-ref (w/solids=0.260), a significantly higher flowability can be achieved. A demonstration of the applicability of this concept in general and mix M-5 in particular was successfully carried out using a conventional 250 liter drum mixer on a construction site.
VERIFICATION OF MECHANICAL PROPERTIES While the primary focus of the study presented in this paper was on the fresh composite properties, the characteristic tensile behavior of ECC in the hardened state must ultimately be confirmed. gr
I Figure 3
Strain (%)
Tensile stress-strain behavior and crack formation in flowable ECC (M-5)
36
Gregor FISCHER, Shuxin WANG and Victor C. L1
Direct tensile tests [5] were conducted on specimens originating from mix M-5 and strain hardening and multiple cracking behavior were confirmed (Fig.3). This particular version of ECC has an ultimate strength of approximately 6MPa at a strain of 4% with an average crack spacing of approximately lmm. CONCLUSIONS An alternative approach to the design of the fresh properties of fiber reinforced engineered cementitious composites has been introduced in this study. The solid particle system of the cementitious matrix consisting of cement, mineral admixtures, and sand with known individual particle size distribution was optimized to achieve a relatively dense microstructure. At a sufficient water content and a certain extent of external disturbance, the cementitious mortar reaches a state of liquefaction, which reduces the mortar viscosity while maintaining a stable consistency without segregation. This concept results in a composite design, which can be mixed in a conventional gravity-based drum mixer, does not require viscosity-enhancing admixtures, has excellent fiber dispersion, superior flowability, and self-compacting capabilities. Strain hardening and multiple cracking behavior of this particular version of ECC in direct tension have been confirmed. REFERENCES 1. Mindess, S., Young, J.F., and Darwin, D., 2003, “Concrete,” 2nded. Pearson Education, Inc., Upper Saddle River, NJ 07458 2. Kong, H.-J., S. Bike, and V.C. Li, “Constitutive Rheological Control to Develop a SelfConsolidating Engineered Cementitious Composite Reinforced with Hydrophilic Poly(viny1 alcohol) Fibers,”J. Cement and Concrete Composites, Vol. 25, 3, pp. 333-341,2003. 3. Kong, H.-J., S. Bike, and V.C. Li, “Development of a Self-compacting Engineered Cementitious Composite Employing Electrosteric DispersiodStabilization,” J. Cement and Concrete Composites, Vol. 2 5 3 , pp. 301-309,2003. 4. Fuller, W.B., and Thompson, S.E., 1907, “The laws of proportioning concrete,” ASCE 59, pp.67-143 5. Li, V. C.; Wu, H. C.; Maalej, M.; Mishra, D. K., “Tensile Behavior of Cement-based Composites with Random Distributed Steel Fibers,” J. Am. Ceram. SOC.,V.79, No.1, 1996, pp. 74-78.
Proc. Int. Symp. ,,BrittleMatri.x Coniposites 7 " A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Puhl.. Warsaw 2003
DRYING SHRINKAGE AND CRACK WIDTH OF ENGINEERED CEMENTITIOUS COMPOSITES (ECC) Martin B. WEIMANN and Victor C. LI The University of Michigan, Ann Arbor, MI, U.S.A. Advanced Civil Engineering Materials Research Laboratory Department of Civil and Environmental Engineering
ABSTRACT Drying shrinkage of an engineered cementitious composites (ECC) leads to eigenstress in the composite when restrained. If the eigenstress is higher than the tensile strength of the composite, crack formation will occur. Due to the engineered design of the composite the crack width is found to be less than 50pm, regardless of the specimen dimensions. From a durability point of view the composite can be considered as an effectively uncracked material. A physical model for the drying shrinkage deformation will be described. It will be demonstrated that at 50% relative humidity or below, the use of a Portland cement with a low alkali content for the ECC matrix reduces the drying shrinkage deformation and the crack width in comparison to an ECC with a normal alkali content cement matrix.
Keywords: drying shrinkage, crack, disjoining pressure, durability, ECC, low alkali cement INTRODUCTION Improvement of the durability of cementitious composites is from an economical and ecological point of view an important issue. An improvement of the durability can be reached with a material which shows a small crack width due to restrained drying shrinkage deformation. In order to achieve this goal it is useful to understand the intrinsic causes of macroscopic drying shrinkage. Moisture exchange of capillary porous cement paste with the environment causes macroscopic deformations of cementitious composites. The microstructure of capillary porous cement paste consists of colloidal CSH-gel particles with at least one dimension of the particles in the range between Inm and Ipm [l]. Different deformation mechanisms operate at this microstructure level depending on the relative humidity (RH). In this paper, we approach the study of drying shrinkage from this microscopic viewpoint. Restrained drying shrinkage deformation of cementitious composites leads to an eigenstress in the material that can cause cracks, if this eigenstress is higher than the tensile strength of the material. In normal concrete or fiber reinforced concrete, the width of shrinkage cracks will depend on the amount of shrinkage and the dimensions of the specimen. The crack width under restrained drying shrinkage of Engineered Cementitious Composite (ECC) investigated here is a material property. This is an outcome of the unique tensile response of ECC. ECC is micromechanically designed [2] with a strain capacity more than 100 times higher than that of a normal concrete. As long as the shrinkage strain remains below the tensile strain capacity, the crack width is a material property independent of the specimen size and shape.
38
Martin B. WEIMAhWand Victor C. LI
A reduction of the drying shrinkage deformation of ECC should lower the crack width. The use of a low alkali content Portland cement (LA-cement) reduces the drying shrinkage compared to a normal alkali content Portland cement (NA-cement) at 50% RH or below. Therefore ECC made with a LA-cement should show a lower crack width compared to ECC made with a NA-cement, at 50% RH or below. The objective of this research is to establish crack width as a material property for ECC under restrained drying condition. It will also be shown that the already small crack width of ECC can be further reduced by the use of LA-cement, at least within a certain humidity range. A clarification of the underlying physical mechanisms of this macroscopic drying shrinkage control of ECC from the microstructural point of view is also part of this research. In the following we will first discuss the physical mechanisms of drying shrinkage, followed by a description of the investigated materials and experiments on free and restrained drying shrinkage. The experimental results and a discussion of them are then presented. Conclusions are drawn in the last section.
REVEEW OF THE PHYSICAL MECHANISMS OF DRYING SHRINKAGE Drying shrinkage in a cementitious material can be attributed to changes in a) surface energy of CSH-gel particles b) disjoining pressure between surfaces of CSH-gel particles, and c) capillary under-pressure [3]. The disjoining pressure defines the force of interaction per unit area of bodies that are separated by a thin parallel interlayer [4], and is a superposition of three forces. These forces are a) an attractive van der Waals force b) a repulsive electrostatic force and c) a repulsive steric force. The steric force may be altered by the introduction of polymers which will not be the focus in this paper. The electrostatic force is influenced by the charge composition ofthe pore solution of the cementitious composite. The importance of the three mechanisms of drying shrinkage varies with the relative humidity. Drying shrinkage for 50% < RH < 100% is caused by an attractive capillary under-pressure which acts simultaneously with a repulsive disjoining pressure [3]. The capillary underpressure leads to a reduction in the pore dimensions of the composite which causes a macroscopic shrinkage deformation. The Laplace equation [ 5 ] describes the under-pressure as a function of the pore radius. The charged surfaces of CSH-gel particles do not coalesce because of the disjoining pressure between the particles. The repulsive disjoining pressure is caused by an electrostatic force between the surfaces of particles which are surrounded by electric charges from the pore solution and by structured water [3]. Structured water is caused by dipole interaction of the water molecules with charged surfaces. The attractive capillary under-pressure acts only in pores which are water saturated. The radius of pores which are empty due to drying depends on the relative humidity. Kelvin’s equation [5] describes the relationship between the radius of the largest water saturated pore as a function of RH. Drying shrinkage for RH < 50% can be described in terms of an attractive capillary underpressure and an attractive van der Waals force in addition to the repulsive part of the disjoining pressure. According to Kelvin’s equation, evaporation of water in pores with a radius smaller than 1.6nm occurs when RH < 50%. It was shown that the smallest pore radius in cement paste is lnm [ 6 ] .(The pore size in ECC has been confirmed to be in the same range as cement paste by mercury intrusion porosimetry measurements.) This means that according to Kelvin’s equation all pores with a radius of lnm are empty at 40% RH. The opposite surfaces of CSH-gel particles can coalesce when the relative humidity reaches 40% due to the
Drying shrinkage and crack width of an Engineered Ceinentitious Composites (ECC)
39
additional attractive van der Waals force which acts between the surfaces. At 40% RH, only adsorbed water on the surfaces of the particles is left. The attractive capillary under-pressure and van der Waals force are no longer responsible for drying shrinkage of RH<40%. Drying shrinkage for RH < 40% is due to a change of surface energy of CSH-gel particles. Evaporation of adsorbed water from surfaces leads to a compression of the particles resulting in a macroscopic shrinkage deformation. The change of the surface energy can be correlated to shrinkage deformation from 40% RH to the dry state (0% RH). The Munich model [6,7] describes hygral deformation as a result of the change in surface energy of CSH-gel particles and disjoining pressure between surfaces of CSH-gel particles in cement paste. In the following we focus on hygral deformation instead of drying shrinkage in order to be able to explain the influence of different pore solutions on the micromechanisms of deformations at changing relative humidity. The concept of hygral deformation can be described as follows. CSH-gel particles in the dry state are under compression due to their surface tension and are held together by chemical and van der Waals bonds. Water adsorption on particles surfaces leads to an expansion of the particles due to surface energy change. For RH > 40% an additional repulsive disjoining pressure act on opposite CSH-gel surfaces which are coalesced due to van der Waals bonds. A release of van der Waals bonds leads to an additional swelling of the cement paste which is superimposed with the swelling of the CSH-gel particles due to surface energy change. The swelling of the cement paste due to moisture uptake causes an expansion of the cementitious composites which can be interpreted as a hygral deformation of the composite. The hygral deformation at a given RH can be computed from the difference between the steady state drying shrinkage value of the dry state and the steady state drying shrinkage value at that RH. The Munich model is adopted here to describe the hygral deformation of ECC: The hygral deformation at 0% < RH < 40% is caused by a change of the surface energy Ay of CSH-gel particles [3]. Bangham [8] describes the hygral deformation &hyg,Surface as a function Ay:
The proportionality constant h was introduced by Hiller [9] for porous materials. h i s a function of the modulus of elasticity, the specific surface area of the porous material, and the density of the nonporous CSH-gel. Ay can be calculated from experimentally determined volume of adsorbed water V at different RH [ 10,11,12]:
R.T 'V(RH) A y ( R H ) = -dP M.A,P(RH)
-j
Here R = universal gas constant, T = absolute temperature, M = mol volume of water, A = specific surface area and P = water vapor partial pressure which depends on RH. RH = 100. P/Ps where P, = saturated water vapor partial pressure. Equation 2 is not valid for water saturated pores because in these pores thermodynamic equilibrium is not attained [ 101. Therefore Ay is not significant for RH > 40%. For RH > 40%, a hygral deformation caused by the disjoining pressure is superimposed onto that due to Ay. The total hygral deformation is
Equation 3 describes the total hygral deformation of cementitious materials for relative humidity's from the dry state (0% I2H) to 100%.
40
Martin B. WEIMANN and Victor C. LI
INFLUENCE OF LA-CEMENT ON DRYING SHRINKAGE In the previous section we noted that the repulsive electrostatic force of the disjoining pressure is influenced by the charge composition of the pore solution. According to the DLVO-theory [ 131 the disjoining pressure depends on the ionic strength of the pore solution and on the surface charge of the colloidal particles. Beltzung et al. [3] investigated the influence of different pore solutions on drying shrinkage of concrete. The DLVO-theory can explain the lower drying shrinkage in a cementitious material made with a LA-cement compared to one with a NA-cement. A cementitious composite has a saturated pore solution of Calciumhydroxid [3]. The amount of divalent ions like Ca2+ dominates the repulsive potential of a double layer compared to monovalent ions [ 131. A reduction in the amount of the monovalent alkalis Na' and K+ leads to an increase of the solubility of Ca2+[3], resulting in a lower repulsive double layer potential. The attractive van der Waals potential is insensitive to the ionic composition of the pore solution [13]. Figure l a shows the repulsive double layer and the attractive van der Waals potentials. A lower repulsive double layer potential during the hydration process at 100% RH leads to a smaller equilibrium distance between the CSH-gel colloids (Fig. Ib). The smaller distance between the gel colloids in a LA-cement will result in a lower macroscopic shrinkage deformation when drying occurs.
7""":
I
\ Double-LayerRepulsion Normal Alkali
,I'
van der Waals Attraction
Low Alkali Content
...
(b)
(a)
Figure. 1: Schematic illustration of total interaction energy as a function of inter-particle distance, adapted from [13] (a) by summing the double-layer repulsion potential and the van der Waals attraction potential and (b) for normal and low alkali content cements at RH 100%
EXPERIMENTS In this research we will investigate an ECC with a normal alkali content (0.9M.-%) Portland cement and an ECC with a low alkali content (0.6M-%) Portland cement. These ECCs are reinforced with 2% by volume of PVA (Polyvinyl Alcohol) fibers. An ECC-Matrix composition with normal alkali content and without fibers will also be investigated. A small amount of HydroxyPropyl-MethylCellulose (HPMC) was added to the ECC-Matrix composition to prevent segregation. Normal concrete is included in these experiments as a control. The mix compositions of the investigated materials are shown in Table 1. Using a uniaxial direct tension test [14], the tensile stress-strain curves of ECC and concrete were determined. The objective of this test in combination with the free drying shrinkage test (described below) is to show that the tensile strain capacity of ECC is higher than the drying
Diyiiig shrinkage and crack width of an Engineered Cernentitious Composites (ECC)
41
shrinkage deformation. This means that the crack width of ECC under restrained drying shrinkage is a material property. The drying shrinkage deformation of concrete is much higher than the tensile strain capacity of concrete implying that the crack width depends on the specimen size and geometry in the case of concrete. Table 1: Mix compositions of the investigated materials (SP = superplasticizer)
Free drying shrinkage measurements were made for all four materials as a function of drying time and RH. Drying shrinkage measurements, with setup shown in Fig. 2a, were conducted based on ASTM C157/C157-99 and ASTM C596-01 [ 151 standards. These measurements clarify the differences in drying shrinkage behavior of the different mixes. In addition, the water mass loss per volume of the specimens was determined in order to calculate the volume content of moisture V, needed to calculate the change of the surface energy at different RH. Specimen
Steel RI
4---+
(a)
(b)
40
Figure 2: Experimental set up: (a) Free drying shrinkage test and (b) Restrained shrinkage ring test. Dimensions in mm.
Measurement of crack width Figure 3: Ring test for determination of the crack width
42
Martin B. WEiMAMVand Victor C. LI
Fourteen specimens for each mix were cast and demoulded after one day. After two days of storage at RH = 100% two specimens of each mix were stored in RH= 93%, 85%, 75%, 66%, 33%, 12% and O%, obtained using oversaturated salt solutions in different desiccators [16,17]. The drying shrinkage deformation and mass loss were measured as a function of drying time until hygral equilibrium was reached. The length change was measured with an accuracy of lpm. The mass loss was measured with an accuracy of lmg. After all specimens had reached hygral equilibrium the specimens stored at 0% RH were dried in an oven at 105C until the mass is constant. After removing from the oven the specimens were allowed to cool down to room temperature in order to measure the hygral length change due to moisture loss. When the specimens reached thermal equilibrium with room temperature the length change and mass loss were determined and considered as values at RH = 0%. In order to investigate the number and width of cracks, the restrained shrinkage ring test [181 was adopted (Fig, 2b). Two specimens of each mix were cast. During casting a thin plastic foil covered cardboard paper cylinder was used as an outer mold which was removed three days after casting. Subsequently, the specimens were exposed to RH = 50%. Drying of the specimen leads to an internal radial pressure in the specimen resulting from the restraint of the hygral deformation by the steel ring. For the dimensions of these specimens, it can be shown that the specimens were subject to an approximately uniaxial tensile stress state during restrained shrinkage. Figure 3 illustrates the measurement of the crack width, determined as an average value for each crack at three different locations as a function of the drying time.
RESULTS & DISCUSSIONS Figure 4 shows the uniaxial tensile stress-strain curve and the crack width for ECC (0.9M.%). For comparison a typical stress-strain curve of a concrete taken from the literature [ 191 is
included. The strain values of the concrete have been expanded to show the curve more clearly. The crack width in the ECC was obtained by monitoring the opening of one of the many multiple cracks as the specimen strain increased. The crack width increases with strain up to about 1% and then stabilizes at a steady state value of about 60pm until fracture localization at ~ 5 . 2 % .
sr.
___.._._ _ . - .
-
- - - Concrete
7
100
-ECC (0.9M.-%) Crack WidthECC (0.9M.-%) --Fit (Crack Width ECC)
O r " " : ' " ' : "
0
I
" " '
2
3 Strain E (YO)
: " ' ' : ' ' 4 5
' 10 6
Figure 4: Tensile stress-strain curve of ECC (0.9M.-%) and concrete. The crack width as a function of tensile strain is also shown for the ECC
Dtying shrinkage and crack width of an Engineered Cernentitious Composites (ECC)
43
Figure 5 shows the calculated change of surface energy according to Eq. 2 for the investigated materials as a function of the relative humidity using the moisture content per volume for the investigated materials measured at 0%, 12% and 33% RH. The dotted lines in Fig. 5 are logarithmic fits to the change of surfaces energy for different RH in the form of Ay = A.ln(RH)+B
(4)
From the experimental data Ay, the values of A and B are determined for each material and reported in Table 2. T
_...__._...--.
..--.**-am ECC (0.9M.-%), (0.6M.-%)
*
ECC-Matrix Concrete -FIT (ECC (0.9M.-%), (0,6M.-%)) .- - FIT (ECC-Matrix) FIT (Concrete)
0
20
40 60 Relative Humidity RH ( O h )
80
I00
Figure 5: Experimental data and theoretical fits of change of surface energy as a function of the relative humidity for the investigated materials Figure 6 plots the hygral deformation of the investigated materials dried to different RH's, calculated from the drying shrinkage data as the difference between the steady state drying shrinkage value in the dry state (0% RH) and the steady state drying shrinkage value at specific RH's. At 100% RH ECC (0.6M.-%) shows a lower hygral deformation due to the lower equilibrium distance between CSH-gel particles (Fig. 1) produced with LA-cement compared to NA-cement. The theoretical hygral deformation curves to be discussed in a later section are also shown in this figure. The measured crack width w as a function of the drying time is shown in Fig. 7. The specimens were exposed to IU-I=50%. 0.4 r
1
2 0.3 -
1
ECC(0.9M.-%)
A
ECC (0.6M.-%)
ECC-Matrix
- ..Equation 1
Concrete
c
O h ' ' 0
'
I
20
6
'
40 60 Relative Humidity RH ("h)
80
,
,
I00
Figure 6 : Experimental data and theoretical curves of hygral deformation as a h c t i o n of the relative humidity for the investigated materials
44
Martin B. WEIMANNand Victor C. LI
. i
-E
A
10.00 :
Concrete -Fit ECC (0.9M.-%) -.- Fit ECC(0.6M.-%) Fit ECC-Matrix -Fit
ECC-Matrix
number of cracks: I0
0.01
+ “ I . {
0
20
40
60 80 Drying Time t (d)
100
120
Figure 7: Crack width development as a function of drying time (at RH=50%) The hygral deformation for the investigated cementitious materials can be described by using the Munich model originally developed for cement paste [6,7]. The expansion of CSH-gel particles is caused by a change of the surface energy of CSH-gel particles and for RH > 40%, due to an additional disjoining pressure between the surfaces of CSH-gel particles. The Munich model originally developed for porous building materials such as brick and concrete [20] is here shown to be applicable to describing the hygral deformation of ECCs. Using Eq. 1 and 3, the total hygral deformation of the investigated materials can be rewritten in the following form: Ehyg,Total = h . ( A . In(RH) + B) + c . (h - ho)2 + d . (h- ho) (5) where c, d are empirical parameters and h, h, are relative humidity’s. The first term is from Eq. 1 and 4. The second and third term represent a second order polynominal fit to the RH dependence of Ehyg,Disjoining-preSsure [20]. Equation 5 is valid for h 2 ho with h,=40. The parametric values h, c and d for the investigated materials shown in Table 2 were obtained by fitting Eq. 5 to the total hygral deformation data reported in Fig. 6. The parametric values of h are on the same order of magnitude as concrete reported in the literature [20].
The average crack width (Fig. 7) in the ECC is almost 20 times smaller compared to the crack width in concrete. A cracked concrete with a crack width smaller than 50pm has been shown to have the same permeability as an uncracked material [21]. From a durability point of view the ECC can be considered an effectively uncracked material. As can be observed in Fig. 6 , the typical drying shrinkage deformations of ECC are lower than 0.3%, so that even a small reduction of the tensile strain has a great influence of the crack width (Fig. 4). This is the reason why an ECC made with a LA-cement shows a lower
Drying slzrinkuge and crack width of an Engineered Cenientitious Composites (ECC)
45
crack width compared to an ECC produced with a NA-cement. Figure 7 shows that the ECC (0.6M.-%) has a crack width of 31pm compare to 46pm for ECC (0.9M.-%). The ECC-Matrix shows a crack width over 5 times higher than the concrete. Clearly, the fibers of the ECC leads to a 100-fold reduction in the crack width compared to the ECCMatrix although the total hygral deformation (100% to 0%) of both is the same. The drying time when the first crack appears shows large differences. For the brittle ECCmatrix the one and only crack appeared after 1 day drying time. The quasi-brittle concrete took seven days of drying before the crack appeared. The first crack for the ductile ECC appeared after four days of drying. These cracks are hardly visible to the naked eyes. An optical microscope is necessary to measure the crack width.
CONCLUSIONS The crack width of ECC under restrained drying shrinkage is a material property and is about 30-5Opm (depending on cement type) at 50% RH for the mix compositions tested. This crack width is below the steady state crack width during strain-hardening and consistent with the crack width at strain value equal to the drying shrinkage strain (Fig. 4). In terms of durability the crack width is more important than the amount of free drying shrinkage, so that ECC should be more durable than concrete despite the higher free drying shrinkage. As a material property, the crack width of ECC is independent of structural dimension or reinforcement ratio. ECC produced with a low alkali content (0.6M.-%) Portland cement leads to a 5% reduction in free drying shrinkage deformation and a 30% lower crack width at 50% RH compared to an ECC produced with a normal alkali content (0.9M.-%) Portland cement. It is desirable to produce ECC with LA-cement in order to improve the durability for RH < 50%. At RH > SO%, the influence of alkali content on free drying shrinkage and crack width of the ECCs investigated is negligible. The hygral deformation of ECC can be explained by an expansion of CSH-gel particles due to a change of surface energy and by a repulsive disjoining pressure for RH > 40%. A reduction of disjoining pressure leads to lower drying shrinkage. Methods to reduce the disjoining pressure include the use of a LA-cement, the use of alkali free mixing water, and the addition of trivalent ions in the concrete composition or any combination of these. The depth of penetration of water and aggressive agents due to capillary suction in a porous material is inversely proportional to the radius of cracks or pores which are assumed as capillary tubes. Treatment of the surface of ECC with a hydrophobic agent may be useful to further minimize penetration of water and aggressive agents into an ECC cover and protect the steel reinforcement from corrosion in reinforced ECC structures. Initial investigations into the use of hydrophobic agents in ECC were conducted by Martinola et al. [22].
ACKNOWLEDGEMENTS Support by the NSF to the ACE-MRL and by the Deutsche Forschungsgemeinschaft (DFG) to M. Weimann to support his studies at the Univ. of Michigan are gratefully acknowledged.
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Martin B. WEIMANN and Victor C. LI
REFERENCES Lide D.R.: “Handbook of Chemistry and Physics 77th,CRC Press, (2002) Li, V.C.: ”Engineered Cementitious Composites-Tailored Composites Through Micromechanical Modeling”, in: Fiber Reinforced Concrete: Present and the Future, Eds. N. Banthia et al., CSCE, Montreal, pp. 64-97, (1998) Beltzung, F., Wittmann, F.H. and Holzer L.: “Influence of Composition of Pore Solution on Drying Shrinkage ”, in: Creep, Shrinkage and Durability Mechanics of Concrete and other Quasi-Brittle Materials, Eds. Ulm, F.-J., Bazant, Z.P. and Wittmann, F.H., Elsevier Science Ltd., pp. 39-48, (2001) Derjaguin, B.V., Rabinovich, Y.I. and Churaev, N.V.: ”Direct Measurement of Molecular Forces ”,Nature, 272,565 1, pp. 3 13-3 18, (1 978) Adamson, A.W.: ”Physical Chemistry of Surfaces”, John Wiley & Sons, Inc., (1997) Wittmann, F.H.: “The Structure of Hardened Cement Paste - A Basis for a Better Understanding of the Materials Properties ”, in: Hydraulic Cement Paste: Their Structure and Properties, Cement and Concrete Ass., pp. 96-1 17, Slough, UK, (1976) Wittmann, F.H.: “Creep and Shrinkage Mechanisms”, in: Creep & Shrinkage in Concrete Structures, Eds. Bazant & Wittmann, Wiley & Sons, pp. 129-16 1, (1982) Bangham, D. and Fakhoury, N.: ”The Translational Motion of Molecules in [he Adsorbed Phase on Solids”, J. Chemical Society, Part I, pp. 1324-1333, (1931) Hiller, K.H.: ”Strength Reduction and Length Changes in Porous Glass Caused by Water Vapor Adsorption ”, Journal of Applied Physics, 35, 5, pp. 1622-1628, (1964) Yates, D.J.C.: ”Molecular Specificily in Physical Adsorption ”, Advances in Catalysis and Related Subjects, 12, pp. 265-312, Academic Press Inc., (1960) Flood, E.A. and Heyding, R.D.: “Stresses and Strains in Ad.sorbent-Adssorbale Sysfems ”, Canadian Journal of Chemistry, 32, pp. 660-682, (1 954) Wittmann, F.H.: “Surface Tension, Shrinkage and Strength of Hardened Cement Paste ”, Materials and Structures, 1,6, pp. 547-552, (1968) Israelachvili, J. N.: “Intermolecular and Surface Forces Acad. Press Inc., (1992) Li, V.C., Wang, S. and Wu. C.: “Tensile Strain-Hardening Behavior of Polyvinyl Alcohol Engineered Cementitious Composites (P K4-ECC) ”, ACI Materials Journal, pp. 483-492, (November-December 2001) American Society for Testing and Materials (US. Code Organization) Greenspan, L.: “Humidity Fixed Points of Binary Salurated Aqueous Solutions ”, J. Research of the NBS - Amer. Physics Chemistry, 81A, 1, (January-February 1977) Schneider, A.: “Diagramme zur Bestimmirng der relativen Lufrfeeuchtigkeit Holz als Roh- und Werkstoff (German Journal), 7, pp. 269-272, (1960) Shah, S.P., Karaguler, M.E. and Sarigaphuti, M.: “EjJect of Shrinkuge-Reducing Admixtures on Restrained Shrinkage Cracking of Concrete ”, ACI Materials Journal. 89, pp. 289-295, (May-June 1992) Wittmann, F.H.: “Structure and Fracture Mechanics of Composite Materials ”, in: Fracture Toughness and Fracture Energy, Eds. H. Mihashi, H. Takahashi and F.H. Wittmann, A.A. Balkema Publishers, pp. 3-12, (1989) Weimann, M.: ‘‘ Vergleichende Stirdie der hygrischen Eigenschafren ausgewaehlter Werhfoffe des Bauwesens ”, Building Materials Reports No. 14, Aedificatio Verlag GmbH, Freiburg, Germany, (2001) Wang, K., Jansen, D.C. and Shah, S.P.: “Permeability Sfu& of Cracked Concrete”, Cement and Concrete Research, 27, 3, pp. 381-393, (1997) Martinola, G., Baeuml, M. & Wittmann F.H.: “ModiJiedECC Applied as an Effective Chloride Barrier ”,Proc., JCI Int’l Workshop on DFRCC, pp. 171- 180, (2002) ’I,
[31
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Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
TIME-DEPENDENT RESPONSE OF HIGHLY DUCTILE FIBER-REINFORCED CEMENT-BASED COMPOSITES Sarah L. BILLINGTON Department of Civil & Environmental Engineering Stanford University Terman 236, Stanford, CA 94305-4020 USA, e-mail: billinaon@,stanford.edu J. Matt ROUSE School of Civil & Environmental Engineering Come11 University 220 Hollister Hall, Ithaca, NY 14853 USA, e-mail:
[email protected]
ABSTRACT The time-dependent response of a ductile fiber-reinforced cementitious composite referred to as Engineered Cementitious Composites (ECC) has been investigated. A series of compressive creep and shrinkage experiments has been conducted on ECC specimens as well as unreinforced specimens (i.e. no fibers). Two different ECC mix designs were investigated along with two corresponding unreinforced mix designs. Experimental results include information about shrinkage, basic creep, drying creep, and creep recovery of the ECC material. It was found that ECC developed greater creep strains than an identical cementitious mix without fibers. Two possible causes for the difference observed in creep response were surface cracking and permeability. Surface cracking was measured and taken into account for an additional assessment of the creep response of the materials. A small set of permeability tests on ECC and unreinforced specimens were also conducted. Keywords: Ductile cement-based composite, engineered cementitious composites, creep, shrinkage, time-dependent response, permeability, fiber-reinforced
INTRODUCTION A class of highly ductile, fiber-reinforced cement-based composites, referred to as Engineered Cementitious Composites (ECC) exhibits a pseudo strain-hardening response and multiple, fine cracking in uniaxial tension. The material is composed of cement, fly ash or silica fume, water, fine sand, and 1.5%-2% by volume of short, randomly distributed polymeric fibers. Background on ECC is given in [I]. ECC is being investigated by the authors for use in structural members that are post-tensioned and thus subjected to considerable long-term compressive loads. It is anticipated that the post-tensioning will cause large creep strains
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because the ECC contains no coarse aggregate. Furthermore, with a 2% fiber volume it is unclear if the fibers will create paths for easier flow of water or if they will control cracking within the matrix to reduce the flow of water through the composite. Pilot creep and shrinkage experiments were conducted to begin assessing the critical, long-term behavior of ECC. Questions raised by the pilot studies led to further investigation of surface cracking and permeability, also reported in part here.
BACKGROUND Creep and shrinkage of fiber-reinforced concrete is a topic of considerable current research and is not yet fully understood. Relatively little research has been conducted on timedependent response of mix designs similar to ECC. Experimental studies on fiber-reinforced concrete have reported conflicting findings on the effect of the fibers on compressive creep and &rinkage. Whereas some researchers have found that long-term compressive creep straiff are higher with (steel and polypropylene) fibers in concrete [2-31, others report that (steel) fibers reduce long-term compressive creep strains [4-51. In ECC, the fibers are considerably finer than steel fibers and traditional polymeric fibers used in fiber-reinforced concrete. The fibers typically used in ECC have a diameter between 8-38 pm. Therefore the microstructure of the cement paste or mortar will be different surrounding these very fine fibers. ECC also exhibits considerably more tensile ductility (up to 3-6% [ 1,6]) and is able to bridge cracks for larger strains than traditional fiber-reinforced concrete. It is expected that cracking from creep and shrinkage will be better controlled by ECC. At the outset of these pilot studies, it was unclear if the fibers would limit long-term deformations through good crack control, or increase long-term deformation through the introduction of porous zones through which water may flow more easily. To assess the time-dependent response of ECC, pilot creep and shrinkage tests were conducted. These pilot tests led to two additional studies, one of surface cracking and one of permeability, to shed light on the creep and shrinkage response measured. The primary motivation for this study was to estimate prestressing losses for applications of ECC to prestressed concrete structures. Therefore the creep results were also compared to two existing models recommended by the American Concrete Institute (ACI) and the ComitC Europeen du Beton (CEB-FIP) for predicting creep in concrete (for lack of well-established models more appropriate for mortars and/or pastes). Selected results of the experiments are presented here. Detailed results and comparisons to the existing models are given in [7].
EXPERIMENTAL PROGRAM Two different mix designs for the ECC were tested along with two corresponding mixes that were identical except they did not contain fibers. The two ECC mixes were similar with the exception that one had a paste matrix consisting of Type I Portland cement, silica fume and water and the other had a mortar matrix of paste as well as fine sand. Mix characteristics are given in Table 1. The fibers used in this study were ultra high molecular weight polyethylene (UHMWPE) fibers that were 6.4 mm long and approximately 8 pm in diameter. These fibers are sold commercially under the trade name Dyneema. The fine aggregate used in the mortar specimens was silica sand uniformly graded between particle si,zes0.3 mm and 0.15 mm.
Time-dependent response of highly ductile fiber-reinforced cement-based composites
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Table 1 Mix Characteristics
1 by volume of cementitious material 2 by total volume of mix
The study presented here includes 12 “triple height” specimens with each specimen representing 3 cylinders stacked end-to-end. Each specimen was nominally 75 mm in diameter by 710 mm in length. Each mix design had a specimen that was tested for creep under a uniform compressive load and a companion specimen that was not loaded so as to be monitored for shrinkage. In addition to the creep and shrinkage specimens of each mix design, four additional fiber-reinforced specimens were sealed with a commercial, paint-on epoxy vapor barrier (Sikagard 62). Of these four additional specimens, two had a paste matrix (one loaded for creep, the other monitored for shrinkage) and two had a mortar matrix (one loaded for creep, the other monitored for shrinkage). The sealed specimens were included in the study to separate basic creep and drying creep by comparing the response of the sealed specimens to that of the unsealed specimens. Table 2 summarizes the characteristics of the 12 specimens.
Table 2: Specimen Summary
1 Naming convention: P-paste matrix, M-mortar matrix, C-creep test, Sh-shrinkage test, F-contains fibers. X-contains no fibers. S-sealed, U-unsealed)
All specimens were cured in a lime-saturated water bath for 14 days (13 days for sealed specimens -after which the coating was applied) prior to testing. After curing, all specimens were stored and monitored in a severe drying environment maintained at approximately 29.5’ C (+/- 3’ C) and roughly 45% (+/- 3%) relative humidity. After 14 days of drying, each creep specimen was loaded to approximately 40% of the 28-day compressive strength of the material (loaded to 25 MPa). Load was maintained by a spring-type creep frame as recommended in ASTM C 512 (Standard Test Method for Creep of Concrete in Compression) and was applied and measured using a 267-kN hydraulic ram and load cell.
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(b) Elevation
c) 1Measurement in progrcss
Figure 1 Specimens and Creep Test Set-up Changes in length in the specimens were monitored over 9 gage locations on the surface of the specimen; 3 equally spaced around the circumference by 3 along the longitudinal axis with 150 mm between them (Fig. 1). Measurements were taken using a hand-held, mechanical strain gage with precision to 1.3 pm. The creep specimens were loaded for 125 days and then unloaded. Measurements were taken throughout the loaded stage and for a minimum of 45 days after unloading. EXPERIMENTAL RESULTS The average of the 9 measurements per specimen for the creep and shrinkage strains is shown for all twelve specimens in Figure 2 (paste specimens on left and mortar specimens on right). The average standard deviation of the 9 strain measurements for all specimens is 14.7 pm. The most striking observation from these results is that the ECC specimens exhibit considerably higher drying shrinkage and creep strains than their corresponding, unreinforced companions. Also clearly evident but much less surprising is that the specimens with a mortar matrix undergo significantly less creep and shrinkage than the corresponding paste specimens. This effect is attributed to the replacement of paste volume with aggregate. It is well known Average of Mortar Specimens
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Figure 2 Resultsfrom compressive creep and shrinkage tests
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Time-dependent response of highly ductile fiber-reinforced cement-based composites
that the aggregate volume can be assumed to behave elastically while the paste phase is the primary agent of creep and shrinkage. Upon unloading, the creep recovery for each unsealed creep specimen ranged from 2533% of the elastic strain recovery. The ECC specimen’s creep recovery-to-elastic recovery ratio averaged 6% lower than that of the unreinforced specimens. The difference between the reinforced and unreinforced response results from elastic strain recovery. The creep recovery strains measured in each ECC specimen were nearly identical to those measured in the corresponding, unreinforced specimens while the elastic strain recovery was slightly higher. From these results, it is not clear that fibers affect creep recovery. Figures 3 and 4 show the basic creep and the drying creep of the ECC specimens with a paste matrix and with a mortar matrix, respectively. Basic creep was taken as the creep strain measured in the sealed specimens. Drying creep was calculated by subtracting the creep strains measured in the sealed specimen from those measured in the unsealed companion specimen for equivalent times. The experiments here were not designed to measure basic and drying creep in the unreinforced materials (i.e. no sealed, unreinforced specimen was fabricated or monitored). The ECC specimen with the paste matrix exhibits similar magnitudes of basic creep and drying creep, with the drying creep reaching a relatively constant value. The ECC specimen with the mortar matrix exhibits higher drying creep than basic creep, with the basic creep reaching a relatively constant value. The drying creep for both ECC specimens is roughly the same, indicating that the major difference in total creep response between the two is due to the basic creep response which is largely affected by sand content in the mix. 0 005
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EFFECT OF SURFACE CRACKING AND PERMEABILITY The differences in total creep and shrinkage among the paste and mortar specimens as explained above was expected due to the replacement of paste with sand in the mortar matrix. As a result, the paste specimens exhibited higher creep and shrinkage than the mortar specimens. The reason for a greater amount of creep and shrinkage in the ECC specimens than in the unreinforced specimens is not as clear. Two hypotheses are considered here. First, there may have been a greater degree of drying shrinkage cracking on the surface of the unreinforced specimens, leading to low values of measured strain. Second, there may be an elevated permeability of the fiber-reinforced specimens. Each hypothesis is examined in more detail next.
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Lo
measured strain, E~ = &,/LO corrected strain, E, = (&,+&)/LO Lo= Initial distance between pins &, measured shortening & = sum of crack openings
Figure 5 Depiction of surface cracking relative to measured deformation
Surface Cracking Surface cracking serves to relieve tensile stresses as the specimen dries and would lead to errantly low values of measured strain. As shown in Figure 5, measured strain would be S,,,/Lo whereas a more accurate strain of the bulk material, as measured on the surface, would be (6,+6,)/Lo. Accounting for cracking in the strain measurements (i.e. “correcting” the measurements) will change the total average shrinkage relationship between the reinforced and unreinforced specimens that was seen in Figure 2. A “correction” such as this is sought here to shed light on the response of these specimens and not to compare these results with values from other tests or materials.
Surface cracking on the four unsealed shrinkage specimens was measured (PShFU, PShXU, MShFU, MShXU) using an x-y-z translation stage and a SOX magnification crack scope with a scale etched on the lens. It is noted that measuring the strain along the centerline of the specimens would also have given useful information, unaffected by surface cracking. However, such internal measurements were not made here. On average, the sum of the crack openings between gage points of the specimens without fibers was over 2.5 times that of the fiber-reinforced specimens. A “correction” was then made to the original shrinkage results (Fig. 2 ) over time. Since the surface crack survey was taken near the end of shrinkage monitoring, the correction was extrapolated back in time to the start of the experiment. This was done by assuming that the crack openings measured at the end of the test developed in time proportionately with the measured deformations (i.e. W6c ult=6m& ud. Using this correction, it was found that the rate of shrinkage was initially higher for the ECC materials, but after some time the unreinforced specimens began to shrink at a faster rate than the ECC specimens [7]. Assuming the method of correction is reasonable, a possible explanation for this behavior is that at early times when surface cracking is minimal, the ECC specimens are slightly more permeable and lose water more readily to the environment. Because the unreinforced specimens experience more extensive surface cracking, their shrinkage rates eventually overtake those of the ECC specimens which have much finer surface cracks. The effect of the shrinkage correction on creep calculations was considered next. To calculate total creep strains, the sum of the total strains measured in the shrinkage specimens and the elastic strains measured upon loading of the creep specimens are normally subtracted from the total strains measured in the creep specimens. The effect of the shrinkage strain correction, by increasing the shrinkage strains, led to lower values of calculated creep (Fig. 6). Here we see
Time-dependent response of highly duetile fiber-reinforced cement-based composites
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Figure 6 Eflect of shrinkage correction on creep response that correcting for surface cracks in fact increases the difference in creep response between the ECC and the unreinforced specimen. It is noted that the presence of surface cracks will also affect the elastic strain measured upon loading. Neglecting the presence of these surface cracks when loading the creep specimens would lead to unexpectedly high measurements of elastic strain. This was, in fact, observed. For example, the apparent elastic modulus of specimen PCFU upon loading was only 10.4 GPa while the average elastic modulus for the strength cylinders of the same mix and age was 12.9 GPa. Clearly surface cracking with this type of test set-up will affect all aspects the time-dependent measurements. Further examination of the importance of surface cracking on determining creep and shrinkage response of ECC is needed.
Permeability A second hypothesis for the differences in behavior between the specimens with and without fibers is permeability. Shrinkage and creep in cementitious materials is highly dependent on the redistribution of water in the gel and loss of water to the environment. The higher the permeability of the cementitious material, the more readily water movement can occur. In ECC, zones of elevated porosity are expected not only between the fine aggregate and the surrounding matrix, but also around the fibers [S]. Therefore it is reasonable to expect an elevated permeability in ECC since the porous zone around the fibers may act as a conduit to promote moisture migration. To begin investigating this possibility, a limited series of permeability tests were conducted. There are numerous experimental methods for determining permeability in cement-based materials [e.g. 9-14]. In this research, falling head permeameter tests were conducted on discs of varying thickness of an unreinforced paste mix and ECC with a paste matrix. The discs were 7.6 cm in diameter and varied in thickness from 0.5 cm to 2.5 cm in increments of roughly 0.5 cm. The discs were fabricated by slicing cylinders and wet-sand-blasting the surfaces of the sliced discs to clean the surfaces while avoiding initial cracking. Each disc was then sealed into a polyvinyl chloride (PVC) tube assembly with a waterproof epoxy sealant and subjected to a roughly 670 cm head of deaerated water. The specimens were cured in a water bath for 14 days prior to testing as were the creep and shrinkage specimens. Measurements were made for 230 days. Permeability was calculated by measuring the head drop, (hl-hz), with time and applying Darcy’s law for a falling head permeameter.
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The test set-up and the results of the tests up to 56 days are shown in Figures 7 and 8, respectively. In Figure 8, PS-PI refers to the paste specimens that were from approximately 2.5 cm (PS) to 0.5 cm (Pl) thick in 0.5 cm intervals. Likewise, E5-El represents the ECC specimens from 2.5 cm to 0.5 cm thick. Note that specimen E4 was cast at the same time as all other specimens, but was 4 weeks older when testing on it began. The steep drop in apparent permeability with time for all specimens is generally attributed to ongoing hydration and densification of the gel structure as the cement continues to cure.
Tape measure (2m longJ
-Top of plug initially Top of plug alhr time, 1
Although the specimens were monitored for 230 days, for clarity in depicting the results, only the first 56 days are shown in Figure 8. Similar trends as seen after 35 days in Figure 8 continued up to 230 days [7]. The average permeability coefficients by the end of the monitoring period (at which point Figure 7 Permeability test set-up the measurements remained relatively constant) calculated for the cement oaste disks were between 0.7-2.4 x lo-'* d s . Thes; values are similar to those reported in [15] but larger than those normally reported such as in [I61 (based on the research of [17]) where permeability of cement paste is reported to be between 1.4-7 x ds.
No significant difference in permeability was found between the ECC and unreinforced specimens of the same thickness. However, the results in Figure 8 suggest a strong dependence on specimen thickness, which is not expected. The ratio of two specimens' permeability at a given time appears to correlate directly with the ratio of their thicknesses. In other words, the flow rate through each specimen is nearly the same regardless of the specimen thickness. 1.OE-I 1
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Time-dependent response of highly ductile fiber-reinforced cement-based composites
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The observed thickness dependence may be attributed to the existence of flaws (e.g. air voids with diameters greater than 1 mm) in the specimens that are of sufficient magnitude relative to the specimen thickness such that the difference in thickness between specimens (0.5 cm) becomes insignificant in this test setup. Such flaws are commonly seen in the casting of these materials. If most of the water that passes through a specimen actually flows through zones where a high density of flaws exists, the permeability calculation will be dominated by this effect. It is noted that extensive testing of the quality of the seals as well as the oil plug’s ability to prevent evaporation was conducted. Curiously, the spacing of the results for the different thicknesses is quite regular. The authors believe that the likelihood of a consistent leak in the set-up in all specimens is much less probable than consistently large material flaws (i.e. entrapped air) in the specimens. It is noted that the “larger-than-normal” permeability values reported in [ 151 that matched the range of those found here were also attributed in part to entrapped air. In neither this nor the study reported in [151 were special casting procedures followed to reduce entrapped air. While this permeability test may yield a reasonable value for the uncracked, structural-scale permeability of this material, the permeability of a micro-scale sample of the material containing no flaws should be much lower. This micro-scale permeability is an important parameter in determining the rate and magnitude of creep and shrinkage. So, while this test was unable to detect significant differences in macro-scale permeability between the unreinforced paste and ECC specimens, it may not disprove the hypothesis that the microscale permeability of the ECC is higher than that of the unreinforced material. Other permeability testing methods [13-141 for this material are being explored by the authors in conjunction with alternate casting procedures. CONCLUSIONS
The conclusions from the research presented herein are: ECC develops greater creep strains than an identical cementitious mix (paste or mortar) without fibers. As expected, small amounts of fine aggregate in ECC can significantly reduce creep and shrinkage of the material. The sum of drying shrinkage crack openings on the surface of unreinforced shrinkage specimens in this study was over 2.5 times that of the corresponding (ECC) specimens with fiber. Surface cracking and the effect of fibers on such cracking must be taken into account when predicting shrinkage behavior. A significant difference in permeability of ECC with a paste matrix and an unreinforced paste matrix was not observed in the falling head permeameter tests conducted here. An observed specimen thickness dependence for measured permeability of ECC and paste specimens is believed to have been caused by relatively large internal flaws (entrapped air) in the specimens. Further time-dependent and permeability testing is necessary to address the many questions raised by these pilot studies.
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ACKNOWLEDGEMENTS This research was sponsored by the Civil Engineering Research Foundation of the American Society of Civil Engineers and in part by The National Science Foundation under Grant CMS9984 127. Material donations from DSM High Performance Fibers are gratefully acknowledged. The authors thank Mr. Tim Bond and Mr. Jonathan Koefman for their careful and creative assistance with the experiments. Fruitful discussions with Prof. George Scherer and Prof. Wilasa Vichit-Vadakan are also gratefully acknowledged. REFERENCES 1. Li, V.C., Reflections on the Research and Development of Engineered Cementitious Composites (ECC),” Proc. JCI Int’l Workshop on Ductile Fiber Reinforced Cementitious Composites - Application and Evaluation (DFRCC-2002), Japan, 2002, pp. 1-21. 2. Balaguru, P.N., Ramakrishnan, R. Properties of Fiber Reinforced Concrete: Workability, Behavior under Long-Term Loading, Air-Void Characteristics. ACI Materials Journal, 1988, 85(3): 189-196. 3. Houde, A., Prezeau, and Roux, R., Creep of Concrete Containing Fibers and Silica Fume. Fiber Reinforced Concrete Properties and Applications, ACI SP-105, American Concrete Institute, Detroit, MI, 1987, pp. 101-118. 4. Mangat, P.S., Azari, M.M., Compression Creep Behavior of Steel Fibre Reinforced Cement Composties. Materiaux et Constructions, 1986, 19(1 13): 361-370. 5. Chem, J.C., Young, C.H., Compressive Creep and Shrinkage of Steel Fibre Reinforced Concrete. International Journal of Cement Composites, 1989, 1l(4): 205-214. 6. Kesner, K.E., Billington, S.L., Douglas, K.S., Cyclic Response of Highly Ductile Fiberreinforced Cement-based Composites. ACI Materials J., to appear, 2003 7. Rouse, J.M., Precast Concrete Bridge Piers using Ductile Fiber-reinforced Cementitious Composites and Unbonded Post-tensioning. PhD Thesis, Cornell U., 2003, in preparation 8. Li, V.C., Chan, Y.W., Effects of Transition Zone Densification on FibedCement Paste Bond Strength Improvement. Advanced Cement Based Material, 1997; 5, pp.’ 8-17. 9. Aldea, C.M., Shah, S.P., Karr, A. Permeability of Cracked Concrete. Materiaux et Constructions, 1999,32, pp. 370-376. 10. Bisaillon, A., Malhotra, V.M., Permeability of Concrete Using a Uniaxial Water-Flow Method, Permeability of Concrete, ACI SP-108. D. Whiting and A. Walitt, eds. American Concrete Institute, Detroit, MI, 1988. 1 1. Janssen, D.J. Laboratory Permeability Measurement. Permeability of Concrete, ACI SP108. D. Whiting and A. Walitt, eds. American Concrete Institute, Detroit, MI, 1988. 12. Schonlin, K., Hilsdorf, H.K., Permeability as a Measure of Potential Durability of Concrete - Development of a Suitable Test Apparatus, Permeability of Concrete, ACI SP108. D. Whiting and A. Walitt, eds. American Concrete Institute, Detroit, MI, 1988. 13. Scherer G., Measuring Permeability of Rigid Materials by a Beam-Bending Method: I, Theory. J. Am. Ceram. SOC.,2000,83(9): 2231-39. 14. Scherer G., Thermal Expansion Kinetics: Method to Measure Permeability of Cementitious Materials: I, Theory. J. Am. Ceram. SOC.,2000, 83(11): 2753-61 15. Banthia, N., Mindess, S. Permeability Measurements of Cement Paste. Proc. Mat. Res. SOC.Symp., 1989, 137,pp. 173-178. 16. Neville, A.M., Properties of Concrete. J. Wiley & Sons, Inc., London, 1996 17. Powers, T.C. Structure and physical properties of hardened Portland cement paste, J. Amer. Ceramic Soc., 1958,41, pp. 1-6.
Proc. Int. Symp. I, Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodliead Publ., Warsaw 2003
PRELIMINARY FINDINGS ON SIZE EFFECT IN ECC STRUCTURAL MEMBERS IN FLEXURE M. LEPECH and V.C. LI The Advanced Civil Engineering Materials Research Laboratory Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI 48 109-2 125
ABSTRACT This article examines the presence of size effect in ECC structurally sized members in flexure. High tensile strain capacity, fracture toughness, and characteristic length make ECC an ideal material for preventing brittle failures responsible for size effects present in concrete members. This study primarily focuses on the structural implications of size effect in ECC and steel reinforced ECC (WECC) members. Three series of beam specimens fabricated of reinforced concrete, ECC, and WECC are tested in flexure to determine the presence and severity of size effect. Preliminary test results of structurally sized members, currently up to 1.4 meters in length, are presented. Correlations between size effect in brittle and quasibrittle materials and material characteristic length are also discussed.
Keywords Engineered Cementitious Composite, ECC, Size Effect, Flexural Strength, Toughness, Characteristic Material Length
INTRODUCTION Current trends in civil engineering are leading towards larger structures with increasing performance demands, however, existing construction materials may not be able to meet these higher requirements. The use of oversized building elements made of high strength concrete to overcome high load requirements in large structural applications illustrates this scenario. While the strength of the building elements, as computed based on material strength, may be adequate, the high brittleness of the members, due to both limited material properties and large member size, may lead to alternative failure modes, ultimately lowering load capacity. The dependence of structural brittleness, specifically upon member size, is of great concern as structural applications grow larger and require higher strength capacity. It is well established that the flexural and shear strength of members made with quasi-brittle materials is not constant with specimen geometry or size, but rather diminishes as specimen size grows larger. This is largely due to fracture failure of the material. This phenomenon, referred to as the size effect, was first quantified in concrete by Hillerborg, et al [ I ] by the definition of the brittleness ratio. This quantity, based on specimen material properties and
58
M.LEPECHand KC. LI
geometry, first captured the effect of specimen size on flexural strength. Further quantification of size effect in concrete was achieved by Bazant et al [2,3] through the introduction of the generalized size effect formula. This non-linear fracture mechanics based theory relates concrete size effect to a characteristic material length, most commonly nominal aggregate size in concrete. Similar results have been found by others, including Carpenteri et al 141. While brittleness is the primary cause for the presence of size effect in most cementitious materials, Engineered Cementitious Composites (ECC), a class of ultra ductile fiber reinforced cementitious composites, exhibit very high fracture energy, up to 34 M/m2 [5]. This high toughness, comparable to the toughness of aluminum, is achievable through the addition of discontinuous short length fibers and a micromechanics based design approach. The design methodology features constituent tailoring and optimization to attain material properties such as high fracture toughness, large tensile strain capacity, and small crack widths. All of these characteristics are achievable due to the formation of closely spaced microcracks, which allow for the formation of large fracture process zones and tensile pseudo-strain hardening of the material. As mentioned, the primary cause for size effect in cementitious materials is brittleness. With a fracture energy roughly 3000 times that of hardened cement paste, the resistance of ECC to fracture failure may lead to a significant reduction or elimination of size effect in ECC when compared to concrete. This effect was demonstrated by Kuneida et a1 [6] through investigation of ECC flexural members ranging from 0.4 meters to 1.2 meters in length. While inconclusive in determining size effect on flexural strength, promising experimental and analytical results were obtained for small-scale ECC members. High fracture energy, in combination with the initial data from Kuneida et al’s small scale element studies, suggest as a minimum a slight reduction of size effect in ECC when compared to plain concrete and quasi-brittle fiber reinforced concrete materials. Analytical work in this regard was performed by Li et a1 [7] on ECC material containing polyethylene fibers. Numerical analysis performed on concrete and various ECC materials demonstrated that in concrete, size effect is dominated by the matrix properties, while for fiber reinforced composites, size effect is increasingly dependent on fiber properties and fiber bridging relationships. As the structural brittleness number decreased for various specimen sizes, the severity of size effect also diminished. For specimens ranging in depth from 2 cm to 10 cm, negligible size effect was seen from ECC while the size effect in concrete specimens of similar size and geometry exhibited a significant reduction in strength. The objective of this study is to clarify experimentally the size effect of structurally sized members made with ECC material. While the value of small-scale studies cannot be underestimated as a basis for larger work, until the phenomenon of size effect is studied in large size components, closer to the scale of building members, its impact on the engineering and construction community cannot be ascertained. This study, and the preliminary results discussed in this article, is focused on the examination of both small and large flexural members fabricated with both un-reinforced and reinforced ECC to examine the effect of size on flexural strength both with and without main reinforcement. The results presented and discussed herein are preliminary and serve as a beginning of larger testing series to follow.
59
Preliminary findings on size effect in ECC structural members in jlexure
EXPERIMENTAL PROCEDURES Materials This study utilized an ECC comprised of 2% by volume poly-vinyl-alcohol (PVA) fibers in random orientation along with standard mortar matrix components, cement, fine aggregate (0.1 mm nominal grain size), water, and various admixtures to improve the fresh properties of the mixture. Mixing proportions are detailed in Table 1. Mechanical properties determined by uniaxial tension testing demonstrated an average first cracking strength of roughly 2.8 MPa at 0.06% strain, an ultimate tensile strength of 4.0 MPa, and a tensile strain capacity of 4.9% (Figure 1). The ductility of this ECC in terms of tensile strain capacity is therefore approximately 500 times that of concrete or normal fiber reinforced concrete (FRC). The ultimate compressive strength of the ECC material was 60 MPa. Table 1. Material Mix Pmportions by Weight for Concrete and ECC
ECC
I
I
1.0
1
0.0
1
1.0
I
0.1
I
0.45
1
I
0.02
5 1
0.0015
I
0.02
I
.I :q : - , ,
0
0
I
2
3
4
5
6
Strain, E (“A)
Figure 1. Tensile Stress-Strain Curve of ECC Material Concrete used in this study for comparison purposes was composed of cement, coarse aggregates (10 mm nominal grain size), fine aggregate, and water. Various admixtures were used as needed to optimize fresh concrete properties. The mix proportions of concrete are also reported in Table 1. While tensile testing was not carried out on concrete specimens, the tensile strength and ultimate strain capacity may be assumed equal to or slightly lower than the first crack strength and first crack strain of ECC, respectively. The compressive strength of concrete used in reference specimens was 45.0 MPa. The longitudinal reinforcement in reinforced ECC specimens consisted of deformed steel reinforcing bars with a yield strength of 410 MPa, yield strain of 0.2%, ultimate strength of 620 MPa, and ultimate strain of approximately 14%. The teinforcing ratio for all specimens was kept constant, however, due to the small size of some specimens, conventional steel reinforcing bars could not be used. In this case, smooth steel rods of comparable strength and strain capacity were used after being mechanically deformed tq more realistically simulate the conventional bars used in larger specimens.
60
M. LEPECHand V.C. LI
Specimen Configuration Three series of flexural specimens were tested in mid- point bending (Figure 2) to determine the load-deflection curve for each specimen, and ultimately the modulus of rupture (MOR). The three series consisted of reference concrete, ECC, and steel reinforced ECC (WECC). Each series consisted of a set of beams with subsequently doubled size for most specimens, e.g. each beam was scaled twice as large as the previous beam. Specimen geometries were sized in two dimensions, beam depth and span, while the beam width was kept constant for all specimens at 0.075m. Test beam sizes are further detailed in Table 2. For RECC specimens, the reinforcement ratio was kept constant at 1.6% for all specimen sizes and at a depth of 85% of overall specimen height. This reinforcement ratio was chosen for convenience as a result of beam dimensions used in this study and standard reinforcing bar sizes. In this article, results from the first four beam sizes for each series are reported. Ultimately, seven beam sizes are planned for testing, up to a beam length of 4.2 meters. P
h = 917
I0.85h
Figure 2. Test Specimen Geometry Table 2. Test Specimen Dimensions and Notation
I
I
Test Series Reinforced Concrete
II I
1
Notation RC-#
Reinforced # : : : : ECC ECC
II
1
TestNumber
2 3 4 5
Span Length, s (meters) 0.175 0.263
I .4
In order to examine the effect of the ductility of ECC on size effect most efficiently, beams were tested at the age of highest material performance. It can be seen from the micromechanical model used in the development of ECC material that a delicate balance exists among PVA fiber properties, the interfacial interaction between fiber and matrix, and the characteristics of the surrounding matrix [8]. While fiber properties are constant, as the matrix matures, the interfacial and matrix fracture properties vary, resulting in a slightly different performance in ECC material at early age. This is most evident in the first three weeks of curing. For testing purposes, optimal performance was assumed to be directly related to ultimate tensile strain capacity. This was determined through direct tension tests of
61
Prelirninatyjttdings on size efect in ECC structirral rrienihers iriflexiire
ECC plate specimens. The development of strain capacity with age is shown in Figure 3. From these tests, the optimal age for testing was determined to be roughly 10 days.
Figure 3. Early Tensile Strain Capacity Development of ECC EXPERIMENTAL RESULTS
Experimental test results are summarized in Table 3. Reported is the modulus of rupture for each specimen. Experimental results from the reinforced concrete control specimens tested are as expected, showing the characteristic size effect seen in other studies of this nature. The failure mode of most concrete specimens was diagonal shear failure, however in the smaller specimens this failure mode was shared by bending failure. These results are similar to those seen by Bazant and Kazemi [9] while studying reinforced concrete beams of similar design.
Series RC- I
MOR (MPa) 19.76 22.92 22.07
Series Ecc-1
RC-2
Not Tested
ECC-2
RC-3
13.88 12.72 15.03
Ec c - 3
MOR (MPa) 12.52 12.84 11.28 15.13 9.88 12.71 16.31 14.45 11.54 12.17
Series R/ ECC- I
WECC-2
R/ECC-3
MOR (MPa) 14.92 16.83 13.49 16.55 12.88 16.79 18.47 18.38 13 14.76
Typical load versus midspan displacement curves for ECC specimens are shown in Figure 4. Similar to the tensile behavior of ECC specimens, the flexural specimens show an elastic pre-
62 M.LEPECHand V.C. LI cracking regime followed by an extensive strain-hardening branch before ultimate failure. This strain hardening is accompanied by the formation of concentrated micro-cracks in beam sections of maximum curvature. After considerable deflection and development of microcracks, a single macro-crack finally localizes and load capacity drops. The failure mode for these specimens is primarily flexural with the macro crack forming near midspan and propagating upward ultimately to specimen failure.
I
31
I
2.5
z2 u 1.5 2
1
15
20
Displacement (mm)
Figure 4. Load vs. Displacement Curves of ECC-3 Specimens
Typical load versus midspan displacement curves for R/ECC are shown in Figure 5. Analogous to ECC beams, the R/ECC specimens exhibit an- initial elastic pre-cracking regime, which is slightly stiffer than seen in ECC beams. This elastic zone is followed by a strain-hardening behavior, together with formation of concentrated micro-cracking in the areas of highest curvature, and therefore maximum moment. While the formation of a localized macro-crack in ECC specimens was indicative of ultimate failure, the localized crack in WECC specimens propagated up to the level of reinforcement. After further load increase, slight yielding of the steel along with hrther extension of the localized macro-crack in shear-like failure was seen up to conclusion of the test at maximum allowable test deflections.
2.5 z
2
0
;1.5
a
0.: 0
0
5
10
I5
20
Displacement (mm)
Figure 5. Load versus Displacement Curves of FUECC-3 Specimens
The overall effect of specimen size on nominal strength is seen when the results from all flexural tests are assembled, as shown in Figure 6. The flexural strength is plotted versus
63
Preliminary findings on size effect in ECC structural members in flexure
non-dimensional specimen depth. The non-dimensional depth is calculated by dividing the specimen depth by width, since the width is kept constant for all specimen sizes. From Figure 6 (a), the presence of size effect in ECC, when compared to reinforced concrete specimens is minimal. While the nominal strength of concrete specimens exhibits a significant decrease through the range of sizes tested, ECC specimens show a remarkably steady nominal strength throughout the range of sizes currently tested. This is also seen in the comparison between reinforced concrete and WECC specimens, shown in Figure 6 (b). While there is a considerable amount of variation in nominal strength among test specimens, even test specimens of the same size, the lack of size effect in this range of beam sizes made of both ECC and R/ECC material is evident.
-
g,
25
0
20
9
&(rinBmed Coaczmk Test Series
;
15
L
5
10
.s
5
2
0
(P
0
0.5
I
1.5
2
Log (dW
(a) Reinforced Concrete and ECC Specimens
I 0
0.5
I
1.5
2
Log WW
(b) Reinforced Concrete and RlECC Specimens Figure 6. Presence of Size Effect in Reinforced Concrete, ECC, and RlECC Specimens
DISCUSSION As mentioned above, the presence of size effect in ECC in comparison to concrete is minimal when dealing with the structurally sized members tested thus far. Over the range of specimens tested, on average, reinforced concrete specimens saw a significant reduction in
64
M.LEPECH and V.C. LI
nominal strength, while ECC and WECC specimens experienced a negligible drop in strength over the same range of beam sizes. While further testing of larger sizes is planned, similar results are anticipated. As structural member sizes increase, the severity of size effect in concrete will continue to become a larger problem, requiring the use of still larger member sizes to overcome lower strength while hrther exacerbating the problem. Through the use of higher toughness materials with less severe, or even negligible size effect, such as ECC and R/ECC, this continual enlarging of member size, or the need for compensating steel reinforcement, can be avoided. Along with the preliminary establishment of the small severity of size effect in ECC material presented in this article, it must be determined whether these results coincide with existing size effect theories. Theories such as those proposed by Bazant or Carpenteri, mentioned eariler, are widely accepted for quasi-brittle materials, however the ductile nature of ECC may violate these theories, thus requiring a modification of existing theory, or complete development of new size effect theory. Current data indicates that a negligible size effect exists in both ECC and WECC flexural members. However, the present set of data is too limited to distinguish whether accepted size effect theories are violated, or this phenomenon is simply not exhibited in the range of sizes yet tested in the laboratory. Current size effect theory is based upon three distinct types of fracture regimes which, when placed in a continuum, form the premise that with increasing size, nominal strength of brittle and quasi-brittle materials diminishes. The three regions which make up the overall size effect law are linear elastic fracture mechanics (LEFM), non-linear elastic fracture mechanics (NLEFM), and strength theory. The combination of these three regions into a continuum is shown in Figure 7. ECC
Reglon
-I --
Clitshon
Mechanics 1
log (ac. 1
Figure 7. Generalized Size Effect Law Normalized by Characteristic Material Length
The portion of size effect theory which predicts the most severe effect is that developed according to LEFM, and corresponding to the largest member sizes. This theory, based upon a Griffith type crack, assumes that in relation to the surrounding material, the fracture process zone surrounding a crack tip is very small, often referred to as having the presence of a Kdominant zone. This allows for the assumption that all fracture energy is consumed at the crack tip, characterizing the material as ideally brittle. From LEFM theory, it can be seen that nominal strength is proportional to the square root of flaw size, and therefore proportional to the square root of specimen size. When plotted on a logarithmic scale, this is characterized by a size effect with a slope of -0.5, as seen in Figure 7.
Prelitninaiyyfindings on size effect in ECC structural members in flexure
65
Moving toward smaller member sizes, or less brittle materials, the size of the process zone at the crack tip becomes more significant in relation to overall member size. This results in a violation of the LEFM assumption that all fracture energy is consumed at the crack tip, and therefore the assumption of an ideally brittle material. Through the application of non-linear fracture mechanics, specifically theories developed by Hillerborg or Bazant such as the fictitious crack tip model, which take into account the larger fracture process zone surrounding the crack tip, a softening in the severity of the size effect is seen with decreasing member size. This dependence of size effect on overall brittleness of the material is captured through measures such as Hillerborg et al’s characteristic length, mentioned earlier and shown in Equation 1
,Z =z
E’G,
(Equation 1)
f; where E’ is effective elastic modulus, Gf is fracture energy, and fl is the tensile strength of the material. As the brittleness of the material decreases and the fracture toughness increases, the magnitude of the process zone surrounding the crack tip increases proportionally. This enlargement of the process zone ultimately leads to a diminishing size effect with smaller member size. Due to large aggregates creating a significant fracture process zone, most commonly sized concrete members are within this region, highlighted in Figure 7.
As member size decreases further, or member ductility increases, NLEFM predicts negligible size effect. The high fracture toughness of ECC, nearly equivalent to aluminum as mentioned earlier, and extremely high value of characteristic length (-100m [7]), may suggest that ECC material lies in the upper left zone on the size-effect plot of Figure 7. For a truly ductile material where the fracture failure mode is suppressed in favor of other types of failure modes (such as compression or buckling) in a structural member, the NLEFM theory of size effect loses meaning. In this case, structural members made with ECC or WECC may not show any size effect. If exhibited, however, the size effect will be governed by phenomenon other than fracture. The Weibull size effect or other concepts may be needed to explain this size effect. This situation remains a possibility for ECC structural members. In this limit, the concepts associated with fracture energy and characteristic length are no longer meaningful. CONCLUSIONS From the range of flexural specimens currently tested, there appears to be negligible size effect in ECC members when compared to reinforced concrete specimens. While reinforced concrete beams exhibited a significant reduction in flexural strength over a series of beams up to 1.4 meters in length, ECC and steel reinforced ECC beams showed no significant change in flexural strength. This phenomenon is due to the ductile nature of ECC material. ECC flexural specimens are highly unlikely to fail in a brittle manner negating brittle failure modes closely associated with size effect in concrete.
66
M. LEPECHand V.C. L1
With the current set of member sizes tested, it is not possible to determine whether ECC will follow current NLEFM based size effect theory. While this theory may apply, it is plausible that ECC members exhibit no size effect due to the full suppression of fracture failures, or are rather subject to other forms of size effect, such as those arising from material variability. REFERENCES 1. Hillerborg, A., Modter, M., and Peterson, P.E. Analysis of Crack Formation and Crack Growth in Concrete By Means of Fracture Mechanics and Finite Elements. Cement and Concrete Res., 6(6), 1976, pp 773-782 2. Bazant, Z. P., and Kim, J. Size Effect in Shear Failure of Longitudinally Reinforced Beams. ACI Journal, 1984, 81(5), pp 456-468 3. Bazant, Z. P., and Sun, H. Size Effect in Diagonal Shear: Influence of Aggregate Size and Stirrups. ACI Materials Journal, 1987,84(4), pp 259-272 4. Carpenteri, A. Fractal Nature of Material Microstructure and Size Effects on Apparent Mechanical Properties. Mech. Mater, 1994, Vol. 18, pp 291-302 5. Maalej, M., Hashida, T:and Li, V.C. Effect of Fiber Volume Fraction on the Off-CrackPlane Fracture Energy in Strain-Hardening Engineered Cementitious Composites. Journal of the American Ceramic Society, 1995, 78(12), pp 3369-3375 6. Kunieda, M., Kamada, T., and Rokugo, K. Size Effects on Flexural Failure Behavior of ECC Members. Proceedings of the JCI International Workshop on DFRCC, 2002, pp 229238 7. Li, V.C., Lin, Z., and Matsumoto, T. Influence of Fiber Bridging on Structural Size Effect. International Journal of Solids Structures, 1998, 35(3 1,32) pp 4223-4238 8. Li, V.C., Wang, S., Wu, C. Tensile Strain-hardening Behavior of PVA-ECC. ACI Materials Journal, 2001,98(6), pp 483-492 9. Bazant, Z. P., and Kazemi, M.T. Size Effect on Diagonal Shear Failure of Beams with Stirrups. ACI Structural Journal, 1991, 88(3), pp 268-276
Proc. Int. Syinp. ,,Brittle Matrix Composites 7 *' A.M. Brandt. V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Ptrhl., Warsaw 2003
STATIC AND DYNAMIC PROPERTIES OF DRY AND WET CEMENT MORTAR Anatoly BRAGOV', Leopold KRUSZKA', Andrey LOMUNOV' Research Institute of Mechanics, State University of Nizhny Novgorod Gagarin Ave. 2,603600 Nizhny Novgorod, Russia, e-mail:
[email protected] Military University of Technology Kaliskiego 2,OO-908 Warszawa, Poland, e-mail:
[email protected] I
'
ABSTRACT Some static and dynamic investigations' results of dry and wet cement mortar in compression and in tension are discussed. This tested material is used to construct some protective walls at buildings. Obtained experimental results are presented in table and graphic forms. Dynamic examinations are realized using the split Hopkinson pressure bar technique. Static investigations are carried out by the standard Instron testing machine. Keywords cement mortar, experimental testing, static and dynamic properties
INTRODUCTION Determination of mechanical properties of building construction materials, such as steels, concretes, bricks or mortars at high strain rates of the order of lo3 11s and larger is of vivid interest for engineering community for many practical reasons. Dynamic properties of the materials are required for reliable prediction of the structure behavior during unexpected impact and explosive loading or other dangerous events. This knowledge in turn permits for increasing safety of the civil engineering structures. Properties of materials at high strain rates of deformation are of natural interest for military industry. The reliable determination of dynamic properties of the materials calls for special experimental techniques different from static testing. There are available a number of experimental techniques for determination of dynamic properties of materials in elastic range of their behavior like free vibrations, resonance method, wave propagation methods. However, the Split Hopkinson Pressure Bar (SHPB) technique is at present probably the most frequently used method for determining the dynamic elastic-plastic properties of various materials at strain rates range of 10' +lo3 11s [l-31. The main aim of this paper is to present static and dynamic properties of dry and wet cement mortar in compression as well as in tension. The purpose is not only to show experimental results of a material investigated, but also to give information useful for various tests using a SHPB apparatus in order to make possible investigations in two different modes of testing the same prepared cylindrical specimens at high strain rates. First, test results together with fracture mechanisms from the dynamic compression of a cement mortar material are compared with those fiom the static testing. Short cylindrical
68
A. M. BRAGOV, L. KRUSZKA arid A . K. LOMUNOV
specimens were dynamically tested in the SHPB set-up. Next, dynamic investigations of cement mortar specimens were performed in tension using the splitting Brazilian test in the same experimental device.
MORTAR AND EXPERIMENTAL SET-UP Mortar and its static properties Cement mortar material designed for 30 MPa compressive strength, of the component ratio w (water) : c (cement) : k (mason's sand of0,25-1 mm) - 1 : 2 : 6, on the basis Polish Portland cement of 35 mark was prepared for testing. For static and dynamic investigations, specimens of cement mortar were produced in the special tubular forms as bars and then they were cut out into separate specimens by diamond disk. The end faces of specimens were grinded and polished. The specimens for tests had the diameter D of 18 mm. In order to investigate the influence of inertia and frictions' effects on dynamical experimental results, the specimens were made of length L = 9 mm and 18 nun. One set of specimens was tested in conditions of delivery, i. e. dry, and second set was stored in water before investigation up to humidity 2 - 4
YO. The static properties of dry cement mortar were investigated under compression until failure. As it was found out, the material has significant diversity of mechanical properties. So, failure stresses in compression changed from 25 MPa up to 80 MPa, failure strain changed from 1,33 YOup to 7 %, module of an initial part of the static stress-strain diagram from 16 MPa up to 104 GPa. On the basis of a series of 17 experiments, the average values of these static strength parameters are determined as follows: a{ = 48,6 MPa - failure stress, E ~ S = 2,3 % - failure strain, and ES= 49,7 GPa - initial Young's modulus.
Experimental set-up of SHPB technique The classical SHPB apparatus consists of two long circular bars between which a specimen is sandwiched (see Fig. 1). The two bars play the role of wave-guides as by striking the end of the "input" (incident) bar with a "striker" bar (projectile) a compressive elastic stress wave is generated that starts to travel towards specimen. At the input bar-specimen interface the wave partially is reflected back as a wave of tension towards the impact end and partially is transmitted still as compressive wave through the specimen and into the "output" (transmitter) bar. The strength of the wave pulse is induced weak enough not to exceed elastic limit of the bars material but is usually strong enough to result in irreversible (plastic) deformation of the specimen. The diameter of the input and output bars was 20 mm, while their length is 1 m. The strain signals in input and output bars are recorded with the aid of two strain gauges glued to the bars. Stored in a computer system strain gauges signals time histories are later processed to recover stress-strain curve of the material tested. General view of two experimental set-ups with 10 and 20 mm gas guns to launch projectiles is presented in Fig. 2.
Striker Bar
Input Bar
I Strain Gauae A
Specimen I
Output Bar
I Strain Gauge B
Figure 1. Operation principle of classic SHPB apparatus
Static and dynatiiic properties of dty and wet cement mortar
69
Figure 2. General view of classical SHPB apparatus The method of splitting test, i.e. the Brazilian test, was proposed to determine the dynamic tensile strength of material tested. Classical compression tests were conducted applying an impact load along the longitudinal axis of a specimen. Splitting tensilc test was carried out turning the specimen through an angle 90' and applying the impact load P along a diameter of the specimen. The scheme of this test is shown in Fig. 3.
Specimen
Figure 3 . Scheme of the Brazilian test When a force, P, is applied to the cylindrical specimen as indicated in Fig. 3, a material element along the diameter is subjected to a compression stress, uC,and to a tensile stress, G, (uniform along the diameter) of following values: 2P D' Gc=-x L D r(D-r)
2P -~ - X L D
(3
where, L and D are respectively, the height and diameter of the cylindrical specimen, and r the distance from the material element to the point where the load is applied. The maximum force recorded, P,, and the geometry of the specimen allow to determine the tensile strength
70
A. M. BRAGOY, L. KRUSZKA and A. K. LOMUNOV
of tested material. Although, it should be kept in mind, that a biaxial stress state is in the specimen, with the compression stress higher than the tensile one. This fact makes impossible a direct comparison between experimental results obtained in these tests with those of simple tensile tests, unless the failure criterion is known.
RESULTS OF DYNAMIC TESTS After the automated computer processing of registered pulses from Hopkinsons' measuring bars, dynamic stress-strain diagrams, as well as, strain rates-strain ones were obtained for each dynamical experiment. As it is just mentioned, one part of specimens prepared was tested under conditions of delivery, i. e. in dry state, and second part of specimens was waterlogged before testing, i. e. in wet state. Experimental dynamic results obtained were differentiated into four main groups: 1. testing of dry specimens with low energy of a loading wave, when specimens didn't disintegrated, 2. testing as above, but wet specimens' tests, 3. testing of dry specimens with high energy of a loading wave, when specimens were completely fractured, i. e. fall to pieces, 4. testing as above, but on wet specimens' tests. Examples of the final stress-time and stress-strain diagrams from dynamical testing showing two typical behaviours of cement mortar specimens tested are presented in Fig. 4, i. e. when specimens didn't disintegrated (curves No l), and when specimens were completely fractured (curves No 2). Strain rate-time and strain rate-strain relations are shown by dotted lines in the lower part of these figures. Maximal stresses omaxobtained during dynamic testing of specimens belong to the .: The point F in Fig. 4. a) represents material groups No 3 and No 4, are failure stresses 0 fracture, for which the appropriate values of time t t and strain E; are determined.
1500 VI
---I)
2~Y
E
0
I I
20
. '
. "
. '
. I
I "
40
.
. '
. '
. "
I '
. '
GO
. "
. "
. '
I '
. "
. '
80
Time, m k s
. '
. '
I I
.
.
.
-.........,_._.._.. -:. . , .
'
100
120
71
Static and dynamic properties of dry and wet cement mortar
.._..__..._.....__.... ._..........._._,_....._..
b)
Figure 4. a), b). Dynamic strength characteristics for two typical cases of cement mortar behaviour: non-fractured (curves No 1) and fractured specimens (curves No 2) aRer testing. In the next Figures 5 + 8 dynamical deformation diagrams of two various size's specimens are given. The average static stress-strain diagram is shown in Fig. 5 in order to compare it with dynamic results. It is possible to observe rather strong intluence of the length L of specimens tested on their dynamic strength characteristics: loading branches of dynamic stress-strain diagrams for longer specimens are larger than for shorter ones.
160
140
'
1,2,3: L=shrm;
i
1500
$
60
1000
40 20 0
0
2
4
6
8
10
strain, Y o
12
14
. m
4
J
*
500
e .g
o
m
&
Figure 5. Dynamic stress-strain diagrams of group No 1 specimens with average static diagram. In the Table 1 there are given the average values of above-mentioned strength parameters for each group of dynamic experimental results.
72
A. M. BRZGOV, L. KRUSZU untl A . K. LOMUNOV
1,2,3: L = h ; 4 , 5 , 6 : L=18mn
0
1
3
2
strain.
5
4
6
Oh
Figure 6. Dynamic stress-strain diagrams of group No 2 specimens.
dry mortar
M, 140f
: L=9mn; L=lBnm
2,2
3,4,5:
0
i
2
3
strain. Y o
4
5
6
Figure 7. Dynamic stress-strain diagrams of group No 3 specimens.
wet mo rta r 150
g too
e 2 F
50
0
t ' 0
.
1
2
.
.
.
.
.
.
3
.
.
.
strain O h
.
.
4
.
.
.
.
.
.
.
.
5
Figure 8. Dynamic stress-strain diagrams of group No 4 specimens.
.
6
Static and rlynaiiiic properties of dry and wet
ceiiieirt
73
iiwrtur
Figure 9 shows failure stress arstress rate 0 dependences for each group of the cement mortar specimens tested. Results can be approximated by linear relations afd = A , & + B
with the parameters presented in the table 2. 200
1 m m a,
2
-
120
a2
2
r;:
1 - D r y , low energy impact; - Wet, low energy impact; 3 - D r y , high energy impact: 4 - W e t , high energy impact,
50-
40
I 0
2
I
I
I
5
10
15
Stress
rate. hiPa/+s
Figurc 9. Stress rate effect on failure stress in cement mortar specimens tested. Table
Besides dynamic testing in compression, the specimens in dry and wet states were subjected to splitting (tension) during the Brazilian tests. Obtained dynamic stress-strain curves are presented in Fig. 10. Above presented experimental results show humidity, stress rate and specimen size effects on dynamical properties of cement mortar. It has also noticed the wet material tested in compression as well as in tension, has lower dynamic strength than dry one by 10-15 %.
74
A. M. BRAGOV, L. KRUSZKA and A. K. LOMUNOV
30 L d 25 PI
=-
20
m
$m
.g
15 10
;?
8
5 0
Figure 10. Dynamic stress-strain dependences for dry and wet cement mortar specimens obtained from splitting tests. CONCLUSION
Cement mortar is a strain rate as well as humidity sensitive material. It is able to explain such behaviour of this material by a dynamic character of loading and two competing sophisticated processes taking place in the specimens, i. e. the process of nucleation, growth and coalescence of microcracks and micropores into macropores and cracks on the one hand, and wave-like increase of loading on the other hand. If increase of stresses is higher than intensity of failure process then the material with already developed failure zones can be overloaded. ACKNOWLEDGEMENTS
Gratitude is expressed to the Military University of Technology, Warsaw for financial supports under the Project No PBS 632. REFERENCES 1. Gary, G.,Bailly, P., Behaviour of a quasi-brittle material at high strain rate. Experiment and modelling. Eur. J. Mech. A Solids, 17, 1998, pp 403-420. 2. Bragov, A.M., Demenko, P.V., Lomunov, A.K., Sergeichev, I.V., Kruszka, L. Investigation of behavior of the materials of different physical nature using the Kolsky method and its modifications. In: New Experimental Methods in Material Dynamics and Impact, W.K. Nowacki and J.R. Klepaczko eds., series: Trends in Mechanics of Materials. Volume 3, Centre of Excellence for Advanced Materials and Structures, Warsaw 2001, pp 337-348. 3. Bragov, A.M., Lomunov A.K., Kruszka, L. Investigation of dynamic properties of microconcrete (in Russian). In.: Proc. 14th International Scientific and Technological Conference on Environmental Engineering in Maintenance of Military, Zakopane, 4-6 October 2000, Military University of Technology, Warsaw 2000, pp 52 1-53 1.
Proc. Int. Sytnp. ,I Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I.H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
INVESTIGATION OF STATIC AND DYNAMIC LOADING OF DIOXIDEZIRCONIUM CERAMICS AND ZIRCONIUM ALUMINA CONCRETE Felix AKOPOV’, Anatoly BRAGOV’, Leopold KRUSZKA3, Andrey LOMUNOV’, Vladimir MINEEV’, Ivan SERGEICHEV’ Institute for High Energy Densities, Russian Academy of Sciences, Izhorskaya 13/19, 127412 Moscow, Russia, e-mail: mineev6Jihed.ras.i-u ’Research Institute of Mechanics, State University of Nizhny Novgorod Gagarin Ave. 2,603600 Nizhny Novgorod, Russia, e-mail:
[email protected] Military University of Technology Kaliskiego 2,OO-908 Warszawa, Poland, e-mail:
[email protected]
’
ABSTRACT The investigations of dioxide-zirconium ceramics and concrete based on zirconium dioxide ZrO2 were performed both at static and dynamic strain rates in compression. For static tests
the standard hydraulic testing machine was used. The Kolsky method that uses the split Hopkinson pressure bar is one of the most developed and widespread procedures for dynamic testing of materials at high strain rates. This experimental method was used to study the dynamic properties of tested materials. Keywords dioxide-zirconium ceramics, zirconium alumina concrete, static and dynamic properties INTRODUCTION Wide application of modem materials in engineering practise requires experimental estimation of the material response in macro-scale. The high performance materials like high strength ceramics or ceramics matrix composites from engineering point of view should be designed to fulfil strength and fracture toughness requirements under static and dynamic loading. The aim of the paper is to analyse experimentally the influence of the loading rate on the strength properties of dioxide-zirconium ceramics and concrete based on zirconium dioxide ZrO2. Static testing was carried out using a standard hydraulic testing machine with a load capacity of 300 kN. Dynamic properties were obtained by application of the split Hopkinson pressure bar (SHPB) technique for testing at high strain rates. To minimize the detrimental influence of inertia and friction, the geometry of specimens was chosen to meet the DaviesHunter criterion [ 11. Three batches of zirconium dioxide ceramic specimens (ZDC) were studied differing in their grain fractional compositions, manufacturing technologies and different initial densities and porosities. Also zirconium alumina concrete specimens (ZAC) were tested. The specimens were prepared from electrically molten zirconium dioxide stabilized with yttrium
76 F.AKOPOV, A. M.BRAGOV, L. KRUSZKA, A . K. LOMUNOV, V. MINEEV, arid. oxide YzO3 (87% Zr02 + 10% YzO3). Barium aluminate (mass fraction 6 %) was used as a binder for ZAC [2]. During the dynamic tests carried out on SHPB experimental set-ups by adjusting the striker velocity, i.e., the amplitude of the incident wave, loading conditions were found under which the specimen either preserved its visual appearance or suffered failure. For each specimen tested, typical dynamic stress-strain curves are presented.
TEST SPECIMENS
ZDC specimens from three batches, differing in fractional composition of grains (Table I), were tested. Some properties of this material from the three batches under ambient conditions are presented in Table. 2. The tested specimens were manufactured in the form of pills: 20 mm in diameter and 10 mm in thickness for ZDC, and 50 mm in diameter and 5 mm in thickness for ZAC. The characteristic deformation and failure properties of brittle materials (such as concrete and ceramics) depended on the condition of the specimens surface. To this end, prior to testing, the specimens were manually polished with sandpaper of 0,OI mm grain size. For static tests, specimens of two sizes were prepared: 20 mni in diameter and height and 30 mm in diameter and height. The choice of various geometric sizes of the specimens was motivated by the desire to examine the effect of the scale factor on the strength and strain characteristics of the ceramics. The specimens of batch No 1 ceramics were tested both in condition of 1D (one dimensional) stress state (without a confining jacket), and in condition of 3D stress and 1D strain states (in a confining jacket). Before installation of a specimen in a working position, 23 layers of thin (10pm) fluoroplastic film were placed between the end faces of Hopkinson’s pressure bars and the specimen to reduce friction and to improve the acoustic contact. In jacket-confined tests, the gap between the rods and the jacket was also filled with above film.
YO).
* - tetragonal phase. The rest of the fractions were cubical structures stabilized with Y2O3, with the molar fraction of 10-1 1 YO.
Primary static tests in tension were also conducted for ceramic specimens. These experimental data obtained allow to conclude that the static failure stresses differ appreciably from each other in compression (38 + 40 MPa) and tension (7 t 10 MPa).
77
Invesligaliotr of static and dynumic loading of dioxirle-zircorzirl,n ceramics and zircotiiutrz . ..
RESULTS AND DISCUSSION Ceramic specimens from the three batches were tested under compression using the apparatus based on the SHPB - see Figs 1-3. Batch No 1 of ceramic specimens were also tested in a rigid jacket. By varying the striker velocities (i.e., the loading wave amplitude), loading modes were selected under which the specimens either retained their apparent integrity and strength or fractured. Visual inspection of the specimens after tests made it possible to assess the level of their damage.
100
20
0 2
0
4
10
8
6
Strain, YO
Figure I . Dynamic diagrams for batch No 1 ceramics
Batch No 2 80
I
0
:
:
.
.
.
2
.
.
.
.
.
4
.
.
.
.
.
.
6
Strain, YO
.
.
.
.
.
8
Figure 2. Dynamic diagrams for batch No 2 ceramics
.
.
.
.
10
78
F.AKOPOV, A . M. BRAGOV, L. KRUSZU, A . K. LOMUNOV, V. MINEEV, und ...
4;
[ceramics]
\3{
BatchNo 3
150
B
ui m
100
&o 50
0
The summary of above diagrams for the three batches of ceramics is presented in Fig. 4, showing two characteristic diagrams for each batch: for the case of apparent integrity of the specimens (the left-hand group) and for their final failure (the right-hand group). To make the figure more clear, the groups were spaced along the strain axis.
3 & 4 - Batch No 2.
150
1 - 180 lk; 2 - 1000 Us; 3 - 150 Us; 4 - 1600 ik; 5 - 200 Us; 6 - 1400 i k
100
0
2
4
6
8
10
12
Strain, 940 Figure 4. Dynamic stress-strain diagrams for the three batches of ceramics: apparent integrity - curves 1,3 and 5; failed specimens - curves 2 , 4 and 6. The effect of a jacket-limited radial deformation of a specimen is clearly illustrated by Fig. 5. If the specimen is tested without a jacket (curve 2), it fractures under stresses of 95 MPa. The similar specimen in a rigid jacket (curve 1) does not fracture under stresses exceeding 200 MPa.
79
I/ivatigafionof stutic and clynumic loading of dioxide-zirconiuin ceramics and zircoiiiutiz ...
1 - specimen in the a d jacket; 2 - specimen without a jacket
. v)
2000
vl' 9
..........................................................
........
0
2
4
6
Strain. %
8
Figure 5. Comparison of dynamic stress-strain diagrams of ceramics (batch No 1) in conditions of restriction of radial strain of the specimen (curve 1) and during traditional loading of the specimen, in conditions of the uniaxial stress state (curve 2). The right hand scale belongs to the dotted curves 1 and 2. Figure 6 shows failure stress orstress rate6 dependences for each batch of the ceramics as well as zirconium concrete specimens tested. Results for ceramics can be approximated by linear relations
of= A - & + B with the parameters presented in the Table 2.
1 - Ceramics, batch No 1; 2 - Ceramics, batch No 2; 3 - Ceramics, batch No 3; 4 - Zirconium concrete
,m
Figure 6 . Failure stress-stress rate dependences for ceramics (batches No 1 , 2 and 3) and zirconium concrete.
80
F. AKOPOV. A . M.RRACOK L. KRUSZKA. A. K. LOMLINOV, v. MINEEV, ant1 ...
Ceramics Batch No I Batch No2 Batch No3
1 I
I
1
A 1 5,47 5,96 6,60
I
I
I
B 53,7 423 63,3
The ceramics of batch No 3 has the highest strength and the lowest deformability in comparison with other batches of ceramics tested and zirconium concrete. Static values of failure stresses (at the stress rate 0) for tested materials are also presented in Fig. 6.
FINAL REMARK The strength properties of ceramics and zirconium alumina concrete detemiined experimentally can be useful to verify a theoretical description of behaviour of those structural and protective building materials subjected to static and dynamic loads.
ACKNOWLEDGEMENTS Gratitude is expressed to the Military University of Technology, Warsaw and the International Scientific-Technological Center for financial supports under the Project No PBS 632 (Poland) and the Project No 425 (Russia).
REFERENCES 1. Davies, E.D.H., Hunter, S.C., The dynamic compression testing of solids by the method of the split Hopkinson pressure bar. J. Mech. Phys. Solids, 1 I, 1963, pp 155-179. 2. Bragov, A., Lomunov, A. Sergeichev, I., Mineev, V., Akopov, F., Kruszka, L., Investigation of strength and fracture of the dioxide-zirconium ceramics under high strain rates, In: Abs. Int. Conf. "Shock Waves in Condensed Matter", A.L. Birukov, A.Y. Dolgoborodov and I.Y. Klimenko eds., St. Petersburg, 1-6 Sept., 2002, pp 16-19.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
THERMAL SHOCK CRACK PROPAGATION IN FUNCTIONALLY GRADED STRIP Tomasz SADOWSKI Faculty of Mechanical Engineering Technical University of Lublin Nadbystxzycka 40,20-618 Lublin, Poland, e-mail: tskms~,archimedes.pol.lubIin.pl Achim NEUBRAND Fraunhofer-Institut f i r Werkstoflhechanik Freiburg 79108, Germany, e-mail:
[email protected]
ABSTRACT The aim of the paper is theoretical modelling of the thermal shock problem in a strip made of finctionally graded composite with an interpenetrating network microstructure of A l z 0 3 and Al. Such a material could be used in brake disks or cylinder liners in the fbture. In both applications it is subjected to thermal shock. As a step towards optimization of the composition gradient with respect to thermal shock sensitivity the stress intensity factors during thermal shock were calculated for different composition profiles The influence of the residual stress resulting from the cooling after the production process was discussed. It was found that residual stresses decrease significantly the stress intensity factors and the length of cracks developing during thermal shock. Also the transition function of the A l 2 0 3 / A l functionally graded material (FGM) has a strong influence on the edge crack propagation. The optimum shape of the property distribution for the best thermal shock resistance of the material will be discussed.
Keywords Functionally graded material, thermal shock problem, thermal stress intensity factors, optimal properties of the material INRODUCTION Brittle surface layers are used in many high temperature applications such as thermal barrier coatings for turbines and combustion engines and chemical reactors because of their superior mechanical properties, oxidation and wear resistance at elevated temperatures. Temperature gradients and differences in thermal expansion can cause high thermal stresses in such layers. Large shear and axial stress concentrations are generated where the interface meets the free edge of the part [l]. These stresses promote crack propagation parallel to the interface [2]. It has been shown that the introduction of a layer with a gradual transition of the thermomechanical properties can greatly reduce these stress concentrations [3]. Additionally, it has been
82
T. SADOWSKlandA. NEUBRAND
observed experimentally that the critical energy release rate for delamination is substantially increased in such a FGM which further impedes delamination [4]. Unfortunately in-plane thermal stresses parallel to the interface are not always reduced [ 5 , 61 and the initiation of vertical surface cracks under transient or constant thermal loads is common in FGMs. In the present work which is based on linear elastic fracture mechanics, it will be demonstrated that the additional degree of freedom provided by the gradation of properties can reduce the driving force for the propagation of such vertical cracks substantially. It will be shown that thermal residual stresses resulting from the production process can play an important role and should be taken into account in investigations of thermal shock crack propagation in FGMs. In combination with the increasing crack growth resistance typically encountered in graded composites, an early crack arrest and a high residual strength after thermal shock can be obtained for an optimized composition gradient.
FORMULATION OF THE PROBLEM OF EDGE CRACK PROBLEM SUBJECTED TO HIGH TEMPERATURE GRADIENr Let us consider an infinitely long strip made of functionally graded material (FGM), which in the initial state is without any crack, Fig. la. Both the mechanical and the thermal properties of the strip change gradually along the x direction. Assume that the strip has initial temperature To. In an unsymmetrical thermal shock one side of strip ( x = 0) is cooled by AT to the temperature T,, whereas the second side of the strip (x = h ) remains under constant temperature To. It is assumed that an edge crack (Fig. 2a) is initiated at the cooling surface due to tensile thermal stress (Fig. lb). This crack can propagate as long as the thermal stress intensity factor exceeds the threshold value of the crack resistance of the FGM. The aim of the work is to estimate the equilibrium length b of the edge crack after thermal shock in particular composition of FGM (A1203/AI).
TO
5 =h X
Fig. 1 Initial configuration of the strip subjected to thermal shock: a) strip dimensions, b) thermal stress distribution during thermal shock
83
Thermal shock crack propagation in functionally graded strip
b
5 =y
Fig. 2 Edge crack formation due to thermal shock a) crack configuration, b) stress applied to the crack surface The theoretical solution of the considered problem is performed in several steps: finding the temperature distribution as a function of time t, Fig. l a calculation of the thermal shock stress distribution as a function of time t, Fig. Ib 0 estimation of thermal residual stress distribution due to technological cooling process calculation of thermal stress intensity factors as a function of time and crack length for an edge crack, Fig. 2 Temperature distribution during thermal shock
The temperature function T(x, y , t ) can be calculated solving the heat conduction equation, which has the following form in the two dimensional case:
Here the thermal diffusivity is equal to K = k / pc, , where k is the thermal conductivity, p is the density and c,, is the specific heat of the material. Taking into account symmetry condition regarding to y axis, Fig. 1, and introducing non-dimensional coordinate dimensional time
K
I' = + t ,
b
5 = 5 and nonh
equation (1) takes the following form for sought temperature
function T = T ( < , t * ) d2T -+dt2
0
1 -d k d T =--1 dT k dtdt ~ d t .
84
T. SADOWSKIandA. NEUBRAND
Here, K~ = K(C = 0) , is the thermal diffusivity at the ceramic side of the strip. The above equation will be solved for the following boundary and initial conditions T(4 = 0, t ) = T. and T({ = 1, t ) = To.The temperature field T = T(4,t') can be obtained by numerical integration of (2) using the Runge-Kutta method for given thermal conductivity and thermal diffusivity functions of the form k(4) = zk,<' and ~ ( 4=) . In the present work the coefficients
ZK,,'
1
I
of these functions were estimated from experimental data. Thermal shock stress Having the temperature field inside the strip T = T(6,t') it is possible to calculate the thermal shock stress by introduction of the Airy stress function [7] into the equilibrium equation
whereJ are components of the body forces per unit mass. Using the Hooke's law in the following form E 6,6, + Ev - a(T - To)uv=(4) (1+v) E [ (1-2v) v (1 - v) %
1
and assuming small strain, i.e. sv = ( u , ,+u,,)/2 ~ one can calculate the thermal shock stress uL(~,t*) from the equation
if body forces are excluded. In equations (4) and ( 5 ) E(5,t') is the Young modulus, v(5,t') is the Poisson ratio and a(T,t')is the thermal expansion coefficient. All of them are in general functions of position and time. Equation ( 5 ) was solved analytically for power law expansions (in x ) for E ( { , t ' ) , v(4,t') a(4,t') and stress free boundary conditions, i.e. no additional mechanical loading on the strip boundary. The particular form of the thermal stress function is the following
Thermal shock crack propagation in functional& graded strip
85
where
Moreover the values EO= E(c = 0, t') and a0 = a(<= 0, t'),i.e. correspond to the ceramic edge of the strip. An example of oL({,t*)distribution is shown in Fig. lb.
Thermal residual stress due to technological cooling process The thermal residual stress created during technological cooling of the FGM from the processing temperature has a significant influence on the material behaviour. According to Ravichandran [8], the thermal residual stress for a strip as shown in Fig. 1 is
01 ( & , t o )= AT,,
E ( 5 , f* )
I
A
a(5,t ' ) - El +
EIE, - Ef
where AT- denotes the difference between the process temperature and room temperature. The expressions for Al and A1 are
and El3E2, E3 are given by
Thermal stress intensity factor during thermal shock As shown in Fig. 2, the crack is perpendicular to the stress-free boundaries, because it was assumed that the problem is symmetric with respect to the y axis. Because the length of the crack after thermal shock is short compared to the specimen dimensions one can simplify the problem by assuming a constant Young modulus E(c = 0, t') = Eo. Then the thermal stress intensity factor in the FGM strip (Fig. 2) can be found in a similar way as described in [7, 9, lo]. The thermal stress intensity factor is found by solution of the integral equation under the given tractions p , ( x , y = 0, t' ) = - D ( ~x . y = 0, t * ) along the crack boundary, Fig 2b. Employing the edge crack opening displacement defined by Vy(x,y=O,f*)=uy(x,+O,t')-uy(x,--O,t*)
for
(O<x
(8)
86
T. SADOWSKIandA. NEUBRAND
the problem can be reduced to the following integral equation = -7r
~ , ~ ( x , t ' )for
(0 < x < b)
(9)
Here K ( x , r ) is the integral kernel given by
K ( x , r ) = K , ( r , ~+)K,( h - r , h - x )
+ K , ( ~ , x+)K l ( h - r,h - X )
1 +--- 12x (r+x)' ( r + x Y
K,( T , x ) = --
122 (r+x)4'
D=l-(4yZhZ+2)e-"''+e4* Normalizing the interval x E (O,6) by defining 6 r = -(I 2 + w)
9
6
x = -(I 2
+ s),
v,(r,t') = -62 f ( w , f ' )
the integral equation (9) becomes
where
Let us assume the solution of the integral equation takes the form f ( w , t * ) =G F ( w , r ' ) , where
is a so called weight function and F(w,t')= Aa,(t*)w"'. Solving (10) we get m=o
the expression for thermal stress intensity factor in the non-dimensional form K;(b,h,t')=
1-vo
K , (6,t') E,~,ATG
87
Theriizal shock crack propagation in functionally graded strip
NUMERICAL SIMULATION OF UNSYMMETRICAL THERMAL SHOCK IN THE STRIP
As an example an A1203/Al FGM prepared by the so called GMFC process [ 1I ] was analysed. This material was chosen because it is one of the rare FGMs for which all thermomechanicnl properties including residual stresses and the crack growth resistance have been studied experimentally in detail [11,12,13]. For the purpose of this work, the properties of the analysed A1203/AI FGM were expressed as a function of the volume content of Al in the composite c I , .The Young's modulus at RT (in GPu) was described by the polynomial E(c,,) = -1482.6(cA,y
+ 1973(c,,)I - 1096.9(~,~,)+ 398.42
(12)
and its temperature dependence was neglected. In a similar manner the thermal expansion coefficient of the composite between 20°C and 620°C was described by a(c,,)=281.24(cA,)1 -102.98(cA,)L +15.112(c,,)+7.71
(in 10-6/K)
(13)
The appropriate function for thermal conductivity k (in W/mK) is given by k ( c A l ) =37.71 + 363(~1~~).exp[-1.5~,,1
(14)
The thermal diffusivity z (in cm2/s) is K(c",)=
0.109+ 1.844(c~~).exp[-2.5cA,]
(15)
The temperature distribution in the strip is presented in Fig. 3 for the time interval t* E (0,l).
) Fig. 3 Distribution of non-dimensional temperature ( T - To)/To= [(T - T o ) / T o ] ( < , t *during thermal shock
88
T SADOWSKIand A. NEUBRAND The crack growth resistance as a function of crack length in the A120,/AI FGMs was determined earlier in [12]. For the calculation of the residual stresses, it was assumed that the composite was stress free at 620°C (at this temperature the aluminium in the composite is still very soft and cannot exert high stresses on the ceramic backbone of the composite irrespective of volume content) and residual stresses during cooling to room temperature were calculated from the thermal expansion coefficients and elastic modulus data. It has been shown for specimens of a different geometry that the stresses calculated with these assumptions are in reasonable agreement with experimental data [ 111.
0.16
1
0.14
{
(Them. shock 600 K ]
Fig. 4 Maximum of the non-dimensional thermal stress intensity factors K,'and corresponding crack resistance curve K; for linear change of Al content in FGM (n = 1); For the calculations of residual stresses during thermal shock it was assumed that the temperature TOwas 620°C and T, was 20"C, i.e. the thermal shock temperature difference AT was 600°C. The strip had a width of h = 10 mm and a composition gradient along the xdirection which could be described by the function C"/
(n,5) =
4+ c;/ .4"
(16)
Here, c:/ ,cfr and n are material parameters describing the composition gradient in the material. By introducing (1 6 ) to (12)-( 15) and varying the material parameters, the thermal shock response of different FGMs can be investigated. In our study, equalled 0.03 and cfl = 0.3 throughout - at such volume fractions the material behaves macroscopically brittle, and thus plasticity could be neglected. For n=l we have a linear composition gradient of the Al in A1203. For n < 1, the metal content increases quickly below the surface, and we have the case
89
Thermal shock crack propagafion in functionally graded strip
of a “metal rich material”, whereas for n > 1 the metal content increases only slowly, and we have a “ceramic rich material”. The thermal stress intensity factor K ; depends on time, crack length and temperature. For a given crack length the stress intensity factor will reach a maximum at a certain time t which will increase with crack length. This non-dimensional maximum of the stress intensity factor K ; is plotted in Fig. 4 as a function of crack length
no residual stress
y
o.20$, 0.00
with residual stress
m
I
El
0.00
G I
El I
I I .oo
I
I
I 2.00
f
3.00
Coefficient n Fig. 5 Equilibrium crack length for different kinds of FGM characterised by coefficient n Fig. 5 presents the equilibrium crack length for different values of n=l, 113 and 3. The crack lengths are much shorter in the graded AI*O,/AI composite than in a homogenous composite with a volume content of Al which corresponds to the surface composition of the FGM, 5 = 0. Residual stresses in the graded composite are typically compressive near the surface and lead to smaller stress intensity factors and equilibrium crack length (for longer cracks the stress intensity factors even become negative indicating very efficient crack arrest). The effect of residual stresses is strongest for n = 1/3 where the equilibrium crack length is reduced by about 60% compared to a hypothetic stress free material. The composite with n = 1/3 shows also the shortest equilibrium crack length. The short crack length is not only caused by the residual stresses, but also by the crack growth resistance of the material which increases quickly due to its metal-rich composition profile. Close examination of Figs. 4 and 5 reveals that the graded material with n = 1/3 would show the lowest stress intensity factors under thermal shock even if residual stresses were absent. The current contribution thus corroborates earlier calculations by Noda [lo], which also predict that thermal shock stress intensity factors can be reduced by gradients. The findings of this work show, however, that significantly shorter equilibrium crack lengths are expected if the rising crack growth (R-curve) of an FGM is combined with a controlled residual stress profile. Residual stress and the rising crack grow
90
T. SADOWSKIandA. NEUBRAND
resistance should thus be included in any analysis of the thermal shock resistance of functionally graded materials. ACKNOWLEDGEMENTS
This research has been supported by the Deutsche Forschungsgemeinschaft (DFG) under contract No. Ne599/4. T.S. has been supported also by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential and Socio-economic Knowledge Base” under contract number HPMF-CT-2002-01859. The authors would like to thank Prof. Dr. J. Rodel, University of Technology, Darmstadt, for valuable discussions.
REFERENCES 1. D.B. Bogy, On the problem of edge-bonded elastic quarter planes loaded at the boundary, International Journal of Solids and Structures 6, 1287-13 13 (1 970) 2. M.S. Hu, M.D. Thouless, A.G. Evans, The decohesion of thin films from brittle substrates, Acta Metall. 36, 1301-1307 (1988) 3. Yang, Y.Y., Munz, D., Reduction of the stresses in a joint of dissimilar materials using graded materials as interlayer, Fracture Mechanics 26, ASTM STP 1256, W.G. Reuter, J.H. Underwood, J.C. Newman, Jr. (Hrsg.), American Society for Testing and Materials, Philadelphia 1995, pp. 1-15 4. Bahr, H.-A., Balke, H., Fett, T., Hofinger, I., Kirchhoff, G., Munz, D., Neubrand, A., Semenov, A. S., Weiss, H.-J., Cracks in graded materials, accepted for publication in Materials Science and Engineering A 5 . Itoh, Y., Kashiwaya, H., Residual stress characteristics of FGMs. J. Ceram. SOC.Jap. 100, 1992, ~ ~ 4 7 6 - 4 8 1 6. Droschel, M., Oberacker, R., Hoffman, M.J., Schaller, W., Yang, Y.Y., Munz, D., Silicon Carbide Evaporator Tubes with Porosity Gradient Designed by Finite Element Calculations, In: Functionally Graded Materials 1998, Proceedings of the 5th International Symposium on FGM, W.R. Kaysser ed., Trans Tech Publications, Schweiz 1999, pp. 820-825 7. Jin, Z. H., Batra, R., Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock. J. Thermal Stress, 19, 1996, pp. 317-339 8. Ravichandran, K. S. Thermal residual stresses in a FGM system. Mat. Sci. and Eng, A201, 1995, pp. 269-276 9. Erdogan, F., Wu, B.H., Crack problems in FGM layers under thermal stresses. J. Thermal Stress, 19, 1996, pp. 237-265 10. Noda, N., Thermal stresses in functionally graded materials. J. Thermal Stress, 22, 1999, pp. 477-512 1 1 . Neubrand, A., Chung, T.-J., Rodel, J., Steffler, E. D., Fett, T., Residual Stresses in Functionally Graded Plates. J. Mater. Res., 17, 2002, pp. 2912-2920 12. Neubrand, A., Chung, T.-J., Lucato, S., Fett, T., Rodel, J., R curve Behavior of Functionally Graded Composites, submitted to J. Amer. Ceram. SOC. 13. Becker, H., Tschudi, T., Neubrand, A., Spatially Resolved Thermal Difhsivity Measurements for Functionally Graded Materials. In: Functionally Graded Materials 2000, Ceramic Transactions 114, American Ceramic Society, Westerville, Ohio, 2001, pp. 571-578
Proc. Itit. Sytirp. ,,Brittle Mutrix Coiiipositer 7 " A.M. Bruritlt. V.C. Li and I. H. Mmslidl, ech. lV(~~\(~\t~, 0ctoht.r 13-15, -7003 ZTUREK HSI arid Woodliead Pirhl.. IVmrciiv 3003
EXPERIiMENTAL TESTING OF CONCRETES SUR.IECTEl) TO IMPACT AND EXPLOSIVE LOADS Anatoly BRAGOV', Pave1 DEMENKO', Leopold KRUSZk4'. Andrey LOMIJNOV', Ryszard REKUCKI' Research Institute of Mechanics, State University of Nizhny Novgorod Gagarin Ave. 2, 603600 Nizhny Novgorod. Russia, e-mail: bragov~mzch.Linii.runnet.ru Military University of Technology Kaliskiego 2, 00-908 Warszawa, Poland, e-mail: I_krtiszkan,ask-kl~iii.iiet.pl
'
'
ABSTRACT Dynamic compressive tests of concrete specimens were carried out on an zxperitnental set-up realizing the traditional Kolsky technique as well as on a stand for testing standard cubic and cylindrical specimens under explosive loads. Determination of structural and sandy concretes strengths in dynamic compression and development of stress-strain relationships, including post-fractured domain, were the main aim of presented investigations. Keywords structural and sandy concretes, experimental testing, impact and explosive loadings
INTKODUCTION
In spite of the very intensive development of the theory of brittle material behaviour (rocks, concretes, bricks and mortars) under dynamic loads, there still exists the need of their experimental verification. The theories of modelling the structural materials especially in the domain of short-term loads cannot be final ones unless they are experimentally verified. To this end, the experimental techniques of testing brittle materials based among others on the Hopkinson bar method [ 1-31, or those with the use of explosive materials have been developed [4-61. In the domain of protective structures, concrete, brick and steel reinforced concrete objects during their lifecycle service can be subjected to pressure wave loads and impacts. Concretes, bricks and mortars used for their construction, besides their static testing, require verification of their strength under impulsive and impact loading with parameters similar to those occurring during their srvice. Modern measurement equipment and loading stands, working with the use of loads generated in the result of rapidly burning powders or impact make it possible to meet those requirements. A pressure explosive load of variable increasing time, up to its maximal value and of duration depending on powder grains diameter is obtained while using nitrocellulose powders of various grain gradient for combustion in a generator of a specially designed loading stand. Measurement o f stresses was carried out directly by recording liquid pressurr changes in the hydraulic servo. Specimens of B30 class structural concrete with Portland cement were
92 M.BRAGOK P. DEMENKO, L. KRUSZKA, A . K. LOMUNOVand R. REKUCKI prepared for testing. The cubic (150 mm x 150 mm x I50 mm) and cylindrical (0150 mm x 300 mm) specimens were placed between two steel interface layers of hardened surfaces. Foil resistance strain gauges of 30 mm measurement basis, posted on the surface of investigated specimen, were used for measurement of concrete deformation. Investigations carried out, have shown that there exists a possibility of conducting verification testing of dynamic strength of structural concrete on compression, on standardized specimens. Impact compressive loads on sandy concrete specimens were realized using two split Hopkinson pressure bar stands with two various diameters of measuring (incident and transmitted) bars, i. e. 20 mm and 60 mm. For study of influence of concrete structure on mechanical properties of tested material, there were made four batches of specimens of various aggregate fractions, separated from one voluinz of sandy soil. For manuhcturing of concrete specimens, Portland cement was also applied. The diameter of specimens for all aggregate fractions was 60 mm, and the thickness of specimens - 20 mm. Above-mentioned experimental set-ups enable conducting of strength testing of concrete materials subjected to impact and explosive loads at a predetermined velocity of load increase, during its increase up to the moment ofspecimm’s fracture.
INVESTIGATIONS OF STRUCTUIWL CONCRETE UNDER EXPLOSIVE LO:\D Experimental set-up A pressure wave load of variable rising time, up to its maximal value and of duration depending on powder grains diameter is obtained while using nitrocellulose powders of various grain gradient for the combustion in a generator in a specially designed loading stand (Fig. l), characteristics of which were presented earlier in [5].
Figure 1. a). Scheme of experimental set-up. 1 -dynamic load generator, 2 -steel columns, 3 lower foundation plate, 4 - lower sliding plate. 5 - top movable plate,.6 - fixed plate, 7 concrete specimen, 8 -hydraulic servo. b). General view of the experimental set up.
-
The loading time up to its maximal value did not exceed 50 ms. During the experiment the specimen did not get fractured, however, distinct cracks could be seen on its surfwes. In fbrther fracturing testing, aimed at the determination of structural concrete strength on compression, only the rising branch of the pressure wave is used of the value equal the
fracturing force; it is controlled by the amount of powder of given grain gradient, portioned into the generator’s combustion chamber. The deterniination of compression strength of structural concrete on under dynamic load of a pressure wave and working out of the stress-strain relationship diagram were main aims of the investigations. Experiments were conducted on standard cubic specimens (1 50 nini x 150 m m x 150 mm). Measurements of stresses were carried out directly by recording liquid pressure p changes in the hydraulic operator (measurement in point 1, Fig. 2). Concrete specimen was placed between two steel interface liners ofhardencd surfaces 8, each being 10 mm thick. Contact surfaces were covered with oil. Such procedure made it possible to partially eliminate tangent stresses occurring at the contact plane: specimcdstreiigth machine plates. The EA-06-1OCBE-I20 foil resistance strain gauges of 30 mm measurement basis and 12042 resistance, posted on the surface of investigated specimen, werc used for nieasureni2nt of concrete strength. During the experiment vertical E strains (point 4) and the horimntal ones (point 5) were measured while connecting strain gauges T, into a full bridge system (Fig. 2) with two compensation strain gauges TI. balancing the cffect of temperature.
Figure 2. Distribution of measurement points on a testing stand. Strain gauges were distributed on opposite walls of the cube. The rccording of global deformation ug of the tested specimen along with the slide of the lower sliding plate were carried out with a transformer differential displacement sensor, while placing it at the point 2. Taking into account sensor’s possible damage, the plate’s sliding distance was limited to 6 mm. In an addition to that the slide velocity of the plate v-point 3 and accelerations a1 and a? during vibrations of the plate in measurement points 6 and 7 were registcrcd. All valucs were registered indirectly as electric potential changes in the function of time, corresponding to changes of individual parameters of physical values. In order to determine static strength, six specimens were subjected static investigations, carried out at the standardized velocity of load increase from 0,2 M P d s to 0,3 MPds. Static tests were made on a hydraulic press, generating forces up to 1500 kN.
94
M.BRAGOV, P. DEMENKO. t.KRUSZlG4. A . K. LOMUNOVud R. REKUCKI
Each physical value investigated was recorded on separate measurement tracks, receiving signals from measurement sensors and processing those input signals into analog output signals of 0,5 V - 10 V. All bridges and amplifiers had a transmission band of 0 - 20 kHz what enabled recording rapidly changing processes. As all recorded signals are in the analog form and because there is no possibility of clear-cut deterniination of the time interval, since the moment of feeding source's switch-on till the ignition of the powder load, a measurement tape-recorder has been chosen as a recording tool. In this case, it is the %channel recorder of the RACAL Company. This recording unit enables a simultaneous recording of runs of eight analog values on a VHS tape of enlianced magnetic properties. The recording is realized in a FM modulation mode in the 0- I00 kNz band. At the output, the analog signal of 1 V amplitude is obtained, which is then subjected to sampling and encoding by the DAS-16F analog-to-digital converter. Further analysis in the domain of time and frequency and appropriate processing were conducted with the use of computer systems or special analyzers. (cg. spectral ones) and the ASYST software. Enamplev of measurement results Twenty specimens of structural concrete of the B30 class. of the component ratio w (watcr):c (cement) : k (aggregate) - I : 2,12 : 11,76, on the basis Polish Portland cement's were prepared for testing. All-in aggregate of a 0,s 8 mm thicknsss fraction was used as a concrete aggregate. Static and dynamic strength tests were carried out with the average load velocity of 0,14 MPds what corresponds the average deformation rate of 52 pm/s. For the investigated specimen series, the average compression strength of the concrete was R, = 30.88 MPa. The maximal increase of local vertical deformations in the analyzzd specimen series was E = 1280 p d m . Average time of load increase up to the fracture was 230 s. Dynamic testing in the case of the specimen's series discussed were conducted only at one velocity of load increase, equaling, on the average, 1505 M P d s (corresponding the load generated by burning of the "Buk"-type powder of the combustible layer thickness averaging 2,2 mm). An examples of the stress runs in the function of time obtained for cubical and cylindrical specimens are presented in Fig. 3. The average load increase time up to the moment of specimen's fracture, was 27 ms. Basing on medium values of courses, determined by digital mcthods with the use of digital filtration and so called smoothing, the final runs of curves of the local stresdstr3in relationships c(&) Fig. 4, were prepared. The average strength of the concrete on compression (as calculated from ten specimens), under the dynamic load was R," = 38,99 MPa. The average value of maximal vertical deformation was E = 1120 pm/ni. The elasticity coefficient E, of the concrete at the compression was determined from the relationship [5]:
-
-
E, =
-
0,4R, -0,5 ~(0,4R,)-E(0,5)
where, E (0,4 RJ strain corresponding the stress of 0.4 R, [MPa/, E(0,j) - strain corresponding the stress of 0,s MPa. Dynamic experiments carried out on structural concrete specimens allow to formulate following conclusions: 1. The investigations carried out have shown that there exists a possibility of conducting verification testing of dynamic strength of structural concrete on compression, on standardized specimens. 2. Along with increasing load rate the concrete undergoes smaller and smaller strains what can be explained by vanishing elasticity phase of the material tested (brittle fracture occurs).
95
E.rperiinenici1testing of concretes subjected to itnpcict unil explosive 1oiiiI.v
30,000
lo.m 5.000 0.000
P
3 55.000
d
L m a Y 2s.m
2o.m 15.m
!
-7-gOlW
IQOQ)
5.WO
J
0.m
. ---
0
.
-.
~
__
. .-. -
.
5
10
...... 15
.......
. ~. . _ .
...
............ 20
25 tinWlIll81
Figure 3. Typical characteristics of the stress-time at the load rate of 1505 MPds ohtaitird during dynamic compression of cubic (a) and cylindrical (b) specimens. For comparison, the stress as a function of time at higher load rate is also presented, corresponding the loid generated by burning of the fine-grained "Wiinia"-type powder. 3. In the investigations presented a compressive strength increase occurred at the dynaniic to static load ratio of 1.26. and adequately the Young modulus increase of 1.7. were to state. 4. The structural concrete belongs to load rate sensitive materials - see Fig. 3. 5. The effect of specimens' geometry on dynamic stren@h characteristics of concrete tested is clearly visible - see Fig. 4.
96 M.BRAGOV, P.DEMENKO, L. KRUSZKA, A. K.LOMUNOV and R.REKUCKl
Figure 4. Average dynamical stress-strain curves for cubic and cylindrical B30 concrete specimens under the loads generated by burning of the "Buk" - type powder.
INVESTIGATIONS OF SANDY CONCRETE UNDER IMPACT LOAD While using the method of split Hopkinson's pressure bar there are carried out the dynamic tests and investigations on the dynamic properties under compression of concrete specimens - Fig. 5.
Gas gun
Incident bar
Stslker
Piezoctystal I
,
I
Specrnen
Transrmtter bar
/
I
Strain gage +50V
116'11
I
I
II
I I
Catbration n
1 I I
1
Figure 5. Scheme of the split Hopkinson pressure bar used during dynamic testing of sandy concrete in compression [7].
97
Experimental testing of concretes subjected to impact and explosive loads
T o study an influence of a sandy concrete structure on strength properties of a material tested there were made four batches of various fractions, separated from one volume of a sandy soil. The size of grains in the first batch (0,2) was from 0,2 mm up to 0,3 15 mni, second batch - from 0.3 I5 mm up to 0,4 mm, third - from 0,63 mm up to 1 mm, and fourth - from 2,5 mm up to 5 mm. The Portland cement M400 was applied to preparation of all specimens. Aggregate, cement and water were mixed up in the proportion of 3 : 1 : 0,65. The diameter of cylindrical specimens was 60 mm, and their length - 20 mm. Additionally, specimens of (0,2) fraction were prepared by the diameter of 20 mm and the length of I2 mm. The deformation diagrams of the sandy concrete tested shows the same behavior for all four batches of various fractions. First parts of stress-strain curves' loading branches are closed to linear, and their modules are rather strain rate non-sensitive - see Fig. 6. Elastic parts those diagrams finish at first local stress maximum. There are partial specimens' failure with microcracking and other defects of their structure at those points. Here, deformations of specimens don't exceed 1 %. Next, it takes place further micro-and macrocracking with stress increasing in specimens deformed dynamically. Specimens' fracture processes begin when stresses decrease with deformation increasing. The maximum achievable degree of specimens' deformation prior to beginning of their fracture is about 3 %. The sandy concrete tested is strain rate sensitive material in particular at post-failed ranges. To study an effect of specimens' scale on dynamic strength properties of the sandy concrete, investigations of (0,2) fraction specimens of 20 mm in diameter were additionally conducted - Fig. 6. d). Differences in behaviour of material tested concern only unloading branches of stress-strain diagrams.
70
I
Concrete, aggregate size of2.5 mm
60
50 40 30
20
15.0
10
12.5
0
10.0
-10
L -2.5
I
98
M. BRAGOV, P. DEMENKO. L. KRUSZU. A . K. L O M U N O V QR. ~ REKUCKI
1
Concrete, aggregte size of 0.315 mm
I
99
Experiinetitul testing of concretes subjected to itnptict a i d explosive loads
Concrete, -e
size of 0.2 mm
dim&erof specimen 20 mm
1
Figure 6. Stress-strain curves for concrete with sand of 0,2 mm, tested at various strain rates. a). Specimens of 60 mm in diameter. b). Specimens of 20 mnt in diameter.
100 M.BRAGOV, P. DEMENKO, L. KRUSZKA. A. K. LOMUNOVand R. REKUCKI FINAL REMARKS The experimental methods presented here enable to determine the strength of the structural and sandy concretes under dynamic loads at a predetermined loading rate up to the moment of specimen’s fracture as well as to obtain post-failed stress-strain relationships. The mechanical properties of cement based materials determined experimentally at high strain rates can be useful to verify a theoretical description of behaviour of those concrete building materials subjected to dynamic loads [S]. ACKNO WL E DC EMENTS Gratitude is expressed to the Military University of Technology, Warsaw and the International Scientific-Technological Center for tinancial supports under the Project No PBS 632 (Poland) and the Grant No 1203 (Russia). REFERENCES 1. Kruszka, L., Nowacki, W.K., Wolna M., Experimental investigations of fracture mechanisms of brittle photoelastic material. In: Proc. 7th European Conference on Fracture “Failure Analysis - Theory and Practice”, E. Czoboly Ed. Budapest 19-23 Sept. 1988, Engineering Materials Advisory Services Ltd., Budapest-Shefield 1988, vol. 2, pp 523-525. 2. Kruszka, L., Nowacki, W.K., Wolna M., Strength and fracture analysis of brittle photoelastic material - static and dynamic tests. Engineering Transactions, 40, 1992, pp 343362. 3. Kruszka, L., Nowacki, W.K., New applications of the Hopkinson pressure bar technique to determining dynamic behaviour of materials. J. of Theoretical and Applied Mechanics, 34, 1996, pp 259-280. 4. Kruszka, L., Rekucki, R., Dynamic behaviour investigations of structural concretes imposed pressure wave (in Polish). In: Proc. 19th Symposium on Experimental Mechanics of Solids. J. Stupnicki Ed. Warsaw University of Technology, 2000, Jachranka 18-20 Sept. 2000, pp 349354. 5. Rekucki, R., Experimental testing method of dynamical properties of brittle materials subjected to explosive load (in Polish). In: Proc. 19th Symposium on Experimental Mechanics of Solids, J. Stupnicki Ed. Warsaw University of Technology, 2000, Jachranka 18-20 Sept. 2000, pp 456-46 I. 6. Cudzib, S., Kruszka, L., Pisera, J., Rekucki, R., Application of explosives to determine resistance of concrete to dynamic loading. Part 11. Experimental testing (in Polish). In: Proc. 7th Scientific and Technological Conference on Military Engineering, Warszawa-Kazuli Nowy 22 November 1994, Military University of Technology, Warsaw 1994, pp 144-151. 7. Bragov, A.M., Lomunov A.K., Kruszka, L. Investigation of dynamic properties of microconcrete (in Russian). In: Proc. 14th International Scientific and Technological Conference on Environmental Engineering in Maintenance of Military, Zakopme, 4-6 October 2000, Military University of Technology, Warsaw 2000, pp 52 1-53 1. 8. Brara, A,, Klepaczko, J. R., Kruszka, L., Tensile testing and modelling of concrete under high loading rates. In: Proc. Int. Symp. “Brittle Matrix Composites Y, A. M.Brandt, V. C. Li and I. H. Marshall eds. Warsaw 13-15 October 1997, Woodhead Publ. Ltd, Cambridge and War~aw1977, pp 281-290.
Proc. Int. Symp. ,,BrittleMatrix Composites 7 A.M. Brandt. V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003 I’
APPLICATION OF UV IMAGE ANALYSIS FOR EVALUATION OF THERMAL CRACKING IN CONCRETE Michal A. GLINICKI I ) and Agnieszka LITOROWICZ ’) Institute of Fundafnental Technological Research, Polish Academy of Sciences, Swiptokrzyska 2 1,OO-049 Warszawa, Poland ’) e-mail:
[email protected] I ) e-mail:
[email protected]
ABSTRACT A method of identification and quantification of crack pattern in concrete is presented. Several concrete cube specimens prepared in the laboratory were exposed to continuous freezing action after 1 hour since concrete mixing in order to induce cracks. Testing of compressive strength of concrete, analysis of crack patterns and permeability testing have been performed on low-temperature damaged specimens and reference specimens. Samples for crack analysis were sawn out from cubes and then impregnated with epoxy resin containing fluorescent dye. Observation of cracks and other microdefects (porosity, air voids) was performed in ultraviolet light using an optical microscope at the magnification of 10 to 63 times. The process of digital image analysis consisted of: extracting the various defects from the observed image, filtering operations and sorting the extracted defects on basis of shape analysis. The use of resin impregnation technique in combination with the computer image analysis technique provided a quantitative determination of the crack system. Keywords Cracks, crack pattern, image analysis, water penetration.
INTRODUCTION Cracks in concrete arise at all stages of life of concrete structures, but well designed and manufactured concrete is originally watertight, containing discontinuous pores and microcracks. Cracks can be induced by loads or volumetric changes due to plastic settlement, high curing temperature, various type of shrinkage, creep and deteriorating mechanisms such as frost, alkali aggregate reactions, etc. Numerous studies have indicated that cracks in concrete structures can have negative effects on important parameters such as permeability, rate of chloride ingress and thus reinforcement corrosion protection [la].The increase in concrete permeability due to crack development allows more water or aggressive chemical ions to penetrate into the concrete, facilitating further deterioration. Research and practical experiences show that the quality and life time of concrete structures largely depend on the curing conditions in the early age of concrete. Inadequate curing leading to cracking or extensive microcracking could considerably decrease durability and service life of structures.
102 Michat A . GLINICKI and Agnieszka LITOROWICZ The tendency of concrete cracking due to temperature changes during hydration and hardening period is a problem known since the beginning of concrete technology. If concrete is exposed to freezing temperatures at its early age there is a danger of irreversible loss of strength [5]. Since conventional protection of concrete from freezing is expensive there are various new low-temperature admixtures [6] and the technology of winter concreting is still being improved. Therefore potential cracking and degradation of concrete due to winter concreting is still to be investigated. Over the past 40 years, several techniques have been developed to detect and measure cracks in cement-based materials. These include acoustic emission [7-81, sonic testing, microscope techniques coupled with dye, fluorescent resin and Wood’s metal impregnation or the replica technique (optical and scanning electronic microscopy) [2,4, 9- 121, x-ray technique [ 131, holographic interferometry, etc. Some of these methods (acoustic and laser speckles methods) can monitor crack propagation but cannot be used to determine the initial or final state of material. Due to availability of modem image analysis systems new methods for crack detection provide quantitative data and in this investigation such a method based on digital image analysis is introduced.
EXPERIMENTAL PROGRAM Xater ials Portland cement CEM I 32,5R from G6raidte cement plant was used. Coarse aggregate used was crushed basalt with the maximum grain size of 16mm. Ordinary river sand with the maximum grain size of 2 mm was used as fine aggregate. A liquid melamine-formaldehyde superplasticizer containing 25-27 % of dry substance was used at a constant ratio to the cement mass. High-zirconia glass fibres ARG 13PH-901X were also added to selected concrete mixes. Mixture proportions and specimens Concrete mixes were designed with constant water to cement ratio of 0.48 (Table 1). reference concrete mix (denoted W) was prepared without any additives. Superplasticizer was used in two mixes (S, SZ) in the same amount of 1% of the cement mass. The mix SZ contained also 0.38 % volume fraction of ARG glass fibres. The concrete mixes were produced in a laboratory mixer (capacity 25 litres). The slump and the density were measured directly after mixing. All tests were performed according to Polish Standard PN-88/B-06250. The concrete was cast in lOOxlOOxl00 mm cubical moulds for compression tests and analysis of crack pattern and also in 150x150~150mm cubical moulds for water penetration tests. In order to induce cracks, concrete mixes were exposed to freezing action after 1 hour since mixing: concrete cubes were kept in the climatic chamber at the constant temperature -5°C. After 2 and 4 days of freezing the specimens were demoulded and stored until the age of 28 days in high humidity conditions (RH>90%) and at temperature of 20°C. The reference specimens were demoulded after 24 hours after mixing and then stored in the same warm and humid conditions.
ne
Test methods The range of the investigation covered the following tests: - Axial compression test, - Water penetration test, - Identification and analysis of crack system.
.4pplication of UV image analysis for evaluation of thermal cracking in concrete
103
Table 1. Composition of the concrete mixes
The compressive strength of three series of concrete (reference, frozen for 2 and frozen for 4 days) was determined on lOOxlOOxl00 mm cubes according to the Polish Standard PN-WB06250 (3 for each series). Water penetration test was performed according to PN-EN 12390-8 on 150mm cubes (reference and frozen for 4 days). The initial water pressure of 0,2 MPa was applied and maintained for 24 hours. Then the pressure was increased by 0,2 MPa every 24 hours up to 0,8 MPa. After perpendicular splitting the specimen to the water exposed surface the maximum depth of water penetration was measured. The result represents the mean value from measurements on 3 specimens. casting surface
@regated ske
water saturating
(width = 20 -)
surface
\
impregnated slice (width = 20 nun) /
Fig. 1. Specimen cutting out of lOOx lOOx 100 mm cubes (a) and out of half of 150x150x150 mm cube after water penetration test (b)
'
For crack detection in concrete the slices were cut and impregnated with a fluorescent epoxy resin. Cutting specimens 100x100~20mm from the 100-mm cubes was done in such way that the specimen surface to be examined was situated as closely as possible to the centre of cube perpendicular to the casting surface (see Figure 1). Specimens 150x75~20mm sawn out from the half of 150-mm cubes after testing water penetration were prepared. After cutting, the surfaces of the specimens were ground, polished and cleaned in order to remove surface irregularities produced by saw and to obtain a smooth flat surface. Impregnation of specimens with an epoxy resin containing fluorescent dye was performed in vacuum (- 1 bar) during 15 minutes. The epoxy penetrated into the specimen and hardened in cracks and other defects. The excess of resin at the surface of specimen was removed by grinding down to 2mm from the surface.
104 Michal A . GLINICIU and Agnieszka LITOROWICZ DIGITAL CRACK IDENTIFICATION AND ANALYSIS impregnated reground polished specimens (IRPS) were subjected to observation in ultraviolet light using a Nikon optical microscope at the magnification in the range of 10 to 63 times. An image was acquired by video camera Sony DXC-950P mounted on the microscope. Identification of cracks in impregnated specimens was carried out on digital images by means of Image Pro Plus image analysis system. For each magnification, the images were acquired in two areas of sample surface (Fig.2). surface subjected :asting surface
A
E
Area 1
! I
10 mm
E *E E
Area 1
ul 0
0 v)
Y
There were taken 2, 4 and 6 images at the magnification of lox, 30x and 6 3 x , respectively. Number of images taken from one area and size of image for two kinds of specimens is given in Table 2.
Magnification
Number of images in each area
Size of image for samples Size of pixel
lOOxlOOx20 mm 100x75~20mm I
10 x
1
25 mm x 61mm
32 mm x 52 mm
8.34 pm
30 x
2
8mmx20mm
11 m m x l 7 m m
2.76pm
63 x
3
4 mm x 10 mm
5 mm x 8 mm
1.34 pm
-
A digital image of a concrete specimen is given in Figure 3, which shows typical multiphase image consisting of bulk cement paste, aggregates and various defects (incl. cracks) filled with fluorescent resin. To assess the characteristics of the crack network, it was necessary to convert the colour image into a binary image. Using the image analysis system, the cracks appearing in a given field were extracted after a series of operation on the binary image (Fig.3). These operations first involved a binary segmentation of the digital image. Black and
white image was derived from the original colour image on the basis of its R (red), G (green) and B (blue) components. In this binary image, the pixels defining the defects are assibwed a value of 1 and the background pixels are given a value of 0.Threshold levels were established to encompass the brightest phase in the image, namely fluorescent resin. The threshold level for cracks identification in this case was set between: R:0-255, G:100-255, B:0-255. Then a series of filtering operations was performed. The remaining objects were classified according to their shapes. The criterion of minimal elongation was: RR > 3, where RR (Radius Ratio) is length-to-width ratio, whilst the roundness factor was: Ro > 2. By applying appropriatc shape criteria, cracks were distinguished from other features - porous zones and spherical air voids (Fig.3b). Next, a skeletonized binary image was obtained by binary thinning (Fig.3~).For every thinning step, pixels that are not relevant to the connectivity of a crack are removed from the object margins - converted into background pixels, thus connectivity of crack is maintained. This process was continued until all objects were reduced to their skeleton (to a width of one pixel). The applied image processing was intended to identify crncks in the image. For distinguishing and description crack pattern in concrete six parameters were used: I . Angle - reports the angle between the vertical axis and the major axis of the ellipse equivalent to the object (i,e. ellipse with the same area, first and second degree moments), where 0" 5 Angle" 5 180". 2. Area - reports the area of each object (any holes in object are not included to object area). 3. Dendritic length - reports the total length of all the dendrites (one-pixel-thick branches). 4. PerArea - reports the ratio between the area of the counted object to the entire area of the active image. 5 . Radius Ratio - reports the ratio between Max Radius and Min Radius for each object. 6 . Roundness - reports the roundncss of each object, as determined by the following formula: perimeter 2/ 4*fI*area. Circular objects have a roundness = I ; others shapes have roundness > I .
'\
Fig.3. The image processing stages: a) original colour image, b) binary image after thresholding, c) binary image after thinning
106
Michut A . GLINICIU and Agnieszka LITOROWICZ
Thus, for each concrete specimen it is possible to determine:
Length of cracks - L [mm] - total length of all the dendrites of each cracks on the image, Average width of cracks - W [mm] - total cracks area per total dendritic length, Area of cracks - A [mm’] - total area of each cracks on the image, Density of cracks - LA [mm/mm2] - total dendritic length of cracks per image area, Areal fraction - AA [mm2/mm2]- ratio between the area of the counted cracks to the entire area of the active image, 6. Orientation of crack system - can be shown by means of “rose of cracks direction”.
1. 2. 3. 4. 5.
TEST RESULTS Compressive strength Table 3 presents the compressive strength data. The strength is given as an average value f, of 3 measurements in each series. Values of the compressive strength obtained for concrete types W, S, S Z were similar. For series of concrete exposed to freezing action after 1 hour after mixing (Wm, Sm, SZm), the compressive strength was significantly reduced - down to 50-55 % of reference (undamaged) concrete specimens. The freezing period (2 or 4 days) had a very small influence on the compressive strength and this influence could be neglected.
Water penetration test Depth of water penetration under pressure was determined on concrete specimens after lowtemperature deterioration and on reference specimens (Table 4). It can be observed that the water penetration depth for undamaged concrete series (W, S, SZ) was similar within the range from 22 mm to 23 mm. Low-temperature damage significantly decreased the resistance to water penetration under pressure: the penetration depth was from 62 to 82 mm that is an increase of 3-4 times in comparison with undamaged concrete. The concrete specimens SZm with glass fibres, which were subjected to freezing, showed the smallest resistance to water penetration. Analysis of crack pattern Cracks were observed in the low-temperature deteriorated concrete only. Table 5 gives the crack characteristic of samples cut from 100-mm cubes. Reference concrete (Wm2, Wm4) prepared without superplasticizer and fibres showed the highest crack density at every magnification, while the lowest crack density was seen in concrete with superplasticizer
107
Application of UV image analysis for evaluation of tkerrnal cracking in concrete
(Sm2, Sm4). The results indicate that the crack density is very sensitive to the magnification factor. Table
days
Concrete
Area bm21
22.00 20.89
Wm2 Wm4 Sm2 Sm4 SZm2 SZm4
0.87 0.81 0.59 0.61 0.59 0.48
Total length Average Density [mml width [mm] [mml mm2]
I I
266.13 273.79
21.50 21.14 14.51 15.60 17.20 16.56
I I
0.082 0.076
0.040 0.036 0.041 0.039 0.034 0.029
I I
0.171 0.176
0.535 0.526 0.361 0.388 0.428 0.412
Areal fraction
I I
0.0 14 0.0 13
0.022 0.020 0.0 15 0.0 I5 0.015 0.012
Average width of cracks decreases with increased magnification and is contained in ranges: 0,71-0,82 mm, 0,54-0,65 mm and 0,29-0,41 mm at the magnification of 10, 30 and 63x, respectively. A higher magnification allows to detect also smaller defects.
108 Michal A. GLINICKl and Agnieszka LITOROWICZ Identification and analysis of cracks was carried out on samples prepared from 150mm cubes subjected previously to water penetration test. There were no cracks in the specimens not subjected to freezing. Results of crack analysis were summarized in Table 6. In this series of specimens the highest crack density was observed in concrete with fibres (SZm4) and the lowest - in reference concrete (Wm4). As it is seen from Table 4 and Table 6 a clear relationship between the water penetration depth and the cracks density is found: the water penetration in concrete increased with an increase of crack density.
I
Table 6. Results of crack analysis (150x150x150mm cubes after water penetration test)
CC ncrete Wm4 Sm4 SZm4
SZm4 Wm4
Area 18.71 37.98 50.63
0.90
Areal
Total length Average width(mm1 [mml 250.9 456.8 593.2 49.4 62.4 124.3 25.9 28.6 46.8
I
0.077 0.082 0.086
0.361
0.051 0.050 0.050
: 9 :
0.034 0.034 0.037
0.673
I
1
0.031
0.035 0.02 1 0.024
CONCLUSIONS A digital image analysis technique for the detection and quantification of cracks in concrete was elaborated using impregnated reground polished sections. Observation in ultraviolet light using an optical microscope at the magnification in the range of 10 to 63 times allowed to detect fine cracks, paste-aggregate transition zones, porous areas and air bubbles. The technique generates images with a good contrast, which are convenient for quantitative analysis. The contrast of the crack images in relation with the adjacent material was strongly dependent on the porosity of the cement paste. Low-temperature action on fresh concrete mix reduced the compressive strength of concrete by 50 - 55 ‘YOand increased the depth of water penetration by a factor of 3 to 4. Such a damage induced a system of cracks in concrete that could be identified and analysed. The crack density and the average width of crack were found to be related to the magnification factor. An increase of the crack density was related to an increase of water penetration depth. The elaborated technique can be used for quantification of cracks in concrete specimens made in the laboratory and also in elements sawn out from existing concrete structure damaged by various mechanisms (mechanical, physical or chemical) e.g. structure exposed to freezing during construction.
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ACKNOWLEDGEMENT The research was performed within the framework of NATO Science for Peace Project No. 97 1888 ,, Diagnosis of Concrete and High Performance Concrete by Structural Examination”.
REFERENCES 1. Samaha, H. R., Hover, K. C., Influence of microcracking on the mass transport properties
of concrete, ACI Materials Journal 89,4, 1992, pp 416-424 2. Jacobsen, S., Marchand, J., Boisvert, L., Effect of cracking and healing on chloride transport in OPC concrete. Cement and Concrete Research, 26,6, 1996, pp 869-881 3. Aldea, C. M., Shah, S. P., Karr, A., Permeability of cracked concrete, Materials and Structures, 32, 1999, pp 370-376 4. Gkrard, B., Marchand, J., Influence of cracking on the diffusion properties of cementbased materials. Part I: Influence of continuous cracks on the steady-state regime. Cement and Concrete Research, 30, 2000, pp 37-43 5. Glinicki M.A., Litorowicz A., Digital analysis of cracks in concrete induced by thermal action, (in Polish), XVIII Scientific-Technical Conference “Concrete and Precasting”, Popowo, April 2002, pp 6. Korhonen, Ch., Ryan R., New low-temperature admixtures, Concrete International, May 2000, pp 33-38 7. Ohtsu, M., Okamoto, T., Yuyama, S., Moment tensor analysis of acoustic emission for cracking mechanisms in concrete. ACI Structural Journal, 95,2, 1998, pp 87-95 8. Popovics, J.S., Song, W-J., Ghandehari, M., Subramaniam, K.V., Achenbach, J.D., Shah, S.P., Application of surface wave transmission measurements for crack depth determination in concrete. ACI Materials Journal, 97, 2,2000, pp 127-135 9. Ammouche, A., Breysse, D., Hornain, H., Didry, O., Marchand, J., A new image analysis technique for the quantitative assessment of microcracks in cement-based materials. Cement and Concrete Research, 30,2000, pp 25-35 10. Nemati, K.M., Monteiro, P.J.M., Scrivener, K.L., Analysis of compressive stress-induced cracks in concrete. ACI Materials Journal, 95, 5 , 1998, pp 617-630 1 1. Sicard, V., Francois R., Ringot E., Pons G., Influence of creep and shrinkage on cracking in high strength concrete, Cement and Concrete Research, 22, 1, 1992, pp 159-168 12. Darwin, D., Abou-Zeid M. N., Ketcham K. W., Automated crack identification for cement paste, Cement and Concrete Research, 25, 3, 1995, pp 605-616 13. Slate, F. O., Olsefski S., X-rays for study of internal structure and microcracking of concrete, Journal of the American Concrete Institute, 60, 5 , 1963, pp 575-587
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
ASSESSING DAMAGE LOCALIZATION IN CONCRETE CYLINDERS TESTED IN COMPRESSION Sunil P U N and Jason WEISS School of Civil Engineering Purdue University, West Lafayette, USA. email:
[email protected]
ABSTRACT The compressive stress-strain behavior of concrete is a critical material descriptor that is used in the design and analysis of concrete structures. While significant research has been performed to illustrate the importance of the peak strength and initial elastic modulus, further work is needed to explain how damage develops, dissipates energy, and results in stiffness degradation. While the stress-strain response has long been considered a material property, recent research has shown that this relationship is dependent upon specimen geometry and size. This research investigated the development of damage, its localization into a band, the size of this band, and the implications of this damage band on the overall stress-strain response. In addition to load and deformation measurements, acoustic emission was used to quantify damage. Specifically, a detailed analysis using acoustic emission activity is presented to describe damage in terms of event amplitude, duration, and energy. To support the correlation between the acoustic activity and physical damage in concrete that was loaded to different levels, the damaged cylindrical specimens were sectioned, ground, polished, and imaged to inspect the extent of cracking and the resulting damage at different locations in the cylinders. Image analysis was compared to the acoustic measurements to present clear picture of how damage develops and localizes in concrete under compressive loading. Keywords Aeal compression, Acoustic emission, Concrete, Damage, Image analysis.
INTRODUCTION The stress-strain behavior of concrete is frequently used in the design of concrete structures. Over the last four decades research has focused on relating the stress-strain behavior of concrete
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Sunil PURIund W. Jason WEISS
to the damage that develops in the specimen (5, 15, 18). The majority of these investigations have modeled concrete as a material that degrades uniformly throughout the specimen. Recent investigations have questioned the use of a uniform damage approach and have advocated the existence of a localized damage region (4, 12, 18, 20). Though the presence of region of local damage has gained acceptance (17), the size of compression damage zone and its role in the stress-strain response has not been fully understood (4). This paper is intended to improve on the fundamental understanding of damage development, localization and the resulting stiffness degradation of concrete when it is tested in compression. A variety of experimental techniques have been used in the past to investigate the development of damage (lo). A real-time, non-destructive technique is beneficial for assessing and locating damage as it develops. Acoustic Emission (AE) is one such technique that provides non-invasive measurement of the material that is being tested. AE has been used to investigate how concrete fractures and degrades (7, 9, 11,22). Previous researchers have offered a variety of characteristics of the acoustic wave form (number of hits, amplitude, and corresponding acoustic energy) in an attempt to separate and quantify the fracture mechanisms (7, 22). Recent work has illustrated that acoustic emission energy can be correlated to the mechanical fracture energy that develops in the specimen (8). While AE provides indirect information about damage development, an optical technique is used in this paper as a secondary method to quantify some of the physical aspects of the damage that develops. RESEARCH SIGNIFICANCE
The design of concrete structures typically utilizes the peak strength and initial elastic stiffness to approximate the stress-strain response of concrete (i.e., Whitney’s stress block) (1). While the stress-strain response is commonly thought of as a material property, it has been shown that the stress-strain response is dependent on the specimen size and geometry (5, 18). This research is aimed at investigating the initiation of microcracks, their coalescence, the development of a localized band of damage, and its effect on the overall stiffness of concrete. This paper describes the use of acoustic emission measurements to quantify the size of the compression damage zone (CDZ). By quantifying the size of the CDZ, a composite modeling approach can be used to quantify the role of the bulk and damage zones for predicting the stress-strain response of concrete. In addition, the relationship behveen optically observed damage and acoustic measurements can be established to indicate how acoustic sensors may be used in structural health monitoring. EXPERIMENTAL PROGRAM Spc cimens were prepared following the RILEM 148-SSC (1997) recommendations for determining the strain-softening response of concrete tested under uniaxial compression. Cylindrical specimens were chosen with a length-to-diameter (L/D) ratio of four in order to provide sufficient space for the compression damage zone (CDZ) to develop. The following sections describe the specimen preparation, experimental procedures, and the experimental results obtained from this study.
Assessing damage localization in concrete cylinders tested in compression
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Specimen preparation The mixture proportions used in this investigation are based on those described in RILEM 148SSC (1997). Type I portland cement was used with a water-to-cement ratio (wk) of 0.50. A locally available sand and coarse aggregate were sieved to obtain gradations similar to those described in RILEM 148-SSC (13, 17). In addition, 50 mm polypropylene fibers (structural fibers manufactured by Grace) were incorporated (0.75% of fibers by volume) into the mixture. Standard practices for making and curing concrete test specimens were followed (2). The specimens were cast in cylindrical molds with a diameter of 76 mm (3 in.) and a height of 406 mm (16 in.). The top and bottom ends of the specimens (approximately 5 1 mm) were removed to attain a specimen with the desired length (304 mm), thereby removing any end-effects that may be present due to the casting process. Specimens were placed in a moist environment (98% relative humidity and 23°C) until the time of testing. After 28 days, the ends of the specimens were ground using a lapping wheel to ensure that ends of the specimen were flat. After grinding, the specimens were placed back in the moist-curing room where they were kept until the time of testing (approximately 90 days). Experimental configuration Results from six specimens are described is this paper. Specimens were loaded in compression using a MTS machine which was equipped with a hydraulic actuator and a 490 kN (1 10 kip) load cell. The bottom platen was fixed against rotation and the top platen was permitted to rotate. Two sheets of teflon (each with thickness of 0.254 mm) were used on each end of the specimen to reduce friction between the ends of the specimens and platens thereby reducing the confining strvses (3, 16, 17). Two linearly variable differential transformer (LVDT) displacement transducers were used to measure platen-to-platen displacement. The LVDTs and load cell were interfaced with a computer for signal conditioning and data acquisition. In addition to the mechanical measurements, four piezoelectric (375 kHz) wide band sensors were used to record the acoustic activity generated in the specimen. The location of sensors and the technique used to attach sensors on the surface of the specimen can be found in Puri and Weiss (13). Initially, a load of 2.2 kN (500 kips) was applied to the specimen to bring the platens (i.e., teflon sheets) in contact with the ends of the specimens. The LVDTs were adjusted to zero and acoustic sensors were activated to record the AE events above 50 dB. Counters on the both the acoustic emission and mechanical testing computers were synchronized at the beginning of the testing. Experimental testing The specimens were tested in compression using displacement control at a rate of 200 pdmin. After reaching predetermined load levels (58% prepeak, 78% prepeak, 98% postpeak, 80% postpeak, 60% postpeak, 38% postpeak), the specimens were unloaded. Mechanical testing data was recorded at intervals of one second. Optical damage assessment After testing the specimens were removed from the testing machine. Thorough visual inspection was performed on each specimen and the extent and location of visible damage was recorded. The specimens were air-dried and kept at room temperature conditions for atleast two weeks. After drying, the damaged specimens were prepared for image analysis using a five step
I 14 Sunil P U U and CY. Jason WEISS
approach: I ) damage stabilization, 2) sample preparation, 3) image acquisition, 4) image processing, and 5) damage quantification (14). Ultra-low-viscosity epoxy resin (Sikadur-55) was used to stabilize the damaged specimens. The specimens were placed in the molds and the ends of the molds were capped and sealed at the top and bottom. Two outlets were left at the top of the mold, one of which was attached to a vacuum pump and the other to the source of epoxy resin. A vacuum was drawn to allow the epoxy (with dissolved carbon black) to enter the damaged specimen at an atmospheric pressure of 25 mm of mercury for 30 minutes. The vacuum was released to 10 mm of mercury as fumes started forming during hardening of the epoxy resin. After the development of fumes stopped, the vacuum level was again increased to 25 mm. This procedure was repeated until bubble formation stopped which hinted that the cracks were filled with epoxy resin. The molds were detached from the vacuum pump and maintained at the room temperature until epoxy hardened. After the epoxy hardened, coordinate axes were marked as vertical grooves on the edges of the stabilized specimens. A diamond tipped saw was used to cut the stabilized specimens into 25 mm (1 inch) thick samples. The rings were labeled and their cut surfaces were coated with black spray paint. Rings were polished on a lapping-wheel using different silicon carbide grits to obtain smooth surface. Light reflection technique was used to verify proper polishing of each surface (6). The surfaces were polished until the spray paint was removed from the surface and a good reflection of light was observed. Colorless varnish was then applied to the final surface. To assess damage on the cut surfaces, the polished surfaces were scanned using a flat-bed scanner. Images (76 mm x 76 mm (3 in. x 3 in.)) were captured at a resolution of 300 pixels/inch. A coordinate axis that matches the groove locations along the specimen was also recorded on scanner surface to ensure that the ring surfaces could be reassembled for threedimensional analysis. The following section describes the results of the experimental program.
EXPERIMENTAL RESULTS
As discussed in the previous section, the specimens were unloaded at different strain values. Figure 1 shows the typical compressive stress-strain response of the cylindrical specimens. The stress measurements were normalized to the peak stress and the strain measurements were normalized by the strain corresponding with the peak stress (i.e., For specimens unloaded in the prepeak region, stress values were normalized by an average peak stress of 39 MPa and strain values were normalized by an average strain of 2500 microstrain. It can be seen in Figure 1 that the specimens have a similar response envelope. The focal point approach has been used for the analysis of unloading stress-strain slopes (13, 21). This approach was used to calculate the fracture energy that was dissipated at each point of unloading. Acoustic sensors recorded the acoustic activity. The acoustic events (hits) were categorized on the basis of their wave characteristics. This included features like amplitude (i.e., the maximum voltage recorded for the particular event) and duration (i.e., the time period for which the voltage of an event remains higher than the threshold value of the voltage). Figure 2 shows the acoustic events categorized on the basis of amplitude, superimposed on the stress-strain response of the specimen. It can be noticed that high amplitude events do not begin until higher strain levels are reached.
115
Assessing damage localization in concrete cylinders tesied in compression
Very high amplitude events (80 dB and above) begin around the time the peak load is reached. This is consistent with the idea that smaller cracks (low amplitude events) occur at low load levels whereas larger cracks (high amplitude events) occur at high stress levels (70% of peak stress and higher). A similar response has been obtained for acoustic events on the basis of their duration (13). To capture aspects of both amplitude and duration, the energy carried in the acoustic wave during the “cracking” process was assessed. Acoustic energy is defined in this paper as the absolute value of area under the acoustic waveform. Figure 3 shows the relationship between the measured acoustic energy and mechanical fracture energy density calculated from the stress-strain curve of the individual specimens (1 3). A relatively linear relationship is observed between acoustic energy and mechanical fracture energy. The triangulation process was used to determine the exact location of acoustic emission with an average velocity of sound (4200 d s e c ) . Figure 4 shows a three dimensional plot of the cumulative acoustic energy and its source location for one specimen as a hnction of increasing strain. It should be noted that not every event could be accounted for since each event must be captured by more than one sensor. It can be noticed in Figure 4 that relatively uniform energy is released along the length of the specimen till the peak stress is reached (&peak). It appears that at the peak load the energy dissipation increases in one region of the specimen (i.e., the upper region in this specimen), however the damage region was found to vary in location from specimen to specimen.
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Figure 3: Relation between acoustic energy and fracture energy density
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1 16 Sunil PUN and W.Jason WEISS
Figure 5 illustrates the formation and development of the CDZ that was obtained from the acoustic energy emission. In the prepeak region the damage is assumed to occur uniformly through out the specimen. After the peak load is achieved, the damage occurs primarily in the CDZ causing a reduction in the stiffness while stiffness in the bulk region remains constant. At peak load the zone of energy emission can be approximated as the top 90 mm of $ the specimen. As the strain increases, this energy emission zone (CDZ) starts expanding and it N’ grows until the strain reaches 1.6 E ‘% &peak at which time it becomes 9 approximately 160 mm long. This demonstrates that the length of CDZ grows till it reaches a length of two times the diameter of cylinder. This is consistent with the assumptions used by Palmquist and Jansen (12) for modeling the Figure 4:Location and size of CDZ postpeak behavior of stress-strain
$ $
’
ciirve.
Using this approach a series model, was used to predict the stiffness degradation of the CDZ after it begins to develop at the peak load (Equation 1). In this equation L refers to length and E to elastic modulus while the subscripts refer to either the CDZ, bulk or total regions respectively. A focal point approach (13) was used to calculate the bulk stiffness. The results of this analysis are shown in Figure 5. It can be noticed that until the peak load is reached the stiffness (damage) is assumed to be uniform throughout the specimen. Immediately after peak, the CDZ forms and the length of the CDZ begins to rapidly increase. The length of CDZ reaches a constant length at approximately 1.6 times the strain at peak.
320
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0.8 1.0 1.2 1.4 1.6 1.8 2.0
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Figure 5: Development of CDZ and its stiffness degradation
Image analysis was used to quantify damage in the specimen. Figure 6 shows a typical image from a slice of the tested specimen taken perpendicular to the axis of testing. While the visible macrocracks appear to be dark, further analysis is needed to describe the remainder of
Assessing damage localization in concrete cylinders tested in compression
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surface. It can be noticed that the epoxy resin seeped through macrocracks, darkens the specimen and makes them distinguishable from the rest of the surface. Macrocracked
While the undamaged region appears lighter, to analyze these different areas, the images of sample surfaces were further studied under optical microscope; examples of which can be seen in Figure 7. While no cracking has been found in lighter area (i.e., Figure 7c), dark gray areas around macrocracks have been found to contain microcracking (i.e., Figure 7b). This signifies that the penetration of epoxy in microcracked region is likely responsible for providing the gray shade around the macrocracks. Each pixel of the captured image was categorized according to intensity on a numerical scale where 0 represents black and 255 stands for white.
(a) Macrocracked Rcgion
Figure 6: Typical ring surface
(b) Microcracked Region
(c) Undamaged Region
Figure 7: Different levels of damage on nng surfaces (each image is 6 mm x 4 mm) The surfaces of the sectioned specimen were categorized as damaged, partially damaged and undamaged based upon the gray scale level. Table 1 provides the gray scale range selected for different areas of ring surfaces. Ring surfaces were processed using Image Pro Plus software to obtain a final image in three colors. Table 1: Color classification for processing image
13 1-200 201-255
.',,
.
Partially damaged (microcracked) Undamaged
Figure 8 shows a typical original image and the corresponding processed image. After processing the image based upon the damage level, the number of pixels corresponding to each
1 18
Sunil P U N and
W.Jason WEISS
color was counted (i.e., damaged, partially damaged, and undamaged). The percentage of pixels corresponding to each color was assessed. To avoid erroneous counting of some of the dark colored aggregates or pores as damaged part, the aspect ratio of each feature was determined. Features with an aspect ratio (i.e., lengthlwidth) of 1.75 or smaller were screened out of damaged category. This process was applied to all the ring surfaces from the tested specimens.
(a) Original image (b) Processed image Figure 8: Processing of images Figure 9 shows the percentage of the area of the surface that was found to correspond to micro (partially damaged) and macro (damaged) level cracking at each section of the specimen which was unloaded at 38% of peak stress in the postpeak region. The bottom half of the specimen has uniform micro and macro cracking while the upper portion of the specimen shows comparatively higher damage level. A uniform level of damage in bottom section is consistent with the existence of bulk or primarily undamaged zone. Percentage Total Damaged Area 20
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Assessing damage localization in concrete cylinders tested in compression
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Damage was assessed at different locations along the length of the specimen. Optical damage assessment obtained from these images was compared with the location of acoustic emission events (Figure 10). The bottom half of the specimen (0-15 cm) shows low acoustic energy. This is consistent with the macrodamage seen in the specimen. The top portion of the specimen experiences severe damage. Figure 10 depicts this both in the form of acoustic energy emission and the percentage damaged area. While the percentage of the damaged region has been found to increase near the end of the specimen, acoustic emission energy depicts an approximate constant trend.
CONCLUSIONS
This paper described the use of acoustic emission to monitor the behavior of concrete tested in compression. Acoustic events were categorized on the basis of their amplitude and duration. It was observed that low amplitude, shorter duration events occur at low stress levels while higher amplitude, longer duration events occur as the load level increases. To capture the characteristics of the waveform, acoustic energy was calculated as the absolute value of the area under the waveform. The acoustic energy was observed to have a linear relationship with the dissipated fracture energy. This implies that the acoustic energy parameter may possess the ability to noninvasively quantify mechanical damage in the concrete specimens. The results presented in this paper indicate that the compression damage zone (CDZ) develops near the peak stress. At peak load, the size of the CDZ is approximately 1.2 times the size of the diameter of the cylinder and it grows until strain reaches approximately twice the diameter of cylinder at 1.6 times the strain at peak. After the strain reaches 1.6 times the peak strain, the length of the CDZ is found to occupy a constant length. Acoustic emission analysis matches with the damage measured by using image analysis. Further work is needed to determine how the observed size of the CDZ changes for different mixture proportions, aggregate size, and length-to-diameter ratios (L/D). ACKNOWLEDGEMENTS
The authors gratefully acknowledge support received from the Center for Advanced CementBased Materials (project C- 1) and the National Science Foundation (NSF). This paper is based in part on work supported by the National Science Foundation Grant No. 0134272: a CAREER AWARD granted to the second author. This work was conducted in the Charles Pankow Concrete Materials Laboratory; as such, the authors gratefully acknowledge the support which has made this laboratory and its operation possible. REFERENCES 1. American Concrete Institute (2002), “Building Code Requirements for Structural Concrete.” ACI 3 18-02. 2. ASTM Standard Designation C192, (2000), “Standard practice for making and curing concrete test specimens in the laboratory.” The American Society for Testing and Materials.
120 Sunil PURI and W. Jason WEISS
3. Choi, S., Thienel, K.C. and Shah, S.P. (1996). “Strain softening of concrete in compression under different end constraints.” Magazine of Concrete Research, Vol. 48, No. 175, pp. 103-115. 4. Jansen, D.C. (1996). “Postpeak properties of high strength concrete cylinders in compression and reinforced beams in shear”; PhD Diss., Northwestern Uni., Evanston, IL. 5. Jansen, D.C., and Shah, S.P. (1997). “Effect of length on compressive strain softening of concrete” Journal of Engineering Mechanics, Vol. 123, No. 1, Jan., 25-35. 6. John, D.A.St., Poole, A.W. and Sims, I (1998), Concrete Petrography, A handbook of investigative techniques. 7. Kim, B., and Weiss, W. J., “Using acoustic emission to quantify damage in restrained fiber reinforced cement mortars.’’ Cement and Concrete Research, Feb, 2003. 8. Landis, E.N., and Whittaker, D.B. (2000). Acoustic emission as a measure of fracture energy. Proceedings: 14th ASCE Engineering Mechanics Conference, Austin, TX. 9. Landis, E.N., Ouyang, C. and Shah, S.P. (1991). “Acoustic emission source locations in concrete. Proceedings.” ASCE Engineering Mechanics Specialty Conference, Columbus, OH., May, 20-22. 10. Malhotra, V.M. and Carino, N.J. (1991). “Handbook on Non-destructive Testing of Concrete”. 11. Ohtsu, M., and Watanabe, H. (2001). “Quantitative damage estimation of concrete of acoustic emission.” Construction and Building Materials, 15, 2 17-224. 12. Palmquist, S.M. and Jansen, D.C., (200 1). “Postpeak strain-stress relationship for concrete in compression” ACI Materials Journal Vol. 98, No. 3, May-June, 2 13-219. 13. Puri. S. and Weiss J., Assessment of localized damage in concrete using acoustic emission, Submitted to A X E Committee for Journal of Materials in Civil Engineering, 2003. 14. Qi, C., Weiss, J. Olek, J. (2002), “Characterization of plastic shrinkage cracking in fiberreinforced concrete using image analysis and a modified weibull function.” Accepted at Materials and Structures. 15. Shah, S.P., and Chandra S. (1968). “Critical stress, volume changes, and microcracking of concrete.” Journal of American Concrete Institute, Vol. 65, 770-78 1. 16. Shah, S.P., and Sankar, R. (1987). “Internal cracking and strain-softening response of concrete under uniaxial compression.” ACI Structural Journal, Vol. 84, No. 3, 200-2 12. 17. Van Mier, J.G.M, Shah, S.P., Arnaud, M., Balayssac, J.P., Bascoul, A., Choi, S., Dasenbrock, D., Ferrara, G., French, C., Gobbi, M.E., Karihaloo, B.L., Konig, G., Kotsovos, M.D., Labuz, J., Lange-Kombak, D., Markeset, G., Pavlovic, M.N., Simch, G., Thienel, K-C., Turatsinze, A., Ulmer, M., Van Geel, H.J.G.M., Van Vliet, M.R.A., Zissopoulos, D. (1997). “Strain-softening of concrete in uni-axial compression.” Materials and Structures, RILEM 148SSC, Vol. 30, May, 195-209. 18. Van Mier, J.G.M. (1984) “Strain-softening of concrete under multiaxial loading conditions.” PhD Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands. 19. Van Mier, J.G.M. (1997), “Fracture process of concrete” CRC Press Inc. 20. Weiss, W.J., Giiler, K. and Shah, S.P. (2001) “Localization and size-dependent response of reinforced concrete beams.” ACI Structural Journal, Vol. 98, No. 5, Sep-Oct, 686-695. 21. Yankelevsky D.Z., and Reinhardt H.W. (1987), “Response of plain concrete to cyclic tension.” ACI Material Journal, Vol. 84, No. 5, Sep.-Oct., 365-373. 22. Yoon, D.-J., Weiss, W. J., and Shah, S. P., (2000) “Assessing Corrosion Damage in Reinforced Concrete Beams Using Acoustic Emission.” J. of Engineering Mechanics Division, ASCE, 126(3), 273-283.
Proc. Int. Sytnp. ((BrittleMatrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
QUANTITATIVE DAMAGE ANALYSIS OF CONCRETE Piet STROEVEN Faculty of Civil Engineering and Geosciences Delft University of Technology Stevinweg 1,2628 CN Delft, The Netherlands, e-mail:
[email protected]
ABSTRACT The load-induced damage structure in concrete can be conceived as a spatial structure of dispersed surfaces of which the connectivity increases during load increase. Quantitative image analysis by line scanning in 'vertical sections' allows determination of crack surface area per unit of volume and degree of crack orientation. This paper presents the methodology, and demonstrates its applicability for assessing damage evolution characteristics in low-cycle compression fatigue domain and in direct tension. The associated tests have been conducted earlier.
Keywords Compression, cracking, damage, modelling, stereology, tension.
INTRODUCTION The damage evolution process can be considered uniquely reflecting certain loading regimes operative under specified circumstances. Vile [l] was probably the first to propose a model for meso-cracking underlying global damage evolution in direct compression. The topic also received attention by Stroeven [2], Newman & Newman [3], and Perry and Gillott [4], providing experimental evidence in support of the model. Analytical support comes from elastic solutions of single inclusions in an infinite matrix the oldest of which dates back some seventy years [5-81. The first systematic experimental investigation into damage evolution of concrete, using different techniques, was performed by the 'Cornell group' [8,9]. Images of sections were analysed two-dimensionally, however. It was concluded, among other things, that 50% of the damage at ultimate loading was already present in the virgin state [8], so not typical of the loading regime. To complicate matters further, the fractal concept has revealed such ratios to be sensitivity-dependent [lo]. Quantitative microscopy is the more common way to quantify local features of damage in concrete [ I 1,121; specimens are easy to handle and grinding and polishing operations can be automated. Applications of quantitative image analysis (stereology) for assessment of three-dimensional global damage parameters are extremely scarce [2,13-161. Yet, results can offer insight into cracking mechanisms underlying mechanical phenomena, or allow structural interpretation of macro-mechanical models.
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QUANTITATIVE IMAGE ANALYSIS Apartially linear system, as a close approximation for the damage structure induced by uniform compression in a cylindrical specimen, can be emphasized as a mixture of 3-D and I-D systems. The cracks are in both systems randomly distributed as to location. In the first case, the cracks are also randomly distributed as to orientation, whereas in the second one all cracks are parallel to a line, the axis of the specimen. In a vertical secfion, the 3-D system yields a random pattern of traces, while the I-D system leads to traces parallel to the axis of the specimen. The number of intersections with a parallel line probe is indicated by P , and its density by P / L = PL. Perpendicular to the orientation axis of the traces the intersection density will have a maximum value, while a minimum is found in an orthogonal direction. It is well known that the intersection density in a certain direction, & ( O ) , is an unbiased estimator of the total projected length of the traces, per unit of area, on a line perpendicular to the grid direction, L;(O + x / 2 ) . Hence, P'(0) =.Li(O + n / 2 ) [2,16]. For the axial and transverse direction it is readily found that
in which LA, and LA, are the areal trace densities in the 1-D and 3-D system, respectively. Obviously, LA = LAI+ LA,, so that
The degree of orientation in the trace pattern can be defined by
The 3-D interpretation of a similar set of observations is equally simple! The same probabilistic principle holds. Hence 1 I F 1 2 PL(0)=-Sv3 and PL(-)=-Sv3 +-S VI 2 2 2 IF
In analogy with the 2-D case:
(4)
Quantitative damage analysis of concrete
123
In case of unifbrm tension, the actual damage structure can be conceived composed of a mixture of 3-D and 2-D systems. Again, cracks in both systems are supposed to be randomly distributed as to location, and in the 3-D set also as to orientation. In the 2-D system, all cracks are developed, however, perpendicular to the loading direction, so parallel to the socalled orientation plane. This is referred to as partially planar crack orientation. The vertical section reveals a mixture of these systems, the pattern of which is equivalent to the one obtained for the partially planar case but rotated in the plane over 90'. In analogy with eqs. (4) and (9,we have 1 R 1 2 PL(0)=-Sv3 and P L ( - ) = - S v 3 + - S v z R 2 2 2
(6)
A comparison between the two- and three-dimensional expressions for w and crack density will reveal the bias of the seemingly (but not really) simpler two-dimensional approach. The partially planar model has been used for evaluation of direct tensile tests on two-sided notched prisms, and the partially linear model for doing so for low-cycle compression fatigue tests on prismatic specimens. EXPERIMENTAL: COMPRESSION CASE Testing was performed in low-cycle compression fatigue to evaluate the effects of average stress level, stress amplitude and frequency on the number of cycles to fracture, N. The frequencies covered were 17.5 Hz and 0.175 Hz. The upper stress level,o,', was taken for all tests at 87.5% of the 28-days short-term compressive strength,o;,, , of prismatic specimens with similar composition. Hence, this is well above the so-called endurance limit. A relative stress amplitude, S, is defined by S = (0,' - o b ' ) / o ) z 8 in,which ob' is the lower stress level. S varied in the investigations between zero and 0.475. Out of the eight stress amplitude cases encompassed in the experiments, three were included in the quantitative image analysis. The selected cases, S O , S0.075 and S=0.35, represent the mechanical states of permanent loading, and of low-cycle fatigue loading with small, respectively, with large load amplitude. A total number of 72 prismatic specimens (100x100~345mm3) were cast from concrete with a maximum grain size of 8 mm and a water to cement ratio of 0.46. Average 28-days compressive strength of reference prisms amounted to 56.2 MPa. The prisms were stored 10 days under water, followed by 7 days under controlled conditions (22' C, 50%RH), whereupon the specimens were placed until the day of testing at about 1 month in the test room. Sieve curves were between the As and Bs curves of DIN 1045. A single specimen whose deformational behaviour was as close as possible to that of the group average was selected for quantitative damage analysis. Deformations were recorded by clip gauges in longitudinal and in transverse direction. Specimens were subjected to sinusoidal load variations in a servohydraulic testing machine. The loading process was automatically stopped when the transverse deformation attained a certain threshold value [ 171. This rendered possible to study the
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Piet STROE VEN
internal damage structure of the specimens without introducing a significant bias in the number of cycles to fracture. Each selected specimen was axially sliced to yield three equally spaced sections at a distance of 27 mm [18]. Specimens were cast, compacted and stored in vertical position. Since the loading was applied also in the same direction, the longitudinal axis of the specimen can be considered an axis of symmetry of the damage structure (excluding boundary zones). Fields of 51x102 mm2 were selected at the centre of each section image. Hence, a sample encompassed three independent so-called 'vertical' fields, which were subjected to intersection counting in the two main directions. The distance between the grid lines was optimised to yield a number of intersections roughly equal to the number of cracks in a field. In doing so, a total test line length of 1734 mm was obtained. Contrast was improved by employing the filtered particle method [2,16]. Mechanical properties were generally found in agreement with published data. They were supported by the stereological outcomes [ 17-19]. Additional information is offered on underlying damage evolution mechanisms, however. Table 1 presents some illustrative data. Note that N A is the number of cracks in the section per unit of area. We will focus on a peculiar phenomenon [ 181, i.e. a prevailing direction of damage evolution perpendicular to the compression direction! This occurred under maximum amplitude (S=0.35) and maximum frequency conditions (17.5 Hz). Average loading was in that case 17.5% lower than under permanent loading (S=O). Nevertheless, these conditions proved very destructive (T is time to fracture). The proposed model by Vile [l] for damage evolution on meso-level, elaborated earlier for general use by this author [2], was applied to the present case [17,18]. The wellknown column-like structure of concrete that is subjected to a uniform state of relatively high compression is effectively broken down by debonding (thus: cracking) at aggregate-matrix interfaces perpendicular to the compression direction. This is the result of secondary tensile stresses initiated under stress release to below the so-called discontinuity point.
Table 1:Low cycle fatigue data at 17.5 Hz S
S"
0 0.075 0.350
[mm-'] 0.561 0.601 0.678
NA
0 3
~ m m - ~ ] [%I 0.127 8 0.113 11 0.151 -3
N 42.800 1361300 4,600
T [set 1 2.446 81246 263
EXPERIMENTAL: TENSION CASE Two-sided notched fine-grained concrete prisms (60x50~250mm3) were subjected to a shortterm direct tensile loading in a servo-controlled system with a maximum capacity of 100 kN. The notches reduced the cross sectional dimensions to 50x50 mm2. Concrete was composed of 375 kg/m3 Portland cement and 905, 363 and 540 kg/m3 aggregate of the size ranges 0-2 mm, 2-4 mm and 4-8 mm, respectively. The specimens were cut from larger 50 mm thick panels that were cast vertically to avoid boundary effects. Average compressive and tensile strength values at 28-days were 47.1 and 3.20 N/mm2, respectively. Specimens were glued between steel platens to promote the fracture process zone to undergo uniform deformations. Deformation measurements were executed by a series of extensometers with a gauge length of 35 mm positioned on both surfaces over the notches.
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Quantitative damage analysis of concrete
From this study six specimens were selected which had been subjected to different postpeak deformational states. The damage state was 'frozen' by gluing aluminium strips to the longitudinal sides of the prisms. Thereupon, four equidistant and parallel 'vertical' sections were prepared of the central portion of the specimens. Spacing between the vertical sections was larger than maximum grain size (8 mm) to obtain statistically independent structural information. The surfaces of the sections were treated with a fluorescent spray [2]. Crack patterns were recorded on slide under illumination by UV light. An area of 48x35 mm2 and a smaller portion of 48x13 mm', located symmetrically with respect to the notch section, were analysed for crack extension. For that purpose Saltikov's method of directed secants was applied to about 7 to 10 times magnified pictures of the designated areas. This was accomplished by projecting a slide on a semi-transparent glass plate. All cracks visible with the unaided eye were taken into consideration, so that the sensitivity will be about a quarter of a millimetre. Rotating the grid allows assessment of the crack orientation distribution. The mechanical experiments revealed the development of a non-uniform distribution of axial deformations over the notch section at yielding (see, e.g. Fig. 4 in [20]). Hence, due to inhomogeneity-induced eccentricity the specimen was subjected to bending. This phenomenon was already known, of course, from experiments using photo-elastic coatings. In [21] this phenomenon was later studied in more detail. Yielding reduced the bending stiffness in the fracture process zone, so that locally a rotation could be accommodated. At larger global deformations, this degree of rotation was maintained. Measurements at front and backside over the notches of the specimens revealed completely different post-peak deformational behaviour even involving compaction [22]. The experimental observations were confirmed by a finite element (FE) simulation based on the smeared out crack approach using the DIANA package. For more details on the mechanical aspects one is referred to [21], and for the FE simulation to [23]. Slides of four vertical sections of the six specimens have been elaborated. Since only single specimens could be selected from the mechanical experiments, scatter between samples (as an average of four images) proved to be too large to draw quantitative conclusions on changes in damage evolution rates during yielding. The scatter was dramatic among the serial sections. For section images, see [16,22]. Table 2 gives some of the damage evolution parameters pertaining to the post-peak range; C-7 and C-5, respectively, C-4 are specimens with a residual load-bearing capacity of 75% and 50% of ultimate. Added are data on a section (C5-4) of a specimen subjected to the same loading history as in case of specimen C-7, but both specimens were unloaded in a different way [ 161. It should be noted that this table reports on data pertaining to the 13 mm wide central zone as well as to the two 11 mm wide boundary zones encompassed in the wider area of 35x48 mm2around the notched section. Table 2: Stereological damage estimates Area location notched zone boundary zone notched zone boundary zone
Damage parameter
S, in mm-l w3 in%
C-7-2 0.333 0.181 18.7 7.6
Specimen number C-7-3 C-5-4 0.543 0.218 0.366 0.146 21.3 9.3 17.5 15.9
C-4-4 0.257 0.193 13.3 3.0
Finally, images were analysed on deviations from symmetry in the damage structure of the so-called Fracture Process Zone (FPZ). Since major cracking will be perpendicular to the
1 26
Piet STROE VEN
e,(O)
global tensile loading direction, the data (in the axial direction) for the more significant cracks (after eliminating the small and widely scattered cracks) are determined separately for the two sides of the specimen [16]. Representative data on C-7-2 and C-5-4 are presented in Table 3. For a selected set of sections also N A was determined. Data obtained in this way for average 2-D crack size (=LA/ N A )fall between 0.5 and 0.7 mm. As an example, [22] gives N A4 . 4 17 mm-' for C-7-2. WithS~4.333mm-' (Table 2), the average crack size in the 13 mm central portion will be 0.65 mm. In [16] the average crack length at DP (assuming completed bond 5 avcracking) was estimated by n d o / 4 , in which do is the sensitivity level. For do~ 0 . mm, erage crack size at DP will be 0.4 mm. Hence, damage evolution between DP and the investigated post-ultimate loading situation is only moderate. The ensemble of 4x6 images reveals a very large amount of structural scatter, as illustrated by presented data (and by earlier published images). Shuffling these images like playing cards would make it impossible to restore their original position in a particular specimen! Systematic features dealing with macro-crack formation only appear in the post-peak range. But a definite delineation of the macro-crack is only found after a considerable amount of yielding has taken place, as can be concluded from a comparison of C-7 and C-4 images. The macro-crack is obviously the final result of a hazardous process of crack coalescence, initially driven by high residual stresses and later primarily by structural stress raisers. The probability of having crack coalescence in the neighbourhood of the notched section is somewhat increased by a 20% higher average stress. The latter leads to a gradually increasing crack density toward the notched section (Table 2), hence to crack concentration, a phenomenon becoming more pronounced during yielding of the specimen. Because the distances between cracks are as a consequence reduced, their interaction will promote further coalescence. The hazardous process of growth and coalescence of the widely scattered cracks on structural level that are only weakly affected by the presence of a notch is alien to the engineering concept of a single crack initiated at a notch and propagating along the notch section. Also, the concept of a fracture process zone symmetric around the notched section is an engineering concept not reflected by the damage structure that, indeed, was found a 'zone spaced without sharp boundaries' [24]. Table 3: Eccentricity in damage evolution Area location
Damage parameter
Specimen number C-7-2 c-5-4 left side right side left side right side
Notched zone
P,(O) in mm-'
0.15
0.06
0.17
0.17
Boundary zone
P,(O) in mm-'
0.12
0.06
0.10
0.14
CONCLUSIONS The interpretation of engineering mechanical behaviour in terms of cracking mechanisms and features of damage evolution by the methodology outlined in this paper allows a structural interpretation of relevant research, and renders possible at least qualitatively estimating mechanical characteristics on the basis of structural modifications. Damage is a fractal-like phenomenon. Hence, observations on damage evolution are resolution-dependent. This also holds
Quantilalive damage analysis of’concrele
127
for the present experiments. Extent of damage and characteristics of the crack orientation distribution are functions of the sensitivity level set by the researcher (here, 0.2 mm). The data presented herein, though of illustrative nature, nevertheless reveal significant structural differences implied by different loading regimes, which allows gaining a clear insight into the operative damage evolution mechanisms.
REFERENCES 1. Vile, G.W.D., Behaviour of concrete under simple and combined stresses, PhD Thesis, Univ. London, UK 1965 2. Stroeven, P., Some aspects of the micromechanics of concrete, PhD Thesis, Delft Univ. Technology, Delft, The Netherlands 1973 3. Newman, K., Newman, J.B., Failure theories and design criteria for plain concrete. In: “Structure, Solid Mechanics and Engineering Design”, M. Te’eni ed. Wiley, New York 1969, pp 963-995 4. Perry, C., Gillott, J.E., The influence of mortar-aggregate bond strength on the behaviour of concrete in uniaxial compression. Cem. Concr. Res., 5, 1977, pp 553-564 5. Goodier, J.N., Concentration of stress around spherical and cylindrical inclusions and flaws, J. Appl. Mech. ASME, 55, 7, 1933, pp 39-44 6. Sezawa, K., Nishimura, G., Stresses under tension in a plate with a heterogeneous insertion. Rep. Aeron. Res. Inst., Tokyo Imp. Univ., 6, 25, 1931, pp 25-43 7. Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen 1953 8. Hsu, T.C., Slate, F.O., Sturman, G., Winter, G., Microcracking of plain concrete and the shape of the stress-strain curve. J. ACI, 60, 2, 1963, pp 209-224 9. Slate, F.O., Olsefski, S., X-ray for the study of internal structure and microcracking of concrete. J. ACI, 60, 5, 1963, pp 575-588 10. Stroeven, P., Fractals and fractography in concrete technology. In: “Brittle Matrix Composites 3”, A.M. Brandt, Marshall I H. eds. Elsevier, London 1991, pp 1-10 1 1 . Ringot, E., Automatic quantification of microcracks network by stereological methods of total projections in mortars and concretes. Cem. Concr. Res., 18, 1988, pp 35-53 12. Saito, M., Characteristics of microcracking in concrete under static and repeated tensile loading. Cem. Concr. Res., 17, 1987, pp 2 11-2 18 13. Stang, H., Shah, S.P., Damage evolution in FRC materials modelling and experimental observations. In: “Fibre Reinforced Cements and Concretes”. Recent Developments, R.N Swamy, B. Barreds. Elsevier, London 1989, pp 378-387 14. Stroeven, P., Application of various stereological methods to the study of the grain and the crack structure of concrete. Journ. Microsc., 107, pt 3, Aug. 1976, pp 3 13-321 15. Stroeven, P., Geometric probability approach to the examination of microcracking in plain concrete. Journ. Mat. Sc., 14, 1979, pp 1141-1 151 16. Stroeven, P., Some observations on microcracking in concrete subjected to various loading regimes. Engr. Fract. Mech., 35,415, 1990, pp 775-782 17. Reinhardt, H.W., Stroeven, P., den Uijl, J.A., Kooistra, T.R., Vrencken, J.H.A.M., Einfluuss von Schwingbreite, Belastungshohe und Frequenz auf die Schwingfestigkeit von Beton bei niedrigen Brucklastweckselzahlen. Betonw. und Fertigteiltechnik, 44, 9, 1978, pp 498503. 18. Stroeven, P., A case of compression failure in concrete due to stress release. In: “Fracture Mechanics of Concrete Structures I”, F.H. Wittmann ed. AEDIFICATIO Publ., Freiburg 1995, pp 461-470
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19. Stroeven, P., Mechanics of microcracking in concrete subjected to fatigue loading. In: “Mechanical Behaviour of Materials 3”, K.J. Miller, R.F. Smith eds. Pergamon Press, Toronto 1979, pp 141-150 20. Cornelissen, H.A.W., Hordijk, D.A., Reinhardt, H.W., Experimental determination of crack softening characteristics of normal weight and lightweight concrete, Heron, 3 1,2, 1986, pp 45-56 21. Hordijk, D.A., Local approach to fatigue of concrete. PhD Thesis, Delft University of Technology, Delft 1991 22. Stroeven, P., Quantitative image analysis of damage in concrete subjected to direct tension. In: “Quantitative Description of Materials Microstructure”, L.J. Wojnar, K. Rozniatowski, K. Kurzydlowski eds. Jagielian Univ. Press, Krak6w 1997, pp 515-522 23. Rots, J.G., Hordijk, D.A., De Borst, R., Numerical simulation of concrete fracture in ‘direct’ tension. In: “Numerical Methods in Fracture Mechanics”, A.R. Luxmore et al eds. Pineridge Press, Swansea 1987, pp 457- 471 24. Buresch, F.E., A structure sensitive Klc-value and its dependence on grain size distribution, density and microcrack formation. In: “Fracture Mechanics of Ceramics 4”, R.C. Bradt, D.P.H. Hasselman, F.F. Lange eds. Plenum Press, New York 1978, pp 835-847
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
IMPLICATIONS OF THE LAW OF AGGREGATION OF MATTER IN CONCRETE TECHNOLOGY
Piet STROEVEN Faculty of Civil Engineering and Geosciences Delft University of Technology, Stevinweg 1,2628 CN Delft, The Netherlands, e-mail:
[email protected] ABSTRACT
This paper introduces some fimdamental issues that govern the reliability of experimental and modelling approaches in concrete technology. These findamentals are frequently violated, so that obtained results will be biased to an unknown degree. Nevertheless, nothing is really new in what is presented. For that reason, basically the philosophy is outlined and the main set up of formulas is given. For further details, reference is made to the relevant literature. Keywords Aggregation, concrete technology, digitisation, fiactality, geometric probability, representativeness, sampling, structural sensitivity.
INTRODUCTION “Concrete in the good old days seemed to be simple, however, concrete was never simple, we were” (Gilkey, 1950)
Concrete is a particulate composite material on different levels of the microstructure. Gravel grains (and eventually macro-fibres) are aggregated on meso-level in a cementitious matrix. Sand grains become discernable upon further increase of resolution in the aggregated mass of particles dispersed in the cement paste. An even more sensitive approach would allow detecting the very particles of this paste in the fresh state, or the hydrate structure of the hardened material. The molecular structure is situated at the lowest micro-structural level. A particulate composite material reveals size segregation of particles near surfaces at a higher level of the microstructure, ranging from boundary effects in structural elements to interfacial transition zones around aggregate grains. The underlying concept of a continuous range of microstructural dimensions and the three discrete levels of aggregation, denoted by macro-, meso-, and micro-level in concrete technology, have been recognized for a long period of time in the physics and mechanics of deformable bodies. Material behaviour under forces is the reflection of material characteristics and of material structure. This behaviour is defined in terms of properties, such as mechanical ones. Properties are denoted as structure-insensitive when solely governed by material composition, e.g. mass and Young’s modulus. Contrary, structure-sensitive properties such as the crack initia-
130 Piet STROEVEN tion strength are affected by the so-called group pattern or configuration of particles. Hence, particle size and spacing are involved. Engineering properties are supposed to reflect certain aspects of the behaviour of material elements of at least representative dimensions. In such representative volume elements (RVE’s) the material parameter at issue can be contracted away. Each geometrical parameter has its independent scale of homogeneity. The same holds for properties with different degrees of structural-sensitivity. RVE’s of structure-sensitive properties will exceed those of structure-insensitive ones to a considerable degree. Heterogeneity inside the RVE will increase with a decline of the micro-structural level taken into .consideration by the selected resolution of observations or measurement equipment (e.g. strain gauges). So, heterogeneity is not a material characteristic, but a jknction of the material parameter and of the ratio of resolution (micro-structural level) and the linear dimension of the RVE involved. Insight into the size of the RVE is important for the sampling strategy, and thus for the economy of the experiment. Particular materials are three-dimensional (3-D) aggregates. Observations should therefore provide 3-D information on material structure. Oblique materials like the cementitious ones do not allow easy access to 3-D material structure, however. Geometrical statistical (i.e. stereological) tools should therefore be applied for this purpose, since they provide means for unbiased estimation of 3-D geometrical parameters of the state of aggregation on the basis of 1-D or 2-D observations. Sampling is in the present context of crucial importance. In discussing fundamentals underlying experimental and modelling approaches to cementitious materials, sampling will receive proper attention in the light of the continuous range of microscopical dimensions. This paper will use fibre concrete (FC) and shrinkage cracking (SC) as reference examples, both in the perspective of material behaviour. Major difference is that fibres are men-made and cracking is a natural phenomenon. The fibre reinforcement structure can be visualized and studied on a discrete level of the microstructure, whereas damage reveals itself differently on a continuous range of microstructures. The implications are far ranging and form the subject of this paper. SAMPLING SCIENCE IN CONCRETE TECHNOLOGY A theoretical concept underlying the dispersion of one phase in a second (in the present case,
fibres or cracks in the matrix) that is generally accepted in modelling and experimental approaches is isotropic uniform randomness (IUR). This implies that sufficiently large samples can provide representative information when drawn at arbitrary location and orientation in bulk of the material. Mostly, this concept is (seriously) violated in practice, however. The production method of the cementitious material can cause fibre anisometry (leading to isotropic behaviour) in the FC example [ 13. Unevenly distributed internal stresses in the SC case will inevitably cause anisometry in the damage structure [2]. Fig. 1 depicts both cases. Care should therefore be bestowed on how to sample (as to location and orientation), since the quality of the estimate can never be better than the quality of the sample. Confronted with structures deviating from the IUR state, quantitative evaluation of structural features in sections is in general only possible by random sampling. This would complicate experimental approaches dramatically, and is therefore in concrete technology avoided. However, serious biases have to be accepted in the three-dimensional estimation procedure when proper precautions are not taken. This author, avoiding random sampling, introduced the correct procedure some 30 years ago [3], but so far most researchers unfortunately neglect this practical proposal. We will come back to this issue later. Of course, a major parameter in the design of experiments is the size of the sample. Together with the afore-mentioned issue, this should
131
Implications of the law of aggregation of matter in concrete technology
guarantee the representativeness of the information derived from the sample. In many cases, use is made of standardized specimens in concrete technology, so that sample size in not designed, and will be found insufficient in many cases (revealed by too large scatter). This inevitably reduces the efficiency of the experimental design.
Freesurface
Slice
I
X-ray direction
I
1 X-raysample
I
Dryingspecimen
I
I Cracking in section I
Fig. 1 (left) FC case: X-ray pattern of vertical slice of fibre concrete (compacted in vertical direction) will reveal partial fibre orientation. Fig. 1 (right) SC case: vertical section of concrete specimen with one free surface reflects anisometry in shrinkage crack pattern.
Orientation sampling strategy Underwood's classical book [4] is one of the very limited stereological literature sources to which researchers in concrete technology refer. Unfortunately, for expenmental methodology, this book is at least partly outdated. New and far more powerful approaches have been developed the last 20 years [ 5 ] . But for the basic set up of stereological theory, relevant for this paper, the book is very useful. Underwood presents the various stereological parameters and the associated correlations in a single table [3,4,6]. For our purpose relevant are the following relationships:
4-
-*
S,=-LA=~PL a
Note that in standardized stereological notation PL = P/L . The bar on top of the expressions implies an averaging operation realized by a proper sampling strategy. The first sequence of formulas represents a complete historical development in volume fraction ( VV)analysis (of
132
Piet STROEVEN
pores, aggregate grains, etc). The oldest approach from 1848 is based on experimental determination of areal fractions (A,) and is due to Delesse [7]. Half a century later, Rosiwall introduced the lineal analysis [8].The method involves coverage of the section image by a randomly oriented or directed line grid, whereupon the line fraction (LL)is determined that covers the sections of the pores or grains. The last development dates back three-quarters of a century (Thomson [9] and Glagolev [lo]), and is referred to as the point counting method; instead of lines, a random (or systematic) point grid is superimposed and the point fraction (Pp) covering the pore or grain sections is determined. The second set of equations is relevant for quantitative damage (crack extension) analysis. Introduced by Saltikov in 1945, this is referred to as the method of random (or directed) secants on a plane [ 111. It allows by simple intersection point counting (PL)to assess the 2-D crack trace extension (LA),or the 3-D crack surface area density (SV).The last equation allows analysing fibre length per unit of volume (Lv) in the FC case by assessment of intersection density in the section plane (PA)[3]. All relationships require random sampling strategies unless one is confronted with the extremely rare situation of an IUR structure. In both reference examples this never occurs. Hence, an appeal is made to the ingenuity of the researcher. Fortunately, solutions, in terms of the economy of the experiment, are available in the literature. Following a suggestion by Saltikov for dispersed surfaces in space, Stroeven has elaborated some 30 years ago a practical approach that can be followed when dealing with fibres or cracks in cementitious materials [1,3,12-141. The basic assumption is that the actual dispersion of structural elements (i.e. fibres or cracks in the reference examples) can be replaced by a linear combination of 1-D, 2D and 3-D ‘random’ structures. In the 2-D and 1-D sets, the structural elements are UR dispersed as to location, but they are parallel to the so-called orientation plane (2-D set), or to the orientation line (1-D set), respectively. The 3-D set is IUR dispersed. Since generally researchers use standardized specimens in materials research (or at least specimens with simple shape), the researcher will mostly be confronted in the actual material system with an orthogonal system of preferred orientations. In the FC case, the compaction direction and the specimen dimensions govern such a Cartesian co-ordinate system of fibre orientations. In the SC case, it is the principal direction of water transport perpendicular to the free surface, and the equality of global tensile stresses parallel to this surface that govern the Cartesian coordinate system of crack orientation. This approach simplifies random sampling to so called ortrip sampling. Hence, in the most complicated case, sectioning will be required in three orthogonal directions. For fibres, the following equations can readily be derived for sections of fibre material with arbitrarily dispersed fibres (Fig. 2). Note that PA is the number of fibres per unit of area, and LV the fibre length per unit of volume.
1 PA,= - L v 3 2 in which it is assumed that the { x,y }-plane can be associated with the orientation plane (generally, perpendicular to the gravitation direction) and the lineal fibre fraction ( L n ) is oriented in the direction of the z -axis (mostly, resulting from restricted specimen dimensions). However, in a large number of cases the researcher can identify an axis of rotational symmetry, which will reduce efforts dramatically, since image analysis can be restricted to so-called vertical sections/slices. This sectiodslice is selected randomly as to location but oriented parallel
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Implications of the law of aggregation of mutter in concrete technology
to the axis of symmetry. This author applied ortrip sampling in a Dutch-Polish co-operation project on FC [13]. But in an earlier research project this could even be avoided by combining counting operations in a section and in the X-ray projection plane of the same slice [ 11. The latter formulas are not presented here, but are quite similar to the ones presented, and can be found in the relevant literature [14]. In the shrinkage cracking case, the co-ordinate axis perpendicular to the free surface could be associated with the axis of symmetry.
.. .
PAy
. -
a
.
Fig. 2. FC case: number of fibres per unit of area, PA,can be determined for fibre concrete in an ortrip sampling scheme (g indicates the gravity force during compaction). When the latter fraction can be neglected, the vertical section is parallel to the z -axis, and P, = PAY.To assess the unknown two fibre fractions, two independent observations are required either counting fibres in two orthogonal sections, or analysing the projection image of a single vertical slice [l]. The fibre system defined by the above set of equations is called a partially linear-planar one. It suits to approach an arbitrary fibre system. When not confronted with very slender elements, we deal with a partially planar system, where Lv, = 0.It constitutes generally the optimum solution for practical applications in terms of the economy of the experiment. Similar sets of equations can readily be derived for cracks [15]. In a Cartesian co-ordinate randomly dispersed traces due to the 3-D sub-set, traces parallel to the z -axis solely stemming system we assume for the most general situation a set of 3-D cracks, hrther a 2-D set parallel to the { x,z }-plane and a 1-D set parallel to the z -axis. All sub-sets of cracks will reveal traces in the { x, y }-plane, i.e. randomly distributed crack traces in the plane due to the 3-D and the 1-D sub-sets, and traces in the y -direction due to the 2-D sub-set. In the { x, z } plane the 2-D and 1-D sub-set yield traces in the z -direction, whereas the 3-D sub-set produces randomly dispersed traces in the plane. Finally, in the { y , z }-plane we find, apart from the randomly dispersed traces due to the 3-D sub-set, traces parallel to the z-axis solely stemming from thel-D sub-set. The set up is given in Fig. 3, also presenting sketches of the aforementioned x -, y - and z -planes. Intersection counts with a superimposed line grid in the { x, y }-plane are indicated by 4. When divided by the grid line length this yields P,, . A line
134
Piet STROEVEN
grid is superimposed in the two respective Cartesian co-ordinate directions and intersection densities are determined. This yields six observations condensed to: 1 P,(x)=-Ss,,+S,, 2 1 P,(y) =-Sva + 2
2
+-S,,
r
,,?!I-+
2 r
1
= P&)=TS,,+s,,
1
= PLY(X) =,S,,
+
2 +-S,,
r 2 +-S,, 7r
1 = pL(z)=-s,, 2
Orientation axis 1-D
+IZI I
Section planes Fig. 3. SC case: intersection counts per unit of grid line length, 4,are determined in two orthogonal directions for concrete with shrinkage cracks subjected to ortrip sampling. Hence, only three independent observations are obtained. Two sections will suffice for determination of the three unknown crack portions. For the constant (projection) factors involved, see the relevant literature [1,3,16]. When symmetry is assumed around the z -axis, as in the case of shrinkage cracking, where the free surface is perpendicular to this axis, we see that S,, 4.We are confronted with apartially linear crack system, allowing determination of the two unknown crack portions from two intersection counts in a single vertical section! Resulting expressions are
Implications of the law of aggregation of matter in concrete technology
135
in which 0 3 defines the degree of orientation in the crack structure (=SV&,). We see that quantitative analysis of cracking at the surface, or alternatively in a parallel plane under the surface, can never yield the full solution in the SC case. Since a crack gradient is formed in z -direction, the solution outlined would just present a global average. Of course, when statistically independent vertical sections are produced, also the independent gradients in both S,, and S,, can be determined. This requires subdividing the vertical section in narrow ‘horizontal’ strips, compromising between sensitivity and representativeness (sample size!). Herewith, we have reduced the requirement of random sampling for deriving threedimensional structural information from the material body to sampling a single (Xrayed) vertical slice in case of FC, and to sampling a single vertical section in the SC case. When detailed information in the latter case on the structural gradient is pursued, it is proposed to analyse narrow strips of a series of vertical sections in combination with sections parallel to the free surface. The replacement of the actual structure by a linear combination of I-D, 2-D and 3-D portions of these structural elements, as developed by Stroeven, in combination with the assumption of an axis of symmetry, renders possible dramatically reducing the complexity of the experimental approach. Since the experimental approach is generally simplified in concrete technology by making unjustified assumptions (IUR state!), the proposed procedure will also dramatically improve the quality of the structural estimates and therefore the reliability of the microphysical or micro-mechanical modelling approach.
Size sampling strategy In addition to correctly sampling with respect to orientation, as discussed in the above section, the size of the sample also governs representativeness. Unfortunately, samples for structural analysis in concrete technology are mostly not designed for size, because standardized specimens are used or specimens designed for material performance. Serial sectioning can help to increase sample size, but the sections should be statistically independent, so spacing is limited to the average size of the largest structural elements at issue. In concrete technology, the rule of thumb is to have minimum sample dimensions exceeding the maximum structural dimension (mostly, maximum grain size) by a factor of 4 to 5 [3,17]. However, this is a proper approach when interested in structure-insensitive properties (such as Young’s modulus). When micro-mechanical or microphysical modelling pursues estimation of structure-sensitive global properties (e.g. crack initiation or ultimate tensile strength), and structural information is as a consequence required on configuration instead of on composition (e.g. volume fraction, specific surface area), sample size should be significantly larger [3,18-211. Scatter in the estimated global geometric parameters of material structure can be theoretically estimated. As a rule, standard deviation s can be considered proportional to the reciprocal square root value of the number of observations [3]. Hence, sample area has to be increased by a factor four when it is pursued to reduce the standard deviation by a factor two. However, this is only relevant when dealing with composition density. Different spacing parameters are available when configuration is at issue. The most common ones are the nearest neighbour distance, A3, and the free interparticle spacing, h . Their global values are directly correlated with global density values of geometrical parameters, i.e.
-
A3
0.553
=-
i/Ny
136
Piel STROEVEN
Configuration homogeneity can be based on representative information as to the distribution of either one (or both) of these spacing parameters. This will require samples significantly larger than the ones used for composition homogeneity. Factors between 5 and 10 should be accounted for [3,18]. Anisotropy in SFRC is disproportionably influenced by the degree of orientation in the three-dimensional fibre structure [ 121. The degree of orientation in the three-dimensional shrinkage crack structure can also be considered a relevant parameter in global modelling of transport of harmhl substances to the reinforcement. Although o, is not a very structure-sensitive parameter, the scatter in global density values in eq (8) should be significantly reduced to yield this parameter with sufficient accuracy. Hence, sample strategy (orientation, location, size) should be part of the design ofexperiments pursuing determination of representative structural parameters. In doing so, the researcher should be aware of the structure-sensitive character of the parameter of interest (and relevance for the physical modelling approach). AGGREGATION IN CONCRETE TECHNOLOGY Continuous scaling Well-known for a long time in the physics and mechanics of deformable bodies is the concept of a continuous linear range of microscopic dimensions, as well as the three levels of aggregation of structural elements of materials. See for this purpose, e.g. Freudental’s book on “The inelastic behaviour of engineering materials and structures”, published in 1950 [22]. This way of emphasizing material structure can also be found in Holliday’s book on Composite Materials published in 1966 [23]. Ample attention to the same topic was given during the Southampton conference on “Structure, Solid Mechanics and Engineering Design” in 1971 [24]. Stroeven [3] more explicitly introduced the ideas in concrete technology in 1973, referring to the various connotations attributed to the three levels in different material technologies. Wittmann was probably the first to refer to the intermediate level in concrete technology as the mesoscopic one [25]. Fundamental to the interpretation of experiments, however, is the continuity in aggregation levels. Changing maximum grain size in experiments would require modifying resolution and sample size to the same degree to be able properly comparing outcomes on the same level of aggregation, unless the sample size is exceeding the linear dimensions of the so called representative volume element for the coarsest-grained material. Hence, “homogeneity and isotropy of concrete on engineering level cannot be qualified as material properties” [3, p.191. Homogeneity of a geometric parameter can only be conceived for samples of representative size. “This volume can be called the representative cell, and is the imaginary unit which represents to a defined and arbitrary probability the heterogeneity of the actual material. In an isotropic material the representative cell can be imagined as a cube... It should be noted that if there are n independent geometrical parameters (such as concentration, particle size, orientation, etc.), there will be n values for the representative cells since each geometrical parameter has an independent scale of homogeneity ... To put this another way, heterogeneity cannot be uniquely described by a single geometrical variable” [22]. These principles are widely ignored in concrete technology, so that outcomes will be biased. Striking examples can be found in [3]. As an example, we can refer here to Keeton’s analysis by photo-elastic coatings of deformations at the surface of cement paste, mortar and finegrained concrete specimens of similar size, and subjected to direct compression [26]. Using the same thickness of coatings (2 mm), Keeton associated the observed increasingly chaotic shear strain contours at larger grain sizes with an increasing degree of inhomogeneity. The observations simply reflect, however, the same phenomenon on different levels of the microstructure! So, Keeton’s conclusions were incorrect. But the underlying fundamental
lmplications of the law of aggregation of matter in concrete technology
137
aggregation rule is violated frequently in concrete technology, like in the SC example, such as treated in [2,27]. This problem does not occur in case of the fibre reinforcement, where fibre volume fraction can be defined and experimentally assessed unambiguously at a single selected resolution level. Continuous scaling plays a major role, however, when dealing with the amount of damage or the total (or specific) crack surface area as in the SC case. The closer the observation, the more heterogeneous and the more extensive will appear the damage structure. Hence, observations on different levels of the microstructure will produce systematically different information on density (extension) and on dispersion (degree of orientation, degree of heterogeneity). When the material structure is modified by hydration or by adding larger sized aggregate (as in [27,28]), a similar level of the microstructure should be adapted for comparison purposes in experimental designs pursuing a study of the effects of such changes on porosity or cracking. Unless this is properly arranged, artificial effects will be mixed with fundamental ones, like in the Keeton case. Fractality A special structural feature linked up with the continuous scaling phenomenon is fractality [29-311. This should be considered highly relevant when researchers are e.g. interested in geometric parameters of cracking. Unfortunately, most researchers only consider the phenomenon of academic interest. Instead, it has fundamental impact on the observations. Still, engineers accept that cracks recorded by naked eye on the surface of reinforced concrete beams subjected to bending forces will be accompanied by smaller cracks in the concrete matrix. Hence, geometric parameters of cracking would change at a lower level of aggregation. The same conclusion should be drawn when sections of relatively small prismatic concrete specimens after test loading are scanned under relatively small magnifications by an optical microscope. Myriads of tiny cracks can be visualized in areas where the naked eye would be incapable of doing so. Hence, intuitively we accept geometric parameters of cracking (density, length, spacing) to depend on sensitivity. This is what is meant by the “coastline of Britain” effect: the coastline’s length will increase steadily starting from observations by satellite, thereupon by plane, and ending up by walking (and measuring!) along the beach [32]. Obviously, length in sections and surface area in space cannot be measured unambiguously. When dealing with (near) fractal properties [3 11, the scaling effect can be quantitatively estimated. As relevant examples, we can mention here that Stroeven has analytically demonstrated the roughness of fracture surfaces [33], the tortuosity of transport routes [34], and the amount of damage [35] to depend on the sensitivity of the experimental or modelling approaches, though none of the cases is generally of ideally fractal nature. A prerequisite is, of course, that the researcher’s design of the experiment will refer to the sensitivity or magnification level employed, thereby acknowledging that experimental ‘findings’ are indeed fundamentally depending on the scaling level. Information concerning the fractal effect on the extent of the fracture surface area and on the amount of damage can be found in the relevant literature [293 13. To get an idea of the significance of the effect, Table 1 presents estimates on the amount of damage (at ‘discontinuity’ in a simple compression test) as a function of sensitivity of the observation method. Note that A4 = d,,,/ d o ,and the particle size distribution function, f ( d ) , for an equal volume fraction mix is given by f ( d ) = 2 S d F Id”’ . Micro cracking is assumed to be restricted to particle-matrix debonding in the modelling concept. We see that over the considered sensitivity range (associated with the range of aggregate grain sizes), damage increases 50 times by reducing (step-by-step) the scaling level of the microstructure.
138
Piet STROE VEN
Magnification Vol. Fraction A4 VV 2 0.1 4 0.2 8 0.3 16 0.4 32 0.5 64 0.6 128 0.7
Size range mm 16-32 8-32 4-32 2-32 1-32 0.5-32 0.25-32
Min. size (do)
Max.size (d,,,)
mm 16 8 4 2 1 0.5 0.25
nun 32 32 32 32 32 32 32
Damage in mm-’ 0.004 0.01 1 0.023 0.044 0.078 0.132 0.217
SV
Automatic quantitative image analysis Automatic quantitative image analysis facilities render possible to significantly reduce the labour intensity of structural approaches. However, it has been demonstrated that this will lead in particular cases to significantly biased results [36,37]. The digitisation operation will not hamper determination of area fraction, but length or area measurements will be significantly biased. Area is involved in the SC case, in which assessment of crack extension is pursued. This contribution will reveal where biases are involved and how to avoid or minimize them. Nowadays available software packages for image processing and quantitative image analysis reduce the work of structural analyses. In standardized situations, hlly automised approaches constitute economic solutions. In non-standardized cases, semi-automatic approaches are preferable [38]. Moreover, the digitisation operation to which field images should be subjected has been proven a serious source of biases [36,37]. For the analysis of numbers, volume fraction, size or spacing, this problem can be overcome. This holds for the FC reference example. But when confronted with (crack or grain perimeter) trace lengths, or surface area in space, this is a major drawback of automation. Digitisation does not influence the total projection of a set of crack traces in the directions of digitisation (conventionally, 4connexity), provided trace length exceeds pixel size considerably. Total projection in any other direction is significantly different from that of the traces, however. Since, the intersection density ( P , ( B ) ) equals the total projection of line traces per unit of area in an orthogonal direction ( L ; ( B + f ) ), the rose of intersections (or intersection densities) of the digitised crack traces will be seriously biased, too. The actual traces can be replaced by a linear combination of L,, and LA3,as we have seen earlier. LA, will not be affected by the digitisation effect. Changing structural parameters, like grain size or volume fraction, will not influence both portions to the same degree. Hence, the changing combination of both portions due to indicated variations in structural parameters is under the impact of unknown digitisation effects. The same will hold, of course, for the specific crack surface area. An elegant way to display the digitisation effect on a partially oriented system of traces in a plane is given in Fig. 4. A mixture of a linear (1-D) and a ‘random’ (3-D) portion is used in Fig. 4 (top). The two circles reflect the roses of intersection of the respective portions [4,37]. The PL-values represent the summation of both roses. This would be the best estimate when the image with crack traces had been manually analysed. In the digitised image, the traces are replaced by orthogonal components only. Hence, we deal with a mixture of oriented portions. The roses of the individual portions are shown in Fig. 4 (bottom). Again, the summation yields the rose of the digitised crack traces. The disparity between the manual and automatic image analysis results for other directions than of the 4-connexity digitisation directions is obvious! When quantitative crack measures are pursued for microphysical modelling of transport phenomena in concrete, the automated approach should be avoided.
139
Implications of the law of aggregation of matter in concrete technologV
+ pLo
X
/
PLr
analogue
/--
a.,-
....
............#* *...<'
*.h
digitised
Fig. 4. SC case: partially oriented system of (crack) traces in a plane. The analogue image analysis results are interpreted as a partially linear pattern on the top. The 4-connexity digitised image analysis results are displayed at the bottom as a bi-linear structure.
140 Piet STROEVEN SPACE STRUCTURE OF CONCRETE As demonstrated above, the fhndamentals are readily available to derive three-dimensional instead of two-dimensional information from structural experiments. As an example, let’s approach the y -plane in the shrinkage cracking reference case. The correct quantitative image analysis approach should also be based on superimposing in x - and z -directions a system of directed secants (ignoring for the time being the gradient in the crack structure). Hence, the analogue of esq. (4-6) is
with the solution:
of This leads to a value of the degree of orientation, w,= LA,lLA,
We note that the same observations are employed, but the result is biased when compared to the spatial parameter, w3. So, why should we decide on two-dimensional results? Of course, the same procedure of serial sampling, outlined before, should be followed for the determination of the gradient damage structure in L A .
CONCLUSIONS Fundamental issues like the sampling design, scaling in complex materials aggregated on continuously changing levels of the microstructure (and not just in three discrete steps), fractality of length (crack traces) in sections and (crack) surface area in space, stereological methods to obtain unbiased three-dimensional structural information, and biases associated with digitisation in automated quantitative image analysis approaches to cracks in concrete have been discussed in the foregoing, because the relevant literature in concrete technology reveals a lack of understanding, insight or even acknowledgment of such fhndamental issues. Still, nothing of what is presented is really new, and reference is therefore given to relevant literature sources, frequently dating back 50 years, or more. This paper is meant to be a guide that - in combination with additional information available in literature sources, of which a significant percentage is outside the hard-core of concrete technology - can help avoiding some of the fundamental mistakes. Micro-mechanical and microphysical modelling to estimate concrete
Implications of the law of aggregation of matter in coricrete technology
141
engineering performance, frequently requires advanced testing and laborious and thus expensive elaborations. The economy of the experiment requires correct design of the various aspects of the experiments (mechanical, physical, and structural), because the result is as reliable as the weakest link. In many cases this concerns the structural aspects, as indicated in this paper. Solutions or solution directions are available, so this can never be an argument for ignoring these fundamental issues. REFERENCES
1. Stroeven, P, Shah SP. Use of radiography-image analysis for steel fibre reinforced concrete. In: “Testing and Test Methods of Fibre Reinforced Composites”. R.N. Swamy, ed. The Constr. Press, Lancaster, 1978,pp. 345-53 2.Bisschop, J. Drying shrinkage microcracking in cement-based materials. PhD Thesis, Delft University of Technology: Delft; 2002. 3. Stroeven, P. Some aspects of the micromechanics of concrete. PhD Thesis, Delft University of Technology, Delft, 1973. 4.Underwood, E.E. Quantitative stereology. Addison-Wesley, Reading (MA), 1970. 5. Gundersen, H.J.G., et al. The new stereological tools. Acta Microbiol. et Immunol. Scand., 96,1988,pp. 379-94and 857-881. 6. Nemati, K.M., Stroeven, P. Stereological analysis of micromechanical behavior of concrete. Mat. struct., 34,2000,pp. 486-494. 7. Delesse, M. Prockddc mkcanique pour dkterminer la composition des roches. Ann. Mines, 13, 1848,pp. 379-388. 8. Rosiwall, A. iiber geometrische Gesteinsanalysen. Ein einfacher Weg zur ziffermksigen Feststellung des Quanti~~tsverhaltnisse der Mineralbestandteile gemengter Gesteine. Verh. K.K. Geol. Reichsanst., 5-6,1898,pp. 143-175. 9.Thomson, E.Quantitative microscopic analysis. J. Geol., 38,1930,pp. 193-222. 10.Glagolev, A. A. Quantitative analysis with the microscope by the point method. Eng. Min. J., 135, 1934,pp. 399-400. 1 1. Saltikov, S.A. Stereometric metallography, sec. edition. Metallurgizdat, Moscow, 1945. 12. Stroeven, P., de Haan, Y.M. Structural investigations of steel fibre reinforced concrete by stereological methods. In: “High performance fibre reinforced cement composites”, H-W. Reinhardt, V.C. Li, eds. E&FN Spon, London, 1989,pp. 407-418. 13. Stroeven, P., Babut, R. Fracture mechanics and structural aspects of concrete. Heron, 31/2,1986,pp. 15-44. 14.Stroeven, P. Geometric probability approach to the examination of microcracking in plain concrete. J. Mater. Sc.,14, 1979,pp. 1141-1151. 15. Stroeven, P. Morphometry of fibre reinforced cementitious materials, Parts I. Mat. Struct., 11/61,1978,pp. 31-38,and Part 11. Mat. Struct., 9,1979,pp. 9-20. 16.Stroeven, P. Structural characterization of steel fibre reinforced concrete. In: “Brittle Matrix Composites 2”,A.M. Brandt, I.H. Marshall IH, eds. Elsevier Appl. Sc., London, 1989,pp. 34-43. 17.Cook, R.W., Seddon, A.E. The laboratory use of bonded-wire electrical resistance strain gauges on concrete at the Building Research Station. Mag. Concr. Res., 8,1956,pp. 31-38. 18.Stroeven, P., Stroeven, M. Size of representative volume element of concrete assessed by quantitative image analysis and computer simulation. In: Proc. “8th. European Congress for Stereology and Image Analysis”, Bordeaux, 4-7Sept. 2001 (available on CDROM).
142 Piet STROE VEN 19. Stroeven, M. Askes, H., Sluys, L.J. A numerical approach to determine representative volumes for granular materials. In: Proc. World Conf. On “Computational Mechanics”, WCCMV, Vienna, July 2002, paper ID: 80395 (http://wccm.tuwien.ac.at). 20. Stroeven, P., Stroeven M. Reconstructions by SPACE of the Interfacial Transition Zone. Cem. Concr. Comp., 23,2001, pp. 189-200. 21. Brown, C.B. Minimum volumes to ensure homogeneity in certain conglomerates. J. Frank. Inst., 279, 1965,pp. 189-199. 22. Freudenthal, A.M. The inelastic behaviour of engineering materials and structures. Wiley, New York, 1950. 23. Holliday, L. Geometric consideration and phase relationships. In: Holliday L, editor. Composite Materials, Elsevier, Amsterdam, 1966, pp. 1-27. 24. Mura, T., Dunders, J. Deformational modes and microstructure, and Murzewski, L. Random structure of a quasi-homogeneous material. In: “Structure, Solid Mechanics and Engineering Design”, M. Te’eni, ed. Wiley, London 1971, pp. 3-12, and pp. 105-116. 25. Wittmann, F.H. Creep and shrinkage mechanisms. In: “Creep and shrinkage in concrete structures”, chapter 6. Z.P. Bazant, F.H. Wittmann, eds.Wiley, London, 1982. 26. Keeton, J.R. Photo-elastic determination of strain distribution in cement pastes, mortars and concretes. Tech Rep R404, US Naval Civil Eng Lab., Port Hueneme (Ca), 1965. 27. Bisschop, J., van Mier J.G.M. Effect of aggregates on drying shrinkage microcracking in cement-based composites. Mat. Struct., 35/252,2002, pp. 453-461. 28. Hu, J. Stroeven, P., Local porosity analysis of pore structure in cement paste. Cem. Concr. Res. (to be published). 29. Stroeven, P. Fractals and fractography in concrete technology. In: “Brittle Matrix Composites 3”, A.M. Brandt, I.H. Marshall, eds. Elsevier Appl. Sc., London, 1991, pp. 1-10. 30. Carpinten, A. Fractal nature of materials microstructure and size effects on apparent mechanical properties. Mech. of Mat., 18, 1994, pp. 259-266. 3 1 . Stroeven, P. Stereological estimation of fractal number of fracture planes in concrete. In: “Disordered materials and interfaces, MRS 407”, H.Z. Cummins, D.J. Durian, D.L. Johnson, H.E. Stanley, eds. MRS, Pittsburgh, 1996, pp. 343-348. 32. Stroeven, P. Coastline-of-Britain aspects of damage in concrete-like composites. In: Proc “6th Nat. Conf. on Mechanics and Technology of Composite Materials”, Y.Simeonov, chief ed. Bulgarian Academy of Sciences, Sofia, 1991, pp. 259-361. 33. Stroeven, P. A stereological approach to roughness of fracture surfaces and tortuosity of transport paths in concrete. Cem. Concr. Comp., 22,2000, pp. 331-41. 34. Stroeven, P. Tortuosity of transport routes for harmfbl substances through cementitious materials. In: Proc Yth.Int. Symp. “Cement and Concrete”. Tongji Univ. Press, Shanghai, 2002, pp. 1206-1210. 35. Stroeven, P. Fractal concept and damage in concrete. In: Proc “CEB Workshop on advanced studies on structural concrete”. LNEC, Lisbon, 1994, pp. 127-139. 36. Chaix, J.M., Grillon, F. On the rose of directions measurements on the discrete grid of an automatic image analyser. J. Microsc., 184, 1996, pp. 208-213. 37. Stroeven, P., Stroeven, A.P., Dalhuisen, D.H. Image analysis of “natural” concrete samples by automated and manual procedures. Cem. Concr. Comp., 23,2001, pp. 227-236. 38. Stroeven, P. Discussion of paper: Automatic quantification of microcracks network by stereological method of total projections in mortars and concretes by E. Ringot. Cem. Corn. Res., 18, 1988, pp. 657-658.
Proc. Int. Symp. Brittle Matrix Composites 7" A.M. Brandt, Y.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003 ,I
THE INFLUENCE OF PARTICLE SIZE DISTRIBUTION ON THE MICROSTRUCTURE OF MODEL CEMENT Jing HU and Piet STROEVEN Faculty of Civil Engineering and Geosciences Delft University of Technology Stevinweg 1, 2628 CN Delft, The Netherlands, email:
[email protected]
ABSTRACT The size distribution and spatial dispersion of Portland cement particles in the fresh state have a significant influence on hydration, microstructure development and ultimate properties of cement-based materials. The relationship between size distribution of Portland cement particles (PSD) and the spatial dispersion of cement particles is quantitatively studied in an analytical approach and verified by computer simulation. The mean free spacing A and the mean nearest neighbour distance
&
between cement particles are adopted to represent the spatial
dispersion of the cement (or aggregate) particles in model cement (or model concrete). This quantitative relationship is discussed for four kinds of particle size distributions, i.e. Rosin-Rammler distribution (widely used for cement particles), Fuller distribution (generally accepted for aggregates), equal volume fraction and equal number fraction mixtures. The influence is studied of microstructure of model cement on the depercolation threshold of the pore phase. The mean free spacing A can be estimated from the particle size distribution function and can offer insight into the morphological evolution and the depercolation threshold of pore structure in cement.
Keywords Depercolation threshold of porosity, mean free spacing, mean nearest neighbour distance, particle size distribution.
INTRODUCTION The microstructure development of cement is of paramount importance for the engineering properties of cement-based materials. Many factors, such as chemical composition, cement
144
Jing HU and Piet STROE VEN
fineness, and water cement ratio, are involved in the development of the cement microstructure during hydration. Among them, the particle size distribution is very important because it determines to some extent the initial packing state of the cement particles and the hydration rate of the cement. Correlations between PSD, the hydration process, and properties of the hardened cement paste have been studied extensively. However, quantitative relationships between PSD of cement and the microstructure of hardened cement (which is partly governed by the spatial dispersion of the cement particles) remain to be established. Due to the complex microstructure of cement, it is not possible to approach this problem by means of experimental techniques. Computer simulation offers a promising alternative for analysing the packing characteristics of cement particles and the evolution of microstructure in hardening cement paste. SPACE system [ 11 (Software Package for the Assessment of Compositional Evolution) has been developed to characterize particle packing of model cements and the microstructure development during the hydration process [2-31. The cement particles with predefined size distribution are generated in the simulation approach within the boundaries of a cubical container (representative volume element). The initial packing state of the cement particles is realized by the “dynamic mixing” algorithm. The mean nearest neighbour distance
xj
of
model cement can be determined in SPACE, characterizing the spatial distribution of the cement particles. In this study, the relationship between PSD and spatial dispersion of cement particles (characterised by h and tools. The calculation of
&
direct measurements. h and
& ) is quantitatively elaborated by means of stereological
is confirmed by SPACE to be a satisfactory approximation of
&
can be directly estimated from the PSD of the cement system.
The discussion covers four kinds of particle size distribution functions, i.e. Rosin-Rammler distribution, Fuller distribution (for aggregates), equal volume fraction and equal number fraction mixtures. The model cement is considered to be composed of solid phase (including unhydrated cement and hydration products) and pore space. The geometrical and morphological properties of solid phase are directly related to those of the pore structure. The influence of h of cement particles on the depercolation threshold of pore phase is studied in this paper. It is found that the value of h can offer insight into the morphological evolution and the depercolation threshold of pore structure in cement.
RELATIONSHIP BETWEEN PSD AND
&
Spherical cement particles distributed in a cubical container (representative volume element) represent the packing state of the model cement. Based on quantitative stereology, Underwood [4] presented a three-dimensional assessment of the geometrical properties of particles embedded in a matrix. It is demonstrated that some particle characteristics can be derived
The influence ofparticle size distribution on the microstructure of model cement
145
without any restrictive assumptions. Foremost among the exact characteristics applicable to systems of particles in a matrix are the volume fraction, VV, the specific surface area, SV,and the mean free spacing, A. The definitions and expressions of these stereological descriptors can be found in [4]. The mean intercept length through the particles,
is the mean value of
z 3 ,
line length intersecting with particles of grids randomly positioned as well as oriented. It appears that average value rather than maximum value of the intercept length across the cement particles is an important quantity when considering bulk properties of a cement system [j]. The mean intercept length
zj
is also related directly to the specific surface area of the ce-
ment. Another spatial parameter of great importance in particulate systems is the mean free spacing 1. This parameter is actually an estimation of the size of pore space. It represents the uninterrupted inter-particle distance averaged over all possible pairs of particles, as opposed to an inter-particle distance between nearest neighbours only. The parameters can be calculated as follows:
I-v, k =4-= S"
1-v, L3 ~
v,
where NV is the number of particles per unit of test volume, VVis the volume fraction of parti-
-
-
cles, SVis the surface area of particles per unit of test volume, d 3 and d 2 are the third and second moments, respectively, of the PSD. In combination with average coordination number,
i 3
was directly measured and em-
ployed to characterize the degree of flocculation of cement particles in model cements with various water cement ratios and finenesses [6]. In this paper,
&
will be calculated from the
PSD of cement (or aggregate) particles and compared with direct measurements.
-
ht is defined as the average distance between nearest neighbour pairs of particles in a
test volume. Strictly speaking, the derived expressions pertain to point particles only, but should apply to aggregates of small, randomly dispersed particles [4].
h, in a uniformly
random distribution of point particles in a test volume is defined in [4] and can be transformed to the following expression:
146
Jing HU and Piet STROE VEN
For model cement or concrete, all stereological descriptors can be easily calculated. However, for a real system of cement particles, very limited information is available about the geometric powder characteristics of cement particles. The PSD curve can be experimentally obtained by sieve analysis or granulometer. In addition, the mass-based specific surface area SC can be either measured directly by experiments or approximately estimated from PSD parameters. The mean free spacing A can be directly estimated from SG [6]:
A=4-
1- V"
s, PV"
and A = 1200/S,
(pm) for w/c=0.3
(4)
where p=3 150 kg/m3 is the density of cement. It can be seen from above-mentioned equations that the value of
z,,h and
i 3
can be
calculated from the moments of PSD of cement (or aggregate) particles. The moments can be calculated according to a specific PSD function.
Rosin-Rammler distribution The Rosin-Rammler distribution is generally accepted as a relatively accurate approximation of the actual system of cement particles. The percentage of the particles by weight retained on the various sieves is plotted on a logarithmic scale. The mass (volume-based) fraction of particles passing a sieve is in the case of the Rosin-Rammler distribution given by: F(V,,) = 1-exp(-bd,")
(5)
where di stands for particle size, a and b are constants for a certain particle system, a representing the degree of uniformity of the size distribution of the cement particles. The values of a and b can be calculated from the measured cumulative PSD curve. The maximum and minimum sizes of particles are incorporated in these two parameters, a and 6. The density distribution function for Vpifollows upon differentiation. Hence,
The density distribution function can be transformed into particle size distribution (PSD) function using the transformation rule: 1 Vp, = - d , ' N , , 6
(7)
where Np, is the number of particles in size range i per unit of volume. The resulting particle size distribution function (number-based) is
147
The influence ofparticle size distribution on the microstructirre of'model cement
6 ~ f(d,) = -n~ b d , " - exp(-bd,")
(8)
The n-th moment ofAdi) is defined as
-
d,
din= Idinf(d,)d(di)
(9)
4
where do and d, are the minimum and maximum diameters of the cement particles, respect ively. Direct integration ofthis equation is not possible. In case of a>l (generally a>l for actual cement), the moments of the Rosin-Rammler PSD can be approximated by means of a Gamma function.
d'
__I
ba
In case of a 4 , Eq. (1 1) is suggested as an approximation [7]: -
d' -= -
__I
b"
I 795 d2 1 . 0 6 5 e x p ( L ) a2
For an actual cement with ~ 1 . 2 4 9and b=0.045 (calculated from the cumulative PSD
-
curve obtained by laser granulometer), the direct calculation revealed d' and 129.70 pm3 and 17.86 pm2, respectively. Thus, the mean intercept length
z 3
d2 to
be
is 4.84 pm. The
estimation by Gamma function (Eqs. 1 and 10) resulted in a value of 4.82 pm. The comparison between Gamma approximation and direct calculation reveals that the estimation of moments by means of Gamma function provides satisfactory results for Rosin-Rammler PSD. Analytical approach to other PSD functions The calculation for Fuller distribution, equal volume and equal number fraction are relatively easy because their PSD functions are simple. The PSDs and expressions for different moments are listed in Table 1.
148 Jing HU and Piet STROE VEN Table 1. Moments of different PSD functions Fuller
2(d, - do 1
-
5d02.’drno.’
d’
dm4 - do4
3d;ln(drnl do)
4(d, - do 1
RESULTS AND DISCUSSION Experimental verification Three particle systems were generated by SPACE with Fuller distribution. The mixtures were subjected to dynamic mixing until a volume fraction of 5 1% was reached.
&
is calculated
for these particle systems according to the equations in section 2. To verify the reliability of calculation by stereological theory,
&
was also directly measured by SPACE system. The
results are presented in Table 2. It is seen that the measurements slightly exceeded the calculated values. This is attributed to increased order in the model cement [8]. C=0.554 is suitable for a randomly dispersed system of particles. However, the packing structure of particles in the actual cement will be governed partly by deterministic and partly by stochastic influences [2]. Therefore, at higher volume fractions of cement particles, order will start to overrule those of random positioning during the packing process. On the other hand, the higher measurement values demonstrate that SPACE offers a more realistic simulation of the particle structure than those obtained by computer systems based on the concept of “random packing” model.
Table 2. Comparison between calculations and measurements of Size range (Pm) 1-20 1-30 3-20
7 ( p m Z ) d?(pm3) 5 5 45
22.36 27.39 348.57
~3
(pm) 2.98 3.65 5.16
h(pm) 2.82 3.45 4.88
&
AJ (Pm)
Calculation Measurement 1.57 I .74 1.70 1.77 3.97 4.62
The influence of particle size distribution on the microstructure of model cetnent
149
Depercolation threshold for equal volume and equal number fraction mixtures It is evident that
&
estimation for point particles (Eq. 3) is not the same as for h (Eq. 2) for
real particles. The latter represents the average uninterrupted surface-to-surface distance between all possible particle pairs, while
&
neighbour pairs of point particles. Therefore,
refers to the average distance between nearest z3
and h are more suitable to characterize the
morphological evolution of solid and pore phase, respectively, during the hydration process. The morphological evolution of pore structure in model cement is briefly discussed in [9] and compared to the results of SEM image analysis on sections of real cement paste. This paper briefly discusses the correlation between
L3
and 1,and the depercolation threshold of pore
space. Garboczi et al. [lo] studied the percolation of pore phase in C3S model cement (cement composed solely of C3S). They found for w/c ratios ranging from 0.3 and 0.6, the curves for the connected fraction of the capillary pore space versus capillary porosity to merge into a single curve (especially at the low porosity part of the curve). This leads to a common depercolation threshold of about 0.22. That implies the capillary pore space to becdme topologically disconnected when its total volume fraction falls below 22% of the total cement paste volume. They also studied the depercolation threshold for ordinary model cement. The resemblance is striking between the percolation curve of the model cement and that of the C3S model cement, whereby very similar percolation thresholds occur at about 21%. The influence of w/c ratio on the depercolation threshold of pore space is negligible as long as the pore space finally depercolates. In case of a higher w/c ratio, it takes more time to reach the depercolation threshold of porosity. This can also be explained by the morphological development of solid structure. For example, in case of a model cement with a moderate fineness of 363 m2/kg, the mean free spacing between cement particles is 4.58, 6.10, 7.63, 9.15 pm for a w/c ratio of 0.3, 0.4, 0.5, and 0.6, respectively. Hence it is expected that the cement with higher w/c ratio needs more time to achieve a low value of h that is corresponding to the depercolation threshold of porosity. The morphological evolution of solid phase and pore structure during hydration, for various w/c ratios, are studied by SPACE simulation and the results are discussed in details in another publication of the authors [ 111. Another interesting observation is that at higher w/c ratios (say, 0.6), the hydrating model cement is sometimes unable to achieve depercolation of the capillary porosity. Even if the model cement hydrates completely, the final porosity is still higher than the depercolation threshold of porosity. To be more specific, Powers’ model [ 121 yields a porosity of 27% after complete hydration of cement paste with a w/c ratio of 0.6. This confirms the concept that depercolation of pore space in cement is a geometry-related rather than a chemistry-related process. Although depercolation of pore space is resulting from increasing volumes of spatially dispersed hydration products, the depercolation threshold of pore space is governed by the size and spatial distribution of the particles at the initial packing
150 Jing HU and Piet STROEVEN state of the fresh model cement. Garboczi et al. [lo] also studied the capillary porosity depercolation for two different cement systems at the same wlc ratio of 0.3. In both cases, only four sizes of particles were used, with diameters of 3, 9, 13, and 19 pm. In one case, equal numbers of each particle size were used, while in the other case, equal volumes of particles were employed. The equal number case had a depercolation threshold of about 16%, whereas the threshold for the equal volume case was about 21%. This can be explained by the stereological parameters of these two systems of cement particles. The mean intercept length of the equal volume mixture is 3.69 pm,'and the mean free spacing between particles is 3.48 pm. For the equal number case, the mean intercept length is 9.53 pm, the mean free spacing 9.00 pm. In the latter case, average particle diameter is heavily relying on the larger particles. So, the average inter-particle spacing (represented by the much larger values of the mean intercept length and the mean free spacing) is much larger. As a consequence, the hydration process needs to be more advanced for closing off capillary pore space.
CONCLUSION The mean intercept length of cement particles, the mean free spacing, and the mean nearest neighbour distance between particles are important parameters to characterize the geometry and morphology of solid phase and pore space in a model cement. In case of actual cements, these parameters can be directly estimated from moments of the PSD, for Rosin-Rammler distribution, Fuller distribution, equal volume fraction, and equal number fraction mixtures. The estimation of mean nearest neighbour distance is verified by direct measurement of model cement with SPACE simulation. Although depercolation of pore space is resulfing from increasing volumes of spatially dispersed hydration products, the depercolation threshold of pore space is governed by the size and spatial distribution of the particles at the initial packing state of the fresh model cement.
REFERENCES 1. Stroeven, M., Discrete Numerical Modelling of Composite Materials. Ph.D. Thesis, Delf? University of Technology, Delft 1999 2. Stroeven, P. and Stroeven, M., Assessment of packing characteristics by computer simulation. Cement and Concrete Research, 29, 1999, pp 1201-1206 3. Stroeven, M., Stroeven, P., Computer-simulated internal structure of materials. Acta Stereologica, 15, 3, 1996, pp 247-252 4. Underwood, E.E., Quantitative Stereology. Addison-Wesley Publishing Company, USA 1970. 5. Myers, E.J., Quantitative metallography of cylinders, cubes, and other polyhedrons. In: Proc. 1'' Int. Conf. for Stereology, Vienna 1963, paper 15 6. Hu, J., Chen, H., Stroeven, P., SPACE simulation of particle flocculation in model cement. Int. Conf. on Advances in Concrete and Structures, Xuzhou 2003, to be published 7. Lu, H., Introduction to Powder Technology. Tongji University Press, Shanghai 1993
The influence ofparticle size distribution on the microstructure of model cement
15 1
8. Stroeven, P., Some Aspects of the Micro-mechanics of Concrete. Ph.D. Thesis, Delft University of Technology, Delft 1973 9. Ye, G, Hu, J., van Breugel, K., Stroeven, P., Characterization of the development of microstructure and porosity of cement-based material by numerical simulation and ESEM image analysis. Materials and Structure, 35, 2002, pp 603-613 10. Garboczi, E.J., Bentz, D.P., The effect of statistical fluctuation, finite size error, and digital resolution on the phase percolation and transport properties of the NIST cement hydration model. Cement and Concrete Research, 31, 2001, pp 1501-1514 11. Hu,J., Stroeven, P., The effects of particle size distribution and water cement ratio on depercolation threshold of pore structure in model cement-approach by morphological evolution during hydration, submitted to Cement Concrete Composites, 2003. 12. Powers, T.C., Structure and physical properties of hardened Portland cement paste. J. Am. Cerem. SOC.,41, 1958, pp 1-6
Proc. Int. Syrvp. ,,Brittle Matris Coinposites 7" A.M. Brandt. V.C. Li and I. lf. Marshall, eds. Warsaw, October 13- 15. 2003 ZTUREK RSI and Woodliead Publ.. Warsaw 2003
ASSESSMENT OF DETERIORATED CONCRETE COVER Francois BUYLE-BODIN*, Bogdan PIWAKOWSKI**, Abdelilah F"E*, Marc GOUEYGOU**, Sidi OULD-NAFFA*'**, * Laboratory of Mechanics of Lille, University of Lillel, CitC scientifique, 59655 Villeneuve d' Ascq, France, francois.buyle-bodin @univ-lille 1.fr ** E M N , Electronics Acoustics group, Ecole Centrale de Lille, BP 48,59651 Villeneuve d' Ascq, France,
[email protected] ABSTRACT Many reinforced concrete structures are suffering from deterioration occurring earlier than their expected service life. The first barrier against attacks of external environmental agents is the concrete cover. The damage mechanisms depend on the microstructure of the cover concrete. This microstructure can be assessed with various measurements. In the present research, concrete and mortar were artificially deteriorated by acid attack. Samples were attacked during different time inducing different depth of deterioration. Different parameters were measured: deterioration depth, velocity and attenuation of compressive, shear and surface high frequency waves, porosity, elastic modulus, compressive strength, water absorption.. These measures are conducted on deteriorated layer, or sound layer, or on a combination of the both layers. The depth of deterioration is well correlated with the acoustic velocities decrease for the three types of waves. The high-frequency ultrasonic wave is thus able to detect changes in the micro-structure of the concrete cover. The surface wave seems to be the most appealing for concrete cover evaluation. The correlations between ultrasonic parameters, and civil engineering parameters like porosity or elastic modulus or compressive strength are evaluated in order to perform the correct interpretation of ultrasonic measurement. The distinctive characteristics of each layer must be deduced from homogenized values measlired on multi-layer samples. For that series or parallel models have been successfully used. Keywords Concrete, degradation, high frequency ultrasonic evaluation, microstructure INTRODUCTION The durability of concrete structures is considerably affected by degradation induced by time variant loading in conjunction with environmental loading processes such as moisture transport, freeze-thaw action, dissolution processes, chemical expansive reactions such as sulphate attack, corrosion of reinforcement or alkali-silica reaction.
154
F. BUYLE-BODIN, B. PIWAKOWSKI, A. FNINE, M. GOUEYGOUandS. OULD-NAFFA
Classically two periods can be distinguished in the service life of concrete structures (Fig. 1). The first is called the initiation period, corresponding to the ingress of aggressive agents into cover concrete. No damage has developed during this period. The second period is called propagation period, when damage is developing and propagating within the structure [I]. For increasing the efficiency of remedial actions, it is interesting to act earlier than the end of the initiation period. The real stage of degradation of the cover concrete must then be evaluated. Visual inspection can give information when concrete surface is cracked, and when corrosion products flow out of structure, but often at this time the initiation period is exceeded. The interest of Non Destructive Evaluation is obvious to conduct detailed inspection on large areas of concrete structures and to allow efficient predictive maintenance 121. For that, a research has been conducted to develop a new high frequency ultrasonic method allowing the assessment of the degradation of the cover concrete. Time t -!
t degradation Figure 1. Two periods of lifetime of concrete structures
COVER CONCRETE The cover concrete is the layer of concrete with a depth of some centimetres between the surface and the more external bars of steel reinforcement. The aggregate cement paste structure of this cover concrete is not isotropic. Variations in the distribution of aggregates will occur within the concrete. The main reason is a skin effect. This effect takes place against the formed face of a concrete section [3]. The skin can be described as a layer that is rich in cement with a low aggregate content. Behind this layer is a zone in which the material consistency is similar to that of a mortar. This anisotropy of the concrete near the surface is a major factor in the durability of concrete structures. And these surface zones are the most prone to poor conditions of cure.
155
Assessment of deteriorated concrete cover
The surface of the concrete is highly susceptible to the cure conditions because of its exposure to the external environment, and the skin is the defence against aggressive environments.
DEGRADATION OF COVER CONCRETE The porous system of cementitious materials is characterized by a very large internal surface which strongly interacts with water. Hence, a state of damage is already induced in the unloaded structure which affects the macroscopic strength, the porosity and the permeability of the material. The contact of a hardened cement paste with aggressive solution leads to the diffusion of different ions and the leaching of this cement paste. As a result, the porosity, the microstructure and the chemical composition of the cementitious skeleton are changed. Consequently, macroscopic mechanical and transport properties also change [4]. An experimental programme was conducted with the aim of observing the deterioration of mortars and concretes. The samples were degraded chemically by immersing half of the sample into an ammonium nitrate (NH3N04)solution with 437 gA density, while the other half remained sound. The degradation procedure was canied out for periods of 15,30 and 45 days. Such procedure is commonly used to accelerate concrete degradation [5-61. The scheme of the degradation tank and the photograph of one section of a degraded mortar sample are shown in Fig.2. a /ample
b
Fig.2. (a) Chemical degradation set-up; (b) Sample of chemically degraded mortar
HIGH FREQUENCY ULTRASONIC EVALUATION Ultrasonic testing methods are non destructive and applicable on site. Low-frequency ultrasound (50 kHz) is routinely used to characterize large defects (a few cm large) at large depths inside the structure [7]. However, such a frequency range is not suitable to the kind of defect to be detected in concrete cover. Preliminary experiments [8] have shown that the sensitivity of ultrasound parameters to cover degradation is higher when the wavelength becomes comparable to the thickness of the degraded layer, i.e. a few millimetres. Given the propagation velocity in concrete, ultrasonic waves with significant frequency components between 0.5 to 1 MHZ are required to characterize concrete cover degradation with high sensitivity. The primary goal is to establish a correlation between acoustic parameters and the growth of the degraded layer. Secondly, it aims at determining the most sensitive evaluation
156
F. BUYLE-BODIN, B. PIWAKOWSKI, A . FNINE, M. GOUEYGOUand S. OULD-NAFFA
method as regards to the wave type (LW, TW or SW) and the measured parameter (velocity or attenuation). The experimental set-up is shown in Fig.3. The measurements were performed on a mortar and on a concrete (with gravel 4/16)). The mix proportion is given in Table 1.
Water Cement Gravel Mortar Concrete
11
22
7
14
0 43
Sand 67 36 0scillo.rcopi.
I
a Grid of mensuremcni
30cm
noitif s . . ..-
=4cm
I Scm Reference half
;
Halfto be degraded
S
Fig.3. (a) Sample of mortar (concrete) used for the experiments (b) Measurement set-up
Determination of acoustic velocity and attenuation The ultrasonic group velocity was measured using the most common mean i.e. directly from the time of flight At between the trigger signal corresponding to the pulse emission and the first received signal. Ultrasonic attenuation seems to be a relevant parameter for degraded material characterization. There are various set-ups to acquire signals for measuring attenuation and different methods for quantitatively estimating the attenuation coefficient. In the present study the correct evaluation of the acoustic attenuation in degraded samples displays a special problem and requires special interest [9]. Fig. 4 presents the measured velocity distributions on the degraded half and on the sound half of the mortar for 15, 30 and 45 days of degradation. A significant decrease of the average velocity with the time of degradation is observed. It is highlighted by the increase of the distance between the peaks of the both histograms. Degradation, though, doesn't seem to have any effect on the variance of the measured velocity. The evolution of the measured velocity with degradation is summarized in figure 4.d. showing the shift of velocity Av relative to the value v, obtained on the sound half. It must be noticed that the greatest variation is observed for the surface wave. It rises up to 24% after 45 days. However, the decrease of SW velocity tends to slow down for longer degradation times. This may be explained by the fact that the SW propagates within a depth of the order of one wavelength.
157
Assessment of deteriorated caricrete cover
As the thickness of the degraded layer increases and goes beyond the depth of propagation of
the SW, the SW tends to sense only one layer of material with identical properties.
h
Velocity ( d s )
8
si?2
8
-0
x
4 2
'8 s?
&
> u
.d Y
m
lY00
1400
1700 2000 Velocity ( d s )
2300
2
Number of days of degradation
Fig 4. Histograms of velocity for the sound mortar and after 15.30 and 45 days (a) longitudinal waves; (b) transverse waves; ( c) surface waves, (d) summary of the results
For concrete it is observed that the dispersion of the results increases and that the velocity shift caused by the degradation is relatively smaller to that of mortar. This observation might be explained by the fact that aggregates are not attacked and that their proportion in concrete is higher than in mortar. Figure 5 shows the attenuation coefficients. The region of validity of the results (indicated by an ellipse) corresponds to the area where the coherence function y reaches maximum values, close to unity. It is observed that the obtained plots of ccv) fit the straight line: o.(fJ = aof thus indicating the dramatic rise of the absorption expressed in terms of (dB/mMHz) as a function of the time of degradation. Fig. 5.d summarizes the increase of attenuation - relative to the attenuation of the sound half of the sample - versus time of degradation. Attenuation values are given at frequencies corresponding to the maximum energy of the wave propagating in the sample. As it may be seen in the plots of coherence function y, the absorption causes the shift of the spectrum towards lower frequencies. The results show a significant increase of attenuation with the time of degradation, specially for the surface wave, where it raises up to 8 times after 45 days of degradation.
158
F. BUYLE-BODIN. B. PIWAKOWSKL A. FNINE. M.GOUEYGOUandS. OULD-NAFFA
I S days of degradatiorl c
-I I -I
L"*
--
-
-
*.I
frequency MHz
'
-
-I
-
-,
.-
-
3
frequency MHz
( 730 days of degradation
frequency MHz
1'
"
&her
30 45 of days of degradatlon
F i g 5 (a), (b), (c) Attenuation a and associated coherence function y vs. frequency, obtained for transversal waves; (d) Summary of results obtained for longitudinal; transverse and surface waves vs. degradation time. OTHER PHYSICAL MEASUREMENTS The depth of the degradation and the open apparent porosity of the degraded mortar samples were measured after each degradation period. The open porosity of the degraded layer can be then calculated by relating to sound and degraded volumes respectively. As shown Fig.6, the global porosity and the depth of the degraded layer increase as a function of the time of degradation, whereas the calculated porosity of the degraded layer remains constant and equal to nearly 24%. n I
1 ..I*
. I
*.".I
.*.I*.
Fig.6. (a) Open porosity vs, time of degradation (b) Depth of the degraded layer vs. square root of the time of degradation
159
Assessment of deteriorated concrete cover
The porosity was also measured by mercury intrusion on bored specimens. The results are for sound mortar equal to 18.6 %, for 15 days degraded mortar 25.4 %, for 30 days degraded mortar 25.2 %, and for 45 days degraded mortar 23.2 %. The comparison of the different measurements of porosity are given Fig. 7. PoroalQ 0.3
0.25
02
iz
{ 0.15 g 0.1
0.05
I
". Wnd
I dsp15d.y.
I
I dep M day.
deg 45 day.
Fig. 7. Porosity measurements for mortar samples Regarding the pore size distribution, the main size of pore of the sound mortar is 1 pm. For degraded mortars this main size is reduced to 0.3-0.4 pm with a less sharp distribution.
MECHANICAL MEASUREMENTS After degradation and acoustic measurement, the samples were sawn up into 4 x 4 x 15 cm specimens presenting a multi-layer configuration. First these samples were tested in bending but the resulting tensile strengths could not be used for analysis. After that, the specimens were tested in compression with different arrangements of the layers: layers in series and subjected to the same stress, or layers in parallel and undergoing the same strain. Strain gauges were bonded on the different faces of the different layers (sound or degraded) in the both directions, parallel or perpendicular to the direction of loading. They gave the local deformations. Moreover the displacement of the compression platen of the loading machine was measured, giving the global deformation of the specimen. With the value of the depth of the degraded layer, it was possible to evaluate the proportions of volume of degraded and sound mortar, and using the parallel or series models to calculate the Young's modulus from the global deformation. Fig. 8 shows the different values of Young's modulus given by strain gauges (parallel and series layers), by using parallel or series models, and by using velocity measurements (see below).
160
F. BUYLE-BODIN, B. PIWAKOWSKI, A . FNINE, M.GOUEYGOUand S. OULD-NAFFA
The strain gauge measurements allow the evaluation of the Poisson's coefficient. Its values stay constant according to the accuracy of the method and equal to 0.3. Young's modulua 4
m
-*
i -
+ c
25ooo
paralldlaye~s
.sadeslam
parslldmodel .Series& - C l m wlwities
Y
-.).I
2
m
15ooo
1CC.X Swnd
15daya
30 days
45 days
Fig. 8. Different evaluations of Young's modulus of degraded mortar
ANALYSIS OF RESULTS The Young's modulus E, the dynamic modulus K and the Poisson's coefficient v can be calculated from velocities using the well-known formulas:
The Poisson coefficient and the density are assumed to be constant with the time of degradation. The parameters E and K computed from the velocity data and expressed as relative values are shown in Fig.9.a. The values of E are also copied out on Fig. 8. The comparison is good, and shows that the pulse velocities are well correlated with the mechanical characteristics. In parallel, the measurements of porosity allow estimating the compressive strength, using the well known formula of Fkret [ 101:
0=oo(I-P)2 : where p indicates the apparent porosity (%) and cq, is the compressive strength of the porosity-free mortar. Fig.9.b. summarizes the relative decrease of ts and increase of P as a function of the time of degradation.
161
Assessment of deteriorated concrete cover
a K/K,
=
WE.
_Number of days of degradation
Number of days of degradation
Fig.9 (a) Normalized elastic modules E and K vs. degradation time; (b) Normalized apparent porosity P and associated compressive strength o vs. time Finally, correlating the time of degradation and the measured acoustic velocities, the relative drops of the Young's modulus and of the compressive strength as a function of the time of degradation are shown in Fig. 10.
Fig.10 (a) Normalized elastic modulus E vs. acoustic velocity; (b) Normalized compressive strength vs. acoustic velocity
CONCLUSIONS The effect of the chemical degradation on the characteristics of cover concrete was studied by different methods at global and local scale. The chemical attack by ammonium nitrate solution creates a degraded layer . Its depth increases following a diffusion law as a function of the square root of the time. The apparent open porosity and the Poisson's coefficient of this degraded layer seems to be constant, while the main size of pore and the elastic modulus decrease. Concerning the high frequency acoustic pulse method, the effect of the degradation is evidenced for the three types of waves. As expected, a decrease of velocity and an increase of attenuation are observed. Similar trends are observed with heterogeneous concrete, but the variance of the results made their interpretation more difficult. In the case of mortar, velocity decrease is 24% for the surface wave, whereas attenuation increased dramatically up by a
162 F. BUYLE-BODIN, B. PIWAKOWSKI, A. FNINE, M. GOUEYGOUand S.OULD-NAFFA
factor of 8 for the transverse wave. The high-frequency ultrasonic wave is thus able to detect changes in the micro-structure of the cover even at an early stage. Furthermore, preliminary experiments using lower frequency (50 kHz) have shown that there is no measurable difference at such a frequency range between the degraded and the sound material. This confirms that the choice of relatively higher frequency is relevant to sense the little depth of degraded layer. Concerning the relations between acoustic and mechanical characteristics, a good correlation is observed, and the sensitivity of all the parameters to the apparent porosity is highlighted.
REFERENCES
1. Basheer, P.A.M., Chidiac, S.E., Long, A.E., Predictive models for deterioration of concrete structures, Construction and Building Materials, 10, 1996, pp 27-37. 2. Bungey, J.H., Millard, S.G., Testing of concrete in structures, Blackie Academic & Professional, Glasgow, 1996. 3. Rendell, F., Jauberthie, R., Grantham, M., Deteriorated Concrete, Thomas Telford, London 2002. 4. Bangert, F., Grasberger, S., Kuhl, D., Meschke, G.,Environmentally induced deterioration of concrete: physical motivation and numerical modelling, Engineering Fracture Mechanics, 70,2003, pp 891-910 5. Torrenti, J.M., Didry, O., Ollivier, J.P., Plas, F., La dkgradation des bttons, Hermes, Paris 1999. 6. Jauberthie, R., Rendell, F., Physicochemical study of the alteration surface of concrete exposed to ammonium salts, Cement and Concrete Research, 33,2003, pp 85-91 7. Krause, F., Comparison of pulse-echo methods for testing concrete, NDT&E International, 30, 1997, pp. 195-204. 8. Ould-Naffa, S., Goueygou, M., Piwakowski, B., Buyle-Bodin, F., Detection of chemical damage in concrete using ultrasound, Ultrasonics, 40,2002, pp 247-25 1. 9. Goueygou, M., Piwakowski, B., Ould Naffa, S., Buyle-Bodin, F., Assessment of broadband ultrasonic attenuation measurements in inhomogeneous media, Ultrasonics, 40, 2002, pp 7782 10. Carde, C., Caracttrisation et moddisation de l’altkration des propri6tks mkcaniques due B la lixiviation des mattriaux cimentaires, Doctoral thesis, Toulouse, 1996.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
MEASUREMENT OF THE DURABILITY OF GLASS FIBRE REINFORCED CONCRETE AND INFLUENCE OF MATRIX ALKALINITY H. CUYPERS and J. WASTIELS Department of Mechanics of Materials and Constructions, Vrije Universiteit Brussel, Belgium J. ORLOWSKY and M. RAUPACH Instita fir Bauforschung, Rheinisch Westfalische Technische Hochschule Aachen, Germany
ABSTRACT Even today, one main topic of consideration regarding glass- fibre reinforced cementitious composites is the durability. At RWTH-Aachen (Germany) the durability of AR-glass yams in concrete is under investigation. The aim of these investigations is to build up a model, allowing prediction of the long-term behaviour of textile reinforced concrete. This model includes the influence of humidity, pH and temperature corditions, combined with stress (constant load). For glass- fibre reinforced cementitious composites, the pH of the matrix has a considerable influence on the durability, since glass fibres can be severely attacked by high alkalinity. To overcome this problem a new cementitious material has been developed at the VUB (Brussels, Belgium). This Inorganic Phosphate Cement (IPC) provides a now alkaline environment after hardening. Since the IPC matrix provides a neutral environment, other effects (humidity, temperature, stress) can be studied. A more common concrete mixture (micro-concrete with Ordinary Portland Cement (OPC), pH 13.5 after hardening) is also tested as a comparison material. The evolution of the tensile strength of IPC composites and OPC composites with AR-glass and with Bglass is measured and discussed. It is shown that the IPC matrix has in comparison to OPC a good durability. Keywords cementitious composite, durability modelling, alkalinity
INTRODUCTION Concrete reinforced with fibres offers several advantages as a building material. Fibre reinforced concrete (FRC) has been known for almost 30 years. Some typical fields of application are claddings, filigree construction elements and industrial floors. Textile reinforced concrete (TRC) represents an interesting new construction material, offering several advantages compared to steel or fibre reinforced concrete. These advantages dominate in those fields of applications where thin- walled, structural elements with a high load-carrying capacity are necessary. The used textiles consist out of continuous fibres (filaments) which are collected to form a yarn (roving). The diameter of the filaments is 12 to 30 pm. A roving with 2400 tex (1 tex = 1 g / 1000 m) has about 2400 filaments. Figure 1 shows on the right side a roving which is embedded in concrete.
164 H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M. RAUPACH
Figure 1. Textile used as reinforcement in c:oncre:te and roving embedded in concrete. In the research project SFB 532 “Textile Reinforced Concrete - Basics of a New Technology” placed at the Technical University of Aachen (financed by the central public funding arganisation for academic research in Germany, DFG) several institutes investigate this new construction material. Some aspects of these investigations are the matrix- fibre bundle bond behaviour, load-bearing capacity, material optimisation, serviceability and durability [l]. The aim of these durability investigations is to build up a model, allowing the prediction of the long-term behaviour of textile reinforced concrete. This model includes the influence of humidity, pH and temperature conditions, combined with stress (constant load). Concerning durability, FRC and TRC are comparable because the same mechanisms of ageing happen. However, the influence on the macro- mechanical behaviour of the composite material may be different. The storage of glass fibre reinforced concrete in a water bath at elevated temperature leads to an accelerated ageing process as it has been shown, amongst others, by Litherland et al. [2]. Depending on the temperature of the water and type of glass and cement, the tensile strength of the composite material decreases with time. Two causes for the loss of tensile strength are described in many papers in different ways [2]-[4]. First the glass is chemically attacked by the high alkalinity of the cement and secondly it is mechanically attacked by hydration products. Pumell [5] is convinced that the local points of flaws in the glass, which are due to the manufacturing process, are the points of attack by chemical and mechanical forces. To protect the glass from chemical attack, 15-20 % zirconium is added to the conventional E-glass mixture. This modified glass is called AR-glass (alkali resistant). It improves the durability of the concrete reinforcement but it does not solve the degradation problems entirely [2]-[6]. To overcome this durability problem, caused by the alkalinity of ordinary cements, a new cementitious material has been developed at the VUB (Brussels, Belgium). This Inorganic Phosphate Cement (IPC) provides a norralkaline environment after hardening. At the VUB ordinary 6glass fibres are applied as reinforcement in IPC. Mechanical modelling of 6glass fibre reinforced IPC composites and possible application as faces in sandwich panels with cementitious faces for building applications have been studied by Cuypers [7]. The advantages of the neutral environment of IPC are now used to study the effect of humidity and temperature on composite materials with Bglass or AR-glass. A more common concrete mixture is also tested as a comparison material. Several testing and measurement techniques are applied to determine the evolution of the matrix, the fibres and their interaction. This paper describes the testing methods and the testing program. Then the results are presented and discussed. Finally conclusions, taken from the experimental program, and future developments are drawn.
Measurement of the durability of glass fibre reinforced concrete and influence of matrix ...
165
TEST METHODS Materials Two different types of glass are used for the investigations: (1) AR-Glass rovings with 2400 tex manufactured by the company Vetrotex (CemFil) and (2) chopped E-glass fibre mats (“2Drandom”) with a fibre length of 50mm and fibre density of 300g/m2 (Owens Coming MK12) with +540 fibres per bundle. The concrete mixture (table 1) with OPC cement, which has been used as a comparison material, was developed by the Institute for Building Materials Research (RWTH-Aachen) as a micro-concrete [8].’The pH value of this mixture is 13.5. Table 1. Composition of the micro-concrete. Binder system
Type of cement
Cement
Additives
content
Fly ash
Silica fume
kglm’
OPC
CEM I52,5
490
175
35
Water reducer
I
Stabilizer
Binder content
w/bratio
max. grain size
kglm’
-
mm
700
0.4
0.6
I’
Test program An overview of the test program is given in table 2. As already mentioned in the introduction, saturation of glass- fibre reinforced concrete, especially in solutions with high alkalinity, leads to degradation of the glass fibres. To accelerate this degradation, the specimens are stored at 50°C in water. Reference specimens are stored at 20 “C in water or in ambient conditions to obtain an idea on the acceleration factor of the experiments. Tests with E-glass in combination with OPC were not carried out since from previous investigations it is well known that Bglass is rapidly degraded in an alkaline environment [ 11, [31.
Reinforcement
AR-glass
Matrix material
OPC
IPC
ambient conditions (20°C and 65 % relative humidity) water 20 “C
90
14, 28, 90
14,90
90
water 50 OC
14, 28, 90
7, 14, 28, 90
storage conditions
E-glass
IPC
storage time in days 7, 14, 28, 56, 90
7, 14, 28, 56, 90
166 H.CUYPERS, J. WASTIELS, J. ORL.0 WSKY and M.RAUPACH IPC: 24 hours post-curing in a oven at 60 "C, followed by storage during 7 days at 23 "C and 50 % relative humidity After the presented storage conditions (table 2) were applied, the specimens were stabilised under ambient conditions for several days. For each test three specimens were used. TSP-Test with AR-glass rovings The TSP-Test (dog bone shaped specimens in tensile test) allows us to draw conclusions concerning the changes in the stress-elongation behaviour, the cracking image and the maximum roving tensile strength after climatic loading. Therefore, statements can be made about the long-term behaviour of textile reinforced concrete [6]. The geometry of the TSP specimens can be seen in figure 2. The specimens have a thickness of 6 mm. Eight single rovings are used, this corresponds to a reinforcement degree of 2,O v01.-%. The change of length is measured on two sides over 250 mm. The rovings, which are sticking out of the sample body, are glued with epoxy resin. This way the individual filaments are fixated at the end of the sample. When stress is applied, individual filaments are unable to slip towards the centre of the sample from the sample edge. Therefore the rovings can reach thkir maximum tensile strength.
I-
I
+*
roving
[mml
gauges
500 250
F-. -_._._._-._-.I-
dl -.-.-I-
fixing of the roving with epoxy resin
O*
-,
fixing of the roving with epoxy resin
Figure 2. TSP-specimens and test set-up. The application of tensile force takes place with rounded off steel elements, shown in figure 2. The TSP samples are charged in displacement control with a speed of 0.5 m d m i n until failure occurs. Figure 3 shows a typical test curve. After a linear elongation, an initial crack in the matrix appears. The curve gradient after this first crack is nearly the same as before, so it is often difficult to determine the first crack point. After the second or third crack appears, the force grows more slowly and a fine crack pattern is build. After introduction of the last crack in the matrix, further load carrying occurs via the 8 rovings until the reinforcement fails. A selE made program finds these described points (force/elongation) automatically (figure 3). The initial stiffness (before the first crack appears) is determined as a measure of the evolution of the matrix properties and the stiffness after the last crack appeared is a measure of the fibre properties.
Measurement of the durability of glass fibre reinforced concrete and influence of matrix ...
5,5 1
167
Force in kN
3-0 €-modulus of the reinforcement
2.5 -
0,O
1.0
2,O
3,O
4,O
5,O
6,O
7,O
8,O
9,0 10,O
11,O 12,O Elongation in mmlm
Figure 3 . Evaluation of the measured results. The number of matrix cracks is determined after failure of the specimen occurred due to mechanical loading. The average crack spacing (
) is, amongst others, function of the matrix-fibre frictional shear stress transfer (z). The relationship between and T is formulated in a rather straightforward way by the well-known ACK (AvestowCooper-Kelly) theory [9]. If this approach is adopted, the average crack spacing at the end of multiple cracking can be determined: (cs) =
1.337 onurV,,, 2zv,
Where: = the average crack spacing at the end of multiple cracking ornu = the matrix failure stress r = the fibre radius V, = the matrix volume fraction Vf = the equivalent fibre volume fraction (including effects of fibre ,orientation and fibre length) z = matrix-fibre interface shear stress All parameters in equation ( 1 ) can be determined easily, except for the matrix- fibre shear stress transfer, 2. This matrix-fibre interaction is function of some aspects that are not easily controlled. In practice fibre bundles are used rather than single fibres. These bundles are usually only impregnated partially, if being impregnated at all. Instead of matrix- fibre interaction, both matrix- fibre and fibre- fibre interaction occurs. Matrix- fibre interaction will be more prominent at the outer fibres of the bundle than at the inner fibres. For this reason z is an average matrix- fibre interaction parameter. If crack counting is performed (determination of ), equation ( 1 ) can be rewritten in order to find the average matrix- fibre shear stress, 2:
168
H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M.RAUPACH
Tests on strip specimens with Eglass fibres The specimens with Bglass fibre reinforcement are laminated by hand layup technique. The amount of matrix used per layer is 800 g/m3. This way, laminates with a fibre volume fraction of about 12 v01.-% are made. After a laminate is fabricated, it is kept in ambient conditions for 24 hours. Afterwards, the laminate is post-cured for another 24 hours at 60 "C to accelerate the hardening process. During the curing and post-curing process, both sides of the laminate are covered with plastic sheets to prevent early evaporation of water. The laminates are cut in strips of 250 mm length and 18 mm width. Tensile tests are performed on the E-glass fibre reinforced specimens by an INSTRON 4505. The force is measured by a load cell and the strains are measured by an extensometer over a length of 50 mm. After loading of the specimens, the average crack spacing is determined and discussed, as explained in paragraph 2.3.3.
RESULTS AND DISCUSSION Measurement of the tensile failure strength Figure 4 shows some load-elongation curves, obtained from tensile testing on TSP specimens with AR-glass. Force In kN micro concretewith OPC
micro concrete wilh OPC
3 tests afler referenz storage: 28d at 23 'C. 95 % r.h. and
0
2
4
6
8
10
12
140
2
4
6
8 10 12 14 Elongationin m d m
Force in kN
I failure at lhe grip
3 tesls aRer referenzswage: 28d at 23 'C. 95 % r.h. and
0
2
4
6
8
10
12
140
2
4
6
8 10 12 14 Elongationin mm/m
Figure 4. TSP tests with different matrix after different storage conditions. Figure 4 top left, shows three tensile test curves with OPC and AR-glass rovings after reference storage. The tests show good conformity. The specimens fail at an average value of
Measurement of the durability of glass'5bre reinforced concrete and influence of matrix ...
169
4.8 kN. At this breaking point, only the reinforcement carries the load so it is possible to
calculate the strength of the rovings, which is then 672 N/mmz. At the top right part of figure 4, the influence of 28 days water storage at 50 "C is shown. After initial cracking, the
specimens also show an evenly distributed cracking image, but the specimens with OPC break already at an average load of 3.1 IcN (Roving strength 434 N/mmz). The results with IPC are presented in figure 4 bottom. After reference storage, the specimens fail at an average value of 5.5 kN (Roving strength 770 N/mm2). This breaking load is significant higher than the OPC specimens. The accelerated ageing storage at 50 "C in water shows no loss of function of the IPC specimens. The average failure load is still 5.5 kN. One of the three specimens of IPC broke at the grip as can be seen in figure 4. Specimens with this kind of failure were not considered in the evaluation. Figure 5 presents an overview of the results with the TSP specimens. In this diagram, the roving strength calculated from the failure force is shown as a function of storage time. The dots at zero days are the reference specimens. For the reference storage, the scatter is also shown. 4 Roving strength in Nlmm'
900
,
I
600 500 400
300 200
W
-
.-._.___
L.-.-.+
'-~
Referenz IPC
-- -65%
- - . - . - _ _- -. - - - - .
4-.Water; 50'C;
IPC
a Water; 20'C; IPC
humidity.; 20°C; IPC ReferenzOPC
4-
65% humidity.: 20%; OPC
--Water;
.Water; 50°C; OPC 20°C: OPC
The roving strength with IPC matrix after reference storage is 140 N/mm2 higher than the roving strength with OPC. This measured roving strength of 790 N/mm2 (IPC specimen) has the same magnitude as the roving strength of a single roving, tested in a tensile test. This means the manufacturing of the TSP-specimens and the IPC matrix itself does not damage the filaments initially. In comparison, the OPC matrix reduces the tensile strength of the reinforcement already after reference storage. One possible reason for the initial strength loss could be the transversal shearing of aggregates and hydration products on the filaments. Further investigations to explain this effect are necessary. The results in figure 5 show that the composite with IPC and AR-glass has a good durability. No significant loss of strength was measured, even when stored in water at elevated temperature. In contrast, specimens with OPC in water at 50 "C show a significant loss of strength. In water at 20 "C these specimens show a strength decrease only after a storage time of 14 days. After this initial decrease, the strength is constant. At 20 "C and 65 % relative humidity the OPC specimens show no loss of strength.
170
H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M. RAUPACH
Figure 6 shows the evolution of the failure stress of the IPC specimens with Erglass fibres. 45
1
I
40
I
I
I
1
I I
I
i
I
I
I
12
14
16
I
I
I
a n 35
rIn 30 3
25
L
20
-$ 15
B
accelerated ageing
10
-ambient
wnditions.averageevolution
5
0 0
2
4
6
10
Figure 6. Evolution of the failure stress of IPC specimens with E-glass. In contrast with IPC with AR-glass, the IPC spepimens with Bglass fibres show ewlution of the failure stress with time. It has been mentioned by some authors [lo] that just the effect of warm water can lead to decreasing strength of glass fibres, even when the fibres are again stabilised under ambient conditions after being kept underwater. The initial composite strength of 35MPa is equivalent to a roving strength of 870 N/mm2, indicating that the initial strength of the Lglass fibres is not or hardly attacked by the IPC matrix. Measurement of stiffness and crack spacing Table 3 sbws the stiffness properties of the composite materials with AR-glass. Table 4 shows the Emodulus measured in the post-cracking zone and the average crack spacing of the IPC composites with Eglass. The E-modulus in the pre-cracking zone and the tensile matrix strength could not be determined clearly for these specimens, since multiple cracking was smeared out over a large stress interval.
'Noevaluation possible (figure 4)
strip specimens.
Measurement of the durability of glassfibre reinforced concrete and influence of matrix ...
171
The roving stiffness of the TSP specimens with IPC and AR-glass does not change significantly with climatic conditioning. The roving stiffness of the TSP specimens with ARglass an3 OPC matrix decreases after 14 days of application of accelerated ageing conditions. This roving stiffness cannot even be determined any more after 28 days. The roving stiffness of the specimens with Bglass and IPC matrix does not change with time. For the TSP specimens with OPC micro concrete the average crack spacing seems to decrease after application of accelerated ageing conditions. A possible explanation for the reduced crack spacing is the increasing hydration of the micro concrete, which results in a higher matrix- fibre interface shear stress (see equation (2)). This increase in matrix- fibre shear stress might lead to early failure due to mechanical attack of the glass fibres by hydration products, as was explained in paragraph 1. The opposite effect can be seen on the specimens with IPC matrix. The average crack spacing is constant or slightly increasing with time of storage. This would mean, according to equation (2), there is hardly any evolution in the matrix-fibre interface interaction (or maybe even a slight loss).
CONCLUSIONS Tensile testing on the different composite materials shows clear results concerning strength. Figure 7 contains an overview of the evolution of the degradation of the tested cementitious composites under accelerated ageing conditions. The strength of OPC micro-concrete reinforced with AR-glass rovings decreases up to 50 'YOof the initial strength after 90 days in water at 50 OC. In comparison, the strength of IPC matrix reinforced with AR-glass rovings stays at nearly 100 YOuntil 28 days. After 90 days at accelerated ageing conditions this composite material shows a small amount of degradation. Tests with Bglass fibre reinforced IPC show in figure 7 also a loss of strength, but the degradation is significantly lower than the combination of OPC and AR-glass. When considering figure 7, one should also keep in mind that the reference failure strength (100% in figure 7) of the OPC specimens with AR-glass (670N/mmz)is already significantly lower than the reference failure strength (100% in figure 7) of the IPC specimens with AR-glass (770N/mmz)and &glass (870N/mmz). The average matrix crack spacing decreases as a function of accelerated ageing time if OPC matrix is used and increases or hardly changes if IPC matrix is used. A possible explanation for the reduced crack spacing in OPC composites is the increasing hydration of the micro concrete, which results in a higher matrix-fibre interface shear stress. This effect is not observed if IPC is used. When IPC is reinforced with AR-glass, no or very limited decrease of failure strength is noted. It has thus been shown that, due to the use of a cementitious material with neutral pH, effects of alkalinity can be studied separately from other effects. This means the IPC matrix can be used as a reference matrix to model long-term behaviour of fibre reinforced concrete and textile reinforced concrete, thereby separating possible effects leading to degradation. If Bglass is used, there is a small decrease in failure strength. However, degradation of 6 glass fibres is rather due to the water and high temperature environment as a chemical reaction (solution of the glass) than to evolutions in the matrix-fibre interface, since no real change in average crack spacing is noted.
172
H. CUYPERS, J. WASTIELS, J. ORLO WSKY and M.RA UPACH
Strength of the composite material compared to the reference in % I
100 I
80
-
60 40
-+IPC-AR-glass
20 -+Storape
.
conditions:water at 50 TI
+IPC-E-glass
-
*OPC-AR-glass "
I
0
20
40
60
80
100 Time In days
Figure 7. Loss of strength of AR-glass and Erglass in OPC or IPC matrix. 5. REFERENCES
[31 [41
r71
PI
r91 r101
Hegger, J. et al, 1. Fachkolloquium der Sonderforschungsbereiche 528 und 532, 15. und 16. Februar 2001 in Aachen. Aachen. Lehrstuhl und Institut f i r Massivbag 2001 Litherland, K.L., Oakley, D.R., Proctor, B.A., The Use of Accelerated Ageing Procedures to predict the Long Tern Strength of GRC Composites. Cement and Concrete Research 11, Nr. 3, 1981, pp 455-466 Majumdar, A.J., Laws, V., Glass Fibre Reinforced Cement. London, BSP Professional Books, 1991 Yilmaz, V.T. , Glasser, F.P., Effect of Silica Fume Addition on the Durability of Alkali-Resistant Glass Fibre in Cement Matrices. Fly Ash, Silica Fume, Slag, and Natural Pozzolans in Concrete. Proceedings Fourth International Conference, Istanbul, May 1992 (Malhotra, V.M.(Ed)), Vol. 2, pp 1151-1166 Purnell, P., Short, N.R., Page, C.L., A Static Fatigue Model for the Durability of Glass Fibre Reinforced Cement. Journal of Materials Science 36,2001, pp 5385-5390 Brockmann, J., Raupach, M., Durability Investigations on Textile Reinforced Concrete. Durability of Materials and Components, 9th International Conference, Brisbane, Australia, 17-20 March 2002, Paper No. 1 11 (CDROM) Cuypers, H., Analysis and Design of Sandwich Panels with Brittle Matrix Composite Faces for Building Applications, Phd. T6esis W B , 2002 Brameshuber, W., Brockmann, J., Development and Optimization of Cementitious Matrices for Textile Reinforced Elements. Proceedings of the 12th International Congress of the International Glassfibre Reinforced Concrete Association, Dublin, 1416 May 2001, pp 237-249 Aveston, J., Cooper, G.A., Kelly, A., Single and multiple fracture, The Properties of Fibre Composites. IPC Science & Technology Press Ltd. London, 1971, pp15-24 Czymai, A., Eine Methode zur Bestimmung von Tiefenprofilen an korrodierten Glasfasern. Clausthal, Technische Universitat, Fakultat fiir Bergbau, Huttenwesen und Maschinenbau, Diss., 1995
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
BRIDGE RECONSTRUCTION WITH ONE LAYER CONCRETE OVERLAY
J. GALIC, I. BANJAD PECUR, N. STIRMER, V. UKRAINCZYK University of Zagreb, Faculty of Civil Engineering KaEiCeva 26, 10000 Zagreb, Croatia, e-mail: [email protected] ABSTRACT
The paper presents the reconstruction of the damaged reinforced concrete bridge with high performance concrete modified with styrene-butadiene latex and fiber reinforcement. ARer 30 years in service the severe damages of concrete cover and reinforcement corrosion were observed. The detailed testing has shown poor quality of concrete, low strength and up to 25% reduction of certain number of reinforcing bars. The bridge reconstruction was executed with one layer concrete overlay 20 cm thick. The repair high performance concrete was designed for the following properties and purposes: - to strengthen the span structure by increasing the depth of cross section by 10 cm replacing partly the damaged concrete, insulating layer and asphalt overlay, - satisfactory resistance to freezing and deicing chemicals, - resistance to wear and abrasion, - to serve as the impermeable overlay replacing the insulation. Keywords bridge reconstruction, repairing impermeable concrete overlay
corroded reinforcement,
polymer
modified FRC,
INTRODUCTION In the past, many bridges were designed and constructed on the basis of safety and bearing capacity proof. The durability of reinforced concrete was not taken into account. ARer some 30 years many of these bridges are heavy damaged. Typical damages result from reinforcement corrosion caused by de-icing salts or carbonation and frost cycles, but also from poor design and construction or lack of maintenance. The methods of reconstruction or rehabilitation or repair of such bridges change from one case to the other. Concretes modified with different admixtures and materials are used in most cases. ARer brief description of the problem, in this paper are presented the reconstruction and repair works of the reinforced concrete bridge with one layer high performance concrete.
174 Jure GALIC, I. BANJAD-PECUR. N. $ T I M E R and V. UKRAINCZYK TEST RESULTS AND EVALUATION OF THE EXISTING BRIDGE Static system is continuous reinforced concrete plate over six spans, L=l1,0+11,5+11,35+11,6+11,75+11,2m =68,4 m, and bridge level line is placed in horizontal S-curve and vertical curve (FIGURE 1). The bridge was concreted in place 30 years ago during the cold weather and the edge parts were damaged by frost. Because the bridge is exposed to heavy traffic load high damage rate was observed. It was necessary to find quick and durable solution for its reconstruction.
FIGURE 1. View of the bridge before reconstruction. In FIGURES 2-4 typical damages are shown. Concrete strength was determined combining the results obtained by Schmidt hammer and drilled cores. Due to the low quality and poor homogeneity of concrete the characteristic strengths of bridge were very low (TABLE 1). TABLE 1. Characteristic concrete strengths
I
.P .A R T --.*
I
fck(MPa)
1
Slabs Columns Abutments
Reinforcement cover depth as measured by rebar locator ((PROCEQ))PROFOMETER 3 showed variations from more than 6 cm to 0 cm. In heavy damaged parts of structure concrete cracks and spalling around reinforcement were significant (FIGURE 3).
175
Bridge reconstruction with one layer concrete overlay
cornice
footway
of
F1 the slab
Concrete carbonation depth was estimated on drilled cores with phenolphthalein. In spite of the similar environmental conditions test results vary in wide range due to the heterogeneity of the concrete quality (FIGURE 5).
carbonatisatondepth (mm) 1501
45 40
35 30 25 20 15 10 5
-,---
0
I-
Ul -~ -
__
S1-J -
-.
- -
-
___
__
r -
S4-J - _. -
FIGURE 5. Carbonation depths
P I -SM
176 Jure GALIC, I. BANJAD-PECUR. N. S T I M E R and V. UKRAINCZYK Chloride ions contents were determined on powder samples taken by drilling subsequently into the depth of bridge parts as described in the TABLE 2. According to these data corrosion of the reinforcement is mainly caused by carbonation.
CODE S1-J u1 u2 PI-s PI-T P 1-SM PS.5-SM
STRUCTURAL ELEMENT
Column abutment abutment Slab Slab I Slab 1 Footway
DEPTH (cm)
I
0-2 . _ 0,002 0,002 0,Ol 0,002 0,0062 0,oo 1 0,006
I
-2-4 .
I
4-6 . -
I
0,002 0,064 0,023 0,002 0,002 0 0,002
0,002 0,os
0,018 0,002 0,0062 0 0,002
Besides the repair in the sense of durability of all parts of the bridge, the recalculation of the existing span structure has shown the necessity of reconstruction and strengthening. THE PRINCIPLES OF REPAIR AND RECONSTRUCTION WORKS The reconstruction principle is visible in the cross-section of the bridge span structure (FIGURE 6 ) . Existing 10 cm of asphalt overlay, waterproofing insulation and 10 cm of the upper part of concrete slab were removed using hydro demolition procedure. These three layers were replaced by new reinforced high performance concrete 20 cm thick. REPAIR PRINCIPLE Before repaii
High-.llulmo q m r m a u i
/ I
FIGURE 6.'Cross-section of the span structure. The high performance concrete was designed for the following purposes: - strengthening the span structure to increase the bearing capacity of the bridge; - specified strength 35 MPa;
- satisfactory resistance to freezing and deicing chemicals, - satisfactory resistance to wear and abrasion, - satisfactory skid resistance;
Bridge reconstruction with one layer concrete overlay
177
- to serve as the impermeable overlay instead of separate insulation.
After hydro demolition the old concrete surface was rough and the bond between old concrete and new concrete overlay was additionally assured with reinforcement web in the contact zone. Concrete curbs were exchanged with steel ones protected with epoxy resin and welded to footway reinforcement. The principles of the repair of corroded steel bars and concrete cover of columns, abutments and bottom part of the bridge deck are shown in FIGURE 9. Contaminated and damaged concrete was removed, steel bars cleaned of rust and new cover of high performance mortar was applied. The depth of cover is increased for 2 cm above the old concrete surface. The high performance mortar was designed for the following purposes: - high-alkaline mortar to recover passive protection; - good bonding between existing concrete and repair mortar in fresh and hardened state; - specified strength 30 MPa; - satisfactory resistance to freezing and thawing.
FIGURE 7. Hydro-demolition of the bottom part of the deck.
FIGURE 8 , Concreting of the bridge deck with polymer-modified FRC.
Along with the deck, new footway was concreted, because the old one was totally damaged by frost. Also, existing steel fence was replaced by new one.
repair
FIGURE 9. Repair principles.
178 Jure GALIC, I. BANJAD-PECUR, N. S T I M E R and V. UKRAINCZYK
DETAILS ON RECONSTRUCTION To fulfill the special concrete requirements, in preliminary tests the following constituents were chosen for mix design: River sand 0.. .4 mm Diabase crushed coarse aggregate 4.. .16 mm Styrene-butadiene latex Steel fibers L/d = 30/0,4 mm Polypropylene fibers L/d = 12/0,02 mm The complete quantity of special concrete for overlay was 120 m3, and the distance from the concrete factory was 100 km. Hence, it was necessary to use setting retarder, and the latex was premixed on the site just before emptying the mixer to avoid the excessive air entrainment of the mixture. The details of the two stages of completing the mix proportions are shown in TABLE 4. Concrete was pumped to its final position, compacted by internal vibrator, then leveled with the screed and again vibrated with the surface vibrating screed. TABLE 4. Mix proportions At mixing plant
Added at construction site
Total
179
Bridge reconstruction with one layer concrete overlay
FIGUIZE 10. Surface treatmznt
FIGURE 1 1. Surface roughncss
Surface roughness was achieved by dragging a broom along the concrete surface until one third of grain size had been visible (FIGURE 10 and FIGURE 11). Two days after final setting the concrete was left to dry, and then it was impregnated with the styrene-butadiene latex solution.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 " A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
CEMENT-BASED THIN BONDED OVERLAYS: NUMERICAL STUDY OF THE INFLUENCE OF BOND DEFECTS AND FIBRE REINFORCEMENT Vincent SABATHIER (1,2,3), Jean-Louis GRANJU (I), Benoit BISSONNETTE (2), Anaclet TURATSINZE (l), B a d e TAMTSIA ( 2 ) (1) Laboratoire Matkriaux et DurabilitC des Constructions (LMDC) Gknie Civil INSA-UPS, 135 av. de Rangueil, 31077 Toulouse Cedex, France (2) Centre de Recherche Interuniversitaire sur le Bkton (CRIB) Dtpartement de Gtnie Civil, UniversitC Laval, QuCbec, G1K 7P4, Canada (3) Saint-Gobain SEVA BP 176, 71 105 Chalon-sur-SaBne Cedex, France
ABSTRACT The aging. of concrete structures raises the problem of repairs. Thin bonded concrete overlaying can be a suitable technique for the rehabilitation of large area structures. A variety of structures or elements are concerned, for instance slabs on grade (mainly industrial floors), pavements, bridge decks, walls and tunnels. Toppings and linings are also relevant to the same issue. The aim of the overlay may be to retrofit a damaged surface, to improve the mechanical capacity of a structure by increasing its thickness, or to do both. The durability of an overlay relies on the durability of the bond with the substrate. In fact, the real issue is this bond. Its strength and durability often remain more or less unpredictable, much more in situ than in laboratory conditions, because of the inherent variable conditions on the work site. Especially, poor preparation of the substrate to be overlaid or its contamination are the cause of local bond defects. Relying on FEM numerical modeling, a quantitative evaluation of the incidence of such bond defects on the further debonding of the overlay is proposed. The modeling tool had been previously validated with experimental results in the absence of bond defects. In the part of the work reported in this paper, bond defects of different sizes were addressed. In addition to the defect size, the influence of the strain softening behavior of the debonding interface, due to bridging and interlocking, and the influence of fiber reinforcement in the overlay by fibers were investigated. The results of this study stresses the importance of taking into account the bridging and interlocking along the debonding interface. They also confirm the beneficial role of fiber reinforcement in the overlay. At last, they demonstrate that, owing to bridging and interlocking mechanisms along the interface, the effect of an initial bond defect vanishes soon while debonding propagates. Keywords Bond, cement, concrete, debonding, defect, fibers, interlocking, modeling, mortar, overlay, reinforcement, repairs.
182
Vincent SABATHIER, Jean-Louis GRANJU, Benoit BISSONNElTE, Anaclet TURATSINZE ...
INTRODUCTION Many concrete structures throughout the world need to be repaired, often only superficially. At the moment, repair is one of the most active fields of research in several construction materials laboratories. The use of a cement-based thin bonded overlay to repair superficially a damaged concrete structure or element is a rather economic technique. It mainly concerns slabs on grade (mainly industrial floors), pavements, bridge decks, walls and tunnels. Toppings and linings are also relevant to the same issue. Since 1990, extensive studies have been performed on the subject by a number of investigators [l-61 who have pointed out that the durability of such overlay relies on the durability of its bond with the substrate structure. This bond is in fact the central issue. The work reported here deals with the overlay mechanical behavior and debonding conditions, the long-term aim being to develop the knowledge and tools that will hopefully prevent debonding from happening. It appears that whatever the cause of debonding (external loading, hygrometric loading, thermal loading, or a combination of these), the involved mechanisms are quite similar. In such a process: - debonding is initiated in the vicinity of discontinuities within the overlay (i.e. cracks); - although the interface between the substrate and the overlay is subjected to both normal and tangential stresses, only the tensile forces perpendicular to the interface will initiate the debonding process; - fiber reinforcement in the overlay delays andor slows down debonding and its propagation by limiting the cracks opening. In order to achieve a successful repair, the thin bonded overlay technique requires from the workers some special care, especially during the surface preparation of the substrate and during the pouring of the new concrete or mortar. Nevertheless, in spite of these efforts, bond defects are practically unavoidable. Since the presence of a defect results locally in a bond sometimes much weaker than elsewhere in the repair, it might play a significant role on the repair (bond) durability. The objective of this study is to evaluate through modeling the effect of a bond defect and the contribution of fiber reinforcement in the general overlay behavior. This paper presents the basics of the model that was used and the results of simulations carried out to quantify the influence of interfacial defects. The effect of fiber reinforcement upon initiation and propagation of debonding caused by this defect was also addressed. BASICS OF THE MODEL
The modeling was based on the FEM code CASTEM 2000. Its methodology is presented in details in [7]. It assumes a crack or a debonding propagation to be controlled by the calculated stresses at first node beyond the crack or debonding tip in the still continuous structure. It is a usual technique to avoid controlling the propagation by the stress state calculated at a node, the tip of the crack or of debonding, where the theoretical stress can reach an infinite value. The crack or debonding therefore propagates to the next node when the stress state at the control node does not anymore satisfy the specified stability criterion. The algorithm used was derived from that developed by Rondeau [8],Chausson [2] and Toumi [9] using the FEM code CESAR (developed by LCPC. France). After evaluating the incidence of the spatial discretization, a distance between nodes along the crack and debonding paths of 1 mm was retained.
183
Cement-based thin bonded overlays: numerical study of the irdluence of b o d s defects ...
Crack propagation in mode I The roughness of the two opposite faces of a crack results in interlocking which is at the origin of a residual strength a, which decreases with the opening of the crack w.The approach used in the present study is that developed by Bazant [lo] and referred to as smeured crack model. The empirical relationship between q and w was obtained from a literature survey. On the basis of the law suggested by Hordijk [ l l ] , the following simplified formulation developed by Toumi [ 121 was used:
where the tern R q is the tensile strength of the material and w /is the opening limits beyond which load transfer through interlocking becomes negligible. For w = wl,the absolute value of q(w) obtained from this formulation is not zero, but it is small enough to be considered negligible. The reduction in the interlocking load capacity with the crack opening corresponds to a damage of the so-called interlocking and it is thus not reversible. As a first approximation, in the phases of closing or re-opening of a crack, provided that its opening remains lower than the maximum value w,,,, previously reached, the following q-w relationship is assumed.
From the proposals of Hordijk [ l l ] , it was estimated that, for an ordinary concrete containing aggregates with maximum size of 10 mm, w~ should be close to 0.1 mm. This value was selected, as it was validated by tests carried out previously [7]. The corresponding q-w plot relationship is presented in Figure 1 (a) and was used to model the interlocking mechanism in the plain concrete. (a) 4
RUL= 3.6 MPa
0.05
Crack opening w (mm)
0.1
I
0
0.1
0.2
0.3
0.4
0.5
0.6
Crack opening w (mm)
reinforced concrete (30 kg of fibers per m' of concrete). In the case of fiber reinforced material, the post-cracking strength is defined as ctfand represents the combined contribution of interlocking and fiber reinforcement. Ribbon-like amorphous metal fibers were used and from the works performed by Chausson [2], a;/-w plot relationship presented in Figure l(b) was chosen (30 kg of fibers by m3 of material). The contribution of these fibers is characterized by an approximately constant stress orf=2.2 MPa up to a critical opening value wCf=0.15 mm, followed by a continuous reduction, assumed as linear, until the limit crack opening of W I / =0.6 mm is reached.
184
Vincent SABATHIER, Jean-Louis GRANJU. Benoit BISSONNETTE, Anaclet TUHATSINZE ...
The following relationships can thus be derived:
) ~ t ( w ) et ) (WQVcr) (Wd <W<WIO orf (w)
otr (w) = ot(w) otr (w) = orf (3) otr (w) = orr .(w-wir)/(wcrwir)
Debonding propagation along an interface Debonding at the interface between the substrate and the repair material is a very complex phenomenon. The interface can be submitted to both tensile and shear stresses, and the debonding propagation process is a result of combined fracture modes (mode I and mode 11). According to the results reported by Uchida [ 131, it was assumed that the evolution of the shear interlocking forces as function of the relative sliding, denoted s, is governed by a law similar to that describing tensile interlocking. The relationships derived from the model previously described (see equations 4 and 5) are presented in Figure 2. The potential closing and re-opening at the interface is dealt with as in the previous model. The term Run corresponds to the tensile strength along a direction perpendicular to the interface, w is the opening of the debonding interface, w,, is the maximum opening previously reached, and w i d the critical opening beyond which there is no more interlocking force. Similar variables can be obtained to describe the corresponding shear behavior and are denoted as R r d , s,,,s and s / d . The values used are from Chausson et al. results [2]. Ran and R r d were available, actually measured by direct tensile and direct shear tests on interface samples. However, the lack of data for WId and Sid have led to the use of values obtained through a reverse analysis of the available flexural data.
In addition, the evolution of tensile and shear interlocking are not independent. For example, an opening w of the debonding interface does not only cause a reduction of the tensile interlocking (according to the empirical relationships described previously), but it also reduces the shear interlocking capacity. Indeed, irrespective of the origin of damage, it breaks local cohesive andor bridging links that affect both the tensile and the shear interlocking. It is proposed to manage this interaction according to the example of tensile interlocking illustrated by the diagram shown in Figure 3. The value of tensile interlocking without considering any interaction is multiplied by a reduction coefficient. This one depends on the maximum shear damage previously reached, itself being a hnction of the maximum sliding previously reached.
The symmetrical approach is applied to the case of shear interlocking.
185
Ceinent-based thin bonded overlays: numerical study of the iifluerrce of bonds defects ...
I I
1.5 I
0
0.01
0.02
0.03
0.04
0
0.C
Opening at the interface w (mm)
0.01
0.02
0.03
0.04
0.051
Sliding at the interfaces (mm)
I
Figure 2. Mechanical characterization of the substrate-overlay interface: (a) bd-w plot relationship (mode I), (b) Td-S plot relationship (mode 11).
7dR7d
t
X
Wld
W
I
Figure 3. Effect of the tensile and shear damage interaction - Example of calculation for tensile interlocking. Modeling of the interfacial residual stresses is performed using so-calledjoint elements in the FEM-based code CASTEM 2000. These elements have normal and transverse (shear) stiffnesses. Initially in accordance with the material characteristics, these stiffnesses are adapted to describe the damage as a hnction of the relative displacements w and s. This evolution is obtained according to the equations presented previously. SIMULATION OF THE ROLE OF FIBERS UPON A BONDING DEFECT
Simulation of the presence of a defect Tests previously carried out by Chausson [2] were simulated. The composite test specimens were made of a cement-based mortar overlay with or without fibers and cast over a stiff steel substrate. The latter was a 100-mm wide hollow steel shape with an effective stiffness comparable to that of a concrete substrate, and its surface was treated to promote the mortar adhesion. The specimens were submitted to three-point flexural tests with the overlay on the tension side. The numerical results reported here are limited to the case of a 20-mm thick overlay on a 50-mm deep substrate. It is a 2-D simulation and it is assumed that a state of plane stress applies. Through a first series of calculations, a good agreement between modeling and experiment was found. Then, a bond defect was introduced and located at the specimen midlength (on the specimen axis of symmetry in the z direction), i.e. at the point of maximum bending moment stresses. It was modeled using interfacial elements having zero tensile and
186
Vincent SABATHIER, Jean-Louis GRANJU, Benoit BISSONNETTE, Anaclel TURATSCNZE ...
shear interlocking stiffness. The different defect lengths considered were respectively 20, 40, 60, and 80 mm. The simulated test is shown with its FEM mesh in Figure 4. The characteristics of the overlay and the interface were already presented and are summarized in Table 1.
Repair mortar General Without fibers E = 25 000 MPa Rot = 3,6 MPa v = 0,2 (not cracked) w1 = 0,l m v = 0 (cracked) p = 2200 kdm3 Bond defect
With fibers cr,.f = 2,2 MPa w,f= 0,15 m m wlf = 0,6 mm
Interface RCJd Rtd
= 0,5 MPa = 1,3 MPa
Wid = 0,05 mm Sld
= 0,05 mm
Imposed displacement
I
!
(with or without fibers) 20 to 80 mm
Figure 4.Illustration of the model developed to study the influence of a bond defect RESULTS AND DISCUSSION
Fiber reinforced overlay, defects with increasing size The results are presented in Figure 5 and show the evolution of the debonding from midlength as a function of the midspan deflection for various lengths of initial bond defect. The following observations can be made: As the size of the defect increases, the subsequent debonding starts less sharply. It may be explained by the increased distance of the debonded edge relative to the point of maximum curvature. That is accompanied by a slight delay of debonding initiation which may also be explained in a similar manner. When an initial bond defect is present, the midspan versus debonding progression curve systematically rejoin that calculated without any defect. The effect of the initial defect vanishes and thereafter causes no significant effect on the overall debonding process. It seems that the debonding length beyond which an initial defect will have no more influence is independent of the defect size. In the present study (50-mm substrate and 20mm fiber reinforced overlay with R,, = 3.6 MPa and S ,= 2.2 MPa, interface characteristics such as defined in Table 1) this length is about 40 mm.
Cement-based thin bonded overlays: numerical study of the influence of bonds defects ...
187
2c
a 0
50
I00
150
200
250
300
350
Mid-span deflection (pm)
Figure 5 . Debonding length from each side of the center crack as function of the midspan deflection (fiber reinforced overlay and various defect lengths)
The role of fibers The results are presented in Figures. 6 and 7. 100 '"Without fibers; No defect '."Without fibers: 40mm defect
-With
50
100
fibers; 40mm defect
150 200 250 Mid-span deflection (rm)
300
I 31
Figure 6. Debonding length from each side of the center crack as a function of the midspan deflection (overlay with and without fibers, 40-mm and 80-mm defects)
188
Vincent SABATHZER, Jenn-Louis GRANJU Betwit BZSSONVETTE, Atlaclet TUM TSZNZE ...
0
50
100
150
200
250
300
351
Mid-span deflection (vm)
Figure 7. Crack opening versus the mid-span deflection (overlay with and without fibers, 40mm and 80-mm defects) The first observation is that reinforcing the overlay with fibers significantly slows down the debonding process. For an identical midspan deflection or an identical curvature, the length of debonding can be reduced by half. The corresponding crack openings are also reduced. Alternatively, at similar overall damage (debonding length and crack opening), fiber reinforcement allows the repaired structure to withstand a much more important curvature. In addition, it appears that the larger the initial defect is, the earlier the effect of fibers arises. When there is no observable initial defect, the separation between the plain mortar and fiber reinforced mortar plots appears only after 18-mm debonding propagation. However, when there is a defect, this separation appears as soon as the debonding starts and is more pronounced as the defect size increases. Nevertheless, the results plotted in Figure 6 clearly show that fiber reinforcement of the overlay (at least for the conditions and assumptions considered in this study) does not affect the debonding length beyond which the influence of the initial defect vanishes.
CONCLUSION This work has confirmed the beneficial role of fiber reinforcement in a thin bonded overlay, Within the conditions of the present study and for a given state of deformation in the overlaid system, it was shown numerically that fibers can reduce by half the extent of debonding. The efficiency of fibers in reducing the effect of a bond defect was also studied. Fibers do not seem to influence the debonding length beyond which the defect has no more effect. Nevertheless, they act against the debonding propagation process as it starts, the effect being more important as the defect size increases. The piece of work reported in this paper is just an early step of a research project that will include laboratory testing of large overlaid concrete structural elements (test series under way). In these experiments, various overlay thickness and defect size values will be investigated. The results will then be used to refine the model.
Cement-based thLi bonded over.la.v.7:nutiierical study ofthe inflirerice of bonds defects ...
189
ACKNOWLEDGMENTS
The authors wish to express their appreciation to Saint-Gobain SEVA and the National Association for Technical Research (ANRT) for their financial support. REFERENCES
Granhaie, F., Granju, J.L., Ringot, E., Durability of pavement repairs, point of view about the role of fibers. In: Proc. "5th International Conference on Concrete Pavement Design and Rehabilitation", Purdue University, West Lafayette, USA,.20-22 April 1993, pp 195202. 2. Chausson, H., Granju, J.L., Rechargements minces adherents en beton renforce de fibres metalliques. Revue Franqaise de Genie Civil, n02, 1997, pp. 309-326. 3. Granju, J-L., Turatsinze, A., Farhat, H., Les paradoxes de la durabilite de l'adherence des rechargements minces adherents. In Proc. 3emeColloque International Francophone sur les Betons Renforces de Fibres Metalliques, Quebec, 11-12 juin 1998, pp. 63-76. 4. Granju, J-L., Thin bonded overlays : about the role of fiber reinforcement on the limitation of their debonding. Advanced Cement Based Materials, vol. 4, no 1, 1997, pp.21-27. 5. Granju, J-L., Debonding of thin cement-based overlays. ASCE Journal of Materials in Civil Enginering, vol. 32, n02, 2001, pp. 114-1 120. 6 . Bissonnette, B., Le fluage en traction: un aspect important de la problematique des reparations minces en bCton. PhD Thesis, Dkpartement de Genie Civil, Faculte des Sciences et de Genie, Universite Laval, Quebec, 1996. 7. Granju, J-L., Sabathier, V., Turatsinze, A., Toumi, A., Structures composites en beton : elements repares par rechargement mince adherent, modelisation de leur delamination.. In Proc. Forum des Associations AFGC/AUGC/IREX, Innovation et Developpement en Genie Civil et Urbain, Toulouse 30-31 mai 2002, on CD, section Materiaux Composites (edited by SCOM - Universite Paul Sabatier - Toulouse). 8. Rondeau, M-C., Modelisation des phknomknes de frottement en mode I d'ouverture de fissure par le logiciel CESAR. DEA, Genie Civil INSA-UPS, Toulouse, France, 1994. 9. Toumi, A., Etude du processus de propagation de fissures par fatigue dans le beton. Thkse de doctorat, Universite Paul Sabatier, Toulouse, France, 1998. 10. Bazant, Z.P., Crack and theory for fracture of concrete. Materials and Structures, vol. 16, 1983, pp. 155-177. 11. Hordjik, D.A., Local approach to fatigue of concrete. Thesis, Delft, Hollande, 1998. 12. Toumi, A., Bascoul, A., Turatsinze, A., Prediction de la duree de vie du beton sous fatigue - paramktres caractkristiques, Revue Franqaise de Genie Civil, vol. 4, 2000, pp. 297-307. 13. Uchida, Y.,Kurihara, N., Pokugo, K., Koyanagi, W., Determination of tension softening diagrams of various kinds of concrete by means of numerical analysis. In Proc. FRAMCOS-2, 1995 (Edit. Aedificatio, 1995), pp. 17-30. 1.
Proc. Int. Symp. brittle Matrix Composites 7 '' A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
DEBONDING OF FRC COMPOSITE BRIDGE DECK OVERLAY Rasmus WALTER, Henrik STANG, John F. OLESEN, Niels J. GIMSING Department of Civil Engineering Technical University of Denmark DK-2800 Kgs. Lyngby, Denmark, e-mail: [email protected]
ABSTRACT A new type of composite bridge deck is currently under research. The concept is to achieve composite action by the adhesion between a thin layer of fiber reinforced concrete cast on a steel plate. Of special concern is the strength of the bond between the concrete and steel plate in the case of vertical cracking of the overlay. Based on a nonlinear 2D finite element model a theoretical parameter study has been conducted in relation to debonding of a concrete overlay. Discrete crack theory was used to model vertical cracking of the overlay and interfacial cracking (debonding) between the steel plate and concrete. Two parameter studies were made. One concerns the fracture energy of the overlay and steel-concrete interface. These results show that the composite performance is dependent primarily on fracture energy of the concrete overlay, and less on the fracture energy of the steel-concrete interface. In the other, the mixed mode behaviour of the steel-concrete interface is studied in relation to the interfacial failure criterion. Keywords Debonding, FRC, fracture mechanics, steel-concrete interface. INTRODUCTION A large number of steel bridge decks suffer significantly from increased traffic intensity and higher wheel loads. This results in fatigue cracks in both welded structures and surfacing. Development of an entirely new concept of deck systems is of interest. A typical deck according to this system consists of a 40-60mm layer of Self-Compacting Steel Fiber Reinforced Concrete, (SCSFRC), bonded to an 8mm steel plate [I]. Whereas conventional composite constructions achieve composite action by mechanical fasteners, the idea here is to achieve composite action only through adhesion. The adhesion between concrete and steel is enhanced by sand blasting of the steel plate. Since a controlling factor of the composite strength is related to the vertical cracking of the overlay, the composite plate subjected to a negative bending moment is of interest. During flexural cracking of the overlay, the distribution of shear and normal stresses along the steelconcrete interface changes dramatically from that of the elastic phase. In the fracture process zone of a discrete crack. high stress concentrations develop in a plane perpendicular to the
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Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jorgen GIMSING
crack direction due to the presence of the steel plate that opposes the opening of the flexural crack. The debonding problem is known from the repairing of existing structures by thin cementbased overlays, see e.g. Granju et al. [2-31. They show that cracking of the overlay induces high interfacial tensile stresses leading to debonding between the two materials. Once initiated, the interfacial crack will propagate in a mixed mode characterized by tensile and shear stresses along the interface. The aim of this paper is to study the behaviour of the interface between concrete and steel with a fracture mechanical approach. In this study the so-called fictitious crack model (FCM) developed by Hillerborg [4]will be applied. The advantage of the model is the simplicity and the good correlation between theory and experimental tests. The basic idea of the FCM is a relationship between the stress and the crack opening. This relationship describes the stresses transferred across the crack. This method has also been applied to fiber reinforced concrete, see e.g. [S]. The two types of cracking - vertically through the overlay and interface debonding between steel and concrete - will be described by the FCM. For small crack openings, an interfacial fracture between steel and concrete shows the ability to transfer stress across the crack. This phenomenon is called ‘interlocking’ and its significance in a debonding process is described in [3]. The ‘interlocking’ effect is synonymous with the FCM. The main focus of the present paper is the presentation of a two-dimensional nonlinear finite element model to simulate the debonding process discussed above. Furthermore, the model is used to carry out two theoretical parameter studies in order to illustrate the influence of debonding on the overall behaviour.
NUMERICAL MODELLING The problem of a vertical crack penetrating a concrete layer bonded to a steel plate and the subsequent debonding is studied in a three point bending set-up according to Figure 1. The modelling is carried out as a two dimensional composite beam model, consisting of a concrete layer bonded to a thin steel plate. The vertical cracking zone in the composite beam under the applied load P corresponds to the zone near a midspan support in a bridge structure. Note that the composite beam is turned upside down for convenience.
Interface crack path, Discrete c d n g
I,_
I Loncrete Linear Elastic
L-Flexural crack path, Discrete craking
~
b
Figure 1: Experimental set-up: Simulating a negative bending moment in a bridge deck The vertical concrete cracking is modelled using standard interface elements as implemented in the applied software Package DIANA [ 6 ] . The interfacial mixed mode fracture is modelled using a composite interface model originally developed by Lourenqo and
j
193
Debonding of FRC composite bridge deck overlay
Rots [7], also implemented in DIANA. The mixed mode behaviour and the significance of constitutive material parameters are investigated through two parameter studies. Firstly, the influence of a tough concrete overlay and different fracture energies of the steel-concrete interface are investigated. Then, a parameter study is carried out concerning the failure criterion for the steel-concrete interface. Material characterisation Considering the concrete-steel interface, the state of stress is described through normal and shear stresses. In many cases the failure surface of the stress state in a steel-concrete interface is well described through a Mohr-Coulomb criterion. The failure criterion in the applied constitutive model, consist of two surfaces, denoted fi and fi, representing shear and tension failure respectively, cf. Figure 2.
Failure surfaces: f i . i=12
Id f
Figure 2: Failure surfaces f,andfi, defined by the cohesion c, slope tan(p), and the tensile strengthf;. Nonlinear softening of the interface is characterized by degradation of the tensile stress J and the cohesion c. The nonlinear softening of the tensile stress and cohesion is assumed to behave according to the following law
where co andl;o are initial values of the cohesion and tensile strength, GJ and Gy represent the fracture energy of MODE I and I1 respectively, s and w represent the slip and opening after crack initiation. The nonlinear exponential behaviour given in Equations 1(a-b), originates from experiments on mortadbrick interfaces by Van der Pluijm [8]. At the intersection between the failure surfacesf1 andfi, cf. Figure 2, a permanent coupling between tension and shear failure is present. The softening of the two surfacesfi and j ; are coupled assuming isotropic softening, meaning that the percentage of softening on the cohesion is assumed to be the same on the tensile strength. This is explained in further details in 161. Furthermore, for simplicity, all calculations are carried out assuming associated plasticity: tan(p)=tan(y), where y is the dilatation angle. Cracking of the overlay is assumed to propagate at midspan O X , using discrete crack theory. Nonlinear effects of the bulk material are not considered in this case. The stress-crack opening relationship of concrete can in many cases be modelled using a bilinear curve [S]. In the present study a bilinear curve is applied according to equation (2).
194 Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jgrgen GIMSING
d w ) -b, - u , w = --
J;
6, -u,w , h2 - U 2 w ,
0I w <w W,
I wI
W?
where 61=1; and the limit w /are given by the intersection of the two line segments and w~ correspond to the intersection by the second line and the abscissa. The steel and concrete outside the crack paths is modelled as a linear elastic materials with the engineering constants E, = 210GPa, vs=0.3, E, = 30GPa and vs=0.15. The elements representing the bulk material are 8-node isoparametric plane stress elements or triangular for mesh refining, cf. Figure 3 for the applied mesh. The two crack paths - the vertical and interface crack - are modelled using so-called interface elements, available in the applied FEM-package [ 6 ] . A two dimensional configuration is considered, where the interface element relates the forces acting on the interface to the relative displacement of the two sides of the interface. In the present case, the interface element is described by a traction vector and a vector which represents the relative displacements. In the elastic regime the relationship between traction and relative displacement is given by:
I:[
=
;[ ;]
I:[
with k,,. and k.? assigned large penalty values to model initial continuous geometry. The interface elements have a thickness of zero and are placed between the steel and concrete and at midspan to represent a possible vertical crack, cf. Figure 3.
Interface elements
/\
P 2
I
Figure 3: Half beam mesh used in FEM calculations, the two thick lines represent interface elements. Study of debond mechanism Consider a load P acting on a composite beam as shown in Figure 1. The load causes a ’negative bending moment’, characterised by tensile stresses in the concrete layer. This will eventually, at some stage, lead to cracking of the concrete. The vertical crack propagates through the concrete overlay, but at some stage it is opposed by the steel plate. The opposition of the steel plate will lead to an increase of normal stress in a plane perpendicular to the vertical crack tip, i.e. in the plane of the steel concrete interface. The horizontal stress intensity is likely to introduce cracking, along the ‘weakest link’ - which in this case is assumed to be the interface between steel and concrete. The initiation of an interfacial crack is illustrated through a case study. A composite beam is studied given the geometry: L=800mm, hC=50mm,hs=8mm, b=lOOmm and a vertical crack
195
Debonding of FRC composite bridge deck overlay
described through Equation (2) given the values: J;=3MPa, a,=lOmm-', a2 =O. lmm", b2=0.5. The distribution of interface stresses is illustrated for different openings of the vertical crack. The opening of the vertical crack, called the crack mouth opening displacement (CMOD), is calculated at midspan, cf. Figure 4-a. For an opening of 0 and 0.03 mm the stress distribution is shown as a function of the x-coordinate normalised with the concrete height h,, cf. Figure 4-b. The x-coordinate is measured from midspan.
I
-2 L 0
--
L
05
1
1.5
I 2
X-coordinale/hc [mmlmm]
(a) (b) Figure 4: Stress distribution along the interface for a CMOD value of zero and 0.03mm (a) Interfacial forces and configuration (b) Stress distribution along the interface versus the xcoordinate normalised with the concrete height h,. Dashed lines represent shear stress r a n d solid line represent the normal stress 0. It is observed that for an uncracked concrete overlay (CMOD=Omm), the normal interface stresses are governed by compression. As the crack is initiated and further opened, the normal stresses changes from compression to tension, in many cases critical to the bond between steel and concrete. Further the shear stresses are significantly increased. PARAMETRIC STUDY I - Fracture energy The purpose of this parametric study is to simulate the global behaviour of the set-up given in Figure 1 for different fracture energies of the overlay and steel-concrete interface. The different simulations performed are grouped into 3 different groups denoted A-C. Simulation A1 is the reference case, and each of the other groups involves simulations where parameters have been changed in relation to this case. The different groups of simulations are: A. Variation of the bilinear (T-wrelation of the vertical crack as defined in Equation ( 2 )
B. Variation of Mode I energy for the steel-concrete interface. The nonlinear softening of the interface in Mode I is defined in Equation (1 -a) C. Variation of Mode I1 energy for the steel-concrete interface. The nonlinear softening of the interface in Mode I1 is defined in Equation (I-b)
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Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jurgen GIMSING
The different groups of simulations and their parameter values are summarized in Table 1. The first case (A) concerns the significance of the toughness of the vertical crack. The vertical crack is characterised by a bilinear crack-opening relationship according to equation (2). The bz-value may be taken as a measure of the amount of fiber used in the material, where a high bz-value corresponds to high fiber content. Finally, the significance of different mode I + I1 energies of the steel-concrete interface is studied through cases B-C. In the reference case, A l , the following numerical values of the geometry parameters were used, cf. Figure 1: L=SOOmm, h,=Smm, hC=50mm, b=l OOmm. The numerical values used for the material parameters in the bilinear 0-w relation of the vertical crack were: J;=3MPa a,=lOmm-', a2=0.1mm-', br=0.5. The numerical values of the steel-concrete interface were, J=2MPa, c=3MPa, tan( p)=O.5, G/'= G/" = 0.1N/mrn. Name
A2 A3
Changing parameter and values Reference 0.2. b, 1.8.b2
B1
0.5. Gi
B2
2.0. Gi
c1
0.5 .Gy
c2
2.0. Gy
A1
Table 1: The Parameter variation of b-Fvalue of the vertical crack and mode I+II fracture energies of steel-concrete interface. Changing the toughness of the vertical crack leads to a change in global behaviour. This is presented in Figure 5 (a), showing the maximum moment versus the opening of the vertical crack. It is observed that changing the bz-value of the vertical crack affects the global ductility significantly.
500
. --:-----. 2
600
A2
,
,'
E
E $ 1.5 E c" - 1 I
s0 P)
100nl " 0
0.5
A3
0.5 1 1.5 CMOD - Vertical crack [mm]
6 I
n
2
"0
0.5 1 1.5 CMOD - Vertical crack [mm]
2
(a) (b) Figure 5 : Graphical representation of three hypothetical cases: -Al, ----A2, -.-.A3. (a) The bending moment M=PL/4 versus the crack opening of the vertical crack - CMOD, (b) The interface crack length normalised with respect to the concrete height versus CMOD.
197
Deboizding of FRC conzposite bridge deck overlay
The relation between the interface crack length and CMOD is shown in Figure 5 (b). Here it is shown that the toughness of the vertical crack has little influence on the relation between the interface crack length and the opening of the vertical crack. Changing mode I+II energy for the interface has a larger effect on the cracklength-CMOD relation than the ductility of the vertical crack. This is illustrated in Figure 6 (b). Furthermore, a higher interfacial mode I energy, has an influence on the Moment-CMOD relationship, cf. Figure 6(a). Comparing cases B and C shows that - for these material properties - the energy consumed at the interface primarily consist of Mode I energy.
-
2
E E
1.5 E c" 1 1 I
5
F
2 0.5 b 0
0.5 1 1.5 CMOD - Vertical crack [mm]
2
0 0
0.5 1 1.5 CMOD - Vertical crack [mm]
2
(4 (b) Figure 6: Graphical representation of five hypothetical cases cf. Table 1 . (a) The bending moment M=PL/4 versus the crack opening of the vertical crack - CMOD, (b) The interface crack length normalised with respect to the concrete height h, versus CMOD. PARAMETRIC STUDY I1 - Failure surface In order to study the degree of mixed mode propagation a second parameter study is carried out. Same reference case as in previous section A l is considered. One group of simulations, denoted D, is performed. This group involves a variation of the slope of failure surfacefl, cf. Figure 2. The parameter values are summarized in Table 2. Name A1
D1 D2
Changing parameter and value Reference 2 . tan( p) 3 . tan(p)
Table 2: Parameter variation of slope of failure surface.fi, tan(a) as defined in Figure 2. For constant cohesion c a change in the slope tan(y) of,fi, will change the position of the corner of the failure criterion. Mixed shear and tension failure takes place in the corner when .fi and ,fr intersects, and is of special interest, since the steel-concrete interface crack propagates in a mixed mode.
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Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jargen GIMSING
The stress distribution during crack propagation is shown in Figure 7. Results for the cases A1 and D1 for a vertical crack opening of CMOD=O.Smm are shown. The interface crack has 1. The peak of tensile normal stresses propagated a length of around (x-coordinatelh,) represents the interfacial crack tip. The corner values for cases A1 and DI differ due to a different slope of surfaceJ. As the crack propagates along the interface, it will try to transfer maximum normal- and shear stress across the interfacial crack. Dominated by mode I fracture, the stress state in the fracture process zone will tend to stay in the corner of failure surfaces fl and fi, cf. Figure 2. Considering the cases A1 and D1, the comer of normal and shear failure before crack initiation is given by: A1 (acorner, zc0,)=(2MPa,2MPa), D 1(a,,,,,, rC,,,,,,)=(2MPa, 1MPa). As the corner values are different, a different stress distribution along the steel-concrete interface is observed. For an opening of the vertical crack (CMOD=O.Smm), the distribution of shearnormal stresses at the crack tip and along the fracture process zone is different. The crack tip is characterised by a peak of normal stress.
Case D1
Case A1 4,
I
I
21
0
0.5 1 1.5 x-coordinate/hc [mm/mm]
2
0.5 1 1.5 x-coordinate/hc [mm/mm]
2
Figure 7: Stress distribution along the interface for cases D1 and A1 for a crack opening of CMOD=O.Smm. The two line types represent the normal and shear stresses acting at the interface between steel and concrete: -0. ----t It turns out that the mixed mode state at the crack tip varies during crack propagation. In order to illustrate varying mixed mode state during crack propagation, the mixed mode state is defined by: ,B = arctan(
t)
(4)
where s and w relates to the crack opening of the interface. The relative deformation s is the cracking deformation related to mode 11 fracture and w is the mode I opening. A failure in pure opening mode (mode I) corresponds to s = 0 a p = 0' and pure shear crack propagation correspond to w = 0 3 p= 90'. The angle /lis plotted versus the crack tip position in order to illustrate the changing mixed mode state during crack propagation of the interface, cf. Figure 8. The curves of Figure 8 are given in terms of the mixed mode angle p, as defined by equation (4) versus the crack tip position. The value of p is calculated at the normal stress peak. The Figure illustrates the three cases A l , DI and D2, each possessing different slopes of failure surface f,.All cases considered start out close to mode I fracture. As the crack tip
199
Debonding of FRC composite bridge deck overlay
propagates along the steel-concrete interface, cases D1 and D2 increase in Mode I1 fracture. Case D2 corresponds to a situation where failure surfacef, intersect the g-axis and propagates almost in pure mode 11.
looi
'
I
...............
,
'
DI
D1
.
' A1
I
I
-800
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
crack tip propagationlhi [mmimml
(a)
(b)
Figure 8 (a) Mixed mode angle p as defined in Equation (4)versus interface crack tip position normalised with the concrete height h, for three hypothetical cases: -A1, ----D I , -.-.D2. The mixed mode angle is calculated at the peak of normal stress, (b) Schematic representation of the three failure surfaces considered. CONCLUSION A model to investigate the debonding process of a concrete overlay cast on a steel plate has been developed. Based on discrete crack theory, the model describes the situation where a vertical crack propagates through the concrete overlay and causes debonding between the steel-concrete interface. The interfacial mixed mode fracture has been modelled using a composite interface model taking into account nonlinear softening of the interface. The debonding process in the case of a negative bending moment has been investigated through two parameter studies. Firstly, the effect of a ductile concrete overlay has been investigated and the results show how it influences the global performance. However, a ductile concrete overlay has little effect on the relation between the interfacial crack length and the opening of the vertical crack CMOD. Secondly, mode I energy of the steel-concrete interface has in the case considered, larger effect on global ductility than mode I1 energy. Furthermore, interfacial mode I energy has a significant influence on the Moment-CMOD relationship. A second parameter study has been carried out in order to study the stress distribution along the interface. The stress distribution during crack propagation has been investigated for different shapes of the failure criterion. It can be concluded that the crack initiates in a mixed mode, where the stress distribution along the steel-concrete is dependent on the intersection between the shear and normal stress failure surfaces. Dependent on the failure criterion, the
200
Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jargen GIMSING
stress state along the interfacial process zone tends to stay in the comer between shear and tension failure. The mixed mode state changes through crack propagation of the interface. From a practical point of view the model carried out attempts to illustrate the role of the different parameters, which might be considered in a design situation. In addition to the significance of high fracture energy of the overlay in the debonding situation considered, this study shows the difference in behaviour for different mode I and I1 energies of the steelconcrete interface.
REFERENCES 1. Walter, R., Stang, H., Gimsing, N.J., Olesen, J.F., High Performance Composite Bridge Decks using SCSFRC. The Fourth International Workshop on High Performance Fiber Reinforced Cement Composites, Ann Arbor, Michigan, USA, June 2003. 2. Granju, J.L., Debonding of Thin Cement-Based Overlays. Journal of Materials in Civil Engineering, 13(2):114-120,2001. 3. Sabathier, V., Granju, J.L., Bissonnette, B., Turatsinxe, A., Repair by Cement-Based Thin Overlays - Interlocking at the Interface and Modelling of Debonding. Industrial Floors’03, Technische Akadamee Esslingen, January 2 1-23,2003, p.62 1-626. 4. Hillerborg, A., ModCer, M., Petersson, P. E., Analysis of Crack Formation and Crack
Growth in Concrete by means of Fracture Mechanics and Finite Elements. Cem. Concr. Res., 6(6):773-782, 1976. 5 . Olesen, J.F., Fictitious Crack Propegation in Fiber-Reinforced Concrete Beams. Journal of Engineering Mechanics, 127(3):272-280, March 2001.
6. DIANA finite element analysis, user’s manual, release 8.1, TNO Building and Construction Research, P.O. Box 49,2600 AA Delft, The Netherlands, January 2003. 7. Lourenqo, P.B., Rots, J.G., Multisurface Interface Model for Analysis of Masonry Structures, Journal Of Engineering Mechanics, 127(7):660-668, 1997. 8. Van der Pluijm, R., Material Properties and its components under Tension and Shear. Proc., 6Ih Can. Masonry Symp., Saskatoon Canada, 1992.
Proc. Int. Symp. ),BrittleMatrix Composites 7” A.M. Brandt, V.C. Li and I. H.Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
PLENARY INVITED PAPER
MULTI-EXPONENTIAL MODELS AS DESCRIPTIVE TOOLS FOR PLAIN CONCRETE AND FRC
Ming Kien LEE and Ben BARR School of Engineering Cardiff University PO Box 925, Cardiff, UK, e-mail: LeeMK@,cf.ac.uk, BarrBIl O.cf.ac.uk ABSTRACT
The paper reports on descriptive tools developed for modelling the response of plain concrete and fibre reinforced concrete (FRC) under various types of loadings. Double and fourexponential models have been developed for use with plain concrete and FRC respectively. The first part of the paper deals with the double-exponential (double-e) model. Three shape parameters are required to fully define the strain-softening response typical of that for plain concrete. Each parameter has a different effect on the ultimate curve shape. An objective method of evaluating the shape parameters, which adds to the attractiveness of the model, is shown. The second part gives details of the four-exponential (four-e) model, which requires six shape parameters. This model was developed specifically to describe the more complex load-deformation response displayed by FRC. Similarly, an objective procedure has been developed for deriving the necessary shape parameters. Comparisons between experimental results and the descriptive models demonstrate the wide applicability of the multi-exponential models. Keywords Modelling, plain concrete, FRC, objective method INTRODUCTION
Loadstress-deformation curves’ obtained from closed-loop tests, be it compression, tensile or flexural (deformation in these cases may mean strain, crack width or deflection) tests, on plain concrete normally exhibit a strain-softening behaviour. On the other hand, the response obtained from fibre reinforced concrete (FRC) specimens is much more complex and diverse. The importance of measuring the response of concrete specimens under loading has grown since the advent of fracture mechanics in the world of concrete. Many attempts have been made to characterise the loadstress-deformation curves using various mathematical functions. Models for describing the complete stress-strain curves for
’ For compression, tensile and flexural tests this may take the form of stress-strain (0-w) and load-deflection
(P-8)curves respectively.
(0-E), stress-crack
width
202
Ming Kien LEE and B. BARR
plain concrete and steel fibre reinforced concrete (SFRC) subjected to compressive loading have been proposed [l-31. Furthermore, as a result of the celebrated work of Hillerborg and co-workers [4], the stress-crack width opening curve of concrete specimens subjected to uniaxial tensile loading have attracted widespread interest. Subsequently, efforts have been expended in characterising the strain-softening curve for specimens under uni-axial tension, in the post-cracking regime. The pre-cracking regime is normally characterised with a simple linear function 14-91. Often, many of these proposed functions are discontinuous i.e. more than one function is required. Furthermore, subjective methodologies have to be applied for the derivation of the model parameters. The objective of the research work reported here was to investigate the possibility of characterising the complete loadstress-deformation curve of plain concrete and FRC using one continuous function. Furthermore, systematic and objective methods of deriving model parameters have been examined to enhance the potential of such a model.
DOUBLE-E MODEL The double-e (short for double-exponential) model has been used to characterise the behaviour of impulse voltages [lo], and has the following general form:
f ( x ) = c, (e-'*' - e-"") where CI,CZ and c3 are independent constants controlling the shape of the f(x) curve. The f(x) curve is a general representation of the possible loadstress-deformation curves which may be measured. In the case of compression, tensile and flexural tests, the f(x) curve may represent G(E), o(u) and P(8) respectively. In this instance, o, E, u, P and 8 mean stress, strain, deformation, load and deflection respectively. The double-e model consists of two exponential functions and a typical shape is as shown in Fig. 1. It is immediately apparent that the double-e model has the ability to model as one continuous function the strain-softening shape typical of that of plain concrete. Furthermore, it has the added significant advantage of being amenable to mathematical procedures such as differentiation and integration. A parametric study has been carried out to study the effects of each model parameter on the ultimate shape of the f(x) curve [ 11,121. The procedure and method of the aforesaid study will not be repeated here in its entirety due to space constraints. Nevertheless, the main findings arising from the study are be reported here. It was found that the parameter cl can be used to take account of the ultimate load capacity of the material, such as tensile strength or compressive strength, for it primarily intluences the peak value of f(x). The parameter c2, on the other hand, significantly influences the tail-end of the f(x) curve whereas c3 influences the initial shape of the f(x) curve. Therefore, a wide range of f(x) curves may be simulated by varying the three model parameters. Additionally, it has been found that by fixing C I and the ratio C~/CZ, it is possible to stretch the f(x) curve in the positive direction of x by varying c2. This finding was significant as it meant that a variety of strain-softening response may be taken into account by simply changing the ratio a (where a = c~/cz).The effect of varying the value of a but maintaining the pre-peak response is shown in Fig. 2. It may be observed that the ratio a can be varied to model approximately brittle to elastic-plastic behaviour. When a approaches unity, the double-e model exhibits a very steep post-peak softening curve. On the
203
Multi-exponentialmodels as descriptive toolsfor plain concrete and FRC
other hand, an elastic-plastic type curve can be obtained by &signing a value of a>>O. Therefore, the ratio a can be said to be a proxy for the level of brittleness.
2
-0.4
J
:
;\
i 4.8 .:
4.8 -
1.2
-~ ~ e - 4 '
1
1
0.8
* a = 10
2 0.0 '4 0.4
0.2
0 0
O.!
0.3
0.2
04
0.5
x
Fig. 2: Plots of various f(x) by varying the model parameters. Proposed objective methodology Following the parametric study, research efforts were directed towards determining a suitable procedure for deriving the model parameters in an objective and simple manner. Such a procedure would be of considerable benefit since it provides a framework for a consistent and systematic means of comparing the performance of different grades of concrete.
Since there are three independent constants, three boundary conditions are required. In the case of testing plain concrete, the most important experimental parameter is the peak loadstress, hence making this parameter an essential boundary condition. Additionally, the value of the deflectiodstrain at which this is achieved is an important parameter as it relates to the initial stiffness of the material. Therefore, the second boundary condition is to define
204
Ming Kien LEE and B. BARR
the gradient to be zero at the deflectionistrain at which the peak loadstress occurs. The first two boundary conditions reflect the response of the material in the pre-cracking regime. The third boundary condition should be indicative of the response of the material in the postcracking regime and thus related to the brittleness of the material. It is well known that a brittle material gives rise to a very steep gradient in the post-cracking region whereas in the other extreme, an elastic-plastic type material would yield a shallow to flat gradient. For a quasi-brittle material such as concrete, the strain-softening behaviour should be captured as accurately as possible for the effective use of fracture mechanics especially in non-linear fracture mechanical analysis. It has been found that it is sufficient to employ a certain point in the post-cracking regime at a pre-determined percentage of the peak loadhtress. The parametric study carried out by the authors found that a value at 20% of the peak loadstress would be adequate for plain concrete specimens. To summarise, the three points required from any experiment to calculate the three parameters for the double-e model are illustrated in Fig. 3.
Xmax
x0.2jmax
X
Fig. 3 : Experimental values necessary to calculate model parameters The model parameters CI,CZ and c3 may be calculated using the following equations: for
[lo4 -I 17
for
for for ii.OOO1
Multi-exponential models as descriptive tools for plain concrete and FRC
where for Equation (2a), the values for xi are tabulated in Table 1. Table 1: Values of Y; for use with Eauation (2al i
0
1
2
3
4
5
xi
285
-10686
183868
-1695374
8564972
-22277264
6 23282310
Example of model application To assess the performance of the double-e model along with the proposed methodology for deriving the parameters, experimental results obtained from three-point bending tests [ 131 have been used as a basis for demonstration. The concrete in this example has a nominal cube compressive strength of 40MPa and was tested in a three-point bending configuration. The actual mix details and test details are not significant, as the aim is to assess only the performance of the double-e model with regards to actual experimental data. Additionally, the effectiveness of the objective methodology in calculating the model parameters may be appraised. Table 2 lists the necessary experimental values for deriving the model parameters and the calculated values of a,CI and c2 using Equations (2a) and (2b).
Table 2: List of experimental data and the associated model parameters.
e Expnmmlal
--Double+
0
model
0.2 0.4 0.0 0.8 1 Avcrsge mid-span dellredon, S(mm)
1.2
Fig. 4: Comparison between the experimental and double-e model P-6 curves, Fig. 4 shows the comparison between the experimental and theoretical curves. It may be observed that there is close agreement between the experimental and the theoretical curves
206
Mirig K i m LEE and B. BARR
hence confirming the applicability of the proposed model as a descriptive tool for strainsoftening responses.
FOUR-E MODEL The limitation of three model parameters has the drawback of not being able to model more complex curves such as those displayed by FRC. For a complex material such as FRC, additional parameters are required to reflect the contribution of the fibres. Therefore, to include additronal parameters to mirror the complexity of fibrous concrete, the authors developed the four-e (short for four-exponential) model [l 1, 141. The four-e model is the result of the superposition of two double-e models and may be expressed as follows:
where C I ,c2, q,c4, c5 and c6 are the model shape parameters. Also, F , ( x ) = cI(e-""-e-c'r) and F2(x) = ~4(e-'~'--e-cwr). Assumption for the four-e model Similar to the double-e model, work was carried out to develop an objective methodology for calculating the six parameters necessary for the four-e model. The task of determining six shape parameters in an objective manner may be tackled by first considering two curves which may be' generally observed for FRC materials: Response A: The initial response is approximately linear up to a peak, fmm.Subsequently, in the post-cracking regime, the f(x) curve achieves a plateau. This is shown in Fig. 5a Response B: The initial response is similar as that described above i.e. an approximately linear response up to a peak, fmax.Thereafter, a second peak is achieved in the postcracking regime. This second peak may or may not be greater than the first peak. This is shown in Fig. 5b.
r
X
X
(a) Response A
(b) Response B
Fig. 5: Schematic diagrams showing the anticipated trends for FRC curves
207
Multi-exponential models as descriptive tools for plain concrete and FRC
The first three parameters (CI,CZ and c3) will be used to reflect the response in the pre-cracking regime. On the other hand, the latter three parameters (c4,c~and cg) will be used to take into account the post-cracking regime. Response A To calculate the model parameters for curves displaying Response-type A, first consider the post-cracking regime i.e. Fz(x). In this case, the gradient is assumed to be approximately zero. This condition may be achieved by taking the ratio ap>O (where a2 = Cg/c5). By fixing the ratio of a2,only two parameters would be required to completely define Fz(x). This may be achieved by specifying two points, say at (Xa, fa) and (xb, fb). Thus:
Subsequently, the pre-cracking regime should be characterised via Fl(x). The value of a1 can be calculated by using the ratio (xmax/xo.gfmax)prepca~ i.e. the ratio of xmaxto the value of x at 90% off,, in the pre-peak region. From simulations, it has been found that the ratio a1 may be calculated using the following equation:
I
1.ooo1
Where the values of 6, and & are given in Table 3. Table 3: Values of 5, and (;k for use with Equation (4b). j/k 0 1 2 5/ -819 1481 -920
3 197 -22977
4 2107
208
Ming Kien LEE and B. BARR
Response B Similar to calculations for Response-type A, the post-cracking regime is first considered. The ratio a 2 is calculated by considering the deformation ratio (~*mJ~*0,9h&,rqe& and using Equation (4b). The term X*m, corresponds to the second peak, P ,, whereas x*o.9fm, is the x-value corresponding to 90% of P , , in the tail region before X*m, as shown in Fig. 6 .
Fig. 6: Schematic representation of various points considered for curves with Response B. The values of cq, c5 and c6 may then be calculated using the following:
Subsequently, the ratio aI (where a1 = c3/c2) can be calculated using the deformation ratio ( ~ ~ ~ / ~ 0 . 9and f ~ using ~ ~Equation ) ~ ~ ~(4b). ~ ~The a kvalues of cl, c2 and c3 may then be calculated using the following:
Example of model application Again, test results obtained from a round-robin test programme involving beams under threepoint loading were used to carry out a comparison [ 131. The materials tested were SFRC with nominal cube compressive strengths of 40MPa (Fig. 7a - Response A) and lOOMPa (Fig. 7b Response B) and a fibre dosage of 25kg/m3. Tables 4a and 4b list the necessary experimental values for deriving the model parameters and the values of C I ,c2 and c3 for the SFRC of 40MPa with 25kg/m3 of fibres. On the other hand, Tables 5a and 5b lists similar values for the SFRC of lOOMPa with 25kg/m3 of fibres. Fig. 7 shows the comparison between the experimental and theoretical curves for the SFRC beams. There is close agreement between the experimental and theoretical curves.
209
Multi-exponential models as descriptive tools,for plain concrete and FRC
Table 4a: Experimental data obtained from beams of 40MPa, 25kg/m3 fibres [ 131.
13.8 0.045 1.45 7.4 1 1.5 6.71 2.5 Table 4b: Four-e model parameters for experimental data from beams of 40MPa, 25kg/mJ. a] a2 CI C2 c4 c5 0.0998 1.0001 1o4 1417733 22.2 8.61 Table 5a: Experimental data obtained from beams of 1OOMPa, 25kg/mJ fibres [ 131. First peak Second peak Pmax
&ax
(mm)
P*max
(W
Pmax
(+)
(A]
(mm)
0 ' 9hax
pmpruk
09t'max
pwpcak
22.0 0.05 17.4 2.13 1.24 2.1 1 Table 5b: Four-e model parameters for experimental data from beams of 100MPa, 25kg/mJ.
a1
1.ooo 1
a2
CI
c2
C4
c5
55.1
552749
20.0
19.1
0.0349
-Four-e
model -Four+
0
2 3 Avenge mid-span defluhon, S(mm) 1
4
0
model
-. . .
2 3 Average mid-span defluhon. S(mm) 1
4
Fig. 7: Comparison between experimental and theoretical P-6 curves for SFRC beams displaying a) Response A and b) Response B behaviour.
CONCLUSIONS The study reported in this paper has demonstrated the feasibility of using multi-exponential models as descriptive tools in modelling the response curves exhibited by plain concrete and FRC. Specifically, the authors have developed the double-e and four-e models. To add to the attractiveness of the multi-exponential models, objective methodologies have been developed for determining the model parameters. Comparisons between experimental results and the models have demonstrated the effectiveness of the multi-exponential functions. Although the
2 10
Mirig Kien LEE and B. BARR
comparisons were carried out using load-deflection curves from flexural tests, the same principles may be applied to test results obtained from compression or tensile tests, which hrther demonstrates the flexibility and versatility of the proposed descriptive model. Thus far, research work has been carried out to develop the multi-exponential models as descriptive tools. Work is currently under way to investigate the possibility of using such models as predictive tools. Such work is of significant value given the potential of the multi-exponential models.
REFERENCES 1. Carreira, D.J., Chu, K.H., Stress-strain relationship for plain concrete in compression. ACI Journal, 82(6), 1985, pp 797-804 2. Van Gysel, A,, Taerwe, L., Analytical formulation of the complete stress-strain curve for high strength concrete. Materials and Structures, 29(293), 1996, pp 529-533 3. Hsu, L.S., Hsu, T.C.C., Stress-strain behavior of steel-fiber high-strength concrete under compression. ACI Structural Journal, 91(4), 1994, pp 448-457 4. Hillerborg, A., Modeer, M., Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 6, 1976, pp 773-782 5. Roelfstra, P.E., Wittmann, F.H., Numerical method to link strain softening with failure of concrete. In: Fracture Toughness and Fracture Energy of Concrete, F.H.Wittmann ed. Elsevier Science, Amsterdam 1986, pp 163-175 6. Olesen, J.F., Fictitious crack propagation in fiber-reinforced concrete beams. Journal of Engineering Mechanics, 127(3), 2001, pp 272-280 7. Du, J., Yon, J.H., Hawkins, N.M., Arakawa, K., Kobayashi, A.S., Fracture process zone for concrete for dynamic loading. ACI Materials Journal, 89(3), 1992, pp 252-258 8. Foote, R.M.L., Mai, Y.W., Cotterell, B., Crack growth resistance curves in strain-softening materials. Journal of the Mechanics and Physics of Solids, 34(6), 1986, pp 593-607 9. Reinhardt, H.W., Crack softening zone in plain concrete under static loading. Cement and Concrete Research, 15, 1985, pp 42-52 10. Kuffel, E., Zaengl, W.S., Kuffel, J., High Voltage Engineering Fundamentals. Butterworth-Heineman, Oxford 2000. 11. Lee, M.K., Testing, Modelling and Applications of Steel Fibre Reinforced Concrete. PhD Thesis, Cardiff University 2002. 12. Barr, B., Lee, M.K., Modelling the strain-softening behaviour of plain concrete using a double-exponential model. To appear in Magazine of Concrete Research. 13. Barr, B., Lee, M.K., Definition of round robin test. Preparation of specimens. Execution and evaluation of round robin testing (beam bending test). Report from Test and Design Methods for Steel Fibre Reinforced Concrete, EU Contract-BRF'R-CT98-8 13, 200 1, pp 105. 14. Lee, M.K., Barr, B., A four-exponential model to describe the behaviour of fibre reinforced concrete. Submitted to Materials and Structures for publication.
Proc. Int. Symp. ,,Brittle Matrix Composites 7” A.M. Brandt. V.C. Li and I. H.Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
PLENARY INVITED PAPER
DESIGN EQUATIONS TO PREDICT THE ULTIMATE PUNCHING SHEAR . STRENGTH OF SLAB-COLUMN CONNECTIONS Dimitrios THEODORAKOPOULOS Department of Civil Engineering University of Patras Patras 26500, Greece, e-mail: [email protected] Narayan SWAMY Department of Mechanical Engineering University of Sheffield Mappin Street, Sheffield S1 3JD, England, e-mail: r.n.swamy @sheffield.ac.uk
ABSTRACT Flat slabs offer an economic and competitive structural form of building construction, but they sometimes fail in a brittle manner without developing an overall yield mechanism at failure. Steel fibre concrete, on the other hand, possesses characteristics of energy absorption capability and ductility, and can transform a sudden structural failure into a ductile mode. However, the use of steel fibre concrete is hampered in practice by the absence of a reliable theoretical model and design equations. Further, existing Code provisions do not account for the presence of fibre reinforcement in concrete. The aim of this paper is to rectify these two situations. The paper presents two design equations to predict the ultimate punching shear strength of slab-column connections - one for plain concrete slabs and the other, for fibre concrete slabs. The former is applied to 20 test results reported in the literature, and the theoretical predictions are compared to those of ACI, BS, CEB-FIP and EC2 Codes. It is shown that the authors’ design equation gives a better prediction of ultimate loads with a smaller standard deviation compared to those of the Codes. The second design equation is applied to 62 fibre concrete slabs with a wide range of test parameters. The theory again predicts the test results extremely well with a mean theorykest ratio of 0.943 and a standard deviation of 0.089. The paper thus provides convincing proof that the design equations presented in this paper are reliable, based on sound engineering principles and reflect the true structural behaviour of slab-column connections. Keywords Slab, punching, design, fibre reinforcement, ultimate strength.
INTRODUCTION Flat slabs, a common form of construction strongly favoured for many reasons, can suffer a rather sudden and catastrophic type of failure. These failures are undesirable since they do not allow an overall yield mechanism to develop. Fibre reinforcement, on the other hand, restrains
2 12 D. THEDOROKOPOULOS and R.N. SWAMY cracking and increases both the tensile strength of concrete and the bond resistance of steel reinforcement. But more importantly, it increases ductility and the energy absorption capability of conventional RC structural members. This, therefore, explains the effectiveness of the use of steel fibres as shear reinforcement in slab-column connections [l-91. Although considerable experimental data exist on the effect of a large number of fibre parameters which affect the punching shear strength, there are, as yet, no Code provisions to account for the presence of fibre reinforcement in predicting the ultimate shear strength of such connections. Recently, the authors have proposed a simple analytical theory and a design model to predict the ultimate punching shear strength of slab-column connections with or without fibres [lo-121. In this paper, a comparison is made between the various Code provisions and the authors' design method against test results of fibre concrete flat slabs in order to evaluate the deficiencies and weaknesses of Code specifications.
EMPIRICAL EXPRESSIONS IN CODES FOR PLAIN CONCRETE SLABS In this paper design recommendations are expressed in terms of nominal shear stress calculated with reference to a control perimeter around the column. The Codes referred to are the American code ACI 318-99, the British code BS 81 10-1985, the CEB-FIP Model Code 1990, and the Eurocode EC2- 1991.
ACI 318-99 The American Building Code for Reinforcement Concrete ACI 3 18-99 [ 131 gives as punching strength, in SI-units, the smallest of V, = (1 + 2 / p, ) (,,@ / 6 ) u d
V, = 2 (,,@/6) u d where
pC = the ratio of the longer to shorter dimension of the loaded area, a, = 40,30 and 20 for interior, edge and corner columns, respectively, fc' = the specified concrete cylinder strength in MPa, d = the average effective depth of slab in mm, u = 4(r + d) for square columns, Fig. 1, u = n(D + d) for circular columns, Fig. 1, r = side dimension of square column in mm, D = diameter of circular column in mm. Eq. (1) shows that ACI 3 18-99 neglects both the influence of flexural reinforcement and the size effect on the punching shear strength. Furthermore, there is no general upper limit of f', ,
&
However, the term in Eq. (1) is limited to 8.3 MPa implying a limit 69 MPa for the concrete strength. It should be also noted that, in Eq. (l), a strength-reduction factor for shear (9= 0.85) is omitted, for the sake of comparison with other Code predictions.
Design equations to predict the ultimate punching shear strength of slab-column connections
ACI 3 18-89
BS 8 1 10 and author's design equations
I
CEB-FIP
EC2
u2
\; I
I
Fig. 1. Basic control perimeter around loaded areas.
2 13
2 14
D. THEDOROKOPOULOS and R.N. SWAMY
BS 81 10-85 The British Code BS 81 10-85 [I41 uses a rectangular control perimeter 1.5d from the loaded area for both rectangular and circular loaded areas. Thus, the punching strength is given by
V, = 0.79 x (4001 d)0'25(p% f,, / 25)'
333
b, d
where f,, = concrete cube strength in MPa, p = percentage of steel reinforcement, b, = 4 (r + 3d) for square columns, Fig. 1 , b, = 4 (D + 3d) for circular columns, Fig. 1, (400/d)0.2'= a size-effect coefficient. The restrictions here are the cube strength f,, I 4 0 MPa , the percentage of flexural steel p % 1 3 and 4 0 0 / d > l . CEB-FIP Model Code 1990 MC 90 In the CEB-FIP Model Code 1990 MC 90 1993 [IS] the design punching shear strength of slabs is determined by
where fck = the characteristic concrete cylinder strength in MPa, U I = 4 r + 4 n: d for square columns, Fig. 1, U I = n: (D + 4d) for circular columns, Fig.1, 1+(200/d)~.~ = a size-effect coefficient. Eq. (3) is subject to restrictions 1 + (200/d)0.5 I 2 and p% I 2 . With regard to the coefficient 0.12 in Eq. (3), which includes a partial safety factor equal to 1.5, Walraven [I61 carried out an evaluation over 1 12 test results and concluded that this value of coefficient is correct. Eurocode EC2 In the European prestandard for the design of concrete structures EC2-1991 [17] the punching shear strength of slabs is given as V,,
= 0.0525
fc2'3 (1,6-d) (1.2 + 0.40 p%) ~2 d
where u2 = 4r + 3xd for square columns, Fig. 1 , u2 = n: (D + 3d) for circular columns, Fig. 1, (1.6-d) = a size-effect coefficient with d in m. Eq. (4) is subject to restrictions 1.6 - d [m] > 1 .O, p 5 0.015 and fck 5 50 MPa .
(4)
Design equations to predict the ultimate punching shear strength of slab-colunzn connections
2 15
Authors' Model The authors have developed theoretical and design expressions to determine the punching shear strength of reinforced concrete slabs with and without fibre reinforcement [ 10-121. Using a control perimeter at 1.5 d away of the load area, as in BS 8 1 10, taking the depth of the compression zone to be the harmonic mean of the compression depths for shear and flexural sections and considering the limiting shear stress equal to 0.27 fc;I3, the following design equation can be derived for plain concrete slabs V,, = 0.234 (100/d)'/6 f,,
213
ah l + a h bP
where pf, 0.145 f,, ' h = 1.60- 0.75~~ for 0.20 < a I 0.50, for 0.50 < a I 1.OO , h = 1.35 - 0.25a h = 1.20 - 0.10a for 1.00 < a I 2 . 5 0 , for 2.50 < a I 0.50, h = 1.30 - 0.14a f,. = the yield stress of steel reinforcement, (100/d)'/6 = a size effect coefficient. a=
The coefficient h in Eq. (5) indicates the effectiveness of the steel stress, i.e., the stress at which the tension steel works at the ultimate stage of punching. Details of calculation of h can be found in [12]. It is also worth reminding that Eq. ( 5 ) indicates that the punching strength of a plain concrete slab is not only proportional to fc:3 but it is also affected by the overall flexural behaviour of the slab, through the coefficient a [lo]. Furthermore, the design expression for punching strength of fibre reinforced concrete slabs is given by ah+P V,, = 0.234(100/d)'/6 fcU2I31+ah+1.25P bPd
d where
'=
(J
cu
0.145fC, ' oCu= the ultimate tensile strength of fibre concrete. It should be noted that both design equations (5) and (6) are by no means based on factors derived empirically from test data. They are, therefore, not subject to any limitation as far as the material properties and steel ratio are concerned.
COMPARISON OF DESIGN METHODS WITH FIBRE CONCRETE SLAB TESTS All four code expressions and authors' design equation have been applied to 62 tests to predict the punching strength of fibre reinforced normal weight and lightweight concrete slabs
2 16
D. THEDOROKOPOULOS and R.N. SWAMY
reported in the technical literature and failing in punching shear [l-91. In addition, the design predictions are compared with 20 test results of the corresponding control slab-column connections (plain concrete slabs) [ 1-91. The comparisons between design rules and tests are based, for the sake of comparison, on the following principles: the code equations are solved with mean values of the concrete strength and not with characteristics values, fc’or fck = 0.80 fCu( if only the cube strength is given for the test slabs), for lightweight concrete slabs a reduction factor 0.85 is used, the upper limits of the flexural reinforcement ratio and the concrete strength are not taken into account in Code expressions. It is desirable to start with the plain concrete slabs. The results are shown in Fig. 2. It can be seen that the mean value for the ratio of predicted to test ultimate load is 0.876, 1.007, 1.112, 0.894 and 0.957 for ACI 318-99, BS 8110, CEB-FIP, EC2 Codes and Eq. (5) respectively, with the greater scattering of test results being for the ACI Code. This is due to the fact that the ACI expression does not consider the size effect or the influence of p. It is also observed that BS 81 10 and Eq. (5) give comparable punching strength predictions, with those of Eq. (5) being on the safe side, and having a smaller standard deviation. For the 62 fibre reinforced concrete slabs, the results provided by the Codes and the proposed model (Eq.(6)) are shown in Fig. 3. As expected, the prediction of the ultimate loads according to the Codes greatly underestimates the true failure loads since the contribution of the fibre reinforcement is not taken into account. A comparison between the average of Vca1JVtest ratios in Fig. 2 and Fig. 3 reveals that for each Code a coefficient can be established relating its predictions for plain and fibre concrete slabs as shown in Table 1. It can be concluded that the ultimate punching strength of a fibre concrete slab can be calculated by using the provisions of each Code for plain concrete slabs multiplied by a factor of about 1.20. Furthermore, from Figs. 2 and 3, it is observed that the mean ratio and standard deviation for the sixty two fibre concrete slabs analysed by authors’ design Eq.(6), are 0.943 and 0.089 respectively and these values are of a comparable magnitude to those of the twenty plain concrete control slabs. This is due to the fact that Eq. (6) accounts for the effect of fibre reinforcement on punching shear. Table.1 Relation between Code predictions for Plain and FRC slabs ACI
BS 81 10
CEB-FIP
EC2
0.876/0.697 = 1.26
1.007/0.833 = 1.21
1.1 12/0.928 = 1.20
0.894/0730 = 1.22
The effectiveness of the design Eq.(6) in predicting the ultimate punching strength can also be seen in Figs. 4 and 5 in which the ratios VcalJVtestare presented as a function of concrete strength fCuand reinforcement ratio p respectively. Fig.4 confirms that concrete strength has an important role in controlling the ultimate strength. In Fig.5, it is observed that the authors’ predictions follow the trend of the test results data with respect to any ratio of the reinforcement p. In addition, one can see that the ACI expression underestimates the test results especially for higher values of p, as expected, whereas the higher underestimation of test results for the BS 81 10 and CEB-FIP expressions is for low values of p. The latter is due to the fact that punching strength is not a simple function of a power of f,, and p but a combined effect of the resistances offered by shear and flexural sections [ 10, 121.
2 17
Design equations to predict the ultimate punching shear strength of slab-coluinn connections
1000
//
z Y
Ave=0.876 S.D=0.265 A.C.1
1000
z Y
100
-m
100
-m
u
0
Y
3 10
100
10
10
1000
Vtest,
10
KN
1000 KN
1000
1000
Ave=l, CEB - FIP 11
2
EC2
1
z
Ave=O,894 S.D=O.178
Y
z
S.D=0.142
Y
-a
100 Vtest,
-m
100
100
0
0
Y
Y
10 100
10
10 10
100
Vtest,
1000
Vtest,
1000 KN
KN
/
Design Eq. ( 5 ) Ave=0,957 S.D=0.096
z Y
10
1000
100 Vtest,
KN
20 plain concrete slabs [I- 91
Fig.2. Comparison between predicted and experimental results: plain concrete slabs.
2 18
D. THEDOROKOPOULOS and R.N. SWAMY
1000
1000
B.S.
A.C.1
z
Ave=0.697 S.D=O.159
Y
-3
z Y
-u3
.,.".
>
aiio
"
100
~
>
loo./ 10
10
1000
1000
,
CEB - FIP Ave=Q.928
Ave=O. 730
z Y
-6m
m
100 -
Y
10
10
100
Vtest,
10
1000
KN
100
Vtest,
1000
KN
1000 -
Design Eq. ( 6 ) 2
Y
-m
100
~
9
10
10
100
Vtest,
1000
KN
-
62 Fibre concrete slabs [I 91
Fig. 3. Comparison between predicted and experimental results: fibre concrete slabs.
Design equations to predict the ultimate punching shear strength of slab-column connections
1.40
2 19
1.40
1
A.C.1
1,20 1.oo
B.S. 8110
1,20
.. . ..' ....;.-:. . . :.'f :: :
1.oo
5
0,80-
0.60 -
.
*
:,?
* .
0.40
-8 0.60 >
-
-
0.40 .
0,20 -
0.20
0,oo
0,oo i
1
1,40
.. .
1,20 . 1.oo
5- 030 3 0.60
1,40 .
W B - FIP
.:...._. _. ;;3:- . .
*
: .*.:?
EC2
1.20
5-
~
. .-f. *'@+ :
0.80
8 >
0.40
' ,'a..
1,oo
.
0.60 -
*
. :
2
0,40 .
020 -
0.20
Design Eq. (6)
1,20
1;: 0.00
1 0
,
20
,
40
fcu,
,
,
60
80
100
Mpa
Fig. 4. Variation of Vcalc I Vtest ratio versus concrete strength for fibre concrete slabs.
220
D. THEDOROKOPOULOSand R.N. SWAMY
-
1,40 1,20
5> 2
1,oo
-
0,80
1.40
.'
A.C.1
0.40
-5z 0,150
*I;. : iji
0.80
$2 i *.
0.20
0.00
7
I
1,40 1,20 1,oo
'
0.80 -
0,60
-
.) f.*
. .:
I
1.40 1,20
FEB-FIP
**
5-
*
5 >
+
1
EC2
1.00 .
--
0.60 -
.*
'i !; . i f . +
0.80
8
0,40
0,40 -
0.20
0,20
0.00
0,oo
j
0,40
0.00
> z
:
>
0,20
5-
* .
1.00
**
0.60
B.S. 8110
1.20
t
7
1.40 1.20
,
1
Design Eq. ( 6 )
A
I .oo
*1 ?i
I:
1. +
?
-
I
,
,
,
2
3
4
0,oo 0
1
5
REINFORCEMENT %
Fig. 5 . Variation of Vcalc / Vtest ratio versus steel reinforcement percentage for fibre concrete slabs
Design equations to predict the ultimate punching shear strength of slab-column connections
22 1
The data presented in Figs. 4 and 5 emphasize that punching shear strength is dependent on both the flexural and shear behaviour of the slab. As pointed out earlier, the ACI expression does not consider size effect and ignores the effect of p. The BS and CEB-FIP Codes, on the other hand, predict that the punching shear strength of a plain concrete slab is proportional to (p%)0.333.This implies that for a flat slab with a reinforcement ratio equal to 2 p%, the percentage increase in punching strength is 26%[(2~/p)O.~~~11, independently of the value of concrete strength and the initial value of p taken. The authors’ design theory Eq. (9,on the other hand, shows that the percentage increase in punching shear strength when the value of p is doubled, depends on the initial value of p. Thus, the increase will be greater for smaller values of p as would be expected. For example, according to Eq. ( 5 ) , slab with a = 1.OO (a is proportional to p) has a punching strength higher by 37.6% than that of a slab with a = 0.50, whereas the strength increase of a slab with a = 2.00, in comparison to one with a = 1.00 is 27.5%. These outcomes result from the structure of the authors’ model that punching shear strength is a h c t i o n of both flexural and shear conditions of the slab. Similar comparisons can be made for slabs with different values of concrete strength and constant value of p. These considerations explain why Code provisions impose restrictions on both f,, and p whereas the authors’ theory has been successhlly used to predict the punching strength of slabs made with high concrete strength (100 MPa) [lo].
CONCLUDING REMARKS Flat slabs offer a popular and economic form of construction with many practical advantages. However, they can sometimes be subject to a major structural weakness of sudden, brittle type of failure. Steel fibre concrete is an exciting construction material that possesses unique properties of high energy absorption and ductility. A combination of the two can therefore lead to a new structural system having a high ultimate strength and characterized by a ductile mode of failure. Many tests on slab-column connections made with steel fibre concrete show that this new structural system can offer distinct advantages of structural integrity and structural stability, particularly when dynamic forces are involved. The use of steel fibre concrete in practice is, however, very much hampered by the absence of a rational theoretical model and design method to predict the ultimate strength of flat slabs made with steel fibre concrete. Current Code provisions such as those of the ACI, BS, CEB-FIP and EC2 do not apply to fibre concrete slabs. The aim of this paper is to present design equations to predict the ultimate punching shear strength of slab-column connections. The design approach is based on the physical behaviour of slab-column connections under load and is, therefore, applicable to both normal weight and lightweight concrete as well as to slabs without or with steel fibres. The proposed design equations are applied to 20 plain and 62 fibre reinforced slab tests reported in the literature. The slabs analysed cover many variables that influence the punching shear behaviour such as type of concrete, the concrete strength, the tension steel ratio, the size of slab and loaded area as well as the type, aspect ratio and volume of fibre reinforcement. It is shown that the authors’ design equation for the ultimate load of plain concrete slabs can predict the test results in a better way than the Codes with a smaller standard deviation. When applied to fibre concrete slabs, the authors’ design equation again predicts the test results extremely well. What is impressive is that the authors’ design equations for the plain and fibre concrete slabs can predict both sets of test results equally well-with a mean theory / test ratio and standard deviation-0.957 and 0.096 for the former and 0.943 and 0.089 for the latter. There is thus convincing proof that the theory and design equations are reliable, based on sound engineering principles and reflect the true structural behaviour of the slab-column connections.
222
D.THEDOROKOPOULOSand R.N. SWAMY
REFERENCES 1. Ito, K., Hirasawa, I. and Aichi, I., Punching shear strength of steel fibre reinforced concrete slab. Transactions of the Japan Concrete Institute, 3, 1981, pp 267-272 (in English). 2. Swamy, R.N. and Ah, S.A.R., Punching shear behavior on reinforced slab-column connections made with steel fibre concrete. ACI Journal, 79-5, 1982, pp.392-406. 3. Walraven, J.C., Pat, M.G.M. and Markov, I., The punching shear resistance of fibre reinforced concrete slabs. Developments in Fibre Reinforced Cement and Concrete, RILEM Symposium, F.R.C. 86, 3rdInt. Symposium 13-17 July 1986, Sheffield.
4. Narayanan, R. and Darwish, I.Y.S., Punching shear tests on steel-fibre-reinforced microconcrete slabs. Magazine of Concrete Research, 39- 138, 1987. 5. Theodorakopoulos, D.D. and Swamy, R.N., Contribution of steel fibres to the strength characteristics of lightweight concrete slab-column connections failing in punching shear. ACI Journal, 90-4, 1993, pp. 342-355. 6. Harajli, M.H., Maalouf, D. and Khatib, H., Effect of fibres on the punching shear strength of slab-column connections. Cement and Concrete Composites, 17, 1995, pp. 161-170. 7. McHarg, P.J., Cook, W.D., Mitchell, D. and Yoon, Y-S., Benefits of concentrated slab reinforcement and steel fibres on performance of slab-column connections. ACI Structural Journal, 97-2,2000, pp. 225-234.
8. Alexander, S.D.B. and Simmonds, S.H., Punching shear tests of concrete slab-column joints containing fibre reinforcement. ACI Structural Journal, 89-4, 1992, pp. 425-432. 9. Shaaban, A.M. and Gesund, H., Punching shear strength of steel fibre reinforced concrete flat plates. ACI Structural Journal, 91-3, 1994, pp. 406-414. 10. Theodorakopoulos, D.D. and Swamy, R.N., Ultimate punching shear strength analysis of slab-column connections. Cement and Concrete Composites, Special Theme Issue, 24-6, 2002, pp.509-521. 1 1. Theodorakopoulos, D.D. and Swamy, R.N., Ultimate punching shear strength analysis of slab-column connections with steel fibres. ACI SP 182-1 1, 1999. 12. Theodorakopoulos, D.D. and Swamy, R.N., A design method for punching shear strength of steel fibre reinforced concrete slabs. ACI SP: Fiber Reinforced Concrete: Innovations for Values, in press. 13. ACI 3 18-99, Building code requirements for reinforced concrete. American Concrete Institute, Detroit, 1999, 355 p. 14. BS 81 10-85. The Structural Use of Concrete. British Standard Institution (1985). 15. CEB-FIB MC 90: CEB-FIP Model Code 1990, London : Thomas Telford 1993. 16. Walraven, L., "Design of Structures for Punching: Present Status of revision of EC-2. International Workshop on Punching Shear Capacity of RC Slabs-Proceedings, Stockholm 2000, pp. 2 1 1-224. 17. EC2-1991. Eurocode 2 : Design of Concrete Structures - Part 1: General Rules and Rules for Buildings. European Prestandards ENV 1992-1-1 : 1991, Comlte Europeen de Normalisation, Brussels, 253 p.
Proc. Int. Syrnp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C.Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTURL?K RSI and Woodhead Publ., Warsaw 2003
Mechanical Properties of Concrete Reinforced with AR-Glass Fibers Tejal DESAI*, Rimpal SHAH*, A h a PELED', and Barzin MOBASHER*
* Dept. of Civil and Env. Eng., Arizona State University, Tempe, AZ, USA +
Structural Engineering Department, Ben Gurion University, Beer Sheva, Israel
ABSTRACT Mechanical properties of concrete mixtures with AR glass fibers are studied. Two types of concrete mixtures representing a lean mixture and an HPC (High Performance Concrete) mixture are used. Two types of AR Glass fibers High dispersion (HD) and High Performance (HP) with different sizing formulations to help with distribution, bonding and durability were considered. High dispersion (HD) AR Glass fibers of several different lengths were used to evaluate the effect of fibers which disperse thoroughly throughout the mixture. These were compared with High Performance (HP) type AR Glass fibers which maintain the bundle characteristics throughout the mixing and casting and are designed to help with long temi strength and ductility. A formulation based on the R-Curves is presented to measure the contribution of the fibers to the overall toughening mechanism.
Keywords Fiber reinforced concrete, cement composites, glass fibers, alkali resistant fibers, toughness, strength, toughening, and mechanical testing. INTRODUCTION Reinforcing ordinary concrete materials with glass fibers has been attempted for more than 20 years [ 1][2][3]. Use of Alkali Resistant (AR) glass fibers in concrete presents an area of opportunity to utilize the strength and stiffness of fibers in reinforcing the brittle matrix. Concrete materials produced with short randomly distributed AR Glass fibers would be superior to other FRC (Fiber Reinforced Concrete) materials for several reasons. In comparison to steel fibers, the small diameter of the individual glass fibers ensures a better and more uniform dispersion. In addition, the high surface area and relatively small size of glass fiber bundles offers significant distribution capability and crack bridging potential as compared to steel fibers. The glass fibers are randomly distributed offering efficiency in load transfer. Furthermore, the bond strength of the glass fiber is far superior to the polypropylene fibers, thus increasing the efficiency of fiber length so that there is limited debonding and l i i x r pullout. Finally, due to the highly compliant nature of the glass fiber bundles which bridge thc matrix cracks at a random orientation, they are able to orient so as to carry thc Ioatl across the crack faces. In the present work, two types of AR Glass fibers are considered as concrete reinforcement, High dispersion (HD) and High Performance (HP) to provide Iioth
224
Tejal DESAI, Rinpal SHAH, Alva PELED and Barzin MOBASHER
strengthening and toughening mechanisms. Various fiber lengths and contents are studied for both fiber types. Two types of concrete mixtures were prepared with the fibers representing a lean mixture and an HPC (High Performance Concrete) mixture. Control specimens without fibers were prepared in both mixtures for comparison. Theoretical modeling of the experimental results is conducted by means of proper determination of response in the context of both strengthening and toughening. The R-curve approach is used for this purpose. The bond parameters of the glass fibers with the matrix affect these models in the context of the closing pressure formulations. Procedures are proposed to back-calculate the materials properties from experimental data.
EXPERIMENTAL PROCEDURE
Specimen Preparation Two different concrete mixtures were selected to cover the wide range of matrix materials and their weight proportions presented in Table 1. The first mixture had characteristics of a high performance concrete mixture with a w/c ratio of 0.4, while the second mixture with a w/c ratio of 0.55, had a characteristic strength of 40 MPa and a slump of 50-55mm. Class F fly ash equivalent to 10% cement replacement was also used. Two types of AR glass fibers were obtained from VETROTEX, Cem-FIL SAINTGOBAIN, HD and HP. High dispersion (HD) AR Glass fibers were used in chopped strand form to evaluate the effect of fibers which disperse thoroughly throughout the mixture. These fibers are formulated for mixing with concrete, mortar, and other cement-based mixes where a uniform dispersion is of primary importance. The effect of sizing is to provide full dispersion characteristics in order to control and prevent early-age cracking in concrete. The dosage of HD glass fiber was limited to 0.6 and 5 Kg/m3 and aimed at early age strength and plastic shrinkage crack control. HP AR glass fibers maintain the bundle characteristics throughout the mixing and casting and were designed for abrasion resistance and integrity during mixing with both concrete and mortar. The dosage of HP glass fiber in this category was in the range of 5-20 Kg/m’ and aimed at long-term strength and ductility. Several different lengths of fibers, 6, 12, 24 and 40 mm were used. After 24 hours, specimens were demolded and placed in a water tank saturated with calcium hydroxide at a temperature of 23°C (700 F) for 3 , 7 and 28 days. Compression and Flexural Tests Compression tests were conducted using a 450 KN closed-loop controlled testing machine. A special ring type fixture was developed to attach two LVDTs (Linear Variable Differential Transducer) to measure the axial strain in the specimen. Three replicate compression cylinders 76.2 mm in diameter by 152 mni long were used for each mixture. A gage length of 64 mm was used for the axial strain using a fixture that permitted the deformations to be measured as the specimen underwent the post peak response. A chain type fixture was placed around the specimen, and an extensometer was used to measure the transverse strain. The axial mode of control operates the test during the prepeakThe post-peak response was obtained by using circumferential microcracking phase. displacement as the controlled variable. The circumferential deformation always increases throughout the test; however, its increase may not be sensitive to the loading during the pre-
225
Mechanical properties of concrete reinforced with AR-glass fibers
peak regime. Obtaining the post peak response clearly demonstrates the behavior of the specimen in terms of its ductility and energy absorption capacity especially when low volume fraction of fibers is used. Dry weight per m3 Cementitious materials (Cement + flyash)
Type #1, Kg
Type #2, Kg
876
341
20-10 mm Aggregates
460
600
10-5 mm Aggregates
300
388
Fine Aggregates 578 75 1 WaterKement Ratio 0.4 0.55 Table 1. Mix design for the two concrete blends used. Flexural beam specimens 368 x 101 x 101 mm in size with an initial notch were tested in a 3-point bending configuration. A test span of 304 mm, and a notch depth of 12.7 mm was used. A three-point bend loading fixture was used to eliminate extraneous support settlements. The crack mouth opening displacement (CMOD) was measured across the face of notch using extensometer. The deflection of the beam was also measured using a springloaded linear variable differential transducer (LVDT) with a 2.54 mm (0.1 in) range. In consideration to the reduced depth of the beam due to the notch, the maximum load was normalized with respect to the modified section modulus of the specimen and referred to as the nominal flexural stress. The area under the load deflection curve was calculated by numerical integration of the load-deflection response. Fracture energy Gf was defined as the area under entire load-deflection curve normalized with respect to crack ligament area. EXPERIMENTAL RESULTS Compression Test Results
A summary of the experimental test data is shown in Table 1. Note that the MIX. ID in the table presents the type of fiber (HP or HD), fiber length (12, 40 or 24 mm) and fiber content (5, 10 or 0.6 kg/m3). For example, the sample HP12-5 is a specimen produced by HP fibers with a length of 12 mm and fiber content of 5 kg/m3. Figure 1 presents the Stress vs. Circumferential Strain for specimens containing 20 Kg/m3 and 10 Kg/m3 HP12mm AR glass fiber reinforced sample for various ages of 3, 7 and 28 days. It is observed that the use of circumferential strain is a successful means of obtaining the post peak response. Several distinct regions are observed in the response. The first region is the initial linear ascending stress strain response. The second region is due to initiation of microcracks that results in a reduction in the stiffness and thus the non-linear behavior of the specimen. This zone terminates at the ultimate strength. In the strain softening region, it is observed that there is significant ductility in the circumferential strain pointing out to the effect of dilatation. The effect of duration of curing is clearly shown in this figure by a significant increase in the strength and toughness of the composite with aging, in both fiber content systems. This is due to the ability of the fibers to bridge the microcrakcs in the pre-peak region of the response. When comparing between the two fiber contents (Figs. l a and Ib) it is observed that the contribution of the fibers in the post peak region of the high volume fraction (Fig Ib) is
226
Tejal DESAI, Rimpal SHAH, Alva PELED and Barzin MOBASHER
not as much as the case with the lower volume fraction shown in Figure l.a., i.e., a better toughening of the lower fiber content system (Fig. la) is observed, this is mainly after 28 day of aging. This is due to the higher strength, a higher magnitude of energy is released, resulting is strengthening but added brittleness since the fibers are unable to absorb the energy released as the specimen enters the post peak response. Figure 2.a shows the effect of length of fiber on the compressive stress strain response at 7 day curing. A comparison is made between HP12, and HP40. It is seen that the concrete with HP12 exhibits significant higher compressive strength and toughness than the concrete with HP40. Comparatively, note that HP12 fibers result in a significantly higher strength and ductility as compared to the control samples with an increase in the compressive strength in the range of 35% as shown in Table 2. The ductility of HP12 is as much as 140% higher than the HP40 and the control samples. This may be due to a better dispersion of the shorter fiber composite, HP12 as compared to poorer dispersion of the longer fiber, HP 40. The closer fiber to fiber spacing for the size of specimen considered with the shorter fibers. Also, differences in fiber failure can occur due to the different in lengths. The shorter fiber may mainly pulled out during testing as the longer fiber may fractured.
“1
Vf
=
1
IOKgim’
L
30 -
=
--
+
HPI210-7 HP1210-3
w/c=o4
to
01
0
’
I
0.002
‘
I
0.004
’
I
0.006
’
( ‘ 1
0.008
Circumferential Strain, mm/mm
0.01
0
0.002
0.004
0.006
0.008
0.01
Circumferential Strain. inrnimm
Figure 1 effect of age on the compressive stress strain response of glass fiber reinforced concrete containing a) 10 Kdm3 b) 20 Kg/m3. Figure 2.b shows the effect of fiber volume fraction on the strength and ductility. Note that as the volume fraction is increased, the strength is increased, however, the ability of the fibers to maintain the cracked specimen together beyond the peak load dirninishcs as the strength of the composite is increased.
227
Mechanical properties of concrete reitforced with AR-Glassfibers
Table 2 Compression Test results 40
30
^^
p\
w/c = 0.55
,
Vr=5Kg/m3
d 20 2
-
5
10
W/C = 0.4
IiP1210-28 HP1220-28
6,:dOO
0.002
0.004
0.006
0,008
Circumferential Strain. m m h m
0.010
~
0
0.002
0.004
0.006
0.008
Circumferential Strain, m n h m
0.01
Figure 2 a) Effect of fiber length on the compressive stress strain response. b) Effect of fiber volume fraction on the strength and ductility. Flexural Test Results A summary of the results of the flexural tests are shown in Table 3. Figure 3 shows the flexural response of the concrete with various lengths of fibers at the same volume fraction. It is shown that the flexural response is significantly increased with the addition of the fibers, however, the magnitude of strength is only slightly improved with increasing the length of fibers. All the samples containing 6 , 12, and 24 mm fiber length behave in a
228
Tejal DESAI, Rimpal SHAH, Alva PELED and Barzin MOBASHER
relatively similar manner. Figure 4 compares the flexural load carrying capacity of concrete with different volume fraction HP glass fibers. As expected, it is shown that concrete with 20 Kg/m3 AR Glass fibers exhibit a higher flexural strength and also ductility after 28 days as compared to the other mixes. The flexural response as a function of age for two sets of fiber composites at different lengths and volume fractions are compared in Figure 5 , by using the entire flexural load canying capacity in terms of load vs. crack mouth opening displacement for 3 , 7 , and 28 days of curing. A comparison of responses as a function of age for 0.6 Kg/m’ of High dispersion fibers (HD24) and 5 Kg/m3 of High Performance (HP40) is presented. It is evident from the graph that both concretes with HD24 and HP40 AR Glass fibers exhibits better flexural strength after 28 days as compared to the other ages. There is only a small marginal difference between the HD12 and HP40 mixtures despite the large difference in the volume fractions. This indicates a benefit in flexural behavior for the shorter fiber, similar to the trend observed in Fig. 2 in compression behavior, while having improved dispersion. The better dispersion of HD type fibers would make it easier for a uniform distribution of the short fibers. The two mixtures are almost equivalent as far as 3 to 28 days strength are concerned. This points out that there might be an optimum level of fiber reinforcement which is a function of volume fraction and also the length of the fibers. Such behavior should further be studied.
A direct comparison of dispersion shown by HD type and maintaining the bundle characteristics are shown in figure 6 where the HP and HD fibers are directly compared at the 5 Kg/m’ level with a control specimen. Note that the HP fibers result in a significantly higher ductility. This is attributed to the bundle effect and fiber pullout, resulting in energy absorption mechanisms. In comparison the HD fibers serve to provide strengthening function due to the good dispersion and bond characteristics.
Age = 28 Days
10
-
. L LHP24
HP12 HP6
+-
8
2--J Control
E
3-
s
AR Glass fibers
6 4
2 n v
-
0
0.2
0.4
0.6
CMOD, mm
Figure 3 . Effect of fiber length at the same volume fraction on the flexural response.
0
0.2
0.4
CMOD, mm
Figure 4. Effect of volume fraction on the flexural response.
0.6
229
Mechanical properties of concrete reitlforced with AR-glass fibers
8000
6000
1 AY6Kg t LW 1 8000
28 days 7 days 3 days
w/c
6000
= 0.55
vf = 5 Kdm3
WIC = u.33
__ 28 days
-
7 days
2 dnvc
z
$4000 e)
$4000
3
nnn
2000I
I
0.0
0.2
0.4
0.6
CMOD,mm Figure 5.a Effect of age on the flexural load-CMOD response.(fiber length 24 mm)
0.0
I
0.4 CMOD,mm
0.2
I 0.6
Figure 5.b Effect of age on the flexural loadCMOD response.(fiber length 40 mm)
Table 3 Summary of the Flexural Test Results.
230
Tejal DESAI, Rirnpal SHAH, Aha PELED and Barzin MOBASHER
.- -
a
Control
HD12 Vf=ZOKg/m3
W/C=04 Age = 28 Days
4
-,
2I " 0 - ' 0 0.1 02
'
'
'
03
I " '
0.4
0.5
0.6
CMOD, mm
Figure 6 Comparison of flexural response of HP and HD fibers.
Figure 7. schematics of crack growth in a fiber reinforced composite
ANALYTICAL SIMULATION OF TOUGHENING A simple model is proposed to address the toughening due to the crack bridging of fibers. The bridging force, expressed as a stress intensity factor, works to reduce the overall applied stress intensity factor. These stress intensity factors are directly obtained from the stresses that are required to pull the fiber out of the matrix, and expressed as:
where P(u) represents the force carried by a bridging fiber as a function of crack opening. The fiber is located at distance "x" from the tip of a crack length "a". Parameter g( l,x/a) represents the green's function representing the stress intensity due to a unit load. The process of toughening can be modeled by means of R-curves and is shown in Figure 7. R represents the increased resistance of the material from the base level R , due to the growth of the crack and increases with incremental crack growth "Aa" due to the presence of bridging. It is observed that as we load the material containing a small flaw, it will begin to grow (under an increasing applied stress intensity factor) until the process zone is fully developed. The crack in the process zone has a different shape because of the forces of the bridging fibers. In figure 7, a simplified approach shows the amount of toughening due to each intersected fiber may be accounted as nlAR. Once the zone has developed fully, then the whole crack may move forward with the process zone size remaining a constant size, at an energy level of R,,,+ nzAR. By controlling the microstructure and properties of the material to result in such an R-curve behavior, we can over certain limits of flaw size ensure that cracks are stable. This mechanism is thus able to explain why for many cement based composites, reduction of inter-fiber spacing results in formation and growth of significant cracking
23 1
Mechanical properties of concrete reinforced with AR-Glass fibers
without causing catastrophic fracture. The criteria for the cracking can be defined in terms of energy balance: d R dG R(a) =G(a) = (K,+K,F)' -=E' * da da A procedure for the modeling of the R-curve has been developed earlier where a closed form solution for the R curve for quasi-brittle materials proposed by Ouyang, Mobasher and Shah [4]. Using this approach the fracture resistance of a material is defined by two parameters Aa, and fJ representing the R-curve. Their magnitudes can be obtained by fitting the loadCMOD or deflection plots and expressed as:
Since R varies with the crack length, it can not be viewed as a single valued function, and the extension of the stable cracking is determined entirely by the geometry and loading. The procedure used in the present approach is based on calculating R parameters corresponding to the load-deformation history of the specimen as suggested by Mobasher, Ouyang and Shah [ 5 ] . The procedure is based on calculation of the fit parameters which describe the effect of fibers in the context of the resistance curve, R and also the amount of critical crack length Aa,.
-Model Prediction 3 Days
0.20
-Model Prediction 28 Days Model Fit, 28 days
0.15
E 2-0.10 c4 0.05
0.00
0
20
40
60
Crack Extension. mm
80
100
0.0
0.I
0.2
0.3
0.4
CMOD, mni
Figure 8 Modeling the effect of age on the flexural and R curves of fiber reinforced concrete. According to Figure 8 it is possible to model the effect of age of the composites by developing a nonlinear curve fit model to the experimental data for the flexural load-CMOD response based on R-curves. Using these R-curves, one can calculate the contribution of fibers to toughening using Equation 3. Figure 9 represents the model fit parameters for the study of the effect of fiber volume fraction on the flexural response. load-CMOD plot and b) the R-curve response. the By conducting a nonlinear fit to the experimental load-CMOD responses, the two parameters, critical crack length Aac, and also the parameter
232
Tejal DESAI, Rimpal SHAH, A h a PELED and Barzin MOBASHER
representing the R-curve are obtained. In this case the ranges of R values obtained are from 5.64 to 6.28 N/m and the range of critical crack extensions are in the range of 20-35 mm. 0.02 *-*-+Control
z
Simulation Sirnulatio
Q - 8 - 0 10 Kg/m3
10
8
M
4
2 0 0
I
0.2
0.6 CMOD, nun 0.4
0.8
1
ole' 10
'
20
'
'
30
'
'
40
'
I
50
Crack Extension, mm
Figure 9 Modeling the fiber volume fraction using R-curves, a) load-CMOD plot and b) the R-curve response.
CONCLUSION Effect of short AR glass fibers on the strength and ductility of concrete was studied and indicate a potential for reinforcing the concrete material both from an early age property modification and also from the strengthening and toughening perspective. Closed loop testing was conducted to characterize the response of specimens in compression, and flexure. It was observed that concrete with 12 mm HP fibers exhibits higher compressive strength than other fiber lengths. During the early ages, due to the fact that the concrete strength is sufficiently low, fibers contribute to toughening, whereas during the later stages of age, the contribution is mainly in increasing the strength. The ability of AR Glass fibers to provide both strengthening and toughening mechanism for concrete was investigated using an RCurve approach. 1. 2. 3. 4.
5.
REFERENCES Frondistouyannas, S., "Flexural Strength Of Concrete With Randomly Oriented Glass Fibers", Magazine of Concrete Research, 29 (100): 142-146 1977. Mobasher, B. and Li, C. Y . , "Mechanical Properties of Hybrid Cement Based Composites," ACIMuterials Journal, Vol. 93, No.3, pp.284-293, 1996. Mobasher, B., and Shah, S. P.,"Test Parameters in Toughness Evaluation of Glass Fiber Reinforced Concrete Panels", ACI Materials Journal, Sept-Oct. 1989, pp. 448458. Ouyang, C. S., Mobasher, B., and Shah, S. P., Eng. Fracture Mech., 37, 4, 901-913, 90. Mobasher, B., Ouyang, C., and Shah, S. P., Int. J. ofFract.. SO: 199-219, 1991.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSIand Woodhead Publ., Warsaw 2003
BEHAVIOUR OF GLASS-FILAMENT-YARNS IN CONCRETE AS A FUNCTION OF TIME AND ENVIRONMENTAL CONDITIONS
J. ORLOWSKY, U. ANTONS and M. RAUPACH Institute of Building Materials Research, Technical University Aachen (ibac), Germany ABSTRACT At the Institute for Building Materials Research of the University Aachen (Germany) the durability of AR-glass yarns in concrete is investigated, within the scope of a large project on textile reinforced concrete. Textile reinforced concrete represents an interesting new construction material which offers several advantages compared to steel or fibre reinforced concrete. These advantages dominate in the field of applications, where thin-walled, structural elements with a high load-canying capacity are necessary. Especially AR-Glass yarns can be used to manufacture the textile reinforcement. These multifilament yarns (rovings) consist of more than 500 filaments with diameters about 12-30 pm. The aim of the durability investigations is to build up a model which allows predictions about the long-term behaviour of textile reinforced concrete. The long-term behaviour of textile reinforced concrete is affected by the chemical attack of hydration products on the glass yarns. Aim of the presented investigations is to determine the influence of static load on the durability of this composite material. The results show the importance to investigate the combination of static load and water. The water changes the bound behaviour of the reinforcement which can lead in the worst case to a failure of the specimens. Keywords concrete, glass fibre, durability, alkalinity
1. INTRODUCTION In textile reinforced concrete steel which is usually used as reinforcement is substituted by technical textiles, which have a defined position and direction in the concrete. One of the advantages is that no minimal concrete cover is necessary because of the lack of possible corrosion. Therefore it is possible to produce thin elements with a high load bearing capacity. In the research project SFB 532 “Textile Reinforced Concrete - Basics of a New Technology” placed at the Technical University of Aachen, financed by the central public funding organization for academic research in Germany, DFG, several institutes investigate this new construction material. At this point in project most of the used textiles are made of glass rovings. Rovings are made out of more than 500 single filaments, which have an average diameter of 12 - 30 pm. Life time and durability predictions are extremely important for the use of this new composite material.
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Jeanette ORLOWSKY, U.ANTONS and Michael RAUPACH
The durability of glass in concrete is mainly dominated by the chemical attack of the hydration products in the concrete, which results in a loss of tensile strength. Storing the composite materials under water at increased temperature (i.e. 50 “C) can accelerate this loss of tensile strength. Because of local cracks and flaws the realistic tensile strength of glass is much lesser than the theoretical tensile strength /Or103/. Pumell /PurO 1/ developed a thesis on the durability of textile reinforced concrete, which bases on the conclusion that the local flaws grow extremely fast under the influence of alkalinity and external applied forces. This leads to an early failure of the composite specimens. This thesis on the fatigue strength of textile reinforced concrete is investigated at the Institute for Building Materials Research (ibac) currently. First results are shown in this paper. 2. MATERIALS
AR-Glass rovings with 2400 tex (1 tex = Ig/km) manufactured by the company SAINT GOBAIN VETROTEX are used for these investigations. To protect the glass from chemical attack, zirconium is added to the conventional E-glass mixture. This modified glass is called AR-glass (alkali resistant). The used 2400 tex rovings are made of more than 1000 single filaments, each of the filaments has a diameter of approx. 27 pm (Internal description of the roving: VET-RO-ARG-2400-1-00). As shown in figure 1 the single filaments are not totally parallel orientated in the roving instead their orientation is “wavy”. Therefore the length of the single filaments varies from the used test length of 500 mm. The tensile strength of this roving at a length of 500 mm is 625 N/mm2. A single filament of the same roving has a tensile strength of approx. 2000 N/mm2. The two reasons that are in charge of this extreme loss of tensile strength, are the wavy orientation and the fracture of single filaments emerged during the production process of the rovings. Less than 50 % of the filaments in the roving are responsible for the breaking load because they are parallel orientated and not damaged. The rest of the filaments fails partly before and after the breaking point /Bra02/.
Figure 1: Filament alignment in a roving with 2400 tex /Bra021 The concrete mixture (table 1) was developed by the Institute for Building Materials Research as a micro-concrete. In order to achieve a total compound a high floating ability and low diameters of aggregate is required. The addition of silica fume and fly ash to the mixture reduces the amount of alkali ions and calcium hydroxide in comparison to Portland cements. The pH value of this mixture is 13.5.
Behaviour of glass7filanient-yarns in concrete as a function of time and environmental conditions 235
Binder
Type of
system
cement
Additives
Cement
content
Fly ash
Silica
fume
Water reducer
35
1'
Stabilizer
kg/m' OPC
CEM152,5
490
175
Binder content
w/bratio
Max.
grain size
kg/m'
-
mm
700
0.4
0.6
The used test specimens (dog bone shaped specimens - called TSP) pass through a two week preparation phase before testing. After the production process the specimens stay in the mould for approx. 24 h at 23°C and 95 YOrelative humidity. After demoulding the specimens are stored for 6 days at 23 "C and 95 % humidity. The final shape of the specimens - at this point they are 500 mm long, 100 mm wide and 6 mm thick - is milled. As shown in figure 2 the central part of the specimen is 250 mm long and 60 mm wide. The transition between the two widths of 60 mm and 100 mm is 75 mm long and formed as a clothoid. The last production step is the fixation of the out sticking VET-RO-ARG-2400-1-00 rovings with epoxy resin. This prevents individual filaments to slip within the sample. During this preparation process, which takes up to 7 days, the samples are stored at 23 "C and 50 % humidity.
500
/
roving
[mml
fixing of the ioving with epoxy resin
Figure 2. Geometry of the TSP-specimens The test setup for static load tests was developed at the ibac and is shown in figure 3. This setup applies the tensile force in the clothoid shaped area of the test specimens. The first load step is applied with a force-controlled hydraulic cylinder. After reaching the desired load this load is constantly adjust with a weight at a crank of a lever. The force- and elongation-curves are measured by one load cell and two different kinds of elongation gauges (strain sensors DDl and inductive gauges). Until the first crack the strain sensors mounted on the center part of the sample determine the elongation curves. The curves are determined as a change of length of the 250 mm long center part based on a homogenous distribution of elongation. After the first crack the inductive gauges mounted on the mounting brackets continue the measurements (figure 4). The two advantages of this setup are, a continuously ongoing
236
Jeanette OIUOWSKK LI. ANTONS and Michael RAUPACH
measurement for underwater storage and the collection of data of cracks in the mounting zone are both possible. The calculated elongations of the first crack can be used for calibrating the inductive gauges. This is required because the mounting brackets might settle during raising the force to its defined level and so the elongations would be increased by mistake.
TSP-specimen
point of load application permanent load tank with water
Figure 3. Setup of the test facility to measure the behaviour of textile reinforced concrete under static load The ibac provides 9 such static load test facilitys, which are in a defined climate of 23 "C and 50 % humidity. The required cylinder for the water storage can be mounted on the lower mounting bracket. In order to avoid a change of the load because of the additional load of the cylinder and the water a hydraulic cylinder is used again. The water temperature can be raised up to 50 "C.
Figure 4. Arrangement of the inductive gauges in the test facility
Behaviour of glass-filainent-yarns in concrete as a function of time and environmental conditions 237
In order to control the functions of the static load setup, especially the force application, some samples were cracked until the total failure. The force-elongation curves were recorded as shown above and compared to curves recorded with a displacement controlled Instron testing machine. Cypers et al /CypO3/ describe the tensile test of TSP samples using the Instron testing machine. The velocity of the displacement controlled test was 0,5 mndmin. The load controlled test was performed at 16 N/sec. Picture 5 shows the accordance of the two curves. Force in kN
0
2
4
6
8
10
12
Elongation in r n d m
Figure 5. Comparison of the failure load a) displacement controlled in the Instron testing machine and b) load controlled in the static load test facility 3. AMOUNT OF TESTS
The following parameters were examined during the test phase:
- Humidity: 50 % relative humidity and water storage - Temperature: 23 "C and 50 "C - Static load: 60 - 85 % of the failure load Each of these parameters was examined with two specimens. This paper only includes a part of the results, because the tests are not finished yet. 4. RESULTS AND DISCUSSION 4.1 Tests at 23 OC and 50 YOrelative humidity The results of the specimens, which were charged with 80 % of the failure load, are shown in figure 6. The diagram shows the percental increase of the elongation over time (creep). The percental increase of the elongation refers to the beginning of the static load phase after the use of the hydraulic cylinder. It can be seen that during the first hours the elongations increase noticeable. After this time the increase of elongation reduces, until after 50 - 100 hours only a small, linear increase remains. Because of difficulties during the test phase the elongation curve of the specimen TSP8O-1 could not be determined completely. But it is still obvious that the two curves are strongly similar - both show a curved area, which leads into a linear area. The percental increase of elongation of specimen TSP8O-1 in the curved area is nearly
23 8
Jeanette ORLOWSKY, U.ANTONS and Michael RA UPACH
twice as high as the increase of specimen TSP80-2, whereby the absolute final elongations of both samples are nearly the same. This shows the reciprocal ratio between percental increase of elongation and absotute values at the beginning of the static load-testing phase. The elongation measurements were stopped after approx. 200 h, but the specimens still remained under load for two more month. A failure of the samples was not predictable. increase of elongation in %
30
20
-
0
.
0
,
50
'
!
100
'
1
150
'
I
'
200
1
.
250 300 time in h
Figure 6. Behaviour of the TSP under static load at 80 % of the failure load and 23 "C, 50 Yo relative humidity The specimens show an average crack distance of 0,8 mm and the cracks are very evenly distributed. The crack wide scatters between 0,05 mm to 0,15 mm wide. 4.2 Tests at 23 "C in water
The results of four TSP-specimens, which were stored under water at 70 YOof their failure load, are shown in the left diagram in figure 7.
time in h
time
in h
Figure 7. Behaviour of the TSP under static load at 70 % of the failure load in water at 23 "C
Behaviour ofglass7filatnen~-yarrlsin concrete as a jirnction oftirne and eirvironmental conditions 239
The storage under water started 24 h after the static load was applied. As seen in the right diagram in figure 7 the curves during the first 24 h are similar to the curves shown in figure 6. Two of the four specimens (TSP70 water sample 1 and 3) stayed under static load and under water for two month and a failure could not be predicted - figure 7 left. The samples TSP70 water 2 and 4 failed within a few minutes respectively a few hours after the storage under water. An obvious increase of elongation (1 5-33 % regarding the elongation at the beginning) while applying the water can be seen in the right diagram of figure 7 for all test specimens. The results of the specimens stored under water at 70 % of their failure load show directly opposite results. One part of the specimens endures a long time under load, the other part of the specimens fails after a short period of time. But all specimens show an obvious increase of elongation after having contact to water (see also figure 8). This increase of elongation can be explained with the geometry of the roving: as seen in figure 1 the roving is made of various single filaments, which lay wavy to each other and are not connected to the concrete over their total length and wide /Rau02: Wa103/. The spaces between the filaments enable the water to flow into them and decrease the friction between the filaments, which leads to an increase of elongation. At this point the tests show that specimens with a crack width of more than 0,l mm fail directly after storing them under load and water, whereby specimens with a crack width below 0,l mm are not affected. So far these tests were only performed with loads 2 70 % of the failure load. At the moment the tests are continued with various crack width and static loads.
4.3 Tests at 50 O C in water The results of a TSP-specimen, which was stored under water at 50 "C and at 70 % of its failure load, are shown in figure 8.
Figure 8. Behaviour of the TSP under static load at 70 % of the failure load in water at 50 "C The specimen were stored under water after 24 h of already being under load. This test also show an obvious increase of the elongation after applying water. The specimen still remains under load for additional 14 days and at this moment there is no loss of fatigue strength detectable. This test points out that Purnell's thesis (the increase of flaws in glass under
240
Jeanette ORLOWSKY,U. ANTONS and Michael RA UPACH
increasing tension which leaves to an early failure) /PurOl/ might not be right. Rather the loss of strength of glass under a static load and accelerated aging (water at 50 "C) seems not as big as the loss of strength of samples, which were aged accelerated without a mechanical influence. During the preliminary tests with small static loads this behaviour was already noticed. Regarding this point more tests are performed.
5. CONCLUSIONS AND FUTURE WORK In order to investigate the durability of textile reinforced concrete under static load a test setup was developed at the Institute for Building Materials Research (ibac). This setup enables to perform tests with concrete specimens reinforced with textiles or rovings under different static loads and in different climates. A reduction of the fatigue strength of the specimens at 23 "C and 50 % relative humidity under a static load of 70-80 % of the failure load could not be detected. The storage of the specimens under water at 23 "C shows different results. One part of the specimens was not affected by water, whereby the other part of the specimens failed nearly directly when they came in water contact. It seems, that the fatigue strength of the specimens, which were tested under water at a temperature of 23 "C, is mainly effected by the crack width after applying a certain amount of the failure load. All specimens show an increased elongation after water contact, which maybe is the result of the decreased friction between the inner filaments. Purnell's thesis /PurOl/ could not be confirmed by the specimen tested at 50 "C under water and a static load. According to this result the static load has no negative effect on the tensile strength of the composite material during the amplified chemical attack caused by the tempered water. In order to verify these early results the tests are continued at this time.
6. REFERENCES Brameshuber, W. ; Brockmann, T.: Development and Optimization of Cementitious Matrices for Textile Reinforced Elements. London : Concrete Society, 2001. - In: Proceedings of the 12th International Congress of the International Glassfibre Reinforced Concrete Association, Dublin, 14-16 May 2001, S. 237-249 Brameshuber, W. ; Banholzer, B. ; Gries, T. ; Al-Masri, A,: Methode zur Untersuchung des Versagensmechanismus unter Zugbelastung von MultijilamentGarnenfir die Betonbewehrzing. In: Technische Textilien 45 (2002), Nr. 2, S. 98-99 Cuypers, H.; Wastiels, J.; Orlowsky, J.; Raupach, M.: Investigations on the Durability of glass fibre reinfoced concrete and influence of matrix alkalinity. In: Brittle Matrix Composites 7, Proceedings of the Seventh International Symposium, Warsaw, Poland, 13 - 15 October 2003 Orlowsky, J. ; Raupach, M.: Einfuss der Umgebungsbedingungen auf die Dauerstandfestigkeit von Textilbeton. Berlin : Deutscher Verband fur Materialforschung und -prufung, 2003. - In: 35. Tagung des DVM-Arbeitskreises Bruchvorg&ge am 18. und. 19. Februar 2003 in Freiburg, S. 325-334 Purnell, P. ; Short, N.R. ; Page, C.L.: A Static Fatigue Model for the Durability of Glass Fibre Reinforced Cement. In: Journal of Materials Science 36 (2001), S. 53855390
Behaviour of glasslfilarnent-yarns in concrete as a function of tirile and environmental conditions 24 1
[6]
[7]
Raupach, M. ; Brockmann, J.: Untersuchungen zur Dauerhafiigkeit von textilbewehrtem Beton : Chemische und mechanische Beanspruchung von Textilien aus Glas. In: Beton 52 (2002), Nr. 2, S. 72-74,76,78-79 Walk-Lauffer, B. ; Orlowsky, J.; Raupach, M.: Verstarkung des inneren RovingVerbundes im textilbewehrten Beton durch Polymerdispersionen. Weimar : BauhausUniversitat, 2003. - In: 15. Internationale Baustofftagung, - ibausil -, 24. - 26. September 2003 in Weimar
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15,2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
DESIGN OF HYBRID-FIBER REINFORCEMENT FOR SHRINKAGE CRACKING BY CRACK WIDTH PREDICTION Michele F. CYR’, Chengsheng OUYANG’ and Surendra P. SHAH’ ‘Center for Advanced Cement-Based Materials Northwestern University2 145 Sheridan Rd., Evanston, IL, 60208, USA, e-mail: [email protected]; [email protected] 2 Office of Materials Iowa Department of Transportation 800 Lincoln Way, Ames, IA, 500 10, USA, e-mail: [email protected]
ABSTRACT The use of fiber reinforcement to reduce shrinkage cracking is becoming increasingly common. The effectiveness of fiber reinforcement can be enhanced using multiple types of fibers. A means of predicting the shrinkage performance of hybrid-fiber reinforcement would facilitate its design. A model to predict shrinkage crack widths in restrained ring shrinkage tests is being developed. The ability of the fibers to transfer stress across a crack and free shrinkage behavior are used to determine crack width. To facilitate calibration of the model, a procedure for establishing tensile performance from flexural test data using fracture mechanics has been developed. The crack width model and the procedure for predicting tensile performance are presented. The initial phase of calibrating the model, verification of the tensile performance prediction, is discussed. Keywords Hybrid-fiber-reinforced concrete and mortar, shrinkage, fracture mechanics
INTRODUCTION As concrete dries, it shrinks due to the loss of water. Shrinkage of concrete is generally classified as autogenous, plastic, or drying. Autogenous shrinkage occurs at low water-tocement ratios due to the consumption of water in hydration. Plastic shrinkage occurs when the concrete is still fresh. Drying shrinkage refers to shrinkage in hardened concrete. If concrete is restrained, it is unable to shrink freely. As a result, tensile stresses will develop, and the concrete might crack. While shrinkage cracks are usually not large enough to compromise structural integrity, they do allow the ingress of water and other corrosive agents, reducing the durability of the concrete. Shrinkage cracking is of particular concern in elements with a high ratio of surface area to volume. Recently, the use of short, discontinuous fibers as reinforcement for concrete has been studied [I]. Because fibers can severely limit the workability of fresh concrete, they can only be added in limited volumes. While these small amounts of fibers cannot provide sufficient
244 Michele F.CYR, Chengsheng OUYANG and Surendra P. SHAH reinforcement to replace conventional steel reinforcing bars, they can significantly reduce shrinkage cracking. In restrained shrinkage tests, fiber reinforcement delays the onset of shrinkage cracking and reduces shrinkage crack widths [2]. In the field, fibers are used as shrinkage reinforcement in slabs, bridge decks, and pavements. Researchers have demonstrated that the performance of fiber-reinforced concrete can be tailored for specific applications with the use of hybrid-fiber reinforcement [3. 41. Two or more different fiber types, sizes, or shapes are combined to achieve the benefits of each. Larger and longer macrofibers, which prevent the opening of macrocracks, can be combined with smaller and shorter microfibers, which limit the growth of microcracks. Stronger but relatively brittle fibers can be combined with weaker, more ductile fibers to enhance both composite strength and ductility. Portions of costly, “high-performance” fibers can be replaced with less expensive fibers. To determine the effect of hybrid-fiber reinforcement on shrinkage crack resistance, restrained shrinkage tests were performed on mortar reinforced with various combinations of glass and polypropylene (PP) fibers and only glass and only polypropylene fibers in the current study. Often, restrained ring shrinkage tests are used to assess experimentally the shrinkage behavior of concrete. Due to the geometry of the test, the rings usually do not crack until at least a week after casting. For design purposes, it would be helpful if shrinkage cracking potential could be assessed more quickly. The effects of different fiber reinforcements could be estimated before large-scale testing was performed. RILEM TC 162-TDF [5] has proposed a model developed by Olesen and Stang [6] to predict shrinkage crack widths in fiber-reinforced concrete slabs. In this paper, the model is adapted for use with a ring geometry. In addition, a method is presented to derive tensile specimen response from flexural test data. This method eliminates the need for uniaxial tension tests, which can be extremely difficult to perform and yield specimen-size dependent results. Ultimately, it is desired to use the model as a design tool to predict the shrinkage performance of various hybrid-fiber combinations.
RESTRAINED SHRINKAGE TESTS Experimental program Restrained ring tests were performed to evaluate the shrinkage resistance of hybrid-fiber combinations of glass and polypropylene fibers. A mortar matrix was used to reduce the age of cracking and amplify the effect of the fibers. A 50 mm-thick mortar ring was cast around a 25 mm-thick steel annulus. The inner diameter of the mortar ring was 300 mm. For each type of fiber reinforcement, two rings were cast and cured in the molds for 24 hours. The molds were removed, and the rings were placed in an environmental chamber at 50% relative humidity (RH) and 22OC. The rings were inspected daily, and the age of cracking was noted. Cracks were measured periodically using a handheld microscope. A schematic of the restrained ring test setup is shown in Figure I .
Figure I . Restrained ring shrinkage test setup.
Design of hybridSfiberreinforcementfor shrinkage cracking by crack width prediction
245
Fiber-reinforced mortar was prepared at I :2:0.5 cement:fine aggregate:water, by weight. To improve the workability of the mortar, 15%, by volume, of the cement was replaced with Class F fly ash. Bundled glass fibers and fibrillated polypropylene fibers were added at 0.38% volume fraction. If the ratio of fibers to cement paste is kept constant, this is equivalent to 0.25% fibers in a I :2:2:0.5 cement:fine aggregate:coarse aggregate:water concrete. Hybrid combinations of I :2, I :1, and 2: 1 glass:PP ratios at a total fiber volume fraction of 0.38%were also tested. Fiber properties are shown in Table I . Filaments Tensile Elastic Fiber Diameter Length Per Strand Strength Modulus TYPe 108 1700MPa 72 GPa Glass 14pm 12 mm N/A 700MPa 5GPa N/A 19mm PP
Results The addition of fiber reinforcement significantly reduces crack widths and induces multiple cracking. Figure 2 shows the total crack widths of mortar with no fibers, only glass fibers, only polypropylene fibers, and several combinations of glass and polypropylene fibers at a total fiber volume fraction of 0.38%. Each curve is an average of the first crack width for two specimens. All of the fiber reinforced specimens showed some degree of multiple cracking. However, for the specimens with polypropylene fibers, the secondary cracks often did not extend the entire length of the ring, and as a result were not measured. The total crack widths for all the fiber-reinforced mortars are significantly smaller than the single cracks that developed in each plain mortar ring. The occurrence of multiple cracking in the rings of fiber-reinforced mortar reduces the permeability of the mortar. Water flow, or permeability, is proportional to crack width cubed [7], which means mortar with multiple smaller cracks is less permeable than that with one larger crack.
1.5 A
-g E E
1.0
i5
-1:ZG:PP *l:1 G.PP -21 GPP
Y
g
.-r
0.5
u. 0.0 0
10
20
-
30
40
Age = t o Age of Cracking (days)
Figure 2. Shrinkage crack widths in restrained ring shrinkage tests of fiber reinforced mortar.
246
Michele F. CYR. Chengsheng OUYANG and Surendra P. SHAH
Figure 2 shows the additive effects of the hybrid-fiber reinforcement. The crack widths of the hybrid specimens fall between those for mortar reinforced with only glass fibers and only polypropylene fibers. Although none of the hybrid combinations tested outperformed the mortar reinforced with only glass fibers, they did have exhibit smaller cracks than the purely polypropylene mixture. If polypropylene were chosen as the primary reinforcing fiber, crack widths could be reduced by replacing a portion of these fibers with glass fibers.
SHRINKAGE CRACK WIDTH MODEL In fiber-reinforced concrete, fibers increase the tensile strength of the matrix by preventing or delaying the coalescence of microcracks and enhance ductility by transferring stress across cracks. Hillerborg's fictitious crack model can be used to describe this stress transfer in the post-peak response of fiber-reinforced concrete in uniaxial tension [8]. Olesen and Stang used the fictitious crack model to develop a method to predict crack widths in fiber-reinforced concrete slabs-on-grade subjected to thermal or shrinkage strains [ 6 ] . Olesen and Stang [6} studied an infinitely long, longitudinally restrained slab. Stress develops when the slab is subjected to thermal or shrinkage strains. This stress is described as a function of the shear between the slab and its substrate. When the stress in the slab reaches the tensile strength of the concrete, the slab cracks, and the stress redistributes. The deformation in the slab, or the crack width, is derived from the stress distribution in the cracked slab, giving crack width as a function of stress. A uniaxial tension test is performed to determine the amount of stress the fibers,can actually carry across a given crack width. Then, from the stress in the slab due to shrinkage strains, the corresponding crack width can be calculated. Two basic changes are made to adapt this model for use with restrained ring shrinkage tests. First, the stress in the concrete ring is expressed as a function of the geometry of the ring and the shrinkage strains that develop, instead of as a function of the interface between the concrete and the restraint. Second, the tensile stress-crack width relationship is approximated as a bilinear relationship, as presented by Olesen [9] and shown in Figure 3, instead of as a constant for all crack widths, which Olesen and Stang used to simplify their model for use in design.
t
=t
t'l
w1=-
a.
bl- bz
,w2=-
al-a2
bz a2
al
Crack Width (w)
Figure 3. Bilinear approximation of post-peak tensile stress vs. crack width, The post-peak tensile stress-crack width relationship is approximated as two lines obtained from a linear regression of experimental data. As in the fictitious crack model, stresses are assumed to be elastic prior to cracking. After cracking, the stress is given by the tensile stress-crack width approximation. Thus, the stress in the ring is written as
Design of hybrid-fiber reinforcementfor shrinkage cracking by crack width prediction
247
o=&E before cracking o = o ( w ) = ( b i -a,w)f, after cracking,
where cs= tensile stress, E = strain, E = elastic modulus, w = crack width, f, = tensile strength, and ai and bi are the parameters for the bilinear approximation of the tensile stress crack width relationship shown in Figure 3. Prior to cracking, the strain, E, is simply the shrinkage strain, which is determined from a free shrinkage profile of the concrete. After the ring has cracked, the strain in the ring-resulting from the restraint that prevents drying shrinkage-is still equal in magnitude to the shrinkage strain, but it is separated into two components: the strain due to the change in the circumference of the ring as a result of the crack and the strain due to the residual stress that the fibers carry across the crack,
where ow(w), the post-peak tensile stress, is a function of crack width as shown in Figure 3, and r is the radius to the center of the concrete ring. If the shrinkage strain as a function of tensile stress and crack width is known, the crack width can be expressed as a function of shrinkage strain. The shrinkage strain at the age of cracking is determined from the free shrinkage profile of the concrete.
MODEL CALIBRATION Required testing To use the model, the shrinkage strain, E,, elastic modulus, E, tensile strength, f,, and the postpeak tensile stress as a function of crack width are required. The shrinkage strain is determined from free shrinkage measurements. For fiber-reinforced concrete, free shrinkage is measured in accordance with ASTM C341-96 [lo]. It is assumed that fiber reinforcement has no effect on free shrinkage. Thus, the measurements for the unreinforced matrix can be applied throughout the study. The elastic modulus, tensile strength, and stress-crack width relationship can all be determined from a uniaxial tension test. However, uniaxial tension tests are extremely unstable and difficult to perform, and the test results can be specimen-size dependent. It would be much easier if the tensile behavior could be derived from material fracture parameters measured based on a more reliable test, such as a flexural test. Some current techniques involve time-consuming, iterative processes with ambiguous results [ I I]. An analytical method developed using R-curves to derive tensile performance from flexural stress vs. crack mouth opening displacement (CMOD) measurements is described below. Tensile behavior from flexural performance An R-curve, fracture resistance as a function of crack extension, can be generated from threepoint bend flexural test data. From this R-curve, the critical stress intensity factor, K,,, and critical crack tip opening displacement, CTOD,, can be calculated. K,,and CTOD, are material parameters, independent of specimen geometry or testing configuration. Once these parameters have been determined, the appropriate equations and geometry factors can be applied to generate the R-curve for uniaxial tension specimens. From the new R-curve, tensile stress and crack width can be calculated. To begin, three-point bending tests are performed on notched beams to generate loadCMOD curves. The span is four times the depth of the beam, and the notch is one-third of the
248
Michele F. CYR. Chengsheng OUYANG and Surendra P. SHAH
depth. An extensometer is mounted across the notch to measure the CMOD and provide feedback to control loading. Two LVDTs are mounted in a yoke on either side of the specimen to measure deflection. A schematic of the test setup and a typical load-CMOD curve for fiber-reinforced concrete are shown in Figure 4.
Y S=4b
CMOD Figure 4. Typical load-CMOD curve and three-point bend test setup.
From the load vs. CMOD data, the flexural stress, ofinex, IS calculated, and crack extension, a, is determined [12, 131. cflex
3PS =2b2t
Then, the stress intensity factor, KI, is determined and used to calculate fracture energy, G.
At fracture, fracture energy is equal to fracture resistance, G = R, so the R-curve for a threepoint bend specimen is plotted. The expression for the R-curve is also written as [ 121
R = pv/(awhere
rn1)L
1 a-1 1 a-1 q 2=-g--+ -i--
a
[4
a
21%
Design of hybrid-fiber reinjorcementfor shrinkage cracking by crack width prediction
249
and a,, = initial notch length. a and p are parameters determined by curve fitting from the Rcurve measured using the three-point bending beam. After a and p are determined, the fracture parameters. Ki, and CTOD,, are back calculated from expressions for a and p.
a=
P=
Kk (d,a - a + 1) Ea(d, -d,)(aa,
where f , and f 2 are geometry factors. For three-point bend beams, fl = I . 123 and f 2 = I .42. For uniaxial tension specimens, fl = I . 123, and f l = 1.454. Once KI, and CTODc have been determined, a and p are calculated for uniaxial tension. Then, the R-curve for uniaxial tension is generated. The R-curve obtained in this manner is based on values of KI, and CTOD,, which are determined by the fracture behavior at peak load. In a fiber-reinforced concrete beam, most of the debonding and slipping of the fibers occurs in the post-peak stage, resulting in inelastic energy. The previously obtained R-curve shall be modified to account for this inelastic energy during the post-peak stage, as shown in Figure 5 . The total energy is considered to be the sum of elastic and inelastic energy contributions. The elastic energy is expressed in the calculated R-curve. The inelastic energy is expressed as the difference between the R-curve generated from experimental data and the calculated R-curve in the post-peak region, the shaded area in Figure 5. The ratio of the inelastic R-curve to the elastic R-curve i s expressed as a power law function of the post-peak crack extension. The inelastic to elastic ratio is determined for the R-curve for the beam and applied to the R-curve for tension. To generate the tensile R-curve, R is taken as the elastic energy before the peak load and t h e sum of the elastic and inelastic energy after the peak.
0.7 0.6
.
0.5
0.4
k 0.3 a
0.2 0.1 ~
0.0 0
20
40
Crack Length
60
(rnrn)
Figure 5. Elastic and inelastic portions of R-curve.
80
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Michele F. CYR, ChengshengOUYANG and Surendra P. SHAH
From the R curve, the tensile stress, 0,for a given crack length, a, is calculated from the energy balance of G = R.
Then, CMOD is calculated using LEFM [ 131.
Finally, the load point displacement, or overall specimen elongation, is determined from compliance [ 121. The energy release rate, G, can also be written in terms of compliance, C.
This expression is integrated to obtain compliance.
c = c, + p d a 02b2t
And, elongation, 6,is simply load multiplied by compliance.
Verification with existing data The accuracy of the tensile performance prediction was verified using data previously obtained by another researcher [14], who performed both flexural and uniaxial tensile tests on concrete reinforced with 0.5% steel macrofibers and 0.29% PVA microfibers. Details of the materials and the experiments performed are discussed elsewhere [ 141. The procedure was applied to derive the tensile stress vs. crack width relationship from flexural stress vs. CMOD test data. Figure 6 shows the derived tensile stress vs. crack width together with experimental data from a uniaxial tension test. Crack width is determined by subtracting the elastic deformation, calculated as stress divided by elastic modulus multiplied by length, from the total displacement. Figure 6 shows excellent agreement between the predicted and actual uniaxial tensile performance. Similarly good results were obtained for a plain concrete specimen and a steel-fiber-reinforced specimen. These results show that this prediction is acceptable. For future work with this model, the tensile stress-crack width relationship will be derived from flexural test data using this technique. It will not be necessary to perform uniaxial tensile tests.
Design of hybrid;fiber reinforcementfor shrinkage cracking by crack width prediction
0.0 I 0.00
0.05
0.10
0.15
0.20
0.25
25 1
0.30
Crack Width (mm)
Figure 6. Experimental [ 141 and predicted tensile performance. From the predicted tensile behavior, a bilinear approximation of the post-peak performance can be made using linear regression. From Figure 6, it is clear where the two lines can be drawn. The bilinear expression of post-peak tensile behavior will be used, together with the free shrinkage strain profile, to calculate total shrinkage crack widths in the next phase of this study.
CONCLUSIONS The additive effect of glass and polypropylene hybrid-fiber-reinforcement is evident in the restrained shrinkage behavior of mortar. The crack widths of the hybrid-fiber-reinforced mortars are larger than those of the glass-fiber-mortar and smaller than those of the polypropylene-fiber-reinforced mortar. The adaptation of Olesen’s and Stang’s shrinkage crack width model to the restrained ring geometry is discussed. The model requires the tensile behavior as input. To facilitate calibration of the model, a fracture-mechanics based technique to derive tensile behavior from flexural test data, using R-curves, is developed. This technique provides excellent agreement between the predicted and experimentally determined uniaxial tensile performance. This indicates that specimens can be tested in a flexural configuration, eliminating the need for unstable, size-dependent uniaxial tensile tests.
ACKNOWLEDGEMENTS This work was supported by the Center for Advanced Cement-Based Materials at Northwestern University. Dr. John S. Lawler provided data to calibrate the tensile curve prediction. Lennart Ostergaard offered a number of helpful suggestions for beginning this work. Their assistant is gratefully acknowledged.
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REFERENCES 1. Balaguru, P., Shah S.P., Fiber-Reinforced Cement Composites. McGraw-Hill Book Co., Singapore 1992 2. Shah, S.P., Weiss, W.J., Yang, W., Shrinkage cracking-can it be prevented? Concrete International, 1998, pp 51-55 3. Lawler, J.S., Wilhelm, T., Zampini, D.. Shah, S.P., Fracture processes of hybrid fiberreinforced mortar. Materials and Structures, 36, 2003, pp 197-208 4. Mobasher, B., Li, C.Y., Mechanical properties of hybrid cement-based composites. ACI Materials Journal, 93, 1996, pp 284-292
5. RILEM TC 162-TDF, Design of steel fibre reinforced concrete using the 0-w method: principles and applications. Materials and Structures, 35,2002, pp 262-278 6. Olesen, J.F., Stang, H., Designing FRC slabs on grade for temperature and shrinkage induced cracks. In: Fibre-Reinforced Concretes (FRC) BEFlB'2000 - Proceedings of the 5Ih International RlLEM Symposium, P.Rossi and G. Chanvillard eds. Lyons 2000. pp 337-346 7. Fox, R.W., McDonald, A.T., Introduction to Fluid Mechanics, 4'h ed. John Wiley & Sons, Inc., New York-Chichester-Brisbane-Toronto-SingaporeI992 p 350
8. Hillerborg, A,, Analysis of fracture by means of the fictitious crack model, particularly for fibre reinforced concrete, The International Journal of Cement Composites, 2, 1980, pp 177184 9. Olesen, J.F., Fictitious crack propagation in fiber-reinforced concrete beams. J. of Engineering Mechanics, 127,2001, pp 272-280 10. ASTM C 341-96 Standard test method for length change of drilled or sawed specimens of hydraulic-cement mortar and concrete. In Annual Book of ASTM Standards, ASTM, Philadelphia, PA 2000 v. 04.02 1 I . Stang, H., Olesen, J.F., On the interpretation of bending tests on FRC materials. In: Fracture Mechanics of Concrete Structures, Proceedings FRAMCOS-3, vol. I . H. Mihashi and K. Rokugo eds. Aedificatio Publishers, Freiburg, Germany 1998 pp 5 I 1-520
12. Shah, S.P., Swartz, S.E., Ouyang, C., Fracture Mechanics of Concrete. John Wiley & Sons, Inc., New York-Chichester-Brisbane-Toronto-Singapore I995
13. Tada, H., Paris, P.C., Irwin, G.R., The Stress Analysis of Cracks Handbook, 2'ld ed. Paris Productions, St. Louis, MO 1985 14. Lawler, J.S., Hybrid Fiber-Reinforcement in Mortar and Concrete. Ph.D. Dissertation, Northwestern University, Evanston, IL 2001
Proc. Int. Symp. ,,BrittleMatrix Coniposites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE CRACKING BEHAVIOUR OF SFRC BEAMS CONTAINING LONGITUDINAL REINFORCEMENT David DUPONT, Lucie VANDEWALLE Department of Civil Engineering Catholic University of Leuven Kasteelpark Arenberg 40,300 1 Heverlee, Belgium, e-mail: David. Uupont(a)bwk.kuleu ven,ac .be ABSTRACT Durability of concrete is in a great extent determined by the crack widths that are formed in the structure and that allow water to infiltrate in the concrete so that corrosion of the reinforcement bars can occur. The analysis of the cracking behaviour in concrete has always been a topic of interest for investigation by many scientists. In general it is assumed that the durability of the structure is assured when the crack widths are limited to 0.3 mm. One of the often-used approaches to limit the crack widths is the use of steel fibre reinforced concrete (SFRC). Steel fibre concrete is generally known to reduce crack widths because of its postcracking tensile strength. At the Department of Civil Engineering of the Catholic University of Leuven, Belgium, a test program has been executed on 19 full-scale SFRC beams containing longitudinal reinforcement. All beams have been tested in four-point bending. The tests were performed in different load steps until failure of the beam. The load steps were chosen so that the beams failed after 10 to 15 steps. At each load step the crack widths and spacing were measured. The results of the test program illustrate the strong beneficial effect of steel fibres on the crack widths as well as on the crack spacing. The addition of fibres to the concrete can lead to a reduction of the crack width of up to 40%. The crack widths of the beams of the test program have been calculated by means of the new Rilem guideline as well as with a newly developed physical cracking model for reinforced SFRC beams. The physical model takes into account the bond between the reinforcement bars and the SFRC matrix as well as the influence of the steel fibres on the stress in the reinforcement bars. A comparison of the calculated results and the experimental results shows that there is a relatively good correlation between the two. The input parameters for the calculation model are the concrete compressive strength, the dimensions of the beam, the position and diameter of the reinforcement bars, the tensile strength and the post-cracking tensile strength of the SFRC material and the bond stress-slip relation. The new calculation model provides a very good understanding of the crack formation process. It also creates the possibility to determine for example the necessary post-cracking strength of the SFRC, given that the crack width of the beam must be lower than a certain value. Furthermore, also the influence of the bond stress-slip relation can be taken into account. This creates the possibility to use the crack model for other types of reinforcement than steel rebars (e.g. GFRF' rebars).
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David DUPONTand Lucie VANDEWALLE
INTRODUCTION It is generally known that steel fibres are a possible way to limit crack widths and enhance the durability of a structure. Crack widths have to be controlled, since if they become too large, it becomes easy for water and other aggressive agents to penetrate into the concrete. This in turn can lead to corrosion of the reinforcement and a fast degradation of the structure. To control the crack width in an economical way, a good calculation method is needed. The formation of cracks is influenced by a large number of parameters. The most important are the dimensions of the cross section, the bond stress-slip relation, the tensile strength and the post-cracking tensile strength. Several calculation methods can be found in literature. These can be divided into semi-empirical relations and physical models. The semi-empirical relations [I, 2, 3, 4, 51 are mostly validated with a large number of experimental results. On the other hand, they can only be applied with great caution for applications in which one of the influencing parameters falls outside the reach of the original collection of experimental results used to derive the empirical relation. To counter this problem, several physical models have been developed [6, 7, 81. These physical models should have the advantage that the influencing parameters are taken better into account, so that the physical model can be extrapolated more safely to other applications. However, after a literature review, the authors have found that most existing physical models are a strong simplification of the reality. Important influencing parameters are often not at all recognised or not taken into account in a proper way. For this reason, the authors have developed a new physical cracking model.
SEMI-EMPIRICAL CALCULATION METHOD The semi-empirical method used in this paper has been first proposed by [S] and later taken over as design recommendation by Rilem TC162-TDF. The method is based on the method of Eurocode 2 [4], with a few small changes to incorporate the influence of the steel fibres. The crack width is calculated as:
= average steel strain;
where ,s,
= average
final crack spacing.
They can be calculated as:
where:
p I is a coefficient to take into account the bond properties of the reinforcing steel; p l is a coefficient to take into account the duration of the load; osis the stress in the reinforcement calculated on the basis of a cracked section (Fig. 1);
The cracking behaviour of SFRC beams containing longitudinal reinforcement
255
osris the stress in the reinforcement calculated on the basis of a cracked section at the moment of cracking (Fig. 1); kl is a coefficient that takes into account the bond properties of the reinforcing bars; k2 is a coefficient that takes into account the f o i p of the strain distribution; 4 is the bar diameter; Lr / dr is the aspect-ratio of the fibre; pr is the effective reinforcement ratio = A, I ACe6 is the concrete section surrounding the tensile reinforcement up to a height of 2.5 times the distance of the centre of the reinforcement to the most stretched fibre.
through the steel stresses osand cssr For the crack The fibres have an influence on spacing the fibres are taken into account by the factor 50 / (Lr I dr). The boundary condition however is that the aspect-ratio is larger than or equal to 50.
---I---\
Figure 1. Stress distribution in a cracked section for plain concrete (a) and SFRC (b).
PHYSICAL CRACKING MODEL The new physical model is made in two steps. In the first step the anchorage length and the crack spacing are calculated. The second step then uses the crack spacing to calculate the crack width for a series of bending moments. Calculation of the average final crack spacing For the calculation of the anchorage length, a part of a beam between a cracked section (section 2) and a section that is just about to crack (section 1) is considered. In section 1 a tensile strength is assumed equal to I .2 times the experimentally determined flexural tensile strength fct,n,while in section 2 a tensile strength is assumed equal to 0.8 times fct,n. This is to take into account the scatter on ths,flexural tensile strength. The position of the neutral axis can be calculated exactly in section 1 and 2. For sections in between it is assumed that the neutral axis is constant over a small distance and evolves stepwise from section 1 to section 2, proportional with the slip 6 between reinforcement and concrete. An important parameter is the post-cracking tensile strength of.It is proposed by the authors to take this equal to 0.39 x fRI [9]. fRI is the residual flexural tensile strength determined on a Rilem 3-point bending test [ 101. The steel strains and concrete strains can be calculated in section 1 and section 2 using a static equilibrium of axial forces and bending moments.
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David DUPONTand Lucie VANDEWALLE
Skss DistfituUon
Seerion I
secrwn 2
(Cracked)
(Uncmckd)
L
I-
I
Fs
i
4-
. .
cc
F, + dF,
ccc
Figure 2. Beam part between a cracked sechon and a section that is just about to crack. One of the most important parameters in the model is the bond stress-slip (r-6) relation. This is taken as [l I]:
where: T =bond stress; 6 = slip; p and h are shape factors. T~~~ = maximal bond stress. For small concrete covers (c < 34), a splitting failure is likely to occur; in this case rmax can be determined as: 1+(1-K).0.3535 ri
1
with c=(rU-q)and4=2ri
K,f. fc
where: ru = distance between the centre of the reinforcement bar and the side of the beam. fct= axial tensile strength. Recent research [ 121 has shown that p is dependent on the fibre dosage and concrete cover, while h is only dependent on the concrete cover. It was shown that for the concrete cover used in this test program, h can be taken equal to 8.25/mm, while p is equal to 0.782
The cracking behaviour of SFRC b e a m containing longitudinal reinforcement
257
for plain concrete and equal to 0.883 for a fibre dosage of 60 kg/m3. For smaller fibre dosages an interpolation is done. The strain in the reinforcement bar is composed of two contributions. The first contribution is the strain in the surrounding concrete, while the second contribution is due to the slipping of the reinforcement bar relative to the surrounding concrete: €, =.5,-+-
d-z
d6(x)
Y
dx
If the horizontal equilibrium of a small part of the reinforcement bar is considered (Fig. 2), the following relation can be found:
where A, = reinforcement section; $ = bar diameter; E, = Young's modulus of steel. By using a static equilibrium of normal forces and bending moments for a section, the strain E~ can be written in fimction of E ~ .If this is then substituted in equation (6), and after that equation (6) is derived for x, then the following differential equation can be found using equations (4) and (7):
The solution of this differential equation is found numerically by using the following boundary conditions:
where: E , ~and are the strains in section 1 in the steel reinforcement, the bottom fibre of the beam, respectively. For the calculation of the anchorage length, the beam is loaded with the cracking moment. In this case the second boundary condition is equal to 0 (the steel strain is equal to the strain in the surrounding concrete).
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David DUPOhTand Lucie VANDEWALLE
The solution of equation (8) gives the slip 6 as a function of x. From this also the bond stress T can be found as a function of x (equation 4). The length L of the model (Fig. 2) can now be determined by considering the global static equilibrium of horizontal forces of the reinforcement bar:
Once the length L is known, it is assumed that this is the minimal crack spacing and that the maximum crack spacing is equal to 2L. The average crack spacing would then be equal to 1.51,.
Calculation of the average crack width at different bending moments. To calculate the average crack width, the length of the model is taken equal to 0.75L (Fig. 3). The position of the neutral axis in section I is assumed at the same level as in the cracked section 2. The calculations have shown that if a slightly different position of the neutral axis is assumed, this only has a negligible effect on the value of the calculated average crack width.
4--. .
I
F, I
ES&A Figure 3. Beam part between a cracked section and a section that liesjust in the middle of two cracks.
The cracking behaviour of SFRC beams containing longitudinal reinforcement
259
In doing this it can no longer be assumed that the strain Etl is equal to the strain at cracking. , Etl are now determined using a static equilibrium of axial Therefore the strains ~ ~ ~~l1 and forces and bending moments in section 1 and using equation (lo), where the integration is now only done up to 0.75L. The crack width is now found as two times the slip 6 in section 2. EXPERIMENTAL PROGRAM To validate the physical model, a test program was executed at the Department of Civil Engineering of the Catholic University of Leuven (Belgium). The test program involved 19 4-point bending tests (Fig. 4) on full-scale SFRC beams containing longitudinal reinforcement. All beams had a cross section of 200 mm x 300 mm. The span of all beams was equal to 2300 mm. The investigated parameters were the fibre dosage (0 kg/m3, 20 kg/m3, 40 kg/m3 or 60 kg/m3), the fibre type (RC 65/60 BN, RC 80/35 BN or RL 45/50 BN), the reinforcement ratio and bar diameter (3 Cp 20 or 3 Cp 16). The tests were load-controlled. The load was applied in 10 to 15 steps until failure (mostly shear failure). After each load step, the load was registered together with the deflection, the strain on top and at the bottom of the beam as well as the crack widths in the zone between the load points. The measurement of the crack width was done at 1 cm above the bottom of the beam with a small, calibrated microscope. The accuracy of the microscope was k 0.02 mm. Furthermore, due to the freaky shapes of the crack, it was sometimes difficult to decide on the crack width. Also the smallest crack that could be detected had already a width of at least 0.02 to 0.03 mm. All smaller cracks could therefore not be detected and not used for the calculation of the average experimental crack width. For all these reasons the authors state that, although the measurements were taken with great care, caution is needed when the experimental results are analysed.
Figure 4. Test set-up for the full-scale beams. Together with each full-scale beam, 8 small Rilem beams were cast to perform a 3point bending test for the characterisation of the post-cracking tensile strength. Also 10 cubes were cast to measure the compressive strength. The experimental results of the crack widths were compared with values predicted by means of the proposed physical model as well as with calculations made with the semi-
260
David DUPONT and Lucie VANDEWALLE
empirical method proposed by Rilem TC162-TDF [5]. The results of the calculations can be seen in Figures 5-7.
No Fibers, 3 4 20
No Fibers, 3 I$ 16
-
0.2
x
I 20 40 60 80 100 Bending Moment (kNm)
0
0
I 20 40 60 80 100 Bending Moment (kNm)
0
Experimental crack width
0
Experimental crack width
-
-Rilem TC162-TDF - - .Physical model
Rilem TC162-TDF
- - .Physical model
Figure 5. Comparison between experimental results and calculations for plain concrete.
-'/I
20 kglm' RC 65/60 BN, 3 4 16
20 kglm' RC 65/60 BN, 3 I$ 20
0.2 T
-
I
g5 Y
Oa2
T
0.15
0.1
! 0.05
0
v
P
P
.Q
0
0
20
40
60
80
100
20 40 60 80 100 Bending Moment (kNm)
0
Bending Moment (kNm) Experimental crack width -Rllem
TC162-TDF
- - .Physical model
0
Experimental crack width
-RilemTCl62-TDF - - *Physicalmodel
Figure 6. Comparison between experimental results and calculations for SFRC with 20 kg/m3 fibres.
The cracking behaviour of SFRC be am containing longitudinal reinforcement 60 k g l d RC 65/60 BN, 3 4 20 0.2
26 1
60 kglm' RC 65/60 BN, 3 4 16
T
-
-5 2
0.2
T
0.15 0.1
*u
2 0.05
0
20
0
40
60
80
100
0
20
0
Experimental crack width
-Rilem
40
60
80
100
Bending Moment (kNm)
Bending Moment (kNm) 0
Experimental crack width
-Rilem TCl62-TDF - - 'Physical model
TCl62-TDF
- - .Physical model
Figure 7. Comparison between experimental results and calculations for SFRC with 60 kg/m3 fibres.
CONCLUSIONS A completely new physical model has been developed to simulate the cracking behaviour of steel fibre reinforced concrete beams containing longitudinal reinforcement. The most important input parameters of the model are the bond stress-slip relation, the tensile strength of the concrete and the post-cracking tensile strength. To validate the model a test program was carried out involving 19 4-point bending tests on full-scale beams. The investigated parameters were the reinforcement ratio, the fibre dosage and the fibre type. The experimentally determined crack widths are compared to calculations done with the proposed physical model as well as with predictions done with the calculation method proposed by Rilem TC162-TDF. The comparison shows that both calculation methods provide relatively good predictions of the average crack width. Since the semi-empirical Rilem method is by far the easiest calculation method of the two, the authors think that this method is the most suited method for standard calculations. For special applications however (glass fibre reinforcement or CFRP sheets), the proposed physical model can be of great interest. The influence of a different bond stress-slip relation can be taken correctly into account.
ACKNOWLEDGEMENTS A part of this study is done in the framework of the Brite Euram project "Test and Design Methods for Steel Fibre Reinforced Concrete", contract no BRPR-CT98-08 13. The partners in the project are: N.V. Bekaert S.A. (Belgium, coordinator), Centre Scientifique et Technique de la Construction (Belgium), Katholieke Universiteit Leuven (Belgium), Technical University of Denmark (Denmark), Balfour Beatty Rail Ltd. (Great Britain), University of Wales Cardiff (Great Britain), Fertig-Decken-Union GmbH (Germany),
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David DUPONTand Lucie VANDEWALLE
Ruhr-University-Bochum (Germany), Technical University of Braunschweig (Germany), FCC Construccion S.A. (Spain), Universitat Polytkcnica de Catalunya (Spain).
REFERENCES 1 . ACI Committee 3 18: Building code requirements for structural concrete (ACI 3 18-95) and commentary (ACI 3 18-95R), American Concrete Institute, Farmington Hills, Michigan 1995 2. Frosch, R.J., Another look at cracking and crack control in reinforced concrete, ACI Structural Journal, Vol. 96 (3), 1999, pp 437-442 3. Frosch, R.J., Modeling and control of side face beam cracking, ACI Structural Journal, Vol. 99 (3), 2002, pp 376-385 4. ENV 1992-1- 1: 199 1 Eurocode 2, Design of concrete structures-part 1 : General rules and rules for buildings, 1991 5. Vandewalle, L., Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers, Materials and Structures, Vol. 33,2000, pp 164-170. 6. Al-Taan, S.A., Al-Feel, J.R., Predictions of crack width in fibrous reinforced concrete members. Fibre Reinforced Cements and Concretes: Recent Developments, Elsevier Science Publishers Ltd.: Essex (UK), 1989, pp 209-218 7. Tan, K-H., Paramasivam, P.& Tan, K-C., Cracking characteristics of reinforced steel fibre concrete beams under short- and long-term loadings, Advanced Cement Based Materials, Elsevier Science inc., Vol. 2, 1995, pp 127-137 8. Padmarajaiah, S.K.& Ramaswamy, A., Crack-width prediction for high strength concrete fully and partially prestressed beam specimens containing steel fibres, ACI Structural Journal, Vol. 98 (6), 2001, pp 852-861 9. Dupont, D. & Vandewalle, L., A practical proposal to derive a stress-strain relation with residual tensile strengths, Annex 5.1.3 of Subtask 3.1 of the Brite Euram project BRPRCT98-0813 “Test and design methods for SFRC”, June 2002, ISBN. 90-5682-358-2. 10. Rilem TC162-TDF 2002, Test and design methods for steel fibre reinforced concrete: Bending test, Materials and structures, Vol. 35,2002, pp 579-582 11. Vandewalle, L., Bond between reinforcement and concrete in normal and cryogenic circumstances (in Dutch), Doctoral thesis, Catholic University of Leuven (Belgium), 1988 12. Dupont, D., The use of steel fibres as reinforcement in structural concrete, Doctoral thesis, Catholic University of Leuven (Belgium), 2003.
Proc. Int. Symp. ,.Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-1S, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
TENSILE BEHAVIOR OF A RECYCLED CONCRETE Hiroshi AKITA, Hideo KOIDE and Mitsuo OJIMA Tohoku Institute of Technology 35-1 Yagiyama Kasumicho, Taihaku-ku, Sendai 982-8577, Japan e-mail: [email protected]
ABSTRACT Tensile behavior of such a recycled concrete in which all the components were reused fine and coarse aggregates after simple crushing was studied. For compressive strength and durability the recycled concrete was already confirmed to be almost equivalent to the original concrete when the water to cement ratio was by 5% lower than original one. The uniaxial tension test showed that tensile strength and fracture energy were reduced considerably in the case of the recycled concrete even though it had the same level as the original concrete in compression and durability Keywords Recycled concrete, tensile strength, fracture energy, uniaxial tension, tension softening
INTRODUCTION
In order to use concrete materials effectively and save space for waste materials, used concrete should be reused as recycled concrete. When used concrete is recycled, it is not a good solution to use much labor or energy for removing mortar from coarse aggregates or throw away fine particles in order to get high quality aggregates. The authors have made a recycled concrete in which all the used concrete was reused as fine and coarse aggregates after simple crushing. For the recycled concrete, it has been confirmed to be almost equivalent to the original concrete in compressive strength and durability when the water to cement ratio was by 5% lower than original in one, [I]. The main purpose of the present study is to examine tensile
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Hiroshi AKITA, Hide0 KOIDE and Mitsuo OJIMA
behavior of the recycled concrete in comparison with the original one. The original concrete was cast and examined by uniaxial tension and other tests to compare its properties before and after recycling. Then the concrete was exposed outdoors for two years in order to make a kind of used concrete. Then the concrete was simply crushed and used as both fine and coarse aggregates. Due to the high amount of mortar attached to the original coarse aggregates, the ratio of recycled coarse aggregates was relatively high. Natural sand was added to balance the sand percentage neglecting the attached mortar. The recycled concrete was examined in the same way as the original concrete. The uniaxial tension test showed that tensile strength and fracture energy were reduced considerably in the case of the recycled concrete. The main reason was estimated to be the relatively small ratio of original coarse aggregates. This was confirmed by the observation of the broken cross-sections where a small number of original coarse aggregate grains were found. Thus, the recycled concrete using additional sand and simply crushed concrete as aggregates was inferior to the original concrete in tensile behavior even though it had the same level in compression and durability.
EXPENMENTAL PROCEDURE The original concrete was cast with mix proportions shown in Table 1. The original concrete was examined by uniaxial tension and other tests and then exposed outdoors for two years before being recycled. The concrete was simply crushed using 30mm and 20mm size crushers without much labor and energy to remove mortar or fine particles. Crushed concrete by the 30mm crusher was sieved and only the particles larger than 20mm were crushed secondarily by the 20mm crusher. The particles larger than 5 mm were used as coarse aggregates and all the remaining were used as fine aggregates. The ratio of recycled coarse aggregates was relatively large, because of the high amount of mortar attached to the original coarse aggregates. Fresh sand was added to balance the sand percentage neglecting the attached mortar. The resulting mix proportions of the recycled concrete are shown in Table 2, adopting by 5% lower amount of water to cement ratio than in original one. Table 1 Mix proportions of original concrete Unit content (kglm’)
Water cement Ratio
Cement
Aggregates
Chemical admixture
0.019
265
Tensile behavior of a recycled concrete
Table 2 Mix proportions of recycled concrete Unit content (kg/m’)
Water cement
Chemical
Ratio
0.0 I 9
The uniaxial tension test was performed by eliminating secondary flexure, using the gear system originally designed by the authors, [ 2 ] . It is essential to eliminate the secondary flexure in order to obtain exact behavior of concrete in the uniaxial tension test. Manual operation of the gear systems was used for the original concrete, whereas automatic controlled gear systems were used for the recycled concrete. Fig. 1 shows the experimental set-up using the automatic controlled gear systems. The specimens were cast in the form of prisms of 100x100x400mm with notches in the center on four laterals as shown in Fig. 2 .
Guide notch
Extensometer
400
Unit: mm
Fig. 1 Experimental set-up
Fig. 2 Prismatic specimen
RESULTS AND DISCUSSIONS Fig. 3 shows the load-deformation curve (P-6 curve) of the original concrete. A smooth curve was obtained despite the elimination of secondary flexure by manual operation. The specimen has reached the peak load equal to 22.5 kN but the first crack appeared near the load of 2 kN.
266
Hiroshi AIUTA, Hide0 KOIDE and Mitsuo OJIMA
Fig. 4 shows the load-deformation curve of the recycled concrete. A complete curve was obtained until the applied load became almost zero. The applied load slightly decreases and increases around peak. This vibration was sometimes observed in the recycled concrete, but hardly observed in the original concrete.
__
I
20?
215: v
a
.
10: 5-
Fig. 4 Load-deformation curve (recycled concrete)
Fig. 3 Load-deformation curve (original concrete)
Fig. 5 shows four tension softening curves (G-w curves) for the original concrete. All specimens were broken around the applied load of 2kN. This was usual when the manually operated gear systems were used for eliminating secondary flexure. Some curves are not smooth and vibrating at times. This shows that secondary flexure was not eliminated smoothly by manual operation. 3.5
3.5 3
3
2.5
2.5
!& v
R
2L 1.5
b. 1
..j
2
1
. . . . . . . . . . .
b
I
\.
\.
. . . .. . . . . . . . .
0.5 0
-
0.5
; . .
-......._. ..__ __ .--.----.
0
0.05 0.1
0.15 0.2 0.25
w (mm) Fig. 5 Tension softening curves (original concrete)
1.5 1 0
.3 0.
0
0.05
0.1
0.15
0.2
0.25
w (mm) Fig. 6 Tension softening curves (recycled concrete)
0.3
267
Tensile behavior of a recycled concrete
Fig. 6 shows four tension softening curves for the recycled concrete. The descending slopes of these curves at the beginning are steeper than those of original concrete shown in Fig. 5. Fracture energy expressed by the area under each softening curve is estimated smaller than that of original concrete. All curves are smooth because of the use of the automatically controlled gear systems. Fig. 7 shows the tensile strengths of the original and recycled concrete with respect to the same four specimens shown in Fig. 5 and 6 . They are presented in descending order. Tensile strength is clearly reduced by recycling.
I
#
1
#
2
#
3
#
4
Specimen
Fig. 7 Tensile strength
#
1
#
2
#
3
#
4
Specimen
Fig. 8 Fracture energies
Significant reductions were found in fracture energies of recycled concrete in comparison with the original concrete as shown in Fig. 8. These reductions can be easily expected after comparison of Fig. 6 and 5. The four points from respective specimens are presented in the same order as Fig. 7. However, they are not always in descending order. It means that large tensile strength does not correlate to large fracture energy.
Fig. 9 Broken cross-section (Original concrete)
Fig. 10 Broken cross-section (Recycled concrete)
268
Hiroshi AKITA. Hide0 KOIDE and Mitsuo OJIMA
Both faces of the broken cross-sections are shown in symmetry in Fig. 9 and 10, correlating to the original and recycled concrete specimen, respectively. In Fig. 9, relatively large numbers of original coarse aggregate grains are found and most of them exhibit symmetrical figures, which express that they were broken without coming out. On the other hand, a relatively small numbers of original coarse aggregates can be found in Fig. 10. The small numbers of the original coarse aggregate grains are considered to be one reason of the low fracture energy of the present recycled concrete.
CONCLUSIONS The recycled concrete made with simply crushed concrete as both fine and coarse aggregates with additional sand was inferior to the original concrete in tensile behavior, even though it had the same level in compression and durability. The main reason for the low fracture energy of the recycled concrete is considered to be the relatively small ratio of original coarse aggregates.
REFERENCES 1. Kitazume, Y., Akita, H. and Tomon, M., “A recycle of used concrete intending zero emission”, Proc. Japan Concrete Institute, V01.2 1, No. 1, 1999, pp. 145- 150. (in Japanese) 2. Akita, H., Koide, H., Sohn, D. and Tomon, M., “A testing procedure for assessing the uniaxial tension of concrete”, ACI International, SP-201, 200 1, pp. 75-91. 3. ACI Committee, “Removal and reuse of hardened concrete”, ACI Mater. J., Vo1.99, No.3, 2002, pp.300-325.
Proc. Int. Symp. I, Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
TOUGHENING MECHANISMS IN CONCRETE: INFLUENCE OF AGGREGATE TYPE Wastimil B ~ L E K Testing Laboratory of Building Materials ZPSV Uhersky Ostroh, a s . Kudelova 8,602 00 Brno, Czech Republic, e-mail: [email protected] ZbynCk KERSNER, Pave1 SCHMID Faculty of Civil Engineering, Institute of Structural MechanicdTesting Laboratory Brno University of Technology VeveiY 95,662 37 Brno, Czech Republic, e-mail: [email protected], schmid,p@fce,vutbr.cz
ABSTRACT The paper is concentrated to identification of the toughening mechanisms of concrete with different type of aggregates and to development/change of these mechanisms during the first months of curing. Concretes with addition of three types of aggregates - river gravel, lightweight aggregate (LiaporB) and glass “aggregates” - were submitted to fracture tests at the ages of 7, 28 and 90 days. The mortadmatrix was also prepared and tested. The self-curing effect of pre-wetted Liapor aggregates was also studied. Keywords Concrete, fracture toughness, fracture energy, glass, light-weight aggregate, toughening mechanisms.
INTRODUCTION It is well known, cement paste shows nearly brittle fracture, while concrete shows significant non-linear behaviour. That is, some toughening mechanisms are active and they control tension softening of these cement-based materials. Four of them are very important distributed interfacial cracking, crack deflection, crack bridging and trapping. The importance of the mechanisms is very strongly influenced by properties of aggregates. On the other hand - shrinkage (especially self-desiccation) affects mechanical properties and especially fracture properties of High Performance Concrete (HPC). To avoid this influence self-curing can be applied. The self-curing can be performed using pre-wetted lightweight aggregates. But these aggregates have poor mechanical properties and they can decrease the mechanical properties of HPC.
270
Vlastirnil BiLEK, Zbyngk KERSNER and Pave1 SCHMID
TOUGHENING MECHANISMS IDENTIFICATION The impact of various toughening mechanisms on fracture parameters of cement-based composites was monitored. The mathematical models by Lange-Kornbak [ l ] based on Li [2] were used. These models can work with the concrete/matrix fracture toughness ratio (rlheor). The effective crack model of Karihaloo and Nallathambi (see e.g. [3]) was used for the determination of effective fracture toughness KlCeof the studied composites and matrix. Thus it is possible to distinguish four toughening mechanisms (M) controlling tension softening: The distributed interfacial cracking (microcracking; with notation A , i.e. MA),crack deflection (MB), crack bridging (Mc) and trappin (MD). In a symbolic way we can write K/cenconcrele/ I/.? K/ce,motrrr = (MA. MB . (Mc+ MD)) . Input variables of these models are summarised in Table 1.
Table 1 Input variables of toughening mechanism models
Variable Unit aggregate content Density of aggregate Poisson’s ratio of matrix Poisson’s ratio of composite Average aggregate size Maximum size of coarse aggregate Fracture toughness of matrix Uniaxial tensile strength of aggregate
Model of mechanism A, B, C, CD A, B, C, CD A, C, CD A, C, CD Mm C, CD Mm C, CD MPa.m’” C, CD C, CD MPa Unit Kg kg/m3
Aggregates: Glass, Liapor, Gravel 1061,350, 1080 2560,850,2600 0.22 0.22, 0.15, 0.22 8,6,6 8, 8, 8 See Table 3 50, 1.1, 10
The theoretically obtained values of the ratio r,heor were compared with the measured value rleslobtained from tests of concrete and matrix (mortar) specimens. This procedure was
repeated for each age of composite. It enabled the distinction of different toughening mechanisms controlling the fracture at different ages. The authors have applied this approach to various types of cement [4].
MATERIALS, MIX PROPORTIONS AND CURING ENVIRONMENTS Three concrete mixtures were prepared by using different types of aggregates - see Table 2 for details of mix proportions. The sand was river sand 0-4 mm in all the mixtures. Glass spheres 8 mm in diameter were used as aggregate. The volume occupied by the glass aggregates is 414 1. The same volume was occupied by lightweight aggregates in the next mixture. The aggregates were produced by expanding clays and they have trade name LiaporB. The fraction of Liapor 4-8 mm was used. Finally, river gravel 4-8 mm was used. Portland cement CEM 142.5 R (EN 197) was used in combination with drinking water and a superplasticizer based on polycarboxylates. The lightweight aggregates are very moisture absorbent and for this reason they were immersed in water 7 days before making of the concrete mix. The water was added to achieve a constant workability (slump 80 20 mm) during mixing.
*
27 1
Toughening mechanisms in concrete: injluence of aggregate type
1
Table 2 Mix proportions (in kg/m3)
CEM 142.5 R Water Superplasticizer Sand 0-4 mm Glass balls 8 mm Liapor 4-8 mm (dry) Gravel 4-8 mm
I
I (Matrix)
Mortar
Glass
I
785 2f
460 ;1
1280
750 1061
-
Liapor
Gravel
460 140;80
460
750
750
1;10 -
350
1080
Concrete and mortar beams 65x65~360mm (depthxwidthxlength) were made for fracture tests. The specimens were stored in foil to avoid moisture exchange with the environment. The effective fracture toughness K/o (and also modulus of elasticity) [3] was determined for ages of specimens 7, 28 and 90 days. Because the load-deflection diagram was continuously recorded, the fracture energy GFcan be computed from the area below this curve [5].
RESULTS AND DISCUSSION Results of fracture tests for three different series are presented: values of modulus of elasticity (Fig. l), values of effective fracture toughness (Fig. 2; Table 3) and values of fracture energy (Fig. 3). Mean values and coefficients of variation are depicted in all these figures. The fracture toughness ratios from tests are given in Table 4 - mean values f standard deviations. The theoretical fracture toughness ratios are presented in Tables 5-7 (possible toughening mechanisms are highlighted). There are different tendencies in fracture toughness and fracture energy development. We can see some decrease of the values for glass and gravel. It is a consequence of shrinkage of the hardening cement paste. Between 28 and 90 days there is significant self-desiccation, because the hydrating cement grains consumed a lot of water. The self-desiccation affects shrinkage and microcracking of the paste. If larger aggregate were used in a previous study, the decrease of fracture toughness and fracture energy were more conspicuous [6] and for this reason we believe that differences in constant volume of aggregates and shrinking paste can control the decrease. But in the present experiments there is small size of maximum aggregate and only shrinkage of the paste can control the decrease. Fracture parameters show lower values for Liapor, but the values don’t decrease between 28 and 90 days. This is a consequence of self-curing of the concrete from the side of lightweight saturated aggregates. The low values of fracture parameters of glass aggregate concrete are very conspicuous. There are not any other toughening mechanisms except microcracking at the interface. Maybe the interface is very weak, because the surface of aggregates is smooth and the glass is not alkali resistant. The Liapor has lower mechanical properties than natural gravel or glass. For this reason no toughening is recorded. The mortar from natural sand has higher values of fracture parameters and Liapor aggregates cause their decrease. A wider study is conducted to investigate the optimum proportion of Liapor coarse aggregate to Liapor fine aggregate.
272
Vlastimil BiLEK, Zbyngk KERSNER and Pavel SCHMID
-
0 Glass COV Glass
0 Liapor 0 COV Liapor
Gravel
El COV Gravel
1
n
1
90
7
Fig. 1 Modulus of elasticity vs. age for different aggregate type OGlass
- OCOV Glass
0 Liapor
aGravel 50
OCOV Liapor
40
F Y
C
.-0 Y
30 .E! 2 LI-
0
20
.-al
g
10
0 7
28
90
Age [days]
Fig. 2 Fracture toughness vs. age for different aggregate type
4
273
Toughening mechanisms in concrete: influence of aggregate type
-
UGlass 0 COV Glass
Liapor 0 COV Liapor
1
80
z
-
3
Y
60
v
30
x
P 5
40
2 =l
Y
U
d
’
20
0
90
Fig. 3 Fracture energy vs. age for different aggregate type
Age [days] 7 28 90
Effective fracture toughness [MPa.m”’] Matrix Glass Liapor Gravel 0.620k0.14 0.686k0.04 0.55 1k0.05 0.870k0.16 0.695k0.02 0.702*0.0 1 0.469k0.04 1.027k0.16 0.460*0.05 0.990k0.15 0.805rt0.07 0.632k0.17
Table 4 Fracture toughness ratio from tests Glass 1.163k0.27
[-I Liapor 0.934k0.23
Gravel 1.475-10.43
1.01 1k0.03
0.675k0.06
1.479k0.23
0.79 1k0.22 0.571 + 1.011)
0.576rt0.08 (0.496 - 0.656)
1.239k0.22 (1.0191 1.459)
rlesl
Age [days] 7
.zx
274
Vlastimil BILEK, Zbyn6k KERSNER and Pave1 SCHMID
7 days
3.513 3.696 3.750 4.039 4.098 4.31 1 4.71 1
28 days
CD AC BC ACD BCD ABC ABCD
3.23 1 3.338 3.387 3.714 3.769 3.893 4.332
90 days
CD AC BC ACD BCD ABC ABCD
2.923 2.939 2.983 3.361 3.410 3.429 3.92
CD AC BC ACD BCD ABC ABCD
Table 6 Theoretical fracture toughness ratio (dimensionless) - Liapor aggregate
7 days
2.487
ABCD
I
2.466
-
90 days
28 days
ABCD
I
2.445
ABCD
Toughening mechanisms in concrete: influence ofaggregate type
275
From the viewpoint of toughening mechanisms, only MA and MBare active for glass balls (see also [7]), especially at the age of 7 days. At 90 days the fracture toughness and fracture energy are lower than for mortar. The weak interface and smooth surface of glass balls affect this behaviour. A similar situation occurs for concrete with Liapor aggregates at age of 7 days. The lowest fracture toughness ratio was recorded for Mc mechanism. All of the Liapor grains on the fracture surface were broken and it is in good accordance with Mc.As the fracture toughness of mortar increases and fracture toughness ratio decreases, there are no indications of toughening at 28 and 90 days. The combination of MA,MBand MCcontrols the toughening of concrete with natural gravel at ages of 7 and 28 days. At the age of 90 days the hardened cement paste around of aggregates is microcracked. For this reason only two mechanisms (iM,, and Mc or MB and Mc) affect the toughening.
CONCLUSIONS The same mechanisms were identified for aggregate with high strength but very smooth surface and for lightweight, low-strength aggregates. However, as natural gravel does not have high strength or a relatively smooth surface, significant toughening is induced by the aggregates (irregular grains). There are some indications of self-curing in the long-tern1 development of fracture characteristics.
ACKNOWLEDGEMENTS The authors thank for funding under grant No. 103/03/1350 from the Grant Agency of the Czech Republic and under the research project reg. No. CEZ: 53-2/98: 261 100007. Financial support of railway sleepers producer, APSV Uhersky Ostroh, a s . , Czech Republic, is also grateful 1y appreciated.
REFERENCES I . Lange-Kornbak, D., Karihaloo, B. L., Design of concrete mixes for minimum brittleness. Advanced Cement Based Materials, No. 3, 1996, pp 124-1 32 2. Li, V. C., Huang, J., Relation of concrete fracture toughness to its internal structure. Engineering Fracture Mechanics, Vol. 35, No. 1/2/3, 1990, pp 39-46 3. Karihaloo, B. L., Fracture mechanics of concrete. Longman Scientific & Technical, New York 1995 4. KerSner, Z., Bilek, V., Influence of microstructure on toughening mechanisms of concretes. Engineering Mechanics, Vol. 5 , No. 3., 1998, pp 199-201 5 . Elices, M., Guinea, G. V., Planas, J. On the measurement of concrete fracture energy using three-point bend tests. Materials and Structures, Vol. 30, 1997, pp 375-376 6. Bilek, V., KerSner, Z., Schmid, P., Mosler, T., The toughness of concrete is not interesting for us, unless it loses it. In: Proc. Int. Symp. Non-Traditional Cements and Concrete, Brno 2002, pp 424-435 7. Merchant, I. J., Macphee, D. E., Chandler, H. W., Henderson R. J., Toughening cementbased materials through the control of interfacial bonding. Cement and Concrete Research. 31,2001, pp 1873-1880
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
FAILURE OF NORMAL AND HIGH STRENGTH CONCRETE UNDER MONOTONIC AND CYCLIC TENSILE LOADING Christoph KESSLER-KRAMER*, Viktor MECHTCHERINE and Harald S. MUELLER Institute of Concrete Structures and Building Materials, University of Karlsruhe, Germany * now: Deutsche Bahn AG (German Railway Construction Inc.), 76139 Karlsruhe, Germany e-mail: [email protected]
ABSTRACT In this investigation the fracture of normal and high strength concrete under monotonic and cyclic tensile loading was studied in order to describe its softening behaviour on the basis of fracture mechanical conceptions. A series of deformation controlled uniaxial tensile tests on notched and unnotched concrete prisms was carried out. The main parameters in the experiments were the number of cycles to failure, the deformation rate, the concrete grade and the curing conditions. Additionally, the fracture surfaces were studied using projected fi-inges technique in order to gain a more detailed glance on the formation and propagation of cracks under tensile loading conditions. The experimental results show in particular that with an increasing number of load cycles the uniaxial tensile strength decreases. Further, for an increasing number of load cycles the corresponding envelope curves differ significantly from the monotonic curve. This clearly shows that the conventional fissumption of a unique envelope curve for the fatigue behaviour of concrete is admissible only for a low-cycle fatigue loading, but cannot be maintained for the high-cycle fatigue. Keywords High strength concrete, fracture mechanics, cyclic loading, fractology, material law.
INTRODUCTION In practice the majority of concrete structures are exposed to more or less severe cyclic loadings, such us traffic loads, temperature changes, wind gusts and in some cases waves or vibrations due to operation of machinery. Therefore, a profound knowledge of the fatigue behaviour of concrete and concrete structures is indispensable for safety and economical reasons. Furthermore, appropriate constitutive laws are required in order to be able to analyse the formation and propagation of cracks in concrete as well as the deformation behaviour or possibly a failure of concrete structures subjected to cyclic loading. The existing constitutive relations are based on experimental investigations with a low number of load cycles which are generally of minor interest for the practical design. Fatigue experiments with a higher number of load cycles have been always performed using stress controlled Wohler tests. Such tests do not allow studying the softening behaviour of concrete
278
Christoph KESSLER-KRAMER, Viktor MECHTCHERINE and Harald S. MULLER
after reaching the peak load. Therefore, in this investigation the fracture of concrete subjected to low-cycle and high-cycle fatigue loading was studied in order to describe the fatigue behaviour of concrete using fracture mechanical approach.
FRACTURE MECHANICAL EXPERIMENTS Geometry and preparation of the specimens In the experimental part of this study deformation controlled uniaxial tension tests on dog-bone shaped as well as on notched concrete prisms were carried out. Figure 1 shows a schematic view of the geometry of the two types of specimens applied in the experimental programme.
Figure 1. Geometrical dimensions of the concrete specimens (thickness of both specimens d = 100; data in [mm]) The dog-bone shaped prisms were used in monotonic tensile tests to study the pre-peak behaviour of the stress-strain relations in order to obtain reliable values of the uniaxial tensile strength f,, the Young's Modulus (tangent modulus of elasticity) and the strain at peak stress c,,, to be used as basic data for the formulation of the material law. On the notched prisms monotonic as well as low-cycle and high-cycle fatigue tension tests were carried out to obtain the softening behaviour of concrete under such loading conditions. Table 1. Composition of the investigated concretes Water
Cement CEM 132.5 R wm31 wm31
Concrete
w/c
HSC
0.30
125
470
NSC
0.55
175
318
Silica fume wm31
Superplasticizer wm31
Aggregate wm31 012 218 8/16
45
21
516
654
551
1.20
555
703
592
The compositions of two investigated concretes, namely a high strength concrete (HSC) and a normal strength concrete (NSC), are given in Table 1. For both mixtures an ordinary Portland cement CEM I 32.5 R was used. As aggregates quartzite Rhine sand and gravel with a maximum aggregate size of 16 mm were applied. For the high strength concrete additionally silica fume was used in the form of a suspension. Further, a sodium naphthalene sulfonate type superplasticizer was added in order to achieve the same consistency for both mixtures.
Failure of normal and high strength concrete under tnonotonic and cyclic tensile loading
279
All specimens were cast horizontally in metal forms. After demoulding at an age of one day, an aluminium foil was glued by means of an epoxy resin to the specimens termed as sealed in order to protect them against desiccation. However, the zones where the crack formation was expected were wrapped with a polyethylene foil before sealing with the aluminium foil. By this measure a contribution of the epoxy resin and the aluminium foil to the bearing capacity of the specimens could be excluded. A continuous control of the specimen weight proofed the quality of the chosen sealing. With this kind of curing the moisture condition in mass concrete was simulated. The specimens termed as unsealed were stored in a climatic chamber at a relative humidity of 65% and a temperature of 20°C immediately after demoulding. These specimens represent the moisture condition in slender concrete members without proper curing. The properties of the investigated concretes in fresh and hardened state are given in Table 2. The compressive strength and the Young’s Modulus were determined at a concrete age of 28 days. The values for the standard deviation are given in parentheses. Table 2. Properties of the fresh and hardened concretes Slump Concrete
[cm]
Air void contents [Vol.-%]
wlc
Gross density Compressive Young’s strength fc,150 Modulus E [kg/m3] , [MPa] [MPaI
HSC
0.30
39 (6.1)
1.6 (0.30)
2467 (15)
109.9 (3.21) 36490 (1280)
NSC
0.55
39 (3.7)
1.2 (0.19)
2407 (9)
50.5 (2.16) 27750 (1270)
Loading regime and test parameters Since a very stiff test set-up is required for the deformation controlled cyclic tests all tests have been performed with non-rotatabre boundary conditions. Therefore, the concrete specimens have been glued to stiff metal adapters applying an extra strong two component adhesive. Finally, the metal adapters were firmly connected to the bearing platens of the testing machine. The mean value of two LVDTs with a gauge length of 250 mm for the dog-bone shaped prisms and 50 mm for the notched prisms (compare Figure 1) was used as a control signal for the testing machine to run the tests with the desired deformation rate. The basic approach for the test control in the fatigue experiments is shown in Figure 2. The increase of the total deformation within the measuring length corresponding approximately to the crack opening is given by the deformation increment A6, which bas kept constant from cycle to cycle (i.e. A6 = d61dn = const, where n = number of load cycles). When the preset value for the deformation A6 in the following cycle is reached, the specimen will .be unloaded until the lower reversal point 6min is attained. The lower reversal point ti,,,, was defined as a function of the lower load level F,i, = const = 0 N. The deformation rate d6ldt was kept constant throughout the complete loading cycle. The deformation increment A6 was determined by dividing the critical crack opening (i.e. the crack opening at which no tensile stresses can be transmitted any more across the crack) as known from the monotonic tests by the desired number of load cycles to failure. As the maximum crack opening in the monotonic case a constant value of wcr= 160 pm was chosen from the literature, see [l]. The main parameters in the experiments were the number of cycles to failure ranging from 1 (monotonic loading) up to 100,000 load cycles, the curing conditions and the grade of concrete.
280
Christoph KESSLER-KRAMER, ViktorMECHTCHERINE and Harald S. MULLER
cr,
s
0
4
deformation 6
time t
Figure 2. Typical load-deformation relation (left) and deformation control procedure (right) in the fatigue experiments The tests were performed applying two different strain rates 8 . For the tests on the dogbone shaped prisms 8 I = lo4 I/s and 8 2 = 10” l/s were chosen. The experiments on the notched prisms were performed with the deformation rates of 6 1 = 5 p d s and 8 2 = 0.5 p d s , which correspond to the chosen strain rates considering the actual gauge length of 50 mm. The age of concretes at testing was 280 days. For each investigated combination of the parameters at least five specimens were tested.
FRACTOLOGICAL STUDIES In order to gain more information on the process of the crack formation and propagation in concrete under cyclic loading phenomenological investigations were additionally performed by means of an acoustic emission (AE) analysis during fracture mechanical tests. Further, the fracture surfaces of the tested concrete specimens were studied using projected fringes technique. In the following the main findings of the fractological investigations will be presented. Concerning the AE analysis, a detailed description of the measurement technique, the used test set-up as well as the applied analytical evaluation may be found in [2].
object
(fracture surface)
;\
i
’\.\
’.
reflector 1
fringe projector
reflector 2
c]
camera
Figure 3. Projected fringes technique: schematic view (left) and photograph (right) of the test set-up
Failure of normal and high strength concrete under monotonic and cyclic tensile loading
28 1
A schematic view of the test set-up using projected fringe technique is shown in Figure 3. Height differences of the surface induce a lateral displacement of the projected strip pattern [3]. Together with the geometrical data of the test set-up the phase shift of the projected fringes allows for the contour information at intervals of 0.16 mm (giving a mesh of 375 x 625 data points for each failure surface). To avoid larger areas of receiving no information due to a shade on the fractured concrete surface a projection from two sides (using the reflectors 1 and 2) was necessary. From the optical measurement data the roughness Rs and the fractal dimension DGSwere determined (Table 3). The roughness RS was defined as the surface area measured with the finest resolution (0.16 mm) divided by the projected area. The determination of the fractal dimension DGSwas performed by means of the grid scaling method [5].
Table 3. Roughness'and fractal dimension of concrete fracture surfaces of the concretes under investigation (standard deviations are given in parentheses) Concrete grade; curing conditions; deformation rate; number of load cycles NSC; sealed; 8 = 5 p d s ; N = 1
[-I
[-I
1.281 (0.003)
2.043 (0.005)
NSC; sealed; S
=5
p d s ; N = 10
1.297 (0.017)
2.043 (0.004)
NSC; sealed; b
=5
p d s ; N = 1000
1.325 (0.032)
2.050 (0.002)
1.335 (0.033)
2.05 1 (0.003)
pds;N=1
1.291 (0.017)
2.047 (0.001)
8 = 0,5 p d s ; N = 1 HSC: sealed; 8 = 5 u d s : N = 1
1.290 (0.030)
2.046 (0.004)
1.245 (0.027)
2.041 (0.003)
8
NSC; sealed;
NSC; unsealed; NSC; sealed;
=5pds;N=
8
=5
100,000
Roughness Rs
Fractal Dimension DGS
As can be seen by the results given in Table 3 an increase of the number of load cycles leads to an increase of both investigated parameters Rs and D G ~Further, . the use of an unsealed specimen as well as a lower deformation rate leads to higher values of the roughness Rs and the fractal dimension DGS,whereas for the high strength concrete lower values of Rs and DGSwere found in comparison to the normal strength concrete.
Figure 4. Typical fracture surfaces of the investigated concretes: high strength concrete (left) and normal strength concrete (right)
282
Ciiristoph KESSLER-KRAMER. Viktoi.MECHTCHERINE and Harald S.MULLER
The differences in the condition of the fracture surfaces of the normal strength concrete and the high strength concrete are illustrated in Figure 4.The effect of the concrete grade is already visible by a close inspection without any fkrther technical aid: high strength concrete shows a smoother surface with a pronounced fracture of aggregates, while the crack propagation in normal strength concrete occurs along the contact zone between coarse aggregates and mortar.
MAIN EXPERIMENTAL RESULTS AND DISCUSSION The uniaxial tension tests on the dog-bone shaped prisms provided stress-strain relations for the HSC always running above the corresponding curves for the NSC. Further, in the case of the high strength concrete the shape of the ascending branch of the o-Erelation remains nearly linear up to a considerably higher stress level in comparison to the corresponding relations for the normal strength concrete. An increase of the strain rate by a factor of 10 resulted in higher values of the uniaxial tensile strength 6, the Young's Modulus E~Jand the strain at peak stress EN. These results agree well with the data given by [4,5].The observed strain rate dependency may be explained by considering the crack development in concrete as a function of time. The cracks always strike the path with the lowest resistance, which runs along the aggregates in the case of normal strength concrete. With increasing rate of loading the cracks can grow faster because of a higher energy supply per time unit. Therefore, some of the cracks go straight through the aggregates following the shortest distance to cover.
6.0 I
I
I
I
I
8 = 0.5 p d s 4 NSC, unsealed, 8 = 5 p d s -0NSC, sealed, 8 = 5 p d s 0 I oo 10' 1o4
l.o
s
I
-0- NSC, sealed,
-0- NSC, sealed,
number of load cycles N
[-I
1o6
8 = 0.5 p d s
1o2 10' number of load cycles N
1
o6
[-I
Figure 5. Effect of the number of load cycles to failure on the net tensile strength (left) and the fracture energy (right) in the uniaxial tension tests on the normal strength concrete and the high strength concrete for different deformation rates and curing conditions The sealed specimens provided in all tests higher values of the uniaxial tensile strength fi, the Young's Modulus & and the strain at peak stress E~ than the unsealed specimens. This can traced back to the fact that the desiccation in the case of the unsealed specimens leads not only to a lower degree of the cement hydration but also to pronounced moisture gradients over the cross section of the specimen, which finally results in stress gradients reducing the bearing capacity of the specimen. Further, due to shrinkage of the cement paste considerable eigenstresses develop
Failure of normal and high strength concrete under monotonic and cyclic tensile loading
283
in concrete leading to the formation of micro cracks in the contact zone between coarse aggregates and mortar. The corresponding crack pattern could be clearly observed in the fractological investigations (see also Table 3). The results obtained from the tests on the notched concrete prisms show that with an increasing number of load cycles the net tensile strength fi, decreases (Figure 5, left). However, in the low-cycle region up to 100 load cycles the fm-valuesremain approximately constant. This observation is in accordance with the experimental findings on three-point bend tests on notched beams [6]. The tensile strength obtained for the unsealed specimens is lower than the corresponding values for the sealed specimens. This agrees well with the results obtained from the tests on the dog-bone shaped prisms. The effect of the strain rate in the experiments on notched concrete prisms is similar to that observed in the tests on dog-bone shaped prisms. In comparison to the values obtained for the normal strength concrete the net tensile strength of the HSC is always higher due to its denser microstructure fixther resulting in a higher capacity to store energy. The denser microstructure of the HSC also lead to smoother fracture surfaces and consequently to lower Rs- and DGs-values (Table 3). Figure 5, right shows a considerable decrease of the fracture energy GF in the high-cycle fatigue tests with an increasing number of load cycles. The GF-values were calculated as the area under the measured stress-deformation curves. In the case of the cyclic tests the envelope curves of the corresponding stress-deformation relations have been chosen for the derivation of the f i x ture energy. Therefore, a possible contribution of the area within hysteresis loops was not considered. Since the decrease of the investigated material parameters with an increasing number of load cycles is approximately the same for the normal strength concrete and the high strength concrete, it can be concluded that the effect of the fatigue loading is similar for the both types of concrete (HSC and NSC).
4.0
1
cyclic tests Lr,
3
envelope curves for monotonic tests, N= 1 low-cycle fatigue tests, N = 10 high-cycle fatigue tests, N = 1000 high-cycle fatigue tests, N = 100,000
0
200
400
deformation 6
600
deformation 6 [pm]
Figure 6. Envelope curves of the stress-deformation relations obtained from the monotonic and the fatigue tests performed on the sealed specimens made of NSC
284
Cliristoph KESSLER-KRAMER. Vibor MECHTCHERINE and Harald S.MULLER
The main finding in the experiments is that for an increasing number of load cycles the envelope curves of the 0-6 relations differ significantly from the corresponding monotonic curve, see Figure 6. The ascending branches show approximately the same shape and the same stifhess for all curves. Because of the lower f,-values for the high-cycle fatigue tests (Figure 5, left) these curves are below the curves for the monotonic and the low-cycle fatigue tests in the first, steeper part of the stress-deformation relation. This also leads to the lower Gpvalues (Figure 5, right) with an increasing number of load cycles which is mainly due to lower energy consumption in this part of the softening curve. Additionally, the curves from the highcycle fatigue tests are steeper than the curves for the monotonic and the low-cycle fatigue tests, see Figure 6. In the second, shallow part of the softening curve the average curves for the cyclic tests are nearly congruent when a deformation of about 150 pm is reached. The curve for the monotonic loading is slightly higher at this deformation region and coincides with the curves for the cyclic loading at a deformation of about 350 pm. Nevertheless, the contribution of the second part of the softening curve to the value of the fracture energy is limited, since it covers a minor amount of energy compared to the first part of the softening curve. The mentioned observations clearly show that the conventional assumption of a unique envelope curve for the fatigue behaviour of concrete cannot be maintained, especially for highcycle fatigue loading. Further results for additionally investigated mechanical and fracture mechanical parameters such as miscellaneous deformations, characteristic length etc. under cyclic tensile loading may be found in [2]. MODELLING THE FATIGUE BEHAVIOUR OF CONCRETE The experimental results obtained in this study restrict the validity of the existing constitutive relations to the range of low-cycle fatigue since they are completely based on the assumption that the monotonic stress-crack opening curve fits the envelopes for fatigue loading regardless of the number of load cycles to failure, see e.g. [ 1, 71. Based on the findings attained in this investigation a new constitutive law on the basis of a rheological-statistical model was currently developed, which considers in particular the number of load cycles, time effects and the heterogeneity of concrete (Figure 7). The model consists of simple rheological elements like springs, friction blocks and dashpots representing the elastic, frictional and viscous deformation components of concrete. The chosen basic model consists of two Kelvin-Voigt elements and three dashpots (in Figure 7 framed with dotted lines). The concrete behaviour resulting in the hysteresis loops is modelled by a serial arrangement of two friction blocks and two Kelvin-Voigt elements. Duda [7], who also used a rheological approach, applied in his model only springs and friction blocks to describe the cyclic tensile behaviour of concrete. In the new material model presented here the dashpots qi,l and qi,2 arranged parallel to the spring elements Ei.1 and Ei.2 enable to consider the rate dependency of concrete behaviour and the effects resulting from the load history. The parallel arrangement o f a further friction block Y ~ Jallows the modelling of the phenomenon that loosened or pulled out aggregates or hardened cement paste particles may dislocate while the crack is open, which leads to local tensile as well as compressive stresses in the case of unloading, i.e. closing of the crack. Since this phenomenon just appears within the hysteresis loops, the associated friction coefficient ~ i . 3is given as a function of the number of load cycles N (Figure 7).
Failure of normal and high strength concrete under monotonic and cyclic tensile loading
285
Figure 7. Rheological-statistical model for the description of the fatigue behaviour of concrete under tensile loading The complete model consists of n basic models arranged parallel. The governing parameters Y, E and q are statistically distributed following an exponential function after Weibull. By this approach the heterogeneity of concrete has been considered. The bulk behaviour of the undamaged concrete is taken into account by an additional spring element Ebulk. A new constitutive law for the description of the stress-crack opening relation of concrete under tensile fatigue loading was developed on the basis of the presented rheologicalstatistical model. Further details concerning the mathematical formulation, the adjustment of the decisive coefficients and the practical application may be found in [2].
SUMMARY AND CONCLUSIONS In this study the effects of the number of load cycles to failure, the strain rate and the curing conditions on mechanical and fracture mechanical parameters of high strength and normal strength concrete under monotonic and cyclic tensile loading were investigated. Therefore, deformation controlled uniaxial tensile tests on dog-bone shaped prisms as well as on notched prisms were carried out. The tests on dog-bone shaped prisms showed a significant increase of the uniaxial tensile strength f,, the Young’s Modulus Eo and the stain at peak stress Etu with an increase of the strain rate by a factor 10. For the sealed specimens the values of these three parameters were found to be higher than for the unsealed specimens. For the high strength concrete the ft-, Eoand q,-values were significantly higher in comparison to those for the normal strength concrete. Concerning the tests on notched concrete prisms the net tensile strength ftnand the critical crack opening w,, decrease with an increasing number of load cycles. The fracture energy GF
286
Clvistoph KESSLER-KRAMER. Viktor MECHTCHERINE and Harald S. MULLER
and the characteristic length lch decrease with an increasing number of load cycles as well. The tests on sealed specimens provided higher GF- and I,h-values as the tests on unsealed specimens. The effect of the number of load cycles on the behaviour of HSC in tension is similar to that of NSC. As a main result it could be shown that for an increasing number of load cycles the envelope curves of the stress-deformation relation differ significantly from the corresponding monotonic curve. This observation restricts the validity of all existing material laws to the low-cycle region. Therefore, a new constitutive law based on a rheological statistical model was developed. Further, the fracture surfaces were studied using projected fringes technique in order to gain a more detailed glance on the formation and propagation of cracks under tensile loading conditions. As a result, strong correlations have been found between the calculated values of the roughness and the fractal dimension, respectively, and the fracture mechanical properties of concrete as measured for different combinations of the investigated parameters. REFERENCES 1. Hordijk, D. A., Local Approach to Fatigue of Concrete. Dissertation, Delft University of Technology, Delft 1991 2. Kessler-Kramer, C., Tensile Structural Behaviour of Concrete under Fatigue Loading (in German). Institute of Concrete Structures and Building Materials, University of Karlsruhe, VOl. 49,2002 3. Gutmann, B., Determination of the Phase Field in the case of Projected Fringe Optical Measurements with an improved Branch-Cut Method (in German). Dissertation, Faculty of Chemical Engineering and Process Technology, University of Karlsruhe, Shaker Publisher, Aachen 2000 4. ACI Committee 446: State-of-the-Art Report on Dynamic Fracture. Report ACI 03.95 R8860,1995 5. Mechtcherine, V., Fracture Mechanical and Fractological Investigations on the Formation and Propagation of Cracks in Concrete (in German). Institute of Concrete Structures and Building Materials, University of Karlsruhe, Vol. 40,2000 6. Kessler, C., Mueller, H. S., Experimental Investigations on Fracture and Damage of Concrete due to Fatigue. In: “Fracture Mechanics of Concrete Structures” (Proc. FRAMCOS-3), H. Mihashi and K. Rokugo eds., Gifu 12-16 Oct. 1998, Aedificatio Publishers, Freiburg 1998, pp 377-386 7. Duda, H., Fracture Mechanical Behaviour of Concrete under Monotonic and Cyclic Tensile Loading (in German). German Association of Concrete Structures (DAfStb), Vol. 419, Beuth Publisher, Berlin, 1991
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE USE OF VISCOSITY ENHANCING ADMIXTURES TO IMPROVE THE HOMOGENEITY OF FIBRE DISTRIBUTION IN STEEL FIBRE REINFORCED CONCRETES Liberato FERR4RA Politecnico di Milano - Department of Structural Engineering Piazza Leonard0 da Vinci 32 20133 Milano, Italy e-maiI : li berato.ferrara@,uolimi.it
ABSTRACT This work presents the early results of a research program aimed at evaluating the influence of viscosity enhancing admixtures (VEA) on the fibre distribution in Steel Fibre Reinforced Concrete (SFRC) elements. First of all their influence has been investigated with reference to fibre distribution along casting direction in cylinder specimens. As a further step of the investigation small-scale prototypes have been cast with the same mixes previously tested and the distribution of fibres, as influenced by the mix-design of concrete, has been evaluated along the thickness, the cross-section and the longitudinal axis of the prototypes. Results are really promising in sight of structural applications. In this framework some full-scale prototypes have been cast with the “optimum” mix, as came out from previous experiments, and the repeatibility of results previously obtained has been checked with reference to them.
Keywords: steel fibre reinforced concretes, viscosity agents, fibre distribution, roof elements
INTRODUCTION Starting from the pioneeristic idea of Batson et al. (1972), relevant studies have been carried out over the past almost thirty years about the partial or even total replacement of conventional shear reinforcement with metallic fibres in reinforced concrete structural elements. Among the several benefits which may come from such an operation, the possibility of achieving a continuous and, hopefully, homegenous distribution of reinforcing “wirelike” elements, spaced closerly than the minimum distance obtainable with the smallest traditional bars (Romualdi and Batson, 1963) was earliest recognised and regarded as a sound motivation for promoting research in this field. Recent experiences, focused on the use of steel fibres as completely substitutive of traditional shear reinforcement in precast prestressed thin web roof elements, have clearly assessed the reliability of this technology (di Prisco and Ferrara, 2001 ; Meda et al., 2002a; di Prisco et al., 2003). The same experiences, together with other studies on steel fibre reinforced concrete prestressed X-beams (Elliot et al., 2002, a-b), have once again confirmed that the homogeneity of fibre distribution inside a structural element, as well as the repeatibility of these homogenity features, stand as a crucial point that must be tackled aiming at efficaciously and efficiently implementing the Steel Fibre Reinforced Concrete
288
Liberato FERRARA
(SFRC) technology in structure building processes, mainly as far as a series production of precast elements is dealt with (di Prisco et al., 2000,a-b; Failla et al., 2000; 2002). It is infact well established that the addition of steel fibres to a traditional concrete may have sever unfavourable effects on the workability and rheology properties of the fresh mix, this negative influence mainly depending on the fibre content and aspect ratio (Bayasi and Soroushian, 1992). The glueing of fibres into bundles, creating a lower aspect ratio during mixing, is surely helpful in avoiding balling and formation of fibre nodules (see for example Ramakrishnan et al., 1980); furthermore the use of superplasticizers (in percentages ranging from 1 to 2% by mass of cement) together with extrafine particles, such as silica fume leads to an improvement of the workability. Nevertheless, whenever it can be guaranteed a homogeneous distribution and random orientation of fibres within the fresh concrete mass when poured out of the mixer, the casting of concrete into formworks and the subsequent compaction by vibration may not only lead fibres to be oriented along preferential directions lying in predictable planes (Edgington and Hannant, 1972) but also to show a not negligible tendency to segregation. These deviations from the homogeneous and random distribution of fibres have been shown to strongly influence the measured material properties, at the laboratory specimen scale, to an extent even such to shadow the effects of other likewise relevant factors (e.g. the specimen size or, in direct tension tests on notched cylinders, the specimen slenderness and notch depth - see Barragin, 2002). Furthermore, when dealing with practical applications to full scale structural elements, the lack of homogeneity in fibre distribution may be called to explain, e.g., non-conventional failure mechanisms accompanied and featured by unattained theoretical strength and ductility levels (di Prisco et al., 2003). In this framework, a sinergy between the technologies of self-consolidating and steelfibre reinforced concrete may by fruitfully employed, leading to an engineered cementitious composite, all the enhanced properties of which may be fully exploited by precast industry (Groth and Nemegeer, 1999; Khayat and Roussel, 1999). On one hand in fact it is dealing with a fresh concrete which, by its own weight, and needing no compaction by vibration, is able to fill any corner of a formwork, whatever its geometry be, perfectly wrapping up the reinforcing bars even when highly congested, and without showing any significant segregation of its constituents. This eliminates, or at least strrongly reduces, the causes which are likely to alterate the homogeneous distribution of fibres, despite introducing some dependence of the orientation of the same fibres on the direction of flow of the fresh concrete in the formworks. On the other hand, the use of fibres may lead to a significant reduction of the production times and workmaship costs due to the placement of traditional reinforcement, furthermore contributing to enchance the performances of concrete, during its settlement, hardening and hardened states. As an obvious outcome of all the "passim" above recalled benefits, the durability of structural elements made with a self compacting steel fibre reinforced concrete is also likewise significantly improved. RESEARCH SIGNIFICANCE AND EXPERIMENTAL PROGRAMME
In order to reliably set up a series production of precast prestressed roof elements in which all transverse reinforcement is replaced by fibres, a crucial role is surely played by the optimisation of the mix design of concrete. The final aim of the whole research project, in the framework of which this work has been conceived, is to achieve an enhanced engineered concrete composite, reinforced with hooked-end steel fibres, furthermore featured, in its fresh state, by high workability and rheological stability. This work focuses on the role which Viscosity Enhancing Admixtures (VEA) may play in enhancing and guaranteeing the above said rheological stability, as far as it is dealt with the positive effects which the enhanced
The use of viscosily enhancing admixtures to improve the homogeneity offibre distribution ...
289
fresh state properties may have on the homogeneous and random distribution of fibres. It can be in fact reasonably hypothesised that the above said correlation between fresh state properties and fibre distribution, when efficaciously established, may also have positive effects on the hardened state properties of the composite, as far as not only their values are concerned but also their repeatability in a continuing production, as typical of precast factories, and their “spatial” dispersion in real scale structural elements. To the above exposed purpose, it has been hence first of all evaluated the effect that vibration times may have on fibre distribution along casting direction in cylindrical specimens. Starting from an ordinary steel fibre-reinforced concrete, the influence of viscosity enhancing admixtures (type and dosage) has been first of all checked. Furthermore, SelfCompacting Steel Fibre Reinforced Concretes (SCSFRC) have been investigated (in these last cases the cylinder specimens have not been vibrated). The influence of mix design on the strength and most of all on toughness properties of the engineered concrete composites has been also evaluated through four point bending tests on notched prisms. For a further check some small-scale prototypes of thin-walled roof elements (4 m span) have been cast, with the different investigated mixes. By coring the prototypes in several suitable positions, information on the distribution of fibres along both longitudinal and transversal directions as well as along the thickness of the thin-walled slabs has been got. It has been also tried to set up some correlation between this information and results from fourpoint bending tests on small thickness slabs, both companion specimens of the prototypes and cored from them. The results obtained in this stage of the work lead to definitively chose one mix, the characteristics of which has been further checked with reference to large scale prototypes (25 m long), further considering the influence of fibre type and aspect ratio.
RESULTS FROM CYLINDER SPECIMENS The first step of the work consisted in evaluating the distribution of fibres along the casting direction in cylinder specimens, as influenced by both viscosity-enhancing admixtures and times of vibration. A reference steel fibre reinforcing concrete, the mix design of which is reported in Table I, was first of all considered. Seven cylinders, 300 tnm high and with a diameter equal to 150 mm, were cast, pouring the mix directly into a plastic tube through a suitable extension and without any manual tamping, so to reproduce as close as possible the real casting conditions of a precast element. The specimens were further submitted to different times of vibration (0, 1, 2, 4, 8 and 16 minutes - 2 cylinders vibrated 8 min). After even only one day of aging, the cylinders were cut into six equally thick. Each slice was then crushed under a press and, by means of a magnet, fibres were separated from the matrix and weighted, their weight being hence referred to the previously measured volume of the slice. The results, in terms of fibre density in the six slices (named downward from A to F) are shown in Figure 1. For longer vibration times, of the same order of magnitude of those generally underwent by precast elements, the random distribution of fibres is significantly altered and a clear tendency of fibres to downward segregate appears. Cement type CEM I 52.5 R Fly ashes Water Steel Fibres type 45/30 (hooked ends- zinc coated)
380 kg/m’ Sieved sand 0/3 mm 60 kg/m’ Natural sand mix 0/12 mm 150 lt/m’ Gravel 8/15 mm
50 kg/m3 Acrylic superplasticiser
Table 1. Mix-design of the reference SFRC
120 kg/m’ 920 kg/m3 865 kg/m’
3,5 1 t h 3
290
Liberato FERRARA 30
z(mm)
casting direction
25
+n
0 0 *.
A
a
+X
20
vibrotion times
0
15
+
t-omin t:lmin
+
0
t=8min
X
t :2mm
10
A 0 0 P+ t=4min
= 16min
t
z (min)
5
m a r
fibre content (kg/m3)
0 0
10
30
20
40
50
60
Figure 1 : influence of vibration on fibre distribution along casting direction - reJ SFRC 30
30
z (mm), casting m +
z(mm)
~
25
\J
direction
25
0
2o
A 15
0
+
0
+m
t=omin t=Zmin
/
I
15 10
t=8min
t I
I
t=16min
5 0
era a63
t=Zmin
= 4 min
+aA
vibration t I mes
20
t=Omin
t
10
‘0 ‘+O
A
vibration times
casting direction
= 4 min
+
t:Bmin
0
t=16min
I30
0
5 1 fibre content (kg/m 3 )
a; ;a
20 30 40 VEA type A
50
0
10
fibre content (kg/m 3 ) e o
0 60
0
10
20 30 40 VEA type B
50
60
Figure 2: influence of vibration and type of VEA on fibre distribution along casting direction
In order to study the influence of viscosity enhancing admixtures, different concrete mixes have been considered, simply adding the chosen dosage of VEA to the reference fibre reinforced concrete. Two types of admixtures have been herein considered, in a dosage such to guarantee their rheological stabilising action without detriment to workability (Table 11). The basic constituent of the first one (named VEA type A in this work) is amorphous silica dispersed in a water solution; the second one (here labelled as VEA type B) mainly consists of water-soluble polymers. Eight cylinders for each VEA-added mix were cast and vibrated 0, 2, 4,8 and 16 minutes respectively (one cylinder for lower times and two cylinders for each of the longer times). The addition of viscosity enhancing admixtures has some quite significant stabilising effects on fibre distribution. The performances of VEA type B, as a matter of fact, appear to be more effective in limiting the downward segregation of fibres even for longer vibration times (Figure 2 - for longer vibration times the mean values of the two cylinders are shown i n the graphs).
The use of viscosi& enhancing admixtures to improve the homogeneity offibre distribution ...
Mix Reference SFRC (mix 1) Reference SFRC + 0.5 It/m’ VEA type A (mix 2) Reference SFRC + 0.5 It/m” VEA tvue B (mix 4)
29 1
Slump (mm) 180 150 140
Table 11. Influence of VEA on workabilihj offi-esli mixes
I Cement tvne < . CEM I
I
1 400 kdin’ 1 Sieved sand 0/3 mm
52.5 R Calcareous fi 11er Water Steel Fibres type 45/30 I (hooked ends- zinc coated)
50 k&-’ Natural sand mix 0/12 mm 160 Wm’ Gravel 8/ 1 5 mm 5o k,,,m3 Acrylic superplasticiser -- - - D... 1 VEA (tvDe A or B)
I
-, r - - -, aiuinp flow diameter (VEA tvoe B)
I
825 kg/m’ 1 190 kg/m’ 135 !@in’ 6 It/m-’ 2 It/m’ I
1
63 cm
Table 111: mix-desigiz and wor-kabili@tesl r-essults,/orself compacting SFRCs 30
z (mm)
casting direction
25
+
a
A
AOM
20
A
r e f sfrc
0
r e f sfrc
+
scc
10
5
u i %
reference sfrc
15
+
veo type A veo type
B
A
O
scc + veo type A +
A
vea type B
10
20
30
O
+
O
4B
fibre content (kg/m3) 0 0
D
40
50
60
Figure 3: distribzitiorz offibre along cylirider lieightjor diflerent mixes (no vibration)
As a further step two self compacting steel fibre reinforced concretes have been designed, each one of them containing one of the two types of the investigated VEA. The mix-design and the results of slump-flow tests for the measurement of workability (Khayat, 1999; Ferraris et al. 1999) are reported in Table 111. Cylinders made with these concretes (one for each mix) have not been vibrated; the distribution of fibre content along the height of the specimens is shown in Figure 3 and compared with the ones detected in not-vibrated specimens made with other concretes. No significant difference can be detected in the random distribution of fibres (except for scc mix with VEA type A which showed some abnormally high content of fibres). The advantage of self compacting mixes stands in the possibility of achieving, as far practical applications are concerned, the same quality of the structural element without any vibration, as it will be further specified, thus removing one of the main causes of fibre segregation. Some tests aimed at assessing mechanical properties of the different investigated mixes have been also performed. Besides compression tests on cubes. four-point bending tests on notched prisms have been performed (see the specimen geometry in Figure 4). Test results are
292
Liberato FERRARA
summarized in Table IV (mean values and corresponding standard deviations, computed on the referred number of tests, are reported). As far these data: - the first-cracking strength fir is defined as the nominal stress stress at a Crack Tip Opening Displacemen (CTOD) equal to 25 microns; - equivalent strengths fq 0-0.6 and fq 0.63 are defined as equivalent stresses computed for CTOD values respectively ranging from 0 to 0.6 mm and fiom 0.6 to 3 mm.
-
ductility indices DOand DI are respectively computed as
feq0-0.6 and
feq0.6-3 ~
flf
fir
Despite some differences have been measured in the compressive strengths, which turned out to be lower in self compacting concretes, no significant differences have been detected as far as the first cracking strength is concerned. Furthermore, and this is even far more signifcant, some improvements for equivalent strengths have been obtained when shifting from ordinary SFRCs, tough added with VEA, to self-compacting ones. The similar tendencies detected for ductility indices, which furthennore result in a percentually larger increase for the second one, may lead to hypothesize that the above measured improvements are due, on one hand, to a better homeogeneity inlhe distribution of fibres within the concrete matrix, and, on the other, to a better bond between the matrix and the fibrous reinforcement (similar to what is well assessed for traditional reinforcement bond with scc matrices; Sonebi and Bartos, 1999; Sonebi et al., 2001). It has to be equally emphasised the lower scattering in test results which has been obtained with self compacting mixes, reliably attributable to an improved stability of the fresh mixes, exerting its positive effects also on the toughness properties of the composite. , 15Omm
I
150mm-
I
150mm - ---
1 --
. ..
I ..
.. ..
-t
mm . _. 450 . . .-._--. -... ..-.- . . ..- .. -_ - . - .... . .600..mm
Figure 4: specimen geometry for 4-point bending tests
no of tests -
I
Mix
I
l 33
RefetenceSFRC
Ref. SFRC + VEA type A
I SCSFRC -
fir
VEA type A
1
5
80.5
4
88. I
I2
68.2
4
75.8
I
fcq0.63
3.3% 5.9
15.1% 6.2
1 18.9% ;;;;2
, 4.95
I;
K3.1%
I
SCSFRC - VEA type B
fqO-O.6
~
5.2 5.1 %
Table IV: results of 4 point bending tests
I .09
The use of viscosity enhancing admixtures to improve the homogeneity offibre distribution ...
293
DISTRIBUTION OF FIBRES IN SMALL SCALE PROTOTYPES The further step of the investigation took into account small scale prototypes of roof elements, having a 4 m span and the cross section skected in Figure 5 , where also the casting direction is indicated by means of arrows. Besides the reference prototype (25 m long) two small prototypes made with SFRC+VEA (one for type A and one for type B) and two small prototypes made with Self Compacting SFRC (one with VEA type A and one with VEA type B) were cast, for a total number of four small scale prototypes, to be compared with the reference real scale one. Prototypes made with ordinary SFRCs have been vibrated 15 minutes, while for SCFRC prototypes vibration was reduced only to one minute. It is by the way significant to remark that even for prototypes made with scc, probably due to the thinwalled thickness and to the quite steeper side slabs, topping-up from the opposite side of the cross section from which fresh concrete were cast together with a short-time vibration were needed. This may callfor a further optimisation of the mix in sight of the structural application at issue or even for some more stringent requirements on the self-compactability of fresh mixes. It may be also called for some dedicated self-compactability tests, besides the ones already accepted in the practice (Khayat, 1999; Ferraris et al., 1999), suitably calibrated on the relevant geometrical features of the structural elements to be cast. 14 cm diameter cores have been extracted from both the wing and the central slabs of the prototypes, according to the scheme in Figure 6 and the content of fibers in each one of them has been evaluated as specified in the previous chapter.
\Il
t
TOPPING-UP
CASTING
i/ '
Figure 5: cross section of t h e p r o t o ~ p e s
_~
............. -. . . . . . . . . .
...
.-
I
,33 34
Figure 6: sclreme ofcores extracted from the prototypes (plari view)
294
I
Liberato FERRARA
The diameter of the cores was chosen as a reasonable compromise between two counteracting needs: on one hand the core size has to be suitably large in order to reliably include the representative volume element of the material and of the structure. On the oher, also in the sight of setting up a "not rmich destnrctive" and cheap test method to be implemented in a statistical quality control procedure for a series production of SFRC precast elements, the core size has to be kept small enough so to induce a moderate damage in the structure which could be furthermore easily repaired. (Meda et al. 2002b). It has to be remarked that cores identified with an even number in the scheme in Figure 6 have been furthermore split into two slices along their thickness, so to have information about the tendency of fibers to segregate along the direction of casting. A first synoptic view of test data is given in table V: the mean values of fiber content, as evaluated from the eighteen cores extracted from each prototype, with the related mean standard deviations, confirm the efficacy of viscosity engancing admixtures, coupled with the self compacting concrete technology, in achieving a more homogeneous distribution of fibers even at the scale of a small roof element prototype. The slightly worst results obtained with self compacting mixes, with respect to ordinary ones simply added with viscosity enhancing admixtures, are adequately compensated by the advantage got with the strong reduction of vibration times.
Prototype
1) reference SFRC
2) ref. SFRC + VEA type A 3) ref. SFRC + VEA type A 4) SCSFRC - VEA type A 5) SCSFRC - VEA type B
(kg/m3)
Fiber content standard deviation (kg/m3)
48.27 46.22 48.73 5 1.95 47.38
8.2 4.1 2.58 4.12 4.84
mean value
variation coeff. 6 17 Yo
9 Yo 5 Yo 8%
~
10 Yo
All the above said statements also holds if the distribution of fiber content in cores extracted from the prototypes are analysed collecting data by rows or columns (Tables VI -VI ). The influence of casting modalities can be clearly got from the lowering values of fiber content when passing from the upper to the lower row of cores in the wing and to the row extracted from the central flat slab. The efficacy of VEA and most of all of the self compactability properties of the mix labelled as 4 and 5 can be clearly appreciated also with reference to this specific problem. The most important effect played by VEA and self compacting concrete techniques stands by the way in the strong reduction of the tendency of fibers to downward segregate. The results of differences in fiber contents obtained from the two slices in which each even-numbered core had been previously cut, gave a strong confirmation to the above said statement, which was, in a sense, the moving idea of all this work (Figure 7). It has been hence attemped to set up some correlation between the results obtained with respect to fiber dispersion within small scale prototypes of structural elements and the ones from four point bending tests on small thickness slabs, which have been either cored from the prototypes and cast at the same type with mixes from the same batches (companion specimens). It has to be remarked that.slabs cored from the prototypes were tested on both sides with respect to the casting direction, in the sense the tests were performed in such a way that the original intradox of the prototype was either the intradox (slabs downward tested) or the extradox (slabs upward tested) of the slabs under test.
The use of viscosity enhancing admixtures to improve the homogeneity offibre distribution ...
295
Table VI: distribution offibre content - ana(iais along longitudinal axis ofprotoppes
I
I
Cores
I
11-21-31 12-22.
Prototype
Mean std. dev.
13-23-33
std. dev.
I
15-25-35 16.26.36 std. dev. 1.57
5?o'
2.82 46.91 2.07
2.37
49.48 3.34 46.86
49.53
3.12 45.42 3.68
Table VI I: disti-ibzitioii offibre content along cr-oss-sectiorialseggmerits ofpi-ototypes 0-
50
E
40
7 0
t
*-
+ +
prototype 1
A
prototype 2
A
prototype 3
+
+
30
Q ) \
u r n
5L k -0
proto4
0
proto 5
& l o * *
2
Q)
y.
+
0
$ a
:0
A
A
a
4
-10
11 13 15
21 23 25
core number 31 33 35
Figure 7: absoltite diflerences i1i.fibr.e content along thickems ofeven-nzmber-ed cores
296
Liberato FERRARA
Slabs were 150 mm wide and 500 mm long, with a thickness equal to 60 mm for companion specimens and to about 75 mm for core ones, and were tested according to the scheme shown in Figure 8, where relevant details of the experimental set-up are also shown. Test results are plotted, in tenns of nominal stress vs. crack opening curves, still in Figure 8. It can be observed that the addition of viscosity enhancing admixtures and the use of self compacting mixes leads to a better uniformity of test results, as far as the behaviour of cores and companion specimens in concerned, and, most of all, to a significantly more homogeneous behaviour between upward and downward tested core slabs. This results is of the utmost importance in sight of the predictable structural applications of the designed enhanced concrete composites. The number of performed test remains by the way quite low and further quantitative confirmation should be needed from a possibly quite large number of test and from statistical interpretation of results.
150mm
CJ
150mm 150mm
1.1.
10
*: '6
A
(MPa)
1~
+
+
ref. SFRC
+
.
+
++
+
I
cores - upward
+
cores - downword
:ACoq(mm7
04 10.1 0.3 0.5
+
companion
A
cores upward
10
CJ
1
companion
A
A
200 mm
COD measurement
10
(MPa)
++
1.2
1.8
+
(MPa)
companion cores - upward
A
~
I
cores -dawnward
5
cores - downward
t +* ++
I
+ +
* - +-
I
+ prototype -I----,
0
ref SFRC + VEA type A
0.1 0.3 0.5
10
CJ
(MPa)
cob (mm)
1.2
+
cores upword
+
cores -downward
A.+
%.
+*
3
---\
A
+*.
-4.
COD (mm)
O*
1.2
0.1 0.3 0.5
10
CJ
(MPa)
-
A
-
11ref SFRC + VEA type B
1.8 companion
+
/
++
++
1.8
+
companion
A
cores - upward
+ +cores - downward
+
+
+
A
COD (mm) 0 0.1 0.3 0.5
1.2
1.8
0.1 0.3 0.5
1.2
Figure 8: geonietr?~-scheine of test specimen and stress-COD ciirves 4pb tessls on small thickness slabs (companion and core specimens)
1.8
The use of viscosity enhancing admi.xtures to improve the homogeneity offibre distribution ...
297
FINAL CHECK ON FULL SCALE PROTOTYPES
In the previous stages of this work it has been - step by step - shown as through a careful calibration of the mix design of concrete, starting from the mere addition of viscosity enhancing admixtures till to the setting up of a full sinergy between self consolidating and fiber reinforced concrete techniques (SCSFRC Self Compacting Steel Fibre Reinforced Concrete), it has been possible to obtain, within small scale prototypes of roof elements, a more homogeneous distribution of fibers than with ordinary SFRC mixes. It has been also shown that the progressive modifications to the composition of the concrete composite, despite some lower values of the cube compressive strength were obtained, lead to a slight but not negligible improveinent of toughness properties of the material, as usually measurable, with a lower dispersion in the results of the material characterization tests. These last statements, despite based on a few number of tests and hence needing of a confirmation based on a larger test number with an eventual statistical interpretation of their results, confirmed the reliable efficacy of the sinergy between self compacting and steel fiber reinforced concrete technologies, mainly in guaranteeing a better cooperation between the concrete matrix and the reinforcement. As a first confirmation of all the above exposed results a check has been made on full scale prototypes of roof elements (25 m span), made with a self compacting steel fiber reinforced concrete containing viscosity enhancing admixture type B (the performances of the two different investigated VEAs were negligibly different; since the research was supported by a company the choice of VEA B was essentially due to marketing reasons). This prototype was hence compared with the analogous reference one, as already done for small scale ones in thc previous chapter. It has been also decided to check the influence of the fiber reinforcement type: beside low carbon hooked-end zinc-coated fibers, 30 mm long and with an aspect ratio equal to 45, as till now used, high-carbon non-coated fibers, 30 mm long and with an aspect ratio equal to 80 were also considered. Fiber dosage was always kept equal to 50 kg/m3. Hence, besides the two above said full scale prototypes, two further ones (one with the reference SFRC mix and the other one with the SCSFRC mix) were cast. All prototypes had the cross section already shown in Figure 5. The number of cores taken from each one of the SCC prototypes in order to evaluate the distribution of fiber content was enlarged according to the scheme shown in Figure 9. Four point bending tests on notched prisms have been also performed for a further check of the properties of self compacting steel fiber reinforced concrete mixes, also taking for the addition of different types of fibers. As far as the homogeneity of fiber reinforcement within the prototype are concerned, the results confirm what has been above said with reference to small scale prototypes. The efficacy of the enhanced mix design in achieving a more homogeneous distribution of fibers can be clearly appreciated from the results summarized in Tables VlII and IX and from results shown in Figure 10 and referring to the fiber distribution along the thickness of the slabs of the prototypes. The above said efficacy appears, by the way,to clearly depend on the adopted type of fibers: the enhancement in the homogeneity of fiber content appear to be proportionally more significant for fibers with a low aspect ratio, this last parameters having, as well known, some negative effects on the workability of the fresh mix. This also appear to be confirmed by results of characterisation tests, summarised in Table X. In the framework of a general improvement of material toughness properties, id est of equivalent post-peak stresses (despite with a lower compressive strength), it can be observed that the improvements are percentually larger for the mix reinforced with fibers type 45/30 than in the other case and that also the positive effects on the experimental scattering are more significant in the first case. This may call for further research work as far as the optimisation of enhanced concrete mixes is concerned with reference to different types of fibrous reinforcement.
298
Liberato FERRARA I 1 12
.
...
.
.
12.1 11.2
. ,= . .... .
,21 .P.
?I
I3 I 4
I 5 I6
3
.= P
24
Prototype
Fibre content
..
+fibre 45/30 . ._. - ... .. .... . . ... . 41 ,a
__
. .
.
.
.
-
10 %
+fibre 45/30
..
6.8 15 % +fibre 80130 d)SCSFRC 54 11 % 5.9 +fibre 80130 1 Figure 9: scheme of cores extracted,fionzfuN Table VIII:,fiberdistribution in cores scale SCCprototypes extracted,fr-ornSCC prototypes SI J?
53 Y
I
I
I I
I I
I
I
1 I
'% 54.49 11% 50.78 15% I56.88! 8% Table VIII: distribution offibre content along longitudinal axis of full-scale proto&ws
53.85
Cores 11-21-31 I 13-23-33 I 15-25-35
I 12.1-12.2-22.1-
Table IX: distribution offibre content along cross-sectional segments offitll-scale prototypes
Table X: results of 4pb tests - mixes offiill scale prototypes
The rise of viscosity enhancing udmixtures to improve the homogeneity offibre distribution ... 50 A
ref SFRC45/30
A
SFSFRC45/30
A
+
ref SFRC 80/30
'8
0
A
A
'
?
299
A
40
A
A
0.
SCSFRC80/30 A '
O A
6
A
n'
0
.zo a
0 L
A
111315
A
212325
corenumber 313335
41
5153
Figure 1 0 difletwices i1i.fibr.e content along thickness ofeven-number-ed cores extracted porn ,fill1 scale prototypes
CONCLUDING REMARKS The present work allowed to check the reliability of a sinergy between self compacting and steel fiber reinforced concrete techniques, in the sight of a possible application to the series prodution of precast prestressed roof elements. The aim was to obtain a concrete composite in which the enhanced toughness properties, which are typical of fiber reinforced concretes and which are responsible of better statical and durability perfonnances of structural elements, are coupled with a better workability of the fresh mix which, on one hand, allow for a reduction of vibration times, and on the other, reduces the sensitivity of the concrete quality to the "human variable". As a matter of factor the enhanced rheological properties of the composite hrthermore allow to achieve a more homogeneous distribution of fibers within a structural element. It is worth remarking that with the enhanced mix design of the concrete it has been possible to sensibly reduce the differences in fiber content along the small thickness of the examined prototypes, thus obtaining an homogenus behaviour of the element, both along its intadox and extradox faces. The obtained better homogeneity of fiber reinforcement, besides guaranteeing a better behaviour of the structural element, also reduces the possibility of defects due to anomalies occurring during casting and vibration operations and thus implies a lower scattering in the experimentally detected behaviour of the prototypes, which is fundamental for a series production. Such a lower scattering has been significantly checked with reference to suitably designed material and structure characterisation tests.
ACKNOWLEDGEMENTS The author wishes to thank Magnetti Larco Building, namely MSc Eng.s Claudio Failla, Sergio Signorini and Francesco Sonzogni, for having supported and promoted this research.
REFERENCES B. BARRAGAN (2002): Failure and toughness of steel fiber reinforced concrete under tension and shear, Doctoral Thesis, UPC, Barcelona, pp. 15I+appendices
3 00 2 3 4
5 6 7 8 9
10 11
12
13 14 15 16 17 I8
19 20 21
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G. BATSON, E. JENKINS, R. SPATNEY ( 1 972): Steel fibers as shear reinforcement in beams, ACI Journal, 69,640-644 .M. Z. BAYASI, P. SOROUSHIAN (1992): Effect of steel fiber reinforcement on fresh mix properties of concrete, ACI Materials Journal, 89, 369-374. M. di PRISCO, C. FAILLA, R. FELICETTI, F. IORIO (2000,a): Precast high strength fibre reinforced roof elements , Studi & Ricerche, 21, 55-94 (in Italian) M. di PRISCO, R. FELICETTI, F. IORlO (2000,b): FRHPS roof elementsa. From constitutive to structural behaviour i n bending, Proc. BEFIB 2000, Lyon, 13-15 September 2000, P. Rossi and G. Chanvillard eds., 253-262 M. di PRISCO, L. FERRARA (2001): HPFRC pre-stressed thin-web elements: some results on shear resistance, Proc. FraMCoS4, Cachan 28 May- I June 2001, R. de Borst et al. eds., Balkema, Rotterdam, 895-902. M. di PRISCO, F. IORIO, G.A. PLIZZARI (2003): HPSFRC prestressed roof elements, in Test and Design Methods for Steel Fibre Reinforced Concrete Background and Experiences -,B. Schniitgen and L. Vandewalle (eds.), Rilem Publications, 161-188 J. EDGINGTON, D.J. HANNANT (1972): Steel fibre reinforced concrete. The effect on fibre orientation of compaction by vibration, Materiaux et Constructions, 5, 41 -44. K.S. ELLIOT, C.H. PEASTON, K. A. PAINE (2002,a-b): Experimental and theorectical investigation of the shear resistance of steel fibre reinforced prestressed concrete X-beams - Part I: experimental work - Part I[: theoretical analysis and comparison with experiments, Materials and Structures, 35, 5 19-535 C. FAILLA, G. TONIOLO, L. FERRARA (2000): Design criteria for structural use of fibre-reinforced concrete in prestressed precast roof elements, BEFIB 2000,253-262. C. FAILLA, G. TONIOLO, L. FERRARA (2002): Structural design of prestressed precast roof elements made with steel fibre reinforced concrete, Proc. BIBM 2002. C. F. FERRARIS, L: BROWER, C. OZYILDIRIM, J. DACZKO (1999): Workability of self-compacting concrete, Symp. Proc. of PCI/FH WA/FIB Int. Symp. on “High Performance Concrete: The Economical Solution for Durable Bridges and Transportation Structures” ,Orlando (FL) September 2527,2000 P: GROTH, D. NEMEGEER (1999): The use of steel fibres in self-compacting concrete, Proc. 1 Int. Rilem Symp. on Self-Compacting Concrete, 497-507. K.H. KHAYAT (1 999): Workability, testing and performance of self-consolidating concrete, ACI Materials Journal, 96, 346-353. K. H. KHAYAT, Y. ROUSSEL (1999): Testing and performance of fiber-reinforced self-consolidating concrete, Proc. 1’‘ Int. Rilem Symp. on Self-Compacting Concrete, 509-52 1. A. MEDA, F. MINELLI, G. PLIZZARI, P. RIVA, C. FAILLA (2002a): Shear Behaviour of precast fibre-reinforced beams, Proc. CTE Conference 2002,453-464 A. MEDA, G. A. PLIZZARI, F. SONZOGNI, T. LAMPERTI (2002b): Fibre distribution in fibre-reinforced structural elements, Proc. CTE Conference 2002, 247256 (in Italian) V. RAMAKRISHNAN, T. BRANDSHAUG, W.V. COYLE, E.K. SCHRADER (1980): A comparative evaluation of concrete reinforced with straight fibers and fibers with deformed ends glued together into bundles, ACI Journal, 77, 3, 135-143 J.P. ROMUALDI, G.B. BATSON (1963): Mechanics of crack arrest in concrete, AASCE Journal of Engineering Mechanics, 89, EM3, 147-168. M. SONEBI, P. J. M. BARTOS (1999): Hardened SCC and its bond with reinforcement, Proc. 1 ’‘ Int. Rilem Symp. on Self-Compacting Concrete, 275-289. M. SONEBI, W. ZHU, J. GIBBS (2001): Bond of reinforcement in self- compacting concrete, Concrete, 7, 26-28
’‘
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H.Marshall, eds. Warsaw, October 13-15 2003 ZTUREK RSIand Woodhead Pirbl., Warsaw 2003
OPTIMISATION OF THE RHEOLOGICAL AND FRACTURE MECHANICAL PROPERTIES OF LIGHTWEIGHT AGGREGATE CONCRETE Viktor MECHTCHERINE, Michael HAIST, Lothar STAERK and Harald S. MUELLER Institute for Concrete Structures and Building Materials, University of Karlsruhe 76 128 Karlsruhe, Germany, e-mail: [email protected]
ABSTRACT In this paper the basic procedure for the development of self-compacting lightweight concrete (SCLC) is presented. By using a rheological optimization approach SCLC with different unit weights could be developed. Further, the experiments carried out on hardened SCLC showed that its mechanical and fracture mechanical properties are comparable to those of LWAC with equal compressive strength. With regard to the brittle failure of LWAC and SCLC the effect of the addition of different amounts of steel, polypropylene and glass fibres on the rheological properties of fresh SCLC as well as on the properties of hardened concrete was investigated. Furthermore, a series of deformation controlled direct tension tests on notched prisms was performed in order to investigate the fracture mechanical behaviour of the developed concretes with and without fibre reinforcement. Keywords: self-compacting concrete, lightweight aggregates, rheology of fresh concrete, fibre reinforcement, fracture mechanics
INTRODUCTION Structural lightweight aggregate concrete (LWAC) possesses a number of favourable mechanical and physical properties such as high compressive strength in combination with a low unit weight and good thermal insulation capabilities. For this reason such a material is especially interesting in the field of renovation and retrofitting of existing structures. However, these advantages are opposed by the fact that the production, placement and compaction of LWAC are afflicted with various problems. Furthermore, at the hardened state, LWAC exhibits a high brittleness and, consequently, a pronounced tendency to the formation of cracks, e.g. due to high moisture or temperature gradients over the cross-section of the concrete structure. The problems concerning the properties of fresh concrete can be attributed to the fact that structural lightweight concrete is normally produced using porous aggregates. Unless stored under dry conditions these aggregates tend to absorb up to 40 mass% of water. This circumstance has to be accounted for in the mix design, for example by pre-wetting the dry aggregates. Used for the production of LWAC, such saturated aggregates reduce the risk of a premature stiffening of the mixture, which may lead to poor compaction (see Figure 1, left).
302
Victor MECHTECHERINE, Michael HAIST. Lothar STAERK and Harald S.MULLER
However, when exposed to accelerations due to the compaction process, the saturated aggregates tend to release parts of the absorbed water resulting in a sudden increase in the water content of the matrix. Strong variations of the effective water-cement ratio, a pronounced softening of the consistency or even segregation (“bleeding”) of the concrete are the consequences (see Figure 1, right).
Figure 1. Typical damages observed on structures made of lightweight aggregate concrete due to insufficient fresh concrete properties and improper concrete placement: poor compaction and leaking formwork (left) and “bleeding” of concrete due to overcompaction (right) Against this background it seems to be possible to strongly improve the quality of LWAC by using self-compacting lightweight concrete and therefore omitting the compaction process. This paper reports on the development and optimization of mixes for SCLC as well as on its rheological and mechanical properties. OPTIMISATION OF THE RHEOLOGICAL PROPERTIES I
Basic approach The principal demands concerning the rheological properties of SCC, like a high flowability, safe de-airing and sufficient cohesion of the batch as well as a high resistance against segregation (see [ 11) also apply to self-compacting lightweight concrete. However, with regard to the development of suitable mixes for SCLC, two major specific phenomena have to be considered: (1) lightweight aggregates absorb parts of the mixing water, which can lead to a premature stiffening of SCLC as well as to the total loss of self-compactability, (2) lightweight aggregates show a pronounced tendency to segregate (attributed to buoyancy). The first phenomenon can be countered by simply pre-wetting the porous aggregates with a defined amount of water. However, in order to inhibit the segregation of the concrete it is necessary to precisely adjust the rheological properties of the fines paste and the mortar, as these are the key to the successhl production of SCLC. For this purpose it is helpful to consider the forces acting on an aggregate grain dispersed in a surrounding liquid, i.e. mortar (see Figure 2). According to this simplified view, segregation, i.e. the reciprocal movement of the aggregate grain and the surrounding liquid, is only possible if the gravitational force G and the outer friction JrdO are exceeded by the buoy-
ancy force B. Therefore, in order to prevent segregation the optimisation of the rheological
Optimisation of the rheological and fracture mechanical properties of lightweight aggregate ...
303
properties of the mortar matrix should be aimed at maximising the outer friction acting upon the grain. However, the de-airing process, which is essential for the self-compaction, underlies the same basic mechanisms, though it deteriorates with increasing friction. It is therefore necessary to find an optimum between these two opposed requirements: a high resistance against segregation and a sufficient de-airing of concrete.
B = G + jr(y).dO 0
Figure 2. Requirements on the rheological properties of SCLC after placing in a formwork Against this background a series of experiments on lightweight pastes, mortars and concretes was carried out. The rheological properties of these materials, the viscosity p and the shear resistance to according to the Bingham model, were determined using a rotational rheometer [2]. By optimising the viscosity and the shear resistance of fines paste and mortar the resistance of SCLC against segregation could be increased significantly while ensuring an excellent workability and sufficient self-compacting properties of the lightweight concrete [2,3]. Composition and properties of fresh concrete Based on the results of the tests on paste and mortar, numerous different concrete mixes were developed by combining the optimized mortars with different kinds and amounts of coarse lightweight coarse aggregates [3,4]. The compositions of two representative mixes for SCLC are given in Table 1. Further, a representative LWAC mixture was investigated for reasons of comparison.
Table 1. Composition of the investigated lightweight aggregate concretes
cement fly-ash mixing water superplasticizer viscosity agent expanded clay sand 014 natural sand 012 expanded clay 418 unit weight of fresh concrete
[kg/m3] [kg/m3] [kg/m3] [kg/m3] [kg/m3] [kg/m31 [kg/m’] [kg/m3] [kg/m3]
SCLC 1 SCLC 2 LWAC 316 318 320 208 208 105 163 171 215 3.1 5.3 3.2 0.47 0.95 329 340 618 425 354 424 1770 1450 1460
304
Victor MECHTECHENNE, Michael HAIST, Lothar STAERK and Harald S.MULLER
In all mixes along with Portland-composite cement also fly-ash was used as binding agent. The use of a great amount of fly-ash leads to an increase in the flowability of SCLC while reducing the mortar density, due to its low unit weight (pra = 2.2 g/cm3). As fine aggregate natural quartzite sand (unit weight of solid particles 2.60 g/cm3, fines content 0.6 vol.%) was chosen for the production of SCLC 1, while for SCLC 2 and LWAC expended clay sand (unit weight of solid particles 1.3 g/cm3, fines content 20 vol.%) was used. Expanded clay with particle sizes ranging between 4 and 8 mm and a unit weight of solid particles of 1.1 g/cm3 was applied as coarse aggregate. All initial weights of the components given in Table 1 refer to oven-dry masses. The coarse aggregates were slightly pre-wetted with 10 mass% of the initial weight in the case of SCLC 1 and SCLC 2, while for the LWAC the pre-wetting amounted to 3 mass%. For the fine aggregates again 10 mass% of water for the pre-wetting were needed for expanded clay sand, whereas the natural sand was not pre-wetted. In order to achieve a good self-compactability 3.1 or 5.3 kg/m3 of a polycarboxilat-ether type superplasticizer and 0.47 or 0.95 kg/m3 viscosity agent were added to SCLC 1 and SCLC 2, respectively. In the case of the LWAC a sodium naphthalene sulfonate type superplasticizer was used. The unit weight of fresh concrete was 1770 kg/m3, 1450 kg/m3 and 1460 kg/m3 for SCLC, SCLC 2 and LWAC, respectively. Table 2 shows the most important results of the experiments on fresh concrete. The developed mixes provided slump flow values between 67 and 72 cm and thus correspond to the usual values for SCC with normal-weight aggregates. In contrast to earlier investigations [2], it was possible to significantly reduce the spreading time t5o and the v-funnel flow time below 10 s. Besides an excellent flowability the self-compacting concretes SCLC 1 and SCLC 2 showed a high resistance against segregation also during the placing by pumping. The results of corresponding laboratory and large scale experiments are presented in [ 5 ] . Table 2. Properties of the fresh self-compacting lightweight aggregate concretes slump flow spreading time t501’ v-funnel flow time [cml Is1 [SI 5 7 SCLC 1 67 SCLC 2 72 8 10 1) time for slump flow to reach a diameter of 50 cm concrete
The properties of the hardened concretes are given in Table 4. They will be presented and didcussed in the next chapter. OPTIMISATION OF FRACTURE MECHANICAL PROPERTIES
The development of self-compacting lightweight aggregate concrete (SCLC) leads to a highperformance building material, which however shows a rather brittle fracture behaviour, typical for all lightweight aggregate concretes. In order to increase the ductility of such concretes a fibre reinforcement may be applied. Within this research project, the effect of the addition of different amounts of steel, polypropylene and glass fibres on the rheological properties of fresh SCLC as well as on the properties of hardened SCLC was investigated.
Optirnisation of the rheological and fracture mechanical properties of lightweight aggregate ...
305
Properties of fresh SCLC with fibre reinforcement For this investigation, SCLC 2 (see Table 1) was chosen as a reference mix, on which the influence of the addition of different types and amounts of fibres was studied. Therefore, the properties of fresh concrete, i.e. the flowing behaviour of mixes containing fibres, were measured using the slump-flow test. Table 4 gives the properties of the fibres used in these experiments. Table 3. Properties of the fibres used in the experiments Properties material of fibres
unit weight wcm31 7.80 0.91 2.70
steel, drawn wire polypropylene glass, alkali-resistant
modulus of elasticity [MPaI 210 000 13 000 72 000
length [mml 35 12 12
Figure 4 shows the effect of the fibre content for various types of fibres on the slumpflow behaviour of the reference mix (concrete SCLC 2, see Table. 1). According to these results, even relatively small additions of polypropylene or glass fibres of up to 0.2 vol.% of the concrete volume cause a reduction of the slump flow of up to 34 %, whereas the effect of the addition of steel-fibres is much less pronounced. This observation was traced back to the fact, that due to their fineness, both polypropylene and glass fibres possess - in comparison to steel fibres - a much larger specific surface, which has to be bedewed by the mixing water. Further, a too high dosage of fibres results in an accumulation of fibres and coarse aggregates in the centre of the slump flow (comparable to hedgehog-like structures) and a very uneven slump flow. This is especially true for mixtures containing steel fibres, which were significantly longer and stiffer than the other fibres used.
80
-s 70 Y
g
60
G=
g 50 40
; 1
+SCLC 2 with steel fibres
I
1 -0-SCLC2withPPfibres
I
I
I
--&-SCLC 2 with glass fibres
30 I 0.00
0.20
0.40
I
I
0.60
0.80
1.oo
fibre content [vol.%]
Figure 4. Effect of the type and content of fibres on the slump flow of SCLC 2 On the basis of the results of the experiments on fresh concrete it can be concluded, that the maximum content of fibres, which can be added to SCLC without affecting its flowability and self-compactability, strongly depends on the type of fibres. This “limit content” is approx.
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Victor MECHTECHERINE, Michael HAIST, Lothar STAERK and Harald S.MULLER
0.5 vol.% for steel fibres and approx. 0.1 vol.% for polypropylene or glass fibres, respectively. Properties of hardened concretes with and without fibre reinforcement For the experiments on hardened concrete SCLC 2 without reinforcement was again chosen as a reference. Based on its composition three further concretes containing the limit contents (compare previous section) of steel, polypropylene and glass fibres, respectively, were produced and tested. In order to clarify the effect of the self-compactability on the mechanical and fracture mechanical properties of lightweight aggregate concrete also the concrete LWAC was tested, both without fibres and with 0.5 vol?? of steel fibres. Furthermore, investigations on the self-compacting concrete with quartzite sand SCLC 1 without fibres were carried out. The compressive strength was determined on cubes with a length of 150 mm, which were demolded one day after concreting, stored in a constant climate at 20°C and 98% r.h. up to the age of 7 days and at 20°C and 65% r.h. up to the age of testing (28 days). Table 4 gives the average values of the compressive strength fc,& and the modulus of elasticity Eo for the investigated concretes. The self-compacting concretes provided higher values of the compressive strength. This holds true especially for the concrete SCLC 1, which was produced using natural quartzite sand. The addition of steel fibres showed practically no effect on this material property in the case of the LWAC. For the self-compacting concrete SCLC 2 however a slight increase of the fc,cuh-valuescould be observed as a result of the fibre reinforcement, both with polypropylene or steel fibres. One reason for this might be the decrease of the effective waterhinder ration due to the “binding” of some part of the mixing water on the surfaces of fibres. On the other hand the fibres seem to hinder the propagation of the cracks at this stage already, which leads to a higher load-carrying capacity of the concrete. In the case of the LWAC, the modulus of elasticity Eo did not change significantly due to the addition of fibres (see Table 4). For the concrete SCLC 2 nearly the same Eo-values were measured as for the LWAC. In the case of SCLC 2 the addition of fibres leaded to a slight but clear increase of the modulus of elasticity, unrespectable of the type of fibres. The highest Eovalues equal to 24.3 GPa were obtained for SCLC 1. The measured Eo-values correspond well to the modulus of elasticity as estimated according to the German building code DIN 1045-1 [6], on the basis of the measured compressive strength of SCLC. Table 4. Results of the mechanical and fracture mechanical experiments Compresive Modulus of strength fc,cuh elasticity Eo WaI [GW LWAC without fibres 33.2 15.7
Type of concrete
Net tensile strength fm WaI 1.55
Fracture energy GF m/m1 31
LWAC with 0.5 vol.% of steel fibres SCLC 1 without fibres
32.8
14.8
1.50
1700
5 1.9
24.3
2.80
51
SCLC 2 without fibres
40.9
15.5
1.70
37
SCLC 2 with 0.1 vol.% of polypropylene fibres
43.7
17.4
1.85
42
SCLC 2 with 0.5 vol.% of steel fibres
47.2
17.1
1.85
2000
Optimisation of the rheological and fracture mechanical properties of lightweight aggregate ...
307
In order to investigate the fracture mechanical behaviour of the concretes deformation controlled direct tension tests were performed on notched prisms. Figure 5 shows the used test set-up. The specimens had a length of 250 mm and an effective cross-section of 60x 100 mmz. All specimens were cast horizontally in metal forms. After demoulding, the specimens were wrapped in a thin plastic sheet in order to protect the concrete against desiccation. All specimens were tested at a concrete age of 28 days. The tension tests were performed with non-rotatable boundaries. For this purpose stiff metal adapters were glued to the specimens. Finally, the metal adapters were firmly connected with the bearing platens of the testing machine. In the tests, the deformation rate was controlled by means of the average signal of two LVDTs with a gauge length of 25 mm, which were placed on the notch tips (LVDTs 1 and 6 in Figure 5). Further LVDTs with a gauge length of 25 mm and 50 mm, respectively were placed on the notch tips, notch mouth and in the middle of the crosssection on both sides of the specimen in order to measure local deformations. Because of the localized cracking due to the notches and the reduction of the gauge length for the control of deformation rate to 25 mm the descending branch of the 0-6 relation could be determined up to nearly complete separation of the specimens into two parts.
-
-
-
100 0
Figure 5. Set-up of the direct tension tests on concrete prisms (left) and schematic view of the positioning of the LVDTs (right, geometrical data in [mm])
308
Victor ivfECHTECHERINE. Michael HAIST, Lothar STAERK and Harald S.MULLER
The tensile tests were performed with a deformation rate of 6 = 5.10' m d s . For each investigated parameter at least three specimens were tested. Further details concerning the test set-up and the carrying out of the experiments may be found in [7]. The mean curves for the stressdeformation relations obtained from the direct tension tests for several of the investigated concretes are given in Figure 6. Special focus was hereby directed at the differences of the curve shape after exceeding the peak stress. The curves for the concretes without fibres - SCLC 1, SCLC 2 and LWAC - do not differ significantly (therefore, for the reason of clearness only the mean curve for SCLC 2 is shown in Figure 6), besides some differences mainly due to the variation of the net tensile strength (see the f,-values in Table 5).
0.00
0.05
0.10
0.15
0.20
0.25
deformation 6 [mm] Figure 6. Mean stress-deformation relations obtained from the direct tension tests on the concrete prisms with and without fibre reinforcement The addition of the polypropylene fibres (0.1 vol.%) to SCLC 2 has only minor influence on the softening behaviour of this concrete: The mean curve for SCLC 2 with fibre reinforcement runs only slightly above the corresponding curve for this concrete without fibres at deformations (or crack openings) of approx. 0.03 mm and greater (see Figure 6). Nearly the same results were obtained also for SCLC 2 with glass fibres (not shown here). However, in the case of concretes with steel fibre reinforcement, a very pronounced increase of the ductility for both the LWAC and SCLC 2 could be observed. The stress-deformation relation for SCLC 2 runs clearly above that curve for the LWAC up to a deformation of approx. 0.8 mm (not shown in Figure 6). Beginning at this deformation the curves for both concretes are nearly identical (at least up to an entire deformation of 1.O mm, at which the experiments were finished, because of the limited capacity of the LVDTs).
Optirnisatiori of the rlieological and fracture mechanical properties of lightweight aggregate ...
309
The observed higher ductility of self-compacting concrete SCLC 2 containing the same amount of fibres as LWAC can be explained by the fact that due to a very high flowability of SCLC 2 a more pronounced orientation of the fibres during the casting process of the forms placed horizontally is achieved. Further, supposedly a better bond between the binder matrix and fibres develops because of a denser structure of the binder lime and a better coating of fibres with the lime in the case of the self-compacting concrete. Table 4 gives the values of the net tensile strength ftn and the fracture energy GF evaluated on the basis of the stress-deformation relations. For both SCLC 2 and LWAC, practically no effect of fibres on the fm-values could be observed. The effect of the composition of nonreinforced concrete is however evident. Self-compacting concrete SCLC 2 provided a higher net tensile strength than the ordinary LWAC. This can be traced back to a lower water/binder ratio of SCLC 2. The highest average ftn-value equal to 2.8 MPa was obtained for SCLC 1, which possesses the mortar matrix with natural quartzite sand. The fracture energy GF is defined as the energy per unit area needed for the separation of a specimen into two parts. This value corresponds to the area under the complete stressdeformation diagram (for this reason an extrapolation of the measured curves was carried out for deformations greater than 1.0 mm in the case of concretes with steel fibres). The fracture energy of the self-compacting concrete SCLC 2 is slightly higher than the corresponding value of the LWAC, but slightly lower than the fracture energy of SCLC 1 (SCLC with quartzite sand). The addition of the polypropylene fibres (0.1 vol.%) to the concrete SCLC 2 leads only to a minor increase of the GF-value from 37 N/m (without fibres) to 42 N/m (with fibres). The addition of steel fibres has a much more pronounced effect on the values of the fracture energy. For the LWAC with 0.5 vol.% of steel fibres an average GF-value equal to 1700 N/m was measured. The self-compacting concrete SCLC 2 with the same fibre content provided the fracture energy of 2000 N/m. CONCLUSIONS
In this study, self-compacting lightweight aggregate concretes were developed and optimized by investigating the rheological behaviour of paste, mortar and subsequently concrete. This approach enables to obtain concretes with the desired properties efficiently and rapidly. Further, the effect of the addition of fibres on the properties of the fresh and hardened SCLC was studied. The workability of SCLC remains sufficient only up to some defined percentage of fibres. This limiting content depends strongly on the type of fibres. Considering the mechanical properties of SCLC, the addition of steel fibres causes a great increase of the fracture energy, whereas with regard to the compressive strength and the net tensile strength of these concretes only a minor improvement could be achieved. The fracture mechanical properties of self-compacting lightweight aggregate concrete are superior to those of ordinary LWAC for the testing conditions used in these investigations. REFERENCES 1. Okamura, H., Ozawa, K., Ouchi, M., Self-compacting concrete. Structural Concrete, Vol. 1, NO. 1,2000, pp 3-17 2. Mueller, H. S., Mechtcherine, V., Haist, M., Development of self-compacting lightweight aggregate concrete. Proceedings of the Second International Symposium on Self-Compacting Concrete, K. Ozawa and M. Ouchi eds., COMS Engineering Corporation, Kochi, Japan, 2001, pp 737-742
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Victor MECHTECHERINE, Michael HAIST, Lothar STAERK and Harald S.MULLER
3. Haist, M., Mechtcherine, V., Mueller, H. S., High performance self-compacting lightweight aggregate concrete with and without fibre-reinforcement. 6* Int. Symposium on Utilisation of High StrengthlHigh Performance Concrete, Conference proceedings, Leipzig, Germany, 2002 4. Mechtcherine, V., Haist, M., Hewener, A., Mueller, H. S., Self-compacting lightweigbt concrete - a new high-performance building material. The First fib Congress, Conference proceedings, Osaka, Japan, 2002 5. Haist, v., Mechtcherine, V., Beitzel, H., Mueller, H. S., Retrofitting of building structures using puntpable self-compacting lightweight concrete. Proceeding of the 3'd International Symposium on Self-compacting Concrete, Iceland, 2003 (accepted for publication) 6. DIN 1045-1, Structures of Concrete, Reinforced Concrete and Pre-stressed Concrete, Part 1: Design Rules (in German). Berlin, Beuth Verlag, Germany, 2001 7. Mechtcherine, V., Fracture Mechanical and Fractological Investigations on the Formation and Propagation of Cracks in Concrete (in German). Institute of Concrete Structures and Building Materials, University of Karlsruhe, Vol. 40,2000
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Wursaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
DESIGN AND TESTING OF SELF-CO IPACTING SIFCO i PRODUCED WITH LOW STRENGTH SLURRY Lucie Svermova, Mohammed Sonebi, Peter J.M. Bartos Advanced Concrete and Masonry Centre University of Paisley Paisley, PA1 2BE, UK, e-mail: [email protected]
ABSTRACT Slurry Infiltrated Fibre Concrete (SIFCON) is produced by a process in which fibres are put into an empty mould, after which the fibre mass is infiltrated by a cement slurry. Generally, the infiltration of the slurry into the layer of fibres is carried out under intensive vibration. Recent research has investigated the development of slurries which do not require to be vibrated when SIFCON is produced. Samples of self-compacting SIFCON were produced and tested for flexural and compressive strength. Three different orientations of fibres in testing samples were obtained. A three-point bending test with displacement control system was used for testing the beams. Basically, the results showed higher flexural strength and energy absorption compared with plain cement slurry. The anisotropy of SIFCON was shown from results of samples which had different orientation of fibres. Keywords Compressive strength, flexural strength. self-compacting SIFCON
INTRODUCTION New developments in steel fibre-reinforced cement composites have appeared during the last forty years. Slurry Infiltrated Fibre Concrete (SIFCON) can be regarded as a special type of steel fibre-reinforced cement composite. Normally, fibre reinforced concrete contains I-3% fibres by volume, while SIFCON contains between 4-25% fibres [I]. The volume of fibres is influenced by fibre type and manner of fibre placing [2]. The first introduction of cement composites with a high content of fibres infiltrated with Portland cement-based materials was made by Haynes in 1Y6X 131. It was first to use the principle of adding fibres into a mould first and then infiltrating the fibre mass by a cement slurry. This approach introduced the possibility 0 1 producing concrete with high volumes c,f' steel fibres and later this kind of material becam: known as SIFCON. Naanian et el proposed the use of SIFCON for 101 . t b in seismic resistant reinfoi,ced concrete frames [4]. SIFCON would be used only in stnall parts of the frames. These parts would be designed to bc affected during seismic 1oadi:ig and form 'plastic hinges', which would ,ibsorb the frachire energy and protect the constructions against coilape. '%r: challenge
3 12
Lucie SVERMOVA. Mohammed SONEBI and Peter J.M. BARTOS
is to ensure that the frame would crack in the areas where moderate/low strength SIFCON has been placed. When hardened, SIFCON exhibits high fractional energy absorption and is capable of transferring load even after considerable deformation. It can also be repaired. Previously, the infiltration of fibres could only be achieved with the assistance of intensive vibration. Bartos and Marrs [ 5 ] came up with the idea of producing SIFCON without vibration. More research on self-compacting SIFCON was carried out, particularly concerning the behaviour of fresh cement slurries containing limestone powder [6,7]. This research brought about the possibility of designing ‘low strength slurry’ for the production of self-compacting SIFCON, which should guarantee the formation of ‘plastic hinges’ in reinforced concrete frames during seismic loading. The aim of this research was the investigation of flexural and compressive strength of self-compacting SIFCON produced with ‘low strength slurry’ and different orientations of fibres, which were obtained by the shape of the moulds. The flexural strength was tested on cut and directly produced beams by a three-point bending test with displacement control. The compressive strength was tested on cut and uncut samples. Cube and beam samples from plain cement slurry were produced and the results of SIFCON samples and plain sluny samples were compared. MATERIALS Slurries were produced from Ordinary Portland cement (class 42.5 N), limestone powder, superplasticiser, viscosity agent, fine sand and tap water. The grading of limestone powder produced from carboniferous limestone of a very high purity was 98% < 45 pn and 25% < 5 pm, and limestone powder was finer than cement. The relative density of the limestone powder was 2.65. Fine sand with a maximal grain size of 0.6 mm was used. A modified polycarboxylate superplasticiser, containing 30% solids by mass and 1.1 1 specific gravity, was used. Powdered microbial polysaccharide welan gum was used as a viscosity agent. Dramix RL-45/35-BN steel hooked fibres with length 35 mm and aspect ratio (1engWdiameter) 48 were used to assess the penetrability of cement slurry measured by the Jfibre penetration test which was introduced in references [6,7] and was used for verification of produced mixes. All samples of SIFCON which were tested for flexural and compressive strength in this study were produced from low carbon steel hooked fibres with a tensile strength 950 MPa Dramix RL-45/50-BN, are 50 mm in length and have an aspect ratio of 48. SHAPE OF SAMPLES Previous researches underlined the anisotropy of SIFCON which is caused by the orientation of fibres in samples [%lo]. The orientation of fibres was influenced by the shape of the mould and turning of the samples after production. The test samples had been produced either in the beam position mould (100 mm high) or the column position mould (350 mm high), which caused different orientations of fibres to the plane of rupture during testing of samples. The beams had dimensions of 100 mm x 100 mm x 350 mm. The other approach for the production of samples was to cut beams and cubes from the block of SIFCON. The reason for this approach was the elimination of the wall effect of fibres in the sides of mould. Three 510 mm x 410 mm x 190 mm prism blocks of SIFCON were produced. One prism was 410 mm high and the other two had a height of 190 mm to obtain the required orientation of fibre. Three beams with dimensions of 100 mm x 100 mm x 350 mm and three cubes 100 mm long were sawed from each block (Figure 1).
Design and testing of self-compacting SIFCONproduced with low strength slurry
313
Straight cast cubes of SIFCON 100 mm long were produced for verification of the difference between straight cast and sawed samples.
<:
<
:: : : : : : :> 510
>
MIX PROPORTIONS
The proportional design of slurry was selected following the previous results obtained from a fractional factorial statistical design model for five independent variables (waterhinder ratio (WE%),proportion of limestone powder (LSP) and sand, and dosage of superplasticiser (SP) and viscosity agent (VA)) [6,7]. The statistical model was valid for mixes with 10-50% limestone powder as replacement of cement, 0.02-0.06% viscosity agent by mass of cement, 0.6-1.2% superplasticiser and 50-150% sand (% mass of binder) and 0.42-0.45 W/B. The selected mix in this study was made with 0.44 W/B (where binder is the content of cement and limestone powder), and 45% of LSP. The dosages of SP and VA were 0.70% and 0.05%, respectively. Finally, the proportion of sand was 50%. The volumes of fibres in the test samples were calculated from the weight of fibres placed into the moulds. The percentage volume of fibres varied from 9.2% to 10.8%0, depending on the shape of mould. The least volume of fibres (9.2%) was obtained when fibres were randomly poured by hand into the column position mould. The samples produced in the beam position moulds had fibre volume of 9.4%. The cubes had fibre volume of 9.7%. Finally, both types of SIFCON blocks had 10.8% volume of fibres. The different percentages of fibres in the different shapes of mould underline the wall effect of fibres at the sides of the moulds, which decreased the volume of fibres in the samples. This claim is apparent from the volume of fibres in the column shape mould, where the volume of fibres was 1.17 times smaller than the samples which were produced from much larger blocks of SIFCON. PRODUCTION OF TEST SPECIMENS
Three blocks of SIFCON, three column samples, six beam samples and six cubes were produced for testing the flexure strength and compressive strength of SIFCON. Three beam and three cube control samples without fibres were produced and their results were compared with the results of SIFCON samples.
3 14
;ucici SVERMOVA. Mohammed SONEBI and Peter J.M. BARTOS
Firstly. the fibres were placed into the mould by hand to make sure that the fibres occupied the entire moulds. The required volume of slurries was calculated and produced. Two 60-litre mixes and one 75-litre mix were prepared for the production of all samples. The following approach was used for production of the slurry mixes: firstly, the dry mix of cement, limestone powder and viscosity agent powder were mixed together. Then, a mix of water and superplasticiser was preparcd in the mixer. The dry mix of cement, limestone powder and viscosity agent was sieved into the mix of water and superplasticiser during mixing. All components were mixed together for 15 minutes. Mixing time was measured from the start of the addition of the dry mix into the mixer. This approach was found useful for producing a homogenous mix of cement slurry which was able to infiltrate the mass of fibres prepared in the moulds. Slurry was cast into the moulds through a sieve to control the speed of pouring and thus prevent the slurry filling the top of the moulds and trapping air among the fibres at bottom. The second reason for sieving the slurry into the moulds was to ensure thorough mixing of all components. The samples were demoulded after two days and left in the same conditions in the laboratory, because the blocks of SIFCON were too big and heavy to be put into a water bath. The blocks were sawed during the four weeks after casting to produce 3 beam and 3 cube test samples. TESTING OF SAMPLES All samples were tested at 28 days. A three-point bending test with displacement control was chosen to obtain ‘post-peak’ behaviour. The speed of loading was 1 mm per minute. The span of roll supports was 300 mm. A 20 mm deep notch was sawed in the middle of each beam sample. Three variables of fibre orientation had been obtained and for each variable three samples were produced. Two different fibre orientations to the plane of rupture were obtained from the moulds in beam position. The first types of beam samples were tested in the classical position for steel fibre reinforced concrete, i.e. the samples were turned in such a way that the casting surface was perpendicular to the notch and loading force (Figure 2a). The second type of samples had parallel orientation of casting surface, notch on beams and loading force (Figure 2b). The beams which were produced in the column shape mould were the third type of test samples (Figure 2c). The beams cut from the blocks of SIFCON were divided into the same three sample types from the point of view of orientation of casting surface and load cell. The only difference was the cutting away of the parts with wall effect at the sides of moulds. The compressive strength was tested with a constant increase of load. The straight cast cubes were tested with two different orientations of fibres. Firstly, the casting surface was turned perpendicular to the loading cells (Figure 3a) and secondly, the load was applied on the casting surface (Figure 3b) The cubes cut from the SIFCON blocks had the same position of casting surface to the loading cells as the straight cast cubes.
315
Design and testing of self-compacting SIFCON produced with low strength d u r n ,
Load cell
25
150
Casting surface
150
Load cell
I00
25
25
w
150
150
25
100
I r
Load cell
25
150
Casting surface
Casting surface
150
25
I00
I
Figure 2: Placing and dimensions (in mm) of beam samples during test (a)
(b) Load cell
Load cell
w Figure 3: Placing and dimensions (in mm) of cube samples during test
TESTS RESULTS AND DISCUSSION Flexural strength The flexural strength f, corresponding to the maximal obtained load was calculated using the following expression:
where F,, = is equal to the highest value of the load (N/mni'), L = span ot the specimen (mm),
3 16
Lucie SVERMOVA, Mohammed SONEBI and Peter J.M. BARTOS
b = width of the specimen (mm), h = distance between tip of the notch and top of cross section (mm). The results of the flexural behaviour are presented in Table 1. Figures 4 and 5 represent the typical displacement vs. load behaviour of the individual types of test beam samples. Each time, three samples were tested and from these samples one was chosen and illustrated in these figures. The values of maximal load, average maximal load with coefficient of variation, flexural strength fl and average flexural strength with coefficient of variation for individual types of samples are shown in Table 1. Volume of fibres
Sample
(“/.I
load (kN)
1
Plain slurry 2
0
3 1
a
2 3
9.4
1
Cast
b
2 3
9.4
1
c
2 3
9.2
1
a Cut
b
2 3
10.8 10.8
2.2 2.3
38.2 40.7 38.8 25.9 26.6 32.0 12’0 10.2 11.6
33.5 32.2 40.1 31.6 31.0
Average Flexural Average Energy Average maximal strength flexural energy absorption load strength absorption ( k ~ ) ( ~ / m m, * m/mm2) ). (N.m) W.m) 0.5 2.1 la4 1.6 o.6 0.7 (9.8 %)
39.2 (3.3 %)
28*o 28.0 25.2
(9.8 %)
0.9
(31.2 %)
27.1
405*8 440.2 434.2
426.7
(6.0%)
(13.9%)
11.3
17” 17.3 21.7 8.3 7.8
(8.4%)
8.0
35.3
24‘4 26.4 28.6 20.5 21.1 4.8 7.0
28‘2 (11.9%)
(12%)
31.3 (1.4%)
1 7.7 2 10.8 9.2 3 7.2 (16.6%) (Bracket values): coefficient of variation c
1.6 1.7
5.0
18.7
8.0
270’6 287.4 333.7
(4.3 %)
297.2 (11.0%)
125.7
(3.1 %)
130.3 131.3
(7.0%)
26.5
367’7 339.8
389.0
(7.9%)
(16.1 %)
(2.0%)
459.5 355.2 345.9
77.6
(21.7%)
72’6 110.6 49.7
20.8
350.6 (1.9%)
(39.6%)
Table 1: Flexural strength of SIFCON Most types of samples had a coefficient of variation less than lo%, which is related to good correlation between the test results of individual test samples. Only the samples which were straight cast and with the casting surface parallel to the load cell had a coefficient of variation for flexural strength equal to 13.9%. The cut samples from the 410 m m high block had the highest coeficient of variation for flexural strength, which was 21.7%. The highest load was transferred by samples which were cast straight to the mould and had the casting surface perpendicular to the load cell. The 39.2kN average maximal load was measured and the calculated flexural strength was equal to 27.1 N/mm2. Similar average
317
Design and testing of self-compacting SIFCONproduced with low strengih slurv
flexural strength of 26.5 N / m 2 was calculated from the samples with the same orientation of casting surface to the load cell, but these samples were cut from a SIFCON block and their average maximal load was 35.3 kN. These samples had the most suitable orientation of fibres to the plane of rupture to transfer increasing load. 3 1.5 kN average maximal load was measured on samples with parallel orientation of the casting surface and the load cell which were cut from a SIFCON block and the average flexural strength was equal to 20.8 Nlmm’. The cast samples in the same position had 28.2 kN average maxima1 load and 18.7 N/mm2 average flexural strength. The volume of fibres turned to the plane of rupture in a suitable direction decreased, which caused decreased flexural strength compared with the previous example. The lowest maximal flexural strength was obtained by the samples which were cast in the column position mould and in the prism block with a height of 410 mm. The cut beam samples produced from these shaped moulds were able to transfer maximal load of 7.7 kN, compared with the 11.3 kN by straight cast samples. Maximal flexural strength was equal to 5.6 N/mm’ for cut beams and 8.0 N/mm’ for beams cast straight into the moulds. The average maximal load and the related flexural strength of the plain cement slurry beams were 2.1 kN and 1.6 N/mm’, respectively. The test results were influenced by volume of fibres in the samples and method of production, i.e. whether they were straight cast or cut from the blocks. The samples which were cut from the blocks did not have the wall effect of fibres at the sides of the mould and the volume of fibres in these samples was higher than in the samples cast straight into the moulds. On the other hand, the fibres on the sides of the cut samples were shorter after cutting and were able to transfer a lower load, mainly during the bending test, because the shorter fibres are easily pulled out from the cement slurry and are not able to transfer high load.
30
1
beam(1a)
ccut
10
0 0
5
10
15
20
25
30
35
Displacement (m)
Figure 4:Typical load-displacement curves for beams cut from blocks of SIFCON
3 18
Lucie SVERMOVA. Mohamtired SONEBI and Peter J.M. BARTOS
...
30
.
-
10
-.
- .
..
-
-
plan slurry (2) cast beam(3c) -V
- ’.._. *,
0 0
5
10
1s
20
25
30
35
Displacement (m)
Figure 5 : Typical load-displacement curves for straight cast beams
Energy absorption The ‘post-peak’ part of the load-displacement curves of SIFCON decrease gradually compared with the example of plain cement slurry. This behaviour was recorded by all SIFCON samples and indicated high ductility and high capacity for energy absorption. This typical behaviour of SIFCON makes it a suitable material to use in seismic resistant frames, because it is able to transfer relatively high load even when broken. The value of energy absorption was calculated as the area under the load-displacement curve for displacement from 0 to 15 mm (Table 1). The highest values of energy absorption corresponded with the highest maximal load and maximal flexural strength. The cast and cut beams with perpendicular orientation of cast surface to the load cell and the notch had average energy absorption of 426.7 Nm and 389.0 Nm, respectively. The beam saniples cut and cast with parallel orientation of cast surface, load cell and notch on beam had energy absorption of 350.6 Nm and 297.2 Nm. The lowest values of energy absorption (125.7 Nm and 77.6 N m ) were calculated on the cast and cut beams produced in the column position mould, respectively. The average value of energy absorption (0.7 Nm) on plain slurry beams wits calculated for the comparison of much lower energy absorption for this type of concrete. Compressive strength The compressive strength of SIFCON (f,) was measured on thc straight cast cubes and cubes which were cut from the blocks. The influence of the fibre orientation in the samples was verified. Table 2 shows the individual and average values of measured maximal load and calculated compressive strength obtained from the three measurements on each type of samples and the average results of the three plain cement slurry samples. The coefficients of variation are also given in Table 2.
319
Design and testing of self-compacting SIFCONprodticed with low strength slurry
Average Volume Maximal Average Compressive compressive offibres load strength f, strength load (%) (m) (kN) (N/m2) (N/mm2)
Sample
1 Plain slurry 2 3
0
1
a
2 3
b
2 3
Cast
9.4
1
9.4
1
a cut
2 3
10.8
321 318 300 273 282 284 343 3 67 543 335 311 316
313.0 (3.6%)
279.7
-
417.7 (26.1 %)
320.7 (3.9 %)
1
793 891.7 904 3 978 (10.4%) (Bracket values): coefficient of variation b
2
10.8
32.1 31.8 30.0 27.3 28.2 34.3 36.7 54.3 32.7 30.3 30.7 80.9 87.3 96.4
31.3 (3.6 %)
28.0 . _-
41.11 (26.1 %)
31.2 (4.1 Yo)
88.2 (8.8 %)
Table 2: Compressive strength of SIFCON The coefficients of variation for results of compressive strength are mostly lower than the coefficient of variation for flexural strength. Only the straight cast cubes with casting surface parallel to the load cell had a high value of coefficient of variation equal to 26.1%. The main influences on the results were the orientation of fibres and the method of sample production. The highest compressive strength (88.2 N/mmz) represented the samples which were cut from the SIFCON blocks and had the casting surface parallel to the load cell. The compressive strength 41.8 N/mm2 represented the cubes which were cast straight in the moulds and also had parallel orientation of the casting surface to the load cell. The samples with perpendicular orientation of the casting surface to the load cell had similar or even smaller compressive strength than the plain cement slurry. The compressive strength of plain slurry and the cube samples cut from a block represented strength of 3 1.2 N/mm2 and 3 1.3 N/mm2, respectively, while the compressive strength of the straight cast sample was 28 N/mm2. CONCLUSIONS Several tests of flexural and compressive strength on SIFCON with different orientations of fibres were carried out and the following conclusions can be made: The test results underline the expected unisotropy of SIFCON. Even though the test samples were produced from the same components and same type of fibres, the results of the maximal flexural strength and compressive strength are different and depend on the orientation of fibres to the plane of rupture. The flexural strength of SIFCON is between 3.7 times and 18 times higher than that of plain cement slurry. This depends on the orientation of fibres to the plane of rupture.
320
Lucie SVERMOVA, Mohammed SONEBI and Peter J.M.BARTOS
Whether the samples were straight cast or cut from a block of SIFCON had no serious influence on flexural strength. The ‘post-peak’ behaviour of all SIFCON samples showed this material to have low brittleness and high ductility and energy absorption, which suggested the suitability of this material for use in seismic areas. The compressive strength of SIFCON was affected by the placing of fibres and by the method of production (straight cast samples or samples cut from a block of SIFCON). The cut cubes with the orientation of fibres mostly parallel to the load cell had 2.8 times higher compressive strength than the plain slurry. On the other hand, the straight cast samples with the casting surface oriented perpendicular to the plane of rupture had compressive strength 1.1 times smaller than the plain cement slurry.
References 1. Naaman, A.E. and Baccouche, M.R., Shear response of dowel reinforced SIFCON, ACI Structural Journal, 92, 1995, pp. 587-596. 2. Reinhardt, H.W. and Fritz, C., Optimization of SIFCON mix, fibre reinforced concrete recent developments, Ed. by Swamy, R.N., and Ban-, B., Elsevier Applied Science, 1989, pp. 11-20. 3. Haynes, H., Investigation of fibre reinforcement methods for thin shell concrete, Naval Civil Engineering Laboratory, Port Hueneme, CA, N-979, 1968, pp. 1-26. 4. Naaman, A.E., Wight, J.K. and Abdou, H., SIFCON connections for seismic resistant frames, Concrete International, 1987, pp. 34-49. 5. Bartos, P.J.M. and Marrs D.L., Development and testing of self-compacting grout for the production of SIFCON, In: Proc.Int.Work. “High performance fibre reinforced cement composites”, Ed. by Reinhardt, H.W. and Naaman, A.E., RILEM, Mainz 16-19 May 1999, pp. 171-179. 6. Svermova, L. and Bartos, P.J.M., Development of in-situ SIFCON for connections in precast concrete and seismic resistant structures. In: Proc.Int.Conf. “27Ih Conference on Our World in Concrete & Structures”, Singapore 29-30 Aug 2002, pp. 553-559. 7. Sonebi M., Svermova L. and Bartos, P.J.M., Development of Cement Slurries Containing Limestone Powder for Self-compacting SIFCON by using Factorial Design Plans. Submitted to ACI Material Journal, 2003. 8. Wang, M.L. and Maji A.K., Shear properties of Slurry Infiltrated Fibre Concrete (SIFCON), “High Performance Fibre Reinforced Cement Composites”, Ed. by Reinhardt, H.W., and Naaman, A.E., RILEM, 1991, pp. 203-212. 9. Van Mier, J.G.M. and Timmers, G., SIFCON subject to shear: effect of material anisotropy on strength and stiffness, “Fibre Reinforced Cement and Concrete”, Ed. by Swamy R.N., Proceedings of the 4Ih International Symposium, Sheffield 1992, pp. 245-256. 10. Svermova, L., Anisotropy of concrete with high content of fibres, the Eleventh Annual BCNConcrete Society Conference on Higher Education and the Concrete Industry, Manchester, Concrete Communication Conference 2001, pp. 367-377.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt. V.C. Li and I. H. Marshall, eds. Warsaw. October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE INFLUENCE OF SELECTED COMPOSITION FACTORS ON THE RHEOLOGICAL PROPERTIES OF FIBRE REINFORCED FRESH MORTAR
Tomasz PONIKIEWSKI, Janusz SZWABOWSKI The Silesian University of Technology, Department of Building Processes Akademicka 5,44- 100 Gliwice, Poland, e-mail:[email protected]; [email protected] ABSTRACT
In the paper the methodology and test results of the investigation are presented and discussed on the influence of fibres on rheological properties of modified standard mortars. The rheological parameters of fibre reinforced fresh mortars (FRFM) - yield value and plastic viscosity were determined. FRFM behaves as a Bingham body, their rheological parameters were determined by using rheometer to pastes and mortars. In the research, an experimental verification of a significance of an influence: WIC ratio, volume fraction of fibres, lengths and kind of materials of fibres on rheological properties of FRFM was investigated. In the paper the results obtained for mixes with polypropylene, steel, carbon and glass fibres are presented. The first step of the procedure was a rheological identification of fiber-mortars, which was completed based on the delimitation of the tension due to an assignment of characteristic dependence - speed of non-dilatational strain, in the form of a curve flow and acceptance of adequate model and rheological equalizations. This equalization is a base to the experimental analyses which influences composition factors of mixtures on the character of their flowing and rheological parameters. The analysis of the results of these measurements permitted on the following qualifications: reliable statistics of rheological parameters from variables, indications of workability forms of mortars with fibres and approximate reliability among rheological parameters of FRFM. Keywords Fresh fibre reinforced mortar, rheology, ANOVA
INTRODUCTION
Fibre-reinforced concrete (FRC) is one of several special concretes that differs significantly from normal concrete with respect to the measurement of workability and mixture proportioning. Fibre parameters such as type, length, aspect ratio and concentration in the concrete matrix have a profound effect on workability measured by any method, [I]. The influence of these factors is still not recognized in sufficient measure. Concrete mixtures are proportioned to provide the workability needed during construction and the required properties in the hardened concrete. The workability of freshly mixed FRC is the property which determines the ease and homogeneity with which it can be mixed, placed, consolidated, and finished, [3][6]. Workability is a function of the rheological properties of concrete. Influence of fibre on FRFM rheological parameters is very significant but presented in only a few publications, [ 2 ] [ 5 ] .
322
Tomasz PONIKIE WSKI and Janusz SZWABO WSKI
Fibers are incorporated in the brittle cement matrix to control cracking, to provide high ductility, improved impact resistance, to increase the tensile and flexural strengths, and to provide a strain-hardening type of response, [4]. However the addition of fibres will cause problems with workability to occur. Many examples of research into the use of fibres in concrete mixes has shown that the stardard test results are unreliable and ambiguous, 171. METHODS AND MATERIALS The rheometrical workability test The main goal for the research presented was the determination of the rheological behaviour of FRFM investigated with a rotary rheometer - Viskomat NT (Fig.l), [3]. It is necessary to qualify the rheological properties of FRFM, using the rheometrical workability test (RWT), described in [3]. The test relies on: - experimental determination of the relation between torque M for the shear resistance of the mortar and the rotational speed N of the impeller rotating in the mortar flow curve, - as fresh mortar and concrete behaves as a Bingham body, their rheological parameters yield value and plastic viscosity can be evaluated from a rearranged Bingham’s (equation 1) by regression analysis experimental data of the relation M-N:
h = K,qpl and K1, KZ- constants of rheometer g and h are rheological parameters which values are respectively proportional to yield value and plastic viscosity q,,, .
0
7
0
-----
-
20
40
80
80
- --r- 100 120 140 160 180 200 220 240 Time Is]
Fig. 1. Measuring procedure and the rotary rheometer - Viskomat NT Materials and methods The investigation was carried out on standard mortar according to PN EN 196-1: 1996, because of the similar nature of mortar and concrete. The lower cost and labour involved was also an advantage. The mortar was modified because of variable W/C ratio (0.45-0.47-0.50-0.53), length and volume fraction (0.1%, 0.3%, 0.5%) of different types of fibres (table 1).
The influence of select composition factors on rheological properties o f j b r e reinforced fresh ...
323
Table 1. Characteristics of the fibers
~~
~~~~~
~~~
The temperature of the mortar was 2W2OC. The content of superplasticizer FM 34 was constant and equal to 1% of the cement weight. Portland sulfate resistant cement, called ,,road" CEM I MSR 42,5 was used. The mixing methods of the components of the samples was according to PN EN 480-1, with exception of fibres, which were added to the dry components (steel and glass fibres) or mixed with water and superplasticizer (another type of fibres) before adding sand and cement to the batch. This paper shows results of research into rheological parameters FRFM: yield value g and plastic viscosity h. All yield value and plastic viscosity results presented are the mean of 3 specimens. The research design is presented in Table 2. The following factors were taken into consideration in researches: - W/C ratio and superplasticizer dosage; - length of fibres; - volume fraction of fibres; - different types of fibres. rable 2. Research desien I. 2. 1.
II
"I
Influence of polypropylene fibres 2. (SP = 1%) 3. 4. Influence ofglass fibres 1. (SP = IYO) 2. I. Influence of steel fibres 2. (SP = IYO) 3. I. Influence of carbon fibres 2. (SP = IYO) 3.
Variables W/C ratio - 0.43-0.454.47-0.50 SP content - 0; 1; 2% W/C ratio - 0.45-0.47-0.50-4.53 Type of polypropylene fibres - fibrillated; monofilament Fibre length - 3; 6; 12; 19 mm Fibre v o l k e fraction - 0.1; 0.3; 0.5% W/C ratio - 0.45-0.47-0.50-0.53 Fibre volume fraction - 0.1; 0.3; 0.5% W/C ratio - 0.45-0.47-0.50-0.53 Fibre length - 6; 13 mm Fibre volume fraction - 0.1; 0.3; 0.5% W/C ratio - 0.45-0.47-0.50-0.53 Fibre length - 3; 6; 10 mm Fibre volume fraction - 0.1; 0.3; 0.5%
The isolated effect of each factor was assessed by eliminating interaction of other factors (all other factors were kept constant in research stage). Having regard to the limited volume of this paper, the results for FRFM with low W/C ratio (0.45 - 0.47) are not presented. In this paper the rheological results only for decreasing velocity of measuring procedure were presented.
324
Tomasz PONIKIEWSKI and Janusz SZWABOWSKI
RESULTS AND DISCUSION Effect of WIC ratio and superplasticizer dosage Analysis of variance (ANOVA) of obtained rheological parameters for mortars without fibres are presented in Table 3. ANOVA shows that W/C ratio have the significant influence on yield value and plastic viscosity of tested mortars without fibres. This is the major reason why the next ANOVA's for mortars with different types of fibres have variable factor W/C ratio.
Sum of Mean Squares d.f* square
Source of variation
I
I
AN OVA^^^:
Sig. Sum of F-ratio Level Squares d.f.
I
Yield value g
Mean square
Sig. F-ratio Level
I
Plastic viscositv h
I
MAIN EFFECTS AWIC B: SP content C:Measurement repetition INTERACTIONS AC
104.334 8.170 1.106
26.084 35.395 0.000 8.170 11.087 0.016 0.553 0.75 0.512
4 1 2
9.800 8 0.369 2 4.422 6 123.428 23
1.225 0.184 0.737
0.267 0.001 0.006
1.662 0.276 0.25 0.787
4 1 2
0.021 8 0.000 2 0.0025 6 0.3153 23
0.067 159.039 0.000 0.001 2.784 0.146 0.003 6.798 0.029 0.003 0.000 0
6.282 0.019 0.03 0.971
Effect of polypropylene fibres addition ANOVA of obtained rheological parameters for polypropylene FRFM are presented in Table 4. ANOVA shows that type of fibres and fibre volume fraction have the significant influence on yield value and W/C ratio have the significant influence on plastic viscosity of tested polypropylene FRFM.
Source of variation ~~
A T O V r
Sum of Squares d.f.
7
Mean square ~~
F-ratio
Sig. Sum of d.f. Level Squares
~
I
Yield value g
Mean square
Sig. F-ratio Level
I
Plastic viscosity h
MAIN EFFECTS A: W I C B: Type of fibres C: Fibre length D: Fibre volume fraction INTERACTIONS BD Residual Total (corrected)
294.400 2855.114 628.107 1388.200
5 58.880 1.036 2 1427.557 25.120 4 157.027 2.763 2 694.100 12.214
1541.723 4 3864.47 68 11236.56 85
378.681 56.831
0.404 0.000 0.034 0.000
6.663 0.000
0.597 0.020 0.142 0.020
5 2 4 2
0.119 0.010 0.036 0.010
11.8 0.991 3.514 0.987
0.043 4 0.6879 68
0.011 0.010
1.072 0.377
0.000 0.377 0.012 0.378
1.6347 85
The results of the rheological investigation of polypropylene FRFM in Fig. 2 and Fig. 3 give additional information. For mortars without fibres, it was observed that their was a small increase of g and h value with a decrease in W/C ratio in the mortar. The rheological
The influence ofselect composition factors on rheologicalproperties offibre reinforced fresh ...
325
properties of polypropylene fibrillated FRFM are better than for FRFM with other types of fibres (Fig. 2). For W/C = 0.53 changes of yield value and plastic viscosity are consequence of fibre volume fraction changes but remain on the same low level for all of the fibre length. For W/C = 0.50 changes of rheological parameters are generally of the same nature and level but for FRFM with H19 fibres increase of yield value was observed. High increase of yield value for polypropylene monofilament FRFM was observed (Fig. 3). Changes of yield value and plastic viscosity are consequence of fibre volume fraction changes but influence of fibre length was observed as well. Increasing dosage of fibres cause increase of yield value. Clearly highest yield values were obtained for FRFM with 0.5% of F12 fibres.
a) b) Fig. 2. Influence the length and volume fraction of polypropylene fibrillated fibres on rheological parameters of FRFM; a) W/C = 0.53; b) W/C = 0.50
%----
-
~
50. 0.5%
-
1 +F3
1
+F6
> 20.
-A-F12,
20
0.3%
15 10.
0.3% 1
92
0,3 0.4 0,5 0.6 0,7 Plasticviscosity h [Nmnin]
0.3
0,4
0.5
0.7 0,8 Plasticvkcdtyh[Nmnin] 0,6
4 b) Fig. 3. Influence the length and volume fraction of polypropylene monofilament fibres on rheological parameters of FRFM; a) W/C = 0.53; b) W/C = 0.50
326
Tomasz PONIKIEWSKIand Janusz SZWABOWSKI
Effect of glass fibres addition ANOVA of obtained rheological parameters for glass FRFM are presented in Table 5 but only for one length of fibres. ANOVA shows that fibre volume fraction have higher influence than W/C ratio on yield value and W/C ratio have higher influence than fibre volume fraction on plastic viscosity of tested glass FRFM. High increase of yield value and plastic viscosity for glass FRFM was observed (Fig. 4). Increasing dosage of fibres cause increase of yield value and plastic viscosity, but for plastic viscosity remain on the same level for all fibre volume fraction.
Sum of Mean Squares d*f. square
Source of variation ANOVA for:
Sig. Sumof Mean F-ratio Level Squares d*f* square
Yield value g
F-ratio
Sig. Level
Plastic viscosity h
MAlN EFFECTS A: W I C B: Fibre volume fraction Residual Total (corrected)
221.340 321.798
3 2
73.780 160.899
62.806
1
62.806
452.468
6
1.175 0.567 2.562 0.398
0.007
0.001 0.001 0.016
3 2
0.002 0.000
1
0.001
1.925 0.470 0.262 0.810
6
Effect of steel fibres addition ANOVA of obtained rheological parameters for steel FRFM are presented in Table 6 and shows that W/C ratio have the significant influence on yield value. While W/C ratio, fibre length and fibre volume fraction have the significant influence on plastic viscosity of tested steel FRFM. The rheological properties of steel FRFM are comparable with properties of polypropylene fibrillated FRFM (Fig. 4). Changes of yield value and plastic viscosity are consequence of fibre length changes but remain on the same low level for all of the fibre volume fraction. Increasing dosage of fibres cause increase of plastic viscosity for FRFM but with 0.3% of S 13 fibres only.
Sum of Mean Squares d*f* square
Source of variation
I
ANOVA for:
I
F-ratio Sig. Sum of Mean Level Squares d*f. square
I
Yield value e
F-ratio
Sig. Level
Plastic viscositv h
1
MAIN EFFECTS 196.727 3 A: W I C 47.649 1 B: Fibre length C: Fibre volume fraction 46.888 2 9.590 2 DMeasurement repetition INTERACTIONS 23.106 3 AB 47.114 6 AD 57.561 2 BC 7.104 2 BD 26.074 4 CD 314.5096 39 Residual 741.29 64 Total (corrected)
65.576 47.649 23.444 4.795 7.702 7.852 28.781 3.552 6.518 8.064
8.132 5.909 2.907 0.595
0.000 0.020 0.067 0.557
0.516 0.107 0.088 0.000
0.955 0.974 3.569 0.44
0.424 0.456 0.038 0.647
0.003 0.006
0.808 0.528
3
I 2 2
3
0.172 110.301 0.000 0.107 68.578 0.000 0.044 28.154 0.000 0.000 0.231 0.795
0.001 0.001
0.708 0.553 0.688 0.661
2 2
0.011
0.000
6.81 I 0.003 0.212 0.81C
0.000 4 0.0608 39
0.000
0.061 0.993
0.021
0.000
6
0.8127 64
0.001
The influence of select compositionfactors on rheological properties ofjbre reinforcedfresh ...
I u s 3 I
321
0
a) b) Fig. 4. Influence the length and volume fraction of glass and steel fibres on rheological parameters of FRFM; a) W/C = 0.53; b) W/C = 0.50 Effect of carbon fibres addition ANOVA of obtained rheological parameters for carbon FRFM (Tabl. 7) shows that carbon fibre volume fraction have the significant influence on yield value. While W/C ratio and fibre volume fraction have the significant influence on plastic viscosity of tested carbon FRFM. The rheological properties of carbon FRFM are the worst than for FRFM with other types of fibres (Fig. 5). For carbon FRFM the yield value g resulted in the highest value. Changes of yield value are consequence of fibre volume fraction changes. Generally increasing dosage of carbon fibres cause high increase of yield value and decrease of plastic viscosity for FRFM was observed. Table 7. Analysis of variance for yield value and plastic viscosity of carbon FRFM. Sum of Squares d.f.
Source of variation
1
AN OVA^^^:
'
MAIN EFFECTS
1
Mean square
Sig. Sum of Mean F-ratio Level Squares d*f* square
Yield value g
I
588.376 3 196.125 2.425 0.078 A: W I C 892.934 3 297.645 3.680 0.019 B: Fibre length 12460.93 2 6230.467 77.041 0.000 IC: Fibre volume fraction 120.005 2 60.003 0.742 0.482 D:Measurement repetition INTERACTIONS 213.676 9 23.742 0.294 0.973 AB AD 330.615 6 55.102 0.681 0.66.5 112.882 6 18.813 0.233 0.964 BD Residual 3639.225 45 80.8716 20991.04 76 Total (corrected)
F-ratio
Plastic viscosity h
0.161 0.101 0.238 0.017
3 3 2 2
0.039 9 0.035 6 0.008 6 0.2823 45 1.2259 76
Sig. Level
I
0.054 8.551 0.000 0.034 5.349 0.003 0.1 19 18.998 0.000 0.008 1.343 0.271 0.004 0.006 0.001 0.00627
0.696 0.709 0.931 0.483 0.208 0.973
328
Tomasz PONIKIEWSKIand Janusz SZWABOWSKI
I
I
+c3
-&-CO I,
I
I
m
-a! 3
F 10.
00,O
.
0,l 0,2 0,3 0.4 0,5 Plastic viscosity h ["nin]
0.6
a) b) Fig. 5. Influence the length and volume fraction of carbon fibres on rheological parameters of FRFM; a) WIC = 0.53; b) WIC = 0.50 Figure 5b also indicates that there is a critical fibre content beyond which yield value g increase very rapidly or resulted in an unmeasurable value. Problems with the rheological measurements from WIC = 0.50 and lower WIC ratio for fibre content of 0.5% by volume especially for carbon (Fig. 5b) and glass fibres (Fig. 4b) were observed. The influence of fibre content and type of fibres on the plastic viscosity h was considerably less than on the yield value g. The increase in plastic viscosity h is connected with the increased content of fibres but only for the steel FRFM. The plastic viscosity h generally is constant for polypropylene monofilament and glass FRFM (Fig. 3, Fig. 4), decrease for carbon FRFM (Fig. 5) and is connected with the increase content of fibres.
CONCLUSIONS It has been shown that in investigated range of composition factors of FRFM the addition of fibres to the fresh mortar changes the composite rheology. Analysis of variances (ANOVA) of obtained rheological parameters for FRFM showed that: - type of fibres and fibre volume fraction have the significant influence on yield value but WIC ratio have the significant influence on plastic viscosity of tested polypropylene FRFM, - fibre volume fraction have higher influence than WIC ratio on yield value but WIC ratio have higher influence than fibre volume fraction on plastic viscosity of tested glass FRFM, - WIC ratio have the significant influence on yield value and WIC ratio, fibre length and fibre volume fraction have the significant influence on plastic viscosity of tested steel FRFM. - fibre volume fraction have the significant influence on yield value but WIC ratio and fibre volume fraction have the significant influence on plastic viscosity of tested carbon FRFM. Yield value g and plastic viscosity h of tested FRFM does not depend significantly on the rheological parameters of the matrix.
The influence of select composition factors on rheological properties offibre reinforced fresh ...
329
The influence of the type of fibre and fibre volume fraction on rheological properties of FRFM are important factors. The length of fibres do not have the significant influence on yield value and plastic viscosity of FRFM. The significant influence of the length of fibres on plastic viscosity of tested steel FRFM was observed only. The rheological properties of polypropylene fibrillated and steel FRFM from workability point of view are better than for FRFM with other types of fibres. In case of glass and carbon fibres the workability of FRFM worsens with the increase of their volume fraction. ACKNOWLEDGEMENT The authors gratefully acknowledge the financial support by the research grant from the State Committee for Scientific Research (KBN-Poland), project: No 8 T07E 033 21. REFERENCES 1. Johnston C.D.: Comparative measures of workability of fibre-reinforced concrete using slump, Ve-Be and inverted cone tests, Special Conretes: Workability and Mixing, edited by J.M.Bartos, E & FN Spon., 1993, pp 107-118. 2. Kucharska L., Logon D.: The influence of fly ash on rheological and mechanical properties of cement mortars reinforced with pitch-based carbon fibres, in: Proc. Int. Symp. ,,Brittle Matrix Composites 5", A.M.Brandt, I.H.Marshal1, V.C.Li eds. Warsaw 1997, pp 113-122. 3. Szwabowski J.: Rheology of cement based mixes, The Silesian University of Technology, Gliwice 1999 (in Polish). 4. Peled A., Shah S.P.: Parameters related to extruded cement composites, in: Proc. Int. Symp. ,,Brittle Matrix Composites 6", A.M.Brandt, V.C.Li, I.H.Marshal1, Warsaw 2000, pp 93-100. 5. Kucharska L., Logon D.: Mixture composition of matrices and the reinforcing effect of thin composite elements by carbon microfibres, in: Proc. Int. Symp. ,,Brittle Matrix Composites 6",A.M.Brandt, V.C.Li, I.H.Marshall, Warsaw 2000, pp 147-157. 6. ACI Manual of Concrete Practice, Part 2: Construction Practices and Inspection Pavements, American Concrete Institute, 200 1. 7. Szwabowski J., Ponikiewski T.: Rheological properties of fresh concrete with polypropylene fibres, 3rd International Conference: Concrete&Concrete Structures, Zilina, Slovakia, 24-25.04.2002 r., pp 33 1-338.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodliead Publ.. Warsaw 2003
MIX DESIGN OF THE SELF-COMPACTING CONCRETE
Maria KASZYIhKA Technical University of Szczecin Piastow 50, 70-3 1 1 Szczecin, Poland e-mail: mkasz@os.@ ABSTRACT
Self-compacting concrete can by made in various ways. The optimum mixtures are sensitive with regard to characteristics of components, such as type of the cement, type and amount of superplasticizer, type of sand and fillers. The fabrication of self-compacting concrete requires a more rigorous quality control of materials and selection of the mixture at all stages of mixing and casting. The objective of this paper is to present the effect of additions and admixtures on performance of the self-compacting concrete. The tests confirmed the importance of the quantity of superplasticizers and of compatibility between cement and superplasticizer. Keywords: Self-compacting concrete, cement, superplasticizer, silica hme, flowability, passing ability, stability, compressive strength. INTRODUCTION
Self-compacting or Self-Consolidating Concrete (SCC) has been described as “the most revolutionary development in concrete construction for several decades”. SCC can be used in precast applications or for concrete placed on site. In designing the mix, the size and the shape of structural elements, dimensions and density of reinforcement and the cover depth should be taken into consideration. The development and use of self-compacting concrete in many countries have shown that it can be successfidly produced from a wide range of component materials but it is difficult and often impossible to predict the final properties of that concrete,
r 1,2,31.
There are no design codes for SCC. This concrete is very sensitive with regard to the proportions of the mix and quality of workmanship. Inaccuracies in proportions of ingredients, varying characteristics of the applied components and varying curing conditions, can result in a failure to obtain the required properties of the SCC, i.e. its filling ability (flowability), its passing ability (free from being blocked by reinforcement) and its resistance to segregation (stability). Many different test methods have been developed in an attempt to specifjr the properties of SCC, but so far there is no single test available to measure all three properties. This paper presents some of the results from a broader study dealing with the relationships between the properties of SCC pastes, mortars and concretes. A similar range of tests have
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Maria KASZYIVSKA
been carried out on both the mortar and concrete i.e. spread and slump flow tests and Vfbnnel tests.
MATERIALS AND MIX PROPORTIONS The tests were performed for paste, mortar and concrete mixtures made using five types of Portland cement. Notation used for the Portland cements is shown in Table 1. Table 1. Notation used for the Portland cements 1
2 3 4 5
Portland Cement CEM 152,s R Goraidze CEM I 52,s R Chelm CEM I 42,s R Goraidze CEM 142,s R Cemcon CEM 132,s R Gorazdze
Notation G 52,s CH 52,s G 42,s C 42,s G 32,s
For the considered mixtures, a superplasticizer and pozzolanic additives: fly ash and/or silica fbme were used. Four different modified polycarboxylic ether superplasticizers were considered: Sika ViscoCrete 3, Isola Polymer BV-10, Woerment FM-787 and Woerment FM 375. The characteristics of the superplasticizers are shown in Table 2.
Superplasticizer Sika ViscoCrete 3 Isola Polymer BV 10 Woerment FM 787 Woerment FM 375
Chemical description Polycarboxylic ether Polycarboxylic ether Polycarboxylic ether Polycarboxylic ether
Notation Si BV WFI wF2
Specific gravity 1.09 1.06 1.07 1.08
The tests were performed for six selected powder compositions for each cement type. Table 3 shows the applied powder compositions. Table 3. Powder compositions
Mortar proportions were identical but with the addition of sand, (mortars are denoted by M1, M2, M3, M4, MS and M6). The volume fraction of sand (> 0.125 mm) in mortars was fixed at 40%. In the first part, the volume of water was calculated on the basis of test executed on
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Mix design of the self-compacting concrete
cement pastes. In the second part of investigation a constant volume of the water in mortars was applied equal to 160 Vm3.
EXPERIMENTAL PROCEDURE In the study, the following parameters were considered: - type of Portland cement: G52,S; G42,S; G35,2; C42,S: CH52,S; - type of superplasticizer: Si; BV; WFl; WF2; - amount of superplasticizer: from 0.5% to 3.0 YOof the cement mass; - addition of silica fume: 10% of cement mass;
Design of paste composition The water to powder volume ratio has to be determined on the basis of paste and mortar flow cone test. Initially the water to powder ratio for zero flow (pp) was determined in the paste, with the selected proportions of cement and additions. The flow cone tests were performed for the watedpowder ratios by volume of 1.1, 1.2, 1.3 and 1.4 for the selected powder compositions. The test results for cement G 32,s are shown in Fig. 1. The point of intersection with the y-axis is designated as pp value, called “water retaining ratio”. 1.5
I
1
7
0,8
1
0,7 0
1 2 3
4 5 6
7 8 9 1 0 1 1 1213
r
1.2
;1,l
0
1
2
3
4
5
6
7
8
P
Fig.2. Test results of determination of the water/powder ratio Pp
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Maria KASZYI~SKA
Figure 2 shows the comparison of the test results for the water retaining ratio pp for all tested mixtures and cements. The mixes with higher amount of fly ash (p1 and P2) had lower values of pp than the mix P6 with silica fume. This means that the pastes with fly ash powder had higher flowability with lower volume of water __ rn P1
P2
0 P3 0 P4 P5 HP6
CEM l52,5R Chehn
CEM I52.5R G6ratdLe
CEM l42.5R G6raZdLe
CEM l42.5R
Cemcon
CEM I32.5R GdraZdte
Portland Cements I
Fig.2. Test values of water retaining ratio Sp for different cements Determination of mortar composition To estimate the optimum volumetric watedpowder ratio and the superplasticizer dosage the tests with flow cone and V-Funnel for mortars were performed for waterlpowder ratios in the range of (0.8 - 0.9)ppand for varying dosages of superplasticizer. Test results for selected Table 4. Slump-flow (r) and V-funnel(t) test results for mortars
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Mix design of the self-compacting concrete
mixtures from different amounts and types of superplasticizer and volume of the water calculated from tests for pastes are presented in Table 4 for cement C 42,5 and G 32,s. All the measurements of slump-flow and v-finnel time were performed within 10, 30 and 60 minutes after mixing the concrete. The comparison of the test results for mixtures with constant amount of superplasticizer are shown in Figs. 3 and 4. I
Cement C 42.6, 1XSuperplasticirerSi
Cement G 32.6, 1.2 % SuperplasticizerBV
-
-.e
60
C
'C
w30
zc
10
0
50100150200250300350
10
0
SLUMP-FLOW [mnf
1
60
50
100 150 200 250 SLUM-FLOW [lnlll]
3M)
350
Fig. 3. Slump-flow test results
I
Cement G 32.6. 12% Superplasticizer BV
30 60 TIME AFTER MIXING [min]
I
Cement C 42.6. 1% Superplasticizr Si
10 30 60 TIME AFTER MIXING [min]
Fig.4. V-funnel time test results The study showed that even for the same type and amount of the superplasticizer and binder the varying proportions of powder had a considerable effect on the slump flow and duration time for the SCC properties. After 60 minutes, some of the mixtures lost their free flow properties required for SCC. This was caused by non-compatibility problems between cements and superplasticizers. The test results for selected mixtures with a constant volume of water but with different amount and type of superplasticizers are presented in Table 5. The best properties of filling ability for each mortar are marked. Target values for the slump-flow are of 24 to 26 cm (r,,, = 5 ) , and V-finnel time of 7 to 1 1 seconds (R,,, = 1).
where: r = 0.5 (rl + rz) rl, rz - measured diameter of the mortar in two perpendicular directions, r,, - base diameter of mortar cone, r, = 100 mm,
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Maria KASZYNSKA
R,=lO/t
where: t - flow time (sec) Table 5. Slump-flow and V-fbnnel test results for mortars with cement G 32,s
Test of concretes The test results are presented here for selected concrete mixtures: M2, M3 and M5. The study focused on the filling ability and the compressive strength of concrete. The fresh concrete mix was tested to establish the required deformability, flowability and segregation resistance properties. The slump flow test was performed using the Abram’s cone. It is the most commonly used test, it gives a good assessment of the filling ability and it may also serve as an indication for the resistance to segregation.
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Mix design of the self-compacting concrete
Time was measured for the concrete to reach a 500 mm spread circle (denoted by T50m) and the final diameter of the concrete in two perpendicular directions was measured (the average value is the slump-flow in mm). Typical range of values for slump-flow for SCC is from 650 mm to 800 mm and for T50cnlfrom 2 to 5 sec, [4,5,6]. All the measurements of spread circle were performed within 10, 30 and 60 minutes after mixing the concrete. To determine the filling ability (flowability) and passing ability of the concrete the Vfunnel test and L-box test are used. The V-funnel is filled with about 12 liters of concrete and the time taken for it to flow through the apparatus is measured. After that, the funnel could be refilled with concrete and left for 5 minutes to settle. If the concrete showed segregation then the flow time increased significantly. For SCC a flow time of 10 seconds and minimum value of H2/Hl = 0.8 were considered as appropriate. The concrete compressive strength was determined after 3, 7 and 28 days of curing. Test results for selected mixtures with G 32,s cement are presented in Table 6.
M2 M3
Workability tests Slump-flow V-funnel T5o [sec] r[mm] [sec] 7.5 760 11.8 6.1 770 13.8
M T
760
Mixture
122
L-box H~/HI 0.89 0.88 094
Compressive strength 2days 7days 28 days [MPal [ma1 [ma] 35 52 69 43 51 66 62
80
81
The concrete reached very high compressive strength. It has been found that the highest strength could be obtained for mixtures that satisfied the self-compacting criterion. Increase or decrease of the slump flow beyond the accepted limits can cause a decrease of the compressive strength. This is due to poor compacting in the case of reduced slump flows and segregation of components for excessive slump flows.
CONCLUSIONS The study showed that even for the same proportions of ingredients, the type of cement has a considerable effect on the slump flow and duration time for the SCC properties. For the selection of the mixture proportions for self-compacting concretes, it was very important to select the most suitable superplasticizer' for the given cement. In addition, the considered mixtures were checked with regard to sedimentation and segregation. The optimum quantity of superplasticizer was determined to maximize the slump flow without segregation. The fabrication of self-compacting concrete requires a more rigorous quality control of materials and an appropriate selection of the mixture proportions for different structural elements. The tests confirmed the importance of the superplasticizer quantity and of the compatibility between cements and superplasticizers. The tests and analyses have shown also that the determination of the optimum properties of self-compacting concrete is most efficient when the paste and the mortar are subjected to preliminary tests.
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REFERENCES 1. Jin, J., Domone, P.L., Relationships between the fresh properties of SCC and its mortar component. Conference Proceedings of First North American Conference on the Design and Use of Self-Consolidating Concrete, 2003,pp 33-38 2. Walraven J., Self-Compacting Concrete in the Nethertands, Conference Proceedings of First North American Conference on the Design and Use of Self-Consolidating Concrete, 2003,pp 399-405. 3. Bui, V.K.,Shah, S.P., Akkaya,Y., A new Approach in Mix Design of Self-Consolidating Concrete, Proceedings of First North American Conference on the Design and Use of SelfConsolidating Concrete, 2003,pp 71-76 4. Okamura, H.,Ozawa, K., Self-Compacting High Performance Concrete, Structural Engineering International 4/96 5. Specification and Guidelines for Self-Compacting Concrete, EF'NARC, 2002. 6. Takada, K., Pelova, G.I., Walraven, J.C.,Development of Self-Compacting Concrete in the Netherlands - 1998 (report from internet).
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
INFLUENCE OF CEMENT AND SUPERPLASTICIZER ON RHEOLOGICAL PROPERTIES OF MORTARS Jacek GOLASZEWSKI Silesian University of Technology Akademicka 544-100 Gliwice, Poland, e-mail: [email protected] Janusz SZWABOWSKI Silesian University of Technology Akademicka $44-1 00 Gliwice, Poland, e-mail: [email protected]
ABSTRACT Effectiveness of superplasticizer is an effect of complex system of factors connected mainly with concrete components properties, concrete composition and concreting conditions. From among these factors the key role for the superplasticizer effectiveness plays interaction of cement and superplasticizer. Selection of cement - superplasticizer system determines also workability of fresh concrete and thus also possibility of performing of HPC. In the paper methodology and results of the investigation into the influence of different superplasticizers on the rheological properties of modified, for the sake of superplasticizer addition and W/C ratio, standard mortars (according PN EN 196-1:1996) with different cements are presented. The rheological parameters of these mortars, yield value and plastic viscosity were determined using a rheometrical methods. In the research program the influence of following factors: chemical origin of superplasticizers (SNF, SMF, PC and PE superplasticizers), cement composition (cements of different C3A, Na20eq and SO3 content) and cement specific surface, superplasticizer dosage and WIC ratio were investigated. On the basis of test results the relationships between cement and superplasticizer properties and rheological properties of cement mortars were defined and discussed. These relationships in form of mathematical models can be used in workability shaping process to select optimal cement - superplasticizer system. Keywords: Workability, High -range water reducers, Rheology, Mortar
INTRODUCTION The definition of workability in concrete technology should be considered in terms of the state of the system concrete mix - method of processing. This state is determined by the interaction between two factors: the rheological properties of given mix and the forces acting on it during processing [ 13. The rheological properties are determined by composition of the mix only. They characterise its strain and flow - stress behaviour. Therefore, concrete mix workability is determined by the reaction of the mix to the forces acting on it during transport and mechanical processing as the resistance of its structure to these forces. Required
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Jacek GOtASZEWSKIand Janusz SZWABO WSKI
workability can be achieved in two ways: rheological properties of concrete mix are adjusted to the given method and conditions of concrete processing or method and conditions of concrete processing are adjusted to the given rheological properties of concrete mix. In practice the first way is usually used. High performance concrete (HPC) is widely used in civil engineering as structural material assuring high strength, durability and reliability of concrete structures [2, 31. To assure required workability of low water cement ratio various superplasticizers are used. Only by using superplasticizers rheological properties of HPC mix can be adequately adjusted to the method and conditions of concrete processing. Effectiveness of superplasticizer is an effect of complex system of factors connected mainly with concrete components properties, concrete composition and concreting conditions [2, 41. From among these factors the key role for rheological properties and workability of fresh HPC plays interaction of superplasticizer - cement system [2,3]. Unfortunately the quantity of experimental data on this topic is limited [5, 6, 71. In the paper influence of cement specific surface, cement composition and superplasticizer on rheological properties of fresh HPC was investigated. The influence of these factors was studied on modified standard mortars (PN EN 196-1:1996), which can be considered as a model of HPC concrete [8, 91. It was proven that influence of superplasticizer and cement characteristics on rheological properties of mortars and concretes is qualitatively the same [9, 10, 111. The rheological properties of superplasticized mortars are described by Bingham's model parameters - yield stress g and plastic viscosity h. The rheological parameters were determined using a rheometrical test. EXPERIMENTAL Testing programme In the research the influence of cement and superplasticizer on rheological properties of cement mixes was investigated. The following factors were taken into consideration: superplasticizer type (see Table 2); specific surface of cement (320; 370; 420 m2kg according Blaine method); chemical and phase composition of cement (C3A content - 2; 7; 12%; alkalis content (NazO,,= NazO + 0.658 K20) - 0.3; 0.7; 1.1% and SO3content 2.5; 3; 3.5% see Table 1); W/C ratio (0.55 and 0.45) and superplasticizer dosage (1,2 ,3% of cement by weight). The range of cement composition changes accepted in tests corresponds to variability of typical commercial cements. All tested cement were specially prepared. The cement clinkers used for cements preparation have similar S03/Na20,, mole proportion - due this soluble alkalis content in total alkalis content was kept on the same level in all tested cements. In order to avoid problems with cement hydration process, the SO3 content in cement was accepted in relatively narrow range of changes. The investigation programme was planned in a manner making possible to define changes of rheological properties of mortars without superplasticizer and with SNF, PE, PC superplasticizers as a function of C3A, NazO,, and SO3 content.. Particular series of tests for different superplasticizers and cements of different specific surfaces were performed on the basis of central composite 2"3 + star experiment design accepting polynomial of a second degree with second order interactions as a response function. Rheological model of fresh mortars It is well documented that fi-esh mortar, like a fresh concrete, behaves as bingham body, whose properties can be expressed by the two fundamental rheological parameters, i.e. yield stress and plastic viscosity according the formula: T = T 0 +Tllpl.Y (1)
34 1
Influence of cement and superplasticizer on rheologicalproperties of mortars
where T (Pa) is the shear stress at shear rate i (Us) and T, (Pa) and qpl (Pas) are the yield value and plastic viscosity respectively [1, 12, 131. The physical interpretation of yield value is that of the stress needed to be applied to a material in order to start flowing. When the shear stress is higher then the yield value the mix flows and its flow resistance depends on plastic viscosity. Detailed rheological properties of fresh mortars and concretes are presented and discussed in [l. 9, 12, 131.
Fig. I . Viskomat PC and its measuring element
Measurements of rheological parameters of fresh mortars Rheological parameters of fresh mortar can be measured by applying a given shear rate and the measuring the resulting shear stress. Because of non-linear character of rheological behaviour of mortar, the measurements should be taken at no less than two considerably different shear rates. In this work rheological parameters were measured using Viskomat PC. (Fig. 1) With this instrument, a rotation rate N is applied to a paddle and the torque T of sample shear resistance is measured. The rheological parameters are determined by regression analysis according to the relation [ 1, 91: T=g+Nh (2) where g (Nmm) and h (Nmmmin) are parameters corresponding to yield value T~ and plastic viscosity qpl, respectively. By suitable calibration of rheometer it is possible to express g and h in fundamental units. In the present investigation, where the object was to determine the character of rheological parameters changes in relation to superplasticizer and cement type, calibration was unnecessary. The two-point test and its principles are presented in [ 1,9]. Cement Cements # I Cements#2 Cements #3 Cements#4 Admixture PC PE I PE2 PE3
SNF SMF
Table I . Chemical and phase composition of cements Chemical composition [%] C,S C2S C3A C4AF Na20eq so3 59.6 19.3 2.01 16.6 0.3 0.7 1 . 1 2.5 3.0 3.5 51.5 27.8 6.9 10.5 0.3 0.7 1.1 2.5 3.0 3.5 58.9 16.4 12.2 8.5 1.1 2.5 3.0 3.5 57.9 14.5 12.1 9.5 0.3 0.7 2.5 3.0 3.5
Specific surface [m2kl 320 370 420 320 370 420 320 370 420 320 370 420
Table 2. Properties of tested superplasticizers Density [g/cm3] Concentration [%I Chemical base polycarboxylate acid I .06 40 polyeter (LMW) 1.09/1.05 17/18 polyeter (MMW) 1.05 polyeter (HMW) I .05 36 naphthalene sulphonate acid 1.11 36 melamine sulphonate acid I .09 36
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Jacek GOEASZEWSKI and Janusz SZWABOWSIU
Materials and mixes Laboratory prepared CEM I type cements and commercial superplasticizers were used for the investigations. Their main properties are presented in Tables 1 and 2. The sand used was PN EN 196:1996 CEN model sand (2 mm max.). The mix proportions of all tested mortars were based on standard mortar proportioning according to PN EN 196:1996 (3: 1 sanacement by weight). Watedcement ratio and superplasticizer type and dosage varied as a part of the programme, this variations is given in the results below. Mortar mixing and testing procedures The PN EN 196:1996 mortar mixer was used. The mixing procedure was according to PN EN 196:1996. Superplasticizer was added with water or delayed 30 s depending on its type and test programme. After end of mixing the sample of mortar was transferred to Viskomat PC and was tested according to procedure presented on Fig. 2. The procedure roughly simulates process of transport in truck concrete mixer. Because measurement at the constant velocity of the impeller rotation for the VISKOMAT PC makes possible the investigation of shear resistance only, which at a given speed consists of yield value and plastic viscosity, at 10 and 60 minutes the speed was changed from 120 to 20 Umin to define the rheological parameters from flow curves. The correlation coefficients calculated from the flow curves used to determine rheological parameters of the mixes were in range of 0.95 0.99 with less then 5% failing below 0.90. In the research range effects of segregation were not observed.
-
I
C .-
E
r
I
2
Time [min]
Fig. 2. Measuring procedure used in investigation.
RESULTS AND DISCUSSION On the base of statistical analysis of obtained results concerning influence of cement specific surface and C3A, NazO,, SO3 content on rheological properties of W/C = 0.55 mortars without superplasticizer, it was found that rheological parameters g and h depends successively on: C3A content in cement, specific surface of cement, interaction of these two factors and NazO,, content in cement. It was found also that in the investigated range of changes influence of SO3 content in cement on rheological parameters of mortars is insignificant. The lack of influence of SO3 on rheology of tested mortars does not mean of course that influence of SO3 content is insignificant at all cases. It means only that when SO3 content in cement is properly adjusted, its other characteristics are decisive for rheological properties of cement mix. The influence of cement specific surface and C3A and NazO,, content on rheological parameters g and h of mortars of W/C=O.55 without superplasticizer is presented on Fig. 3 and 4. Increasing C3A content increases g value of cement mortars. The range of this increase depends on cement specific surface and alkalis content in cement but obtained relationships show ambiguous trends. Increase of specific surface of cement from 320 to 370 m’kg cause
343
Influence of cement and superplasticizer on rheologicalproperties of mortars --c Na20q - 0.3%; 320 m’ikg -m- Na20, - 0.3%; 370 rn’lkg
0.5
120
-&-
+
100
-
*
0.4
+ -a-
80
-A-
.-
E
-
Na20q 0.3%; 420 rn’ikg - 0.7% 320 rn2/kg Na20, - 0.7%: 370 rn’lkg Na20, 0.7%; 420 m’ikg Na20, 1 .l%; 320 rn’ikg Na20q 1.1%; 370 rn‘ikg Na20q 1.1%: 420 rn’ikg
+ NarO,
-
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C
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I
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0 C,A content [“%I
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cement of smific surface 320 rn‘/ka glo =-49.O7+O.87A+31.916+39.92~-1.O8A6-O.27AC-13.046C+O.51A2-l.09B2-4.44C?; = 0.990 P = 0.938 hio = 1.~-0.021A-0.518B-0.373C-O,010AB-O, 004AC+O,0316C+O.OOlA’+O. 27082+0.053C?; cement of specific surface 370 m’/kg gro = 273.1-3.16A-113.00B-138.00C+3.28AB-0.25AC-4.44BC+O.51AZ+49.0082+22. 85c‘; 8 = 0.975 hw = -O.049+8.979A-O.392B+O.246C+O.OO8AB+O.OOOAC+O.128BC+0.000A‘+0.004B2-0.055C?; = 0.880 cement of specific surface 420 m‘/kg gro = 117.5+24.05A-90.80B-67.89C+2.04AB-1.47AC-12.176C-1.00A2+72.766’+13.33C?; ? = 0.996 hm = 0.781-0.076A-0.518B-0.179C+0.024AB+0.009AC+0. 1836C+0.002A2-0.1096‘+0.004C?; P = 0.877 where A CJn content in cementfi]; 6 Na20, content in cement [%I; C - SO, content in cement [%]
r
-
-
Fig. 3. Influence of cement specific surface and C3A and NazOcqcontent in cement on rheological properties of W/C = 0.55 mortars 10 min after end of mixing (cements of S03=3%)
’1 1-51
-A-
-03
I . . . . . . .4
Na20,-
1.1%
-5
0
4 8 C A content [“h]
12
0
I
4
8
CSA content [%I
12
Fig. 4. lnfluence of C3A and NazOcqcontent in cement on rate of rheological properties changes in time of cement mortars with and without PEI superplasticizer (cements of specific surface = 320 m’kg, S03=3%)
344
racek GOLASZE WSKI and Janusz SZWABO WSKI
120
- 0.3Oh;320 m2kg - 0.3%; 370 rn‘kg - 0.3%; 420 m2kg + Na20, - 0.7%; 320 m2kg 4 a - Na20, - 0.7%;370 m’kg + NalO, - 0.7%; 420 m’ikg -0Naa, - 1.1Oh; 320 m2kg + Na20, - 1.1%; 370 rn‘ikg + Na20, - 1.1%; 420 rn’kg --t Nap, -WNa20, -t- Na20,
0,s
100 0.4
80
-
P
E
3
60
W
--
0.3
E E
!?
=
0.2
40
0,1
20
0
0 4
8
C A content ph]
12
I
0
8
4
12
C A content p/.]
cement of smiric surface 320 m2ka gro = 32.34+6.27A- 16.226+22.09~2.8OAB+O.17AGl.56BC-0.1 2A2+18.376‘-3. 47c‘; ? = 0.992 hro = -0 408-0.019A+O.~86+O.388C+O.0l2AB+O,000AC-O,0166C+O.001A2-0.00282-0.083~; ? = 0.891 cement of specMc surface 370 d k g gro = 168.W.45A-122.106-77.37C+4.64AB+1.13AC+22.35EC+O.17A2+27.236’+9.48c‘; ? = 0.900 hro = 0.729+0.011A-0.2656+0.62BCO.00SAB-O.010AC+0.0906C+0.OO1A2+0.01BB1-O. 1lOc‘; ? = 0.897 cement of spec& surface 420 d k g gio = 123.5+12.79A-83.876-78.87Gl.OMB+O. lOAC+9.306C-O.823A2+37.5382+12.38c‘; ? = 0.924 hra = 0.239+0.001A+0.253B-O.193C+O~005AE+O.OOlAGO.055BC-O.OOlA2-0.08&+0.039c‘; ? = 0.907 when, A C A content in cemen@6]; 6 - Na20, content in cement C SOscontent in cement
-
m]; -
Fig. 5. Influence of C,A and Na20, content in cement and cement specific surface on rheological properties of mortars with PEI superplasticizer 10 min after end of mixing (W/C = 0.55; SP = I%, cements of S03=3%
slight decrease of g value of mortars. Further increase of specific surface to 420 m’kg cause distinct increase of g value. It is worth to notice that effect of specific surface on g value of mortars is negligible when cements of low C3A content are used. Effect of alkalis content on g value of mortars is ambiguous and disclose generally for cements of high C3A content. Generally value of g trends to decrease with increasing alkalis content when cements of 2 and 7% C3A are used, and shows minimum for 0.7% alkalis content when cements of 12% C3A are used. Plots on Fig. 3 show that h value of cement mortars depends mainly on specific surface of cement, C3A and NazO,, content are for h value factors of minor importance. Increasing specific surface of cement cause tendency to decrease of h value of mortars. Influence of C3A and NazO, content in cement on h value shows ambiguous trends and generally from workability shaping point of view is out of importance. Influence of cement composition on rheological parameters rate of changes with time was determined only for mortars with cements of specific surface 320 m’kg. Increase in cement specific surface accelerates rate of changes of g and h values with time and causes rapid increase of shear stress of cement mortars. By reason of this measurements of rheological parameters of mortars with cements of specific surface 370 and 420 m’kg after 60 min were not possible to manage. As can be seen on Fig. 4 cement composition influencing mainly changes of g value with time, its influence on changes of h value with time are negligible. Decisive for the rate of g changes with time is C3A content. Value of g always increases with time and rate of this increase increases in direct proportion to C3A content. Influence of NazOeq content is significant only for mortars with cements of 2% C3A content - for such mortars rate of g value increase decreases with increasing NazOe, content.
345
Influence of cement and superplasticizer on rheological properties of mortars
Influence of addition of SMF, SNF and PEl superplasticizers on rheological properties of W/C=0.55 mortars is presented on Fig. 5 and 6. Generally addition of superplasticizer cause drop of g and h values of W/C=0,55 mortars. Only in case of mortars with cements of high C3A content and with SMF superplasticizer g value after 10 min from end of mixing increases in comparison to mortars without superplasticizer. This increase is caused by accelerating action of SMF superplasticizer on cement setting [4]. Effectiveness of PE1 superplasticizer is always higher then of SNF and SMF superplasticizers. It is also worth to underline that low h value of superplasticized mortars creates segregation effects. On the ground of statistical analysis and plots on Fig. 5 and 6 it was found that rheological parameters g and h of superplasticized W/C = 0.55 mortars depend on superplasticizer type and successively on C3A content, NazO,, content, specific surface of cement and interaction of these factors. Content of SO3 in cement in tested range, likewise for mortars without superplasticizer, doesn't influence rheological properties of superplasticized mortars. Value of g of superplasticized W/C=0.55 mortars increases with increasing content of C3A. This increase depends on superplasticizer type and is clearly lowest in case of PE1 superplasticizer addition. Plots on Fig. 5 and 6 well illustrate importance of cement selection for effective usage of superplasticizer and workability shaping. Mortars with cements of 7 and 12% C3A content have, despite superplasticizer addition, higher g value then mortars with cement of 2% C3A content and without superplasticizer. The influence of NazO,, content on g value of W/C=0.55 mortars with SMF and SNF superplasticizers has extreme character and increases with increasing C3A content. For these mortars minimum g value occurs when NazO,, content is 0.7%. 120
-
P
100.
-
-
0.3.
'5
E
--C Na20,
- 0.3%
--tNa20,+Na20, NazO, -ANa20, +Na20, +Na20, +Na20,-
1.1% 0.3% 0.7% - 1.1% - 0.3% - 0.7% 1.1%
i
+Na20, - 0.7% ~
-
E
60
40
0.4
-
80.
4m
0,s
E
z =
-
0.2.
p~
SM F
0.1
20.
0 4
0
0
8
4
CIA
12
content [ O h ]
0
-
I
4
8
C,A
12
content ph]
mortars with SNF superplasticizer gro = 219.0~.01A-97.928-119.2OC+1.87AB+O. 68AC-0.23BC+0.42A2+63.66Bz+19.186; P = 0.925 hro = -0.630+0.025A+0.3628+0.4 13C-O,008AB+O.002AC+0,023BC-O.O02A2-0.290B2-0.0716; ? = 0.966 mortars with SMF superplasticizer gro = 341.90+6.27A-l35.90B-211.30C+6.81AB-0.68AC+lO. 70BC-0.04Az+55.57B2+34.6 2 e ; ? = 0.933 hm = -0.442+0.014A+0.4688+0.282C-0.01lAB-0.006AC-0.064BC-0.002AZ-0.142BZ-0.0456: P = 0.900 .. ~ mortars with PE1 superplasticizer 910 = 163.50-1.07A-180.20B-68.863C+5.83AB+0.04AC+21.04BC+0.18A2+67.88B2+9.266; P = 0.904 hro = 1. 172-O.O38A+O.25O8-O.6OlC-O,OlOAB+O.OO3AC-O.OO38C+O.W2Az-O. 137B2+0.096~; ? = 0.960 where A CIA content in cementfi]; B NazO, content in cement fi];C - SO3content in cement PA] ~~
-
.
-
Fig. 6 . Influence of cement specific surface and CpA and Na20,, content in cement on rheological properties o f mortars with SNF, SMF and PEI superplasticizers 10 min after end o f mixing. (W/C = 0.55; SNF, SMF = 2%; PEI = I%, cements of specific surface = 370 m'kg, S03=3%)
346
Jacek GOLASZE WSIU and Janusz SZWABO WSIU
-
120
0.5
-
100. 0,4.
80
10.3-
1
e=
60I
D
OV2
--t Na20,
0.1 20.
0
1
-
:
-
:
-
1
- 0.3%; 320 m2kg
+ Na& - 0.3% 370 m2kg + Na,O, - 0.3%; 420 m'kg + Na20, - 0.7% 320 m'kg
40
.*
d- Na&-0.7%;
Nap, -0- Na20, -a- Na20, --b Na20,
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- 0.7%; 420 m'kg
- 1.l%; 320 m2kg - 1.I%; 370 m'kg - 1.I%; 420 m'kg 1
Influence of cement and superplasticizer on rheological properties of mortars
347
possible to obtain mortars with negligible low changes of g value with time. When the cements of 7% C3A content are used rate of g value increase with time for mortars with SNF and SMF superplasticizers average appropriately 0.79 and 0.90 N m d m i n and is clearly higher then rate of g increase of mortars without superplasticizer (0.60 Nmdmin) and mortars with PE1 superplasticizer (0.3 Nmdmin). When the cements of 12% C3A content are used rate of g value increase with time for mortars without superplasticizer average 0.80 N d m i n , for mortars with SNF superplasticizer and cement of 0.7% NazO,, content 1.3 N d m i n and for mortars with PE1 superplasticizer - 0.65 N d m i n . Content of NazO,, is important factor for mortars with SNF and SMF superplasticizer rate of g changes with time. For mortars with cements of 2 and 7% C3A rate of g changes with time decreases with increasing NazO,, content. In case of mortars with PE1 superplasticizer the same trend can be observed but influence of NazO,, on rate of g increase with time is weaker. Changes of h value with time of superplasticized W/C = 0.55 mortars shows ambiguous trends depending on superplasticizer type, NazO,, and C3A content. (Fig 4) Value h of mortars with PE1 superplasticizer increases or doesn't changes with time, while h value of SNF and SMF mortars decreases with time. Generally range of h value changes with time is generally low and doesn't influence workability. Character of influence of superplasticizer on rheological properties of cement mix changes depending on W/C ratio [12, 151. Comparing to high W/C ratio mixes, mixes of low W/C ratio are distinguished by considerably higher h value and higher range of changes of g and h values with time [12, 151. Influence of specific surface and cement composition on rheologicat properties of W/C = 0.45 mortars with PE1 superplasticizer is presented on Fig. 7. It is worth to notice that at 3% addition of PE1 superplasticizer mortars of W/C = 0.45 after 10 min from end of mixing characterise by lower g values and considerably higher h values then corresponding mortars of W/C = 0.55 and 1% of PE1 superplasticizer. On the base of statistical analysis was established that g value of W/C=0.45 mortars with PE1 superplasticizer depends successively on: C,A content in cement, NazO,, content in cement, interaction of these two factors and, but in a lesser degree, on cement specific surface and interaction of cement specific surface and C3A content. Simultaneously h value of such mortars depends successively on: specific surface of cement, Na20eqand C3A content. Character of influence of cement composition on rheological properties of W/C=0.45 mortars with PEl superplasticizer changes depending on cement specific surface. In case of mortars with cements of specific surface 320 m2kg g value after 10 min practically doesn't depend on cement composition while h value depends on NazO,, content and increases with its increasing content. Also C3A content influences h value. Character of this influence depends on Na20, content - for cements of low NazO,, content increase of C3A content cause increase of h value, while for cements of high Na20eq content increase of C3A content cause decrease of h value. In case of mortars with cements of specific surface 370 and 420 m2kg its rheological parameters are more strongly influenced by cement composition. Value g of these mortars increases with increasing C3A and NazO,, content. Simultaneously h value increases with increasing C3A content and decreases with increasing NazO,, content. Specific surface of cement alone only slightly influences g value of W/C=0.45 mortars with PEl superplasticizer - increase of specific surface of cement increases g value. In the same time increase of specific surface of cement causes significant drop of h value. Range of h value chan5es due cement specific surface variations is higher then range of h value changes due variations of cement composition.
348
Jacek GOLASZEWSKIand Janusz SZWABO WSH
+Na20,
- 0.3%
100
+Na20,-Na20,
- 0.3%
80
-&-NaZO-, +Na20,
120
1.1%
-
+Na20,-
z $
0.5
0.4
1.1% 0.3%
-B
1.1%
B =
60
0.3
L.
I
3
m
0.2
40
0,1
20
Y
0
0
I
8
4
I
12
4 8 CIA content ph]
C,A content ph]
mortars with PE2 superplasticizer gro = 74.65+0.98A+24.89B-50.5lC-O,03AB+0.20AC-5.41BC-0.01AZ-3.75P+9.04cZ; ? = 0.953 hro = -0.118-0.033A+0.2228+0. l89C4,Ol5AB+O,OllAC-O,O42BC+O.00lAz4.O33BZ-O.035cZ~? = 0.887 mortars with PE3 superplasticizer gro = 156.3(r2.4OA-45.748-85.79C+4.38AB-O.17AC+O.66BC+O. 16A2+26.9682+13.62C1; f = 0.934 hro = ~.278+0.002A+O.089B+O.431C-O.O1OAB-O.001AC+O.062BC+O.000AZ-0. 166Bz-0.078cf; f = 0.895 mortars with PC superplasticizer gro = 141.4-2.13A-76.348-72.O3C+3.3BAB+O.26AC+8.29BC+O.O8Az+31.62~+1O. 75cZ; ? = 0.921 hro = 0.O95-0.~2A+0.4328+0.006C+0.wOAB-0.004AC-0.074BC+0.001Az-0.156B2+0.012 e ; f = 0.917 where A C A content in cementi%]; B NazO, content in cement [%I; C SO, content in cement [%I 8. Influence of CjA and NazO, content in cement on rheological properties of cement mortars with PC,
-
Fig.
12
-
-
PE2, PE3 superplasticizers 10 min after end of mixing (W/C=0.45; SP-2%; cements of specific surface = 370 m2/kg, S03=3%) 120
100
E E
3
NaSO,
- 0.3%
--tNa20,-9-Na20, +i+ Na20, +Na20,+Na20, +Na20, -Na20,-
- 0.3% - 0.7% 1.1% - 0.3% - 0.7%
-4-
80
0.5
1.1%
0.4
-
1.1%
0.3
B
1
60
3
m
=
0.2
40
0.1
20
I
0 0
4
8 C,A content ph]
12
0
4 C,A
12
content [%I
Fig. 9. Influence of C,A and Na20, content in cement on rheological properties of cement mortars with PC, PE2, PE3 superplasticizers60 min after end of mixing (W/C=0.45; SP-2%; cements of specific surface = 370 m’kg, SO&%)
Influence of cement and superplasticizer on rheological properties of mortars
349
Value g of WIC = 0.45 mortars with 3% PE1 superplasticizer addition increases with time, while h value of these mortars, in opposite to WIC = 0.55 mortars with PEl superplasticizer, strongly decreases. Character of changes of g value with time of WlGO.45 mortars with 3% PE1 superplasticizer is generally similar to changes of g value of WlC=O.55 mortars without and with 1% PE1 superplasticizer. (Fig. 4) Rate of g value increase with time of W/C=O.45 mortars with 3% PE1 superplasticizer depends on specific surface of cement - increases from 0.20 Nmm/min for mortars with cements of 320 m’kg to 0.42 Nmdmin for mortars with cements of 420 m2ikg, on C3A and NazO,, content - increases with increasing C3A and Na20, content, and on interaction of these factors. Rate of h value decreases with time depending on complex interaction of specific surface of cement and C3A and NazO,, content and reach minimum for mortars with cements of specific surface 320 m2/kg, 2% C3A and 1.1% Na20e, content. Generally h value rate of decrease increases with increasing specific surface of cement and C3A content and decreasing Na20, content. Statistical analysis of obtained results and plots on Fig. 8 and 9 indicate that for particular specific surface (in discussed case 370 m2/kg) character of influence of cement composition on rheological parameters of W/C=O.45 mortars with PC, PE2, and PE3 superplasticizers is qualitatively similar. Rheological properties of these mortars depend successively on: g value - C3A and Na20eq content and interaction of these factors, h value - NazO,, content, interaction between C3A and Na20eqcontent and C3A content. There are the same factors and in the same order like in case mortars with PEl superplasticizer. Also for mortars with PC, PE2, and PE3 superplasticizers it was found that, in investigated range of changes, SO3 doesn’t influence rheological parameters. Values g of WIC = 0.45 mortars with PE3 and PC superplasticizers 10 min after end of mixing are similar. In that case g value increases with increasing C3A and NazO,, content and influence of increasing NazO,, content is especially meaningful when cements with high C3A content are used. Values g of WIC = 0.45 mortars with PE2 at a lesser extend depends on C3A content, showing in the same time strong dependence on Na20eq content and tendency to increase with increasing NazO,, content. Values h of WIC = 0.45 mortars with PE2, PE3 and PC superplasticizers 10 min after end of mixing depends mainly on type of superplasticizer. In case of superplasticizers PE3 and PC addition, which characterise by higher then and PE2 molecular weight, h value of mortar is clearly higher. Character of cement composition influence on h value of mortars with PE2, PE3 and PC superplasticizers depends on type of superplasticizer added. Increasing C3A content in cement causes decrease of h value of mortars with PC and PE2 superplasticizers, while h value of mortars with PE3 superplasticizer increases or decreases depending on NazO,, content. Increase of Na2Oeq content doesn’t influence or decreases h value of mortars with PC and PE superplasticizers. Rate of g value increase with time of W/C = 0.45 mortars with PC and PE3 superplasticizers is lower then mortars with superplasticizer PE2. Rate of increase of g value in time of these mortars increases with increasing C3A content and reach maximum for cements with 0.7 YO NazO,, content (PC 1, PE3 superplasticizers) or 1,1% NazO,, content (PE2 superplasticizer). The least changes of g value with time proceeds for mortars with cements of 2% C3A content and 0.3% Na20eq content. Value h of all tested WIC = 0.45 mortars, independently on cement composition and superplasticizer type, decreases with time. The rate of h value decrease depends first of all on superplasticizer type and is clearly higher for mortars with PC superplasticizer then for mortars with PE2 and PE3 superplasticizers. Rate of h value decrease depends also on C3A and Na20,, content - in case of mortars with PE2 superplasticizers decreases with increasing C3A content, in case of mortars with PE3 and PC superplasticizers minimum rate of h value decrease appears for cements of 7% C3A. Higher Na20eqcontent in cement foster higher rate of h value decrease.
3 50
Jacek GOtASZEWSKI and Janusz SZWABOWSKI
On the base of obtained relationships a simple mathematical models can be developed. Such models, developed for mortars without and with SNF, SMF, PC and PE superplasticizers (see Fig. 3 8), include wide range of C3A, Na20, and SO3 contents in cements and can be successfblly used for initial selection of cements and superplasticizers from point of view of its compatibility and character of its influence on rheological parameters of cement mixes. Simultaneously, for the sake of possibility of significant differences between effectiveness of different superplasticizers and omission of influence of form of gypsum and interaction of cement specific surface and cement accuracy of such selection of cement and superplasticizer should be experimentally confirmed.
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SUMMARY Workability shaping of fresh HPC should be conducted on the ground of rheology - required workability can be achieved by adjusting rheological properties of concrete mix to the given method and conditions of concrete processing. Basis of fresh concrete rheological properties shaping are data and relationships from rheological studies performed using rheometrical methods. In the presented investigation basic relationships of influence of cement specific surface and cement chemical and mineral composition on rheological parameters of superplasticized model mortars were defined using rheometrical test. These relationships provide unequivocal physical information on character of cement and superplasticizer influence on properties of HPC concrete and can be used for choice of compatible cement superplasticizer system and for workability of HPC shaping.
LITERATURE [ l ] Szwabowski J.: Rheology of cement based mixes (in Polish). Wyd. Politechniki Slqskiej, Gliwice, 1999. [2] Aitcin P-C.: High Performance Concrete, EF&N SPON 1998. [3] Aitcin P-C.: Durable high performance concrete art and knowledge (in Polish). Conference ”Beton na progu nowego milenium”, Krakow, 2000, pp. 383 - 413. [4] Ramachandran V.S.: Concrete Admixtures Handbook. Properties, Science and Technology, Ed. V.S. Ramahandran, Noyes Publications, Park Ridge, New Jersey, USA, 1995. [5] Proceedings of the International RILEM Conference ,,The Role of Admixtures in High Performance Concrete” Ed. J.G. Cabrera and R. Rivera - Villarreal. Monterrey, Mexico, 1999. [6] Proceedings of International Congress “Creating with Concrete” Ed. Ravinda K Dhir & others, Dundee, Scotland, UK, 1999. [7] Proceeding of Sixth CANMET/ACI International Conference on Superplasticizers and Other Chemical Admixtures in Concrete. Ed. V.M. Malhorta, Nice, France, 2000. [8] Teubert J.: Measuring the consistency of concrete mortar and its importance to the workability of fresh concret, Betonwerk + Fertigeil Technik, (4), 1981, p. 6. [9] Banfill P.F.G.: The rheology of fresh mortar. Mag. of Concrete Research, Vol. 43, No 154, 1991, pp.13-21. [lo] Meader U., Kustrerle W., Grass G.: The rheological behaviour of cementitious materials with chemically different superplasticizers, in Proceedings of the International RILEM Conference ,,The Role of Admixtures in High Performance Concrete”, ed J.G. Cabrera and R. Rivera - Villarreal, Monterrey, Mexico, 1999, pp. 357 - 316. [ l 11 Giergiczny Z., Matolepszy J., Szwabowski J., Sliwihski J.: Cements with mineral additives in concretes of new generation (in Polish). Wydawnictwo Instytut Sl4ski sp. z 0.0. w Opolu, Opole 2002, p 189. [12] Faroug F., Szwabowski J., Wild S.: Influence of Superplasticizers on Workability of Concrete, Journal of Materials in Civil Engineering, Vol. 11, No. 2, 1999, pp. 151-157. [ 131 Tattarsall G.H., Banfill P.F.G: The Rheology of Fresh Concrete, Pitman Books Limited, Boston 1983. 1141 Jiang S.; Kim B-G.; Aitcin P-C.: Importance of adequate soluble alkali content to ensure cernenthperplasticizer compatibility. Cement and Concrete Research. Vol. 29, 1999, pp. 71-78. [15] Golaszewski J, Szwabowski J.: Rheological behaviour of fresh cement mortars containing superplasticizers of new generation. Kurdowski Sympozjum. Science of cement and concrete. Krakow, 2001, pp. 1 11- 135.
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Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, KC. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
ANALYSIS OF CONCRETE PROPERTY FIELDS AND SEARCH FOR THE BEST COMPOSITIONS USING MONTE CARL0 METHOD Tatiana LYASHENKO, Vitaly VOZNESENSKY Odessa State Building and Architecture Academy PO Box 76 Main Post Office, Odessa 65001, Ukraine, e-mail: [email protected] Shimon BOIKO Concretec Ltd. Har-Hozvim, PO Box 45010, Jerusalem 91450, Israel David SHTAKELBERG Standard Institution of Israel 7 Yad Harutzim St., PO Box 10258, Jerusalem 93420, Israel ABSTRACT Rational compositions that would guarantee the required levels of six properties of ready-mix in-situ concrete for framed buildings have been determined. To do this computational experiments on property fields in composition coordinates have been carried out using experimental-statistical models and Monte Carlo method. For compositions providing a fixed level of specific property isoparametric analysis has been fulfilled to evaluate the variations in other properties. Keywords In-situ concrete, guaranteed quality, computational experiment, optimization, isoparametric analysis.
INTRODUCTION The concept of fields Y(x) of composite properties Y in coordinates of mix proportions and technological parameters (vector x) is aimed at deriving, as much as possible, information about multi-component materials behavior from experimental data [ 13. For this purpose computational experiments on property fields, described by structured multifactor experimental-statistical (ES) models [2], are carried out. They allow materials science regularities to be evaluated and solutions that would guarantee required quality of the material to be found with specified risk taken into account. To account for the risk the modeldeterminate level of property field at any point in the region of composition and process parameters is transformed into random value by inclusion of the model error related to experiment [3]. So, analysed in computational experiments, using Monte Carlo method, are full and local fields, which can be random or “of guaranteed level”[ I]. Generalising numerical indices of the fields [4] make it possible to compare the fields, to estimate their transformations as composition and technological factors change, to evaluate changing
352
T. LYASHENKO,
v. VOZNESENSKY, s. BOIKO, D. SHTAKELBERG
correlation between the properties [3, 51. Thus the concept and special means of its operation allow rational compositions and technological parameters to be assigned that would provide required levels of properties. The analysis of property fields described on the data of designed experiments has made it possible to evaluate the influence of composition on properties of mixes, characteristics of structure and hnctional properties for a number of composites [ 11. Such analysis helps to find optimal compositions, with levels of quality criteria guaranteed, for some jobs that impose specific requirements on the materials, in particular, on in-situ concrete for framed buildings. CONDITIONS OF EXPERIMENT AND MODELLING The experiment was carried out at the Standard Institution of Israel (by international and Israel standards). Mix components and base mix proportions were received from ready-mix producer. Variables in the experiment (according to optimal design) were the quantity of cement (C), XI= 280 -I 30 kg/m3, crushed aggregate-sand ratio (CNS, by mass), X2 = 2.23 ? 0.25, and two modification factors - dosages of admixture (A, of D-G type), X3 = 0.56 0.14, and of fine-grained dolomite filler (F, 190 m2/kg), X4 at levels of 10, 50, 60 kg/m3. Constant content of water, 200 dm3/m3,was conditioned by NMR-procedures used to analyse structure formation process [6]. Based on values of properties of concrete mix and hardened concrete of 18 compositions, corresponding to optimal design of experiment, four-factor non-linear ES-models (with normalized I x, 151) were built to describe the property fields in composition coordinates. Such model (presented in [3] in structured form) for strength R (MPa) of 28-day concrete has 8 significant terms (at experimental error SR =1.34 MPa and one-sided risk 0.1):
R = 24.74 + 4.27~1- 0.71~2+ 1.90~:
+ 1.58xlX4 + 1.15X2X3 + 0 . 7 6 ~ 2 ~+40 . 6 6 ~ 3 ~ 4
The main generalizing indices of the field “composition - compression strength”, R(x), estimated by the model above, are: R,, = 34.4 at X I = x2 = x3 = x4 = +1 (C=310, CA/S=2.48, A=0.70, F=60), R,,, = 18.1 at X I = x3 = -1, xz = 0.29, x4 = +1, absolute increase AR= 16.3 MPa, relative increase 6R= 190%. To determine the rational compositions of the concrete the fields of six properties have been analysed in computational experiments on the fields, using Monte Carlo method with ES-models analogous to equation R(x) shown above. The levels of three from six criteria were specified. Firstly, the concrete had to be of grade B-20 (Israeli Standard 118), i.e., to provide average strength R 1 2 4 . It was decided, however, to set harder requirement, since R levels estimated by ES-model for any composition xu, when searching for the best one, would be within confidence interval R, = R(x,) k AR(x~),where AR(x,) = s R tu . [d(~”)]’.~,ta - quantile of standard normal distribution corresponding to certain risk a (acceptable when making technological decision), d - depending on xu prediction variance hnction (defined by experiment design and model structure). So average value (over region of x, with a = O.l), AR = 1.72, has been added to specified level of R, giving the lowest value of R = 25.72 that would guarantee required 24 MPa. Secondly, the slump (S) of concrete mix had to be not less than 12 cm (Israeli Standard 26). To guarantee this level more severe requirement has been fixed, S 2 12.6 cm. Thirdly, special requirement was imposed on mixes for in-situ construction of framed buildings. Column specimens 2.4 m high were made from each of the 18 mixes, by vertical placement of concrete in pipe forms of 10 cm diameter, to be cut into cylinder slices after 28
353
Analysis of concrete property fields and searchfor the best compositions using Monte Carlo ...
days of hardening. As agreed with the customer the ratio of strength in lower cylinder (RL)to that of upper cylinder (Ru), KLU = 100(Rr/RU), had to be within 95-105%. This would eliminate the occurrence of substantial gradients in the fields of strength along the vertical concrete elements of building frames. The inclusion of confidence intervals AKLUhas led to harder requirement, 98 I KLUI 102%. No rigid requirements have been posed for three other criteria but it has been proposed to improve their levels, with respect to median level, Y M=~O.S(Y,,+Y,i,), of the fields of these criteria in coordinates of mix proportions. Thus, it would be useful to maximize elastic modulus of the concrete, beyond E = 16.1 GPa, minimize the shrinkage, to E less than 0.53 m d m , and minimize special index of non-uniformity in pole element, defined as the ratio of strength in strongest and weakest fragments, 6 = 100(RmaX/R"'"),below 6 ~ , = 114%. OPTIMISATION
Prior to multi-criterion search for rational compositions of the concrete, the compositions optimal by each individual quality criterion (Table 1) have been analysed. Table 1
Characteristics of optimal compositions by individual criteria of concrete quality
Levels of )articular criteria
Quality criteria of in-situ concrete for framed buildings sei :rely specified S, crn
:optimised
P
23.3 -
10.3 14.1
0.39
18.2
0.36 -
20.9
0.42
12.6
0.53
104
1
114
As it could be expected none of the five compositions in Table 1 would satisfy the stringent standard requirements for all three criteria. In particular, the composition of Em, (XI= +1, x2 = x3= x4 = -1; C=310, CA/S=1.98, A=0.42, F=lO), which complies with requirements for R and S, would be unacceptable by KLU. Multi-criterion search for admissible compositions in four-factor region ( X I , x2, x3, xd} of property fields has been fulfilled with algorithm using Monte Carlo method iteratively (for multi-dimensional random scanning). At first iteration N = lo4 uniformly distributed random points (compositions) have been generated in the intervals -1 I X I , x2, x3, I + I and for them 10000 values of each quality criterion (S, R, KLU,E, E, 6) have been calculated. The generated compositions (with added 16 at vertices of 4-dimension cube) which would not comply with all the requirements defined above were deleted. All guaranteeing requirements (on S, R, KLU) would be fulfilled only by 169 compositions (out of 10016), the greatest elimination being by strength gradient oriented
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T. LYASHENKO, V. VOZNESENSKY,S.BOIKO, D. SHTAKELBERG
down along the pole (violating KLU 102). The algorithm determined automatically the volume of permissible compositions region R 1.7% (of all the region of compositions). If the requirements have not been stringent the size of permissible region would be near 8%. Accounting for three additional quality criteria (requirements for E, E, and 6 being not worse than their median levels) reduce the number of acceptable compositions to 22. These present the region of compromise; its volume R, 0.2%. Table 2 shows some results of the first iteration. After reducing the region of search almost 500 times a number of compositions have been found which not only meet the stringent requirements for S , R, and KLU,but have three optimality criteria at levels not less than median as well. The composition providing Rm,, = 30.7 MPa and all other properties approaching their best levels has been of special interest, but corresponded to increased level of cement, 3 10 kg/m3. Table 2
Characteristics of compromise compositions obtained at 1-st iteration
Levels of Darticular criteria
Limits
-
Quality criteria of in-situ concrete for framed buildings severely specified to be optimised
Factors
XI
1
x2 x3 x4 1 0.9
0.2 -1
0
1
-1 -0.E
1 0 - 1
12.8
25.9
98.2
16.1
0.41
105
16.4
26.3
100.8
16.5
0.52
114
18.2
0.42
109
18.1
0.41
107
16.6
0.46
105
1 1 - 1 1
Best value
1
-1
0
-1
1
-1
0
-1
12.8
30.2
98.2
1 1 - 1 1
15.1
30.7
99.0
1
15.8
28.5
99.0
1
I
-1
1
-1
1
The analysis of the location of compromise region along the axis of each factor allows the results to be refined at the second iteration. Helpful in the analysis are frequency polygons (Fig. 1) for values of factors corresponding to compositions obtained at the first iteration (22 points enclosed in region of compromise). These polygons define the shortened intervals in which next lo4 random points could be generated. Thus amount of cement can be varied as 0 I X I S +I (the lower limit being offset by average step of scanning at previous iteration, Ax = 0.2). Since values of three other factors (CNS, A, F) for promising compositions have grouped near the boundaries of factor intervals, three possible combinations fotm compositions clusters A, B, C: A + x2 from 0.8 to+1, x3 from -1 to-0.7, x4 from 0.8 to+1; B + x2 from0.8 to+1, x3 fromO.l to +1, ~4 fkom-1 to-0.5; C -+ x2 from -1 to -0.3, x3 from 0.1 to + I ; x4 from -1 to -0.5. Between these three clusters 10000 random points have been distributed at the second iteration of the search for adequate compositions, the proportion being 1:2: 19 (accounting for number of compositions in respective zones after 1'' iteration). Guaranteeing requirements have appeared to be fulfilled by 915 of 10016 concrete
Analysis of concrete property fields and search for the best cornpositions using Monte Carlo ...
355
Figure 1. Distributions of factor values in compromise compositions found at the 1'' iteration compositions analysed at the 2"d iteration. To choose the best from them by optimality criteria (E, E, and 6 ) step-by-step reduction of compromise region has been carried out, starting with median levels of the criteria as boundary levels. In particular, minimal level set for E could be increased by O.l.(E,,,m-E~e) = (26.0-16.1) = 0.1 GPa at each step. Only 10 compositions have been left within the final zone of compromise, where 18.11 E 5 18.7,0.411 E 1 0.44, and 1.07 5 6 5 1.09. Nine of them have approximately the same C N S = 2.48, quantities of admixture, A = 0.42 kg/m3, and filler, F = 60 kg/m3 (XI= x4 = +I, x3 = -1; with accuracy equal to step of scanning at 2"d iteration Ax = 0.08), minimal amount of cement being about 290 kg/m3 (XI= 0.7). This composition meets all the requirements imposed on the concrete. It has S = 15 cm, R = 29 MPa, KLU= 99%, and rather high levels of the properties which have been optimised: E -1 8.5 GPa, E = 0.44 m d m , and 6 = 106.
ISOPARAMETFUC ANALYSIS
To make the final choice of the composition it has been reasonable to analyse the local fields of six properties Y(x1, x2) at x3 = -1 and x4 = +1, in coordinates of cement content and crushed aggregate-sand ratio at low concentration of the admixture and high quantity of the filler. The fields are represented in Figure 2 (heavy net corresponds to forbidden compositions and the star to the optimal one). The difference in shape of the fields substantiates the complexity of the problem - to provide the necessary levels for many criteria of concrete quality through controlling concrete composition. The requirement KLU = 100 f. 2 imposed on concrete in the column elements has proved to be extremely tough. This can be seen in Figure 2. So, it has been reasonable to estimate the changes of other properties in this narrow range of KLU. The problem is solved with isoparametric analysis [7]. The movement along the line KLU = 100 (along projection of the arrow shown in Fig. 2) on the field of respective property could be realized in computational experiment, by increasing cement content from X I = -1 to + I . To keep KLU at indicated level the crash aggregate-sand ratio should be varied by non-linear dependence XI = 0.71 + 0.15X1+ 0 . 1 6 ~ 0~. ~ 12~1 ~0.16~1~. Monte Carlo method provides rather simple way to obtain the information on variations in properties of compositions that would give the same level of some property (KLU= loo), with isoline being transformed into the strip (KLU= 1OOf.2, formed by required boundaries).
356
T.LYASHENKO, V. VOZNESENSKY, S. BOIKO, D. SHTAKELBERG
1
1
1
1
1
1
1
1
Figure 2. The fields of concrete properties in coordinates of C and C N S at fKed dosages of modifiers Shown in Figure 3 are the results of isoparametric analysis of five quality criteria of ready-mix concrete at conditions providing practically the same values of concrete strength in lower and upper fragments of the column. Placed inside a given corridor, along the line KLU(X~, x2) = 100, are 200 of 2500 generated points. The values of five properties for these 200 compositions also form the corridors in which properties change as quantities of components are varied. Concrete strength grows, naturally, as the content of cement increases (at constant water
Analysis of concrete property fields and searchfor the best compositions using Monfe Curlo ...
S
357
6
"1
I
E
KLU
30 28 26 24 22 20
I8 16
1
0.5
0
-0.5
-1
Figure 3. Isoparametric analysis (along the line KLU= 100) of ready mix concrete properties (at A = 0.4 and F = 60 kg/m3) content) and achieves the level R = 25.6 (marked with star in Fig.' 3), that would guarantee standard requirement of 24 MPa, at C > 280 kg/m3 ( X I > 0). The levels of all other properties therewith also comply with the requirements discussed above. It should be noted that R grows throughout cement content range, whereas the increase of E and decrease of slump stop just from C = 280. The results of isoparametric analysis allow the composition of ready-mix concrete for insitu construction of framed building, found after two iteration of multi-criterion search with the use of Monte Carlo method, to be accepted as guaranteeing multi-criterion requirements.
CONCLUSION Computational experiments on the fields of composites properties in coordinates of compositions, specifically, using Monte Carlo method, serve as effective means of computational materials science. The tools presented make possible the controllable multicriterion search for optimal compositions and evaluation of relations between composite properties when one of them is invariable. Determined have been the rational compositions of ready-mix concrete with account for criteria of uniformity of the material in pole elements.
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T. LYASHENKO, V. VOZNESENSKY, S. BOIKO, D. SHTAKELBERG
REFERENCES 1. Lyashenko, T.V. Building Materials Property Fields (Concept, Analysis, Optimisation). Abstract of Thesis for Doctor of Science Degree (in Ukrainian). Odessa State Building and Architecture Academy, Odessa, 2003, pp 34 2. Lyashenko, T.V. Brittle matrix composites optimization on the base of structured experimental-statistical models. In: Proc.Int.Symp. “Brittle matrix composites 3”, A.M. Brandt and I.H. Marshall eds., Elsevier Applied Science, London 1991, pp 448-457 3. Lyashenko, T.V., Voznesensky, V.A. Modelling and analysis of varying correlation between properties of brittle matrix composites. In: Proc.Int.Symp. “Brittle Matrix Composites 5”, A.M.Brandt, V.C.Li, and LH.Marshal1 eds., Woodhead Publ. Ltd. - Bigraf, Cambridge-Warsaw 1997, pp 417-426 4. Voznesensky, V.A., Lyashenko, T.V., Modelling, analysis and optimization of brittle matrix composites properties fields. In: Proc.Int.Symp. “Brittle Matrix Composites 4”, A.M.Brandt, V.C.Li, and I.H.Marshal1 eds., Woodhead Publ. Ltd. - BigraE CambridgeWarsaw 1994, pp 255-263 5. Lyashenko, T.V, Voznesensky, V.A, Krovyakov, S.A. Analysis of water effect on fracture toughness in cement-based composites using computational materials science methods. In: Proc.Int.Symp. “Brittle Matrix Composites 6“,A.M.Brandt, V.C.Li, and I.H.Marshal1 eds., Woodhead Publ. Ltd. - ZTUREK, Warsaw 2000, pp 210-219 6. Lyashenko, T., Voznesensky, V., Boiko, S., Shtakelberg, D. Experimental-statistical modeling and analysis of the chain “composition - NMR-signal - properties” of cement composite. In: Proc.lOth Int. Congress on Chemistry of Cement, V.3., Gothenburg 1997, pp 4~003,s 7. Voznesensky, V.A., Lyashenko, T.V., Ivanov, Y.P., Nikolov, I.I., Computers and Optirnisation of Composite Materials (in Russian). Budivelnik, Kiev 1989, pp 240
Proc. Int. Symp. ,,BrittleMatrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
CEMENT-BASED MATERIALS INCORPORATING RUBBER AGGREGATES: SHRINKAGE LENGTH CHANGES Anaclet TURATSINZE'", Sandra BONNET (I9*) and Jean-Louis GRANJU ( I ) ( I ) Laboratoire Matkriaux et Durabilitk des Constructions (LMDC) 135, av de Rangueil, 31077 Toulouse cedex 04, France (*)Agence De I'Environnement et de la Maitrise de I'Energie (ADEME) 2, Square Lafayette, 49004 Angers, France ABSTRACT Cement-based materials are brittle. As a consequence to their poor straining capacity and their sensitivity to shrinkage, they generally present cracking detrimental to the durability of structures. Nowadays, a solution to prevent or to delay the shrinkage cracking remains a research issue. Fibre reinforcement, restraining the crack opening, is one of the most documented way to partly reach this objective. This paper focuses on a second option to decrease the brittleness of cementious materials: the incorporation of low modulus aggregates. The study aims to design a composite exhibiting a high straining ability before macrocracking localisation. It has been assumed that incorporating aggregates with low deformation modulus should succeed with the challenge. Rubber aggregates were chosen. They confer to the work a second facet: the opportunity to recycle rubber tyres, fulfilling a demand of clean environment conservation. The results presented compare the properties of a plain mortar with the ones of two mixes obtained by partially replacing the sand aggregates by rubber aggregates. Two ratios of sand replacement, 20 and 30 % by volume, were investigated. In both cases (natural sand and rubber aggregates), a maximum grain size of 4 mm was used. Previous results had shown that rubber aggregates are strongly detrimental to the composite strength. In return, the modulus of elasticity of the mortar incorporating rubber aggregates is substantially decreased and its straining capacity before failure is significantly increased. On another hand rubberised mortars suffer higher length changes due to shrinkage than plain mortar. In order to weigh up benefits and deficits, ring tests have been carried out and their results clearly demonstrate the benefit: the straining capacity enhanced by rubber aggregate substitution widely offsets the additional shrinkage length changes. The future prospects are the combination of the beneficial effects of both the fibre reinforcement and the rubber aggregate substitution to design a cimentitious composite exhibiting enhanced ductile failure. Keywords Brittleness, straining capacity, modulus of elasticity, compressive and tensile strengths, length changes, rubber aggregates, shrinkage cracking, ring test, ecology.
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Anaclet TURATSINZE, Sandra BONNET and Jean-Louis GRANJU
INTRODUCTION Cement-based materials, the prominent fraction of construction materials, are perfectible. Due to their poor straining capacity and their low tensile strength, they are sensitive to cracking particularly to shrinkage cracking. For instance, large area elements (slabs on grade, pavements.. .) are often cracked, this cracking being strongly marked in the case of restrained shrinkage. The cracking of cement based repairs also is relevant of a similar problematic. It has been evidenced that such a cracking is the main cause of their debonding initiation and, consequently, of the limitation of their service life [ 1-21. Fibre reinforcement is generally used to limit the detrimental effect of cracking, but the ideal solution to avoid the handicaps would be to improve the straining capacity of the material before cracking localisation. In this regard, it has been assumed that incorporation of aggregates with low deformation modulus would be a solution. In our research programme rubber aggregates obtained from shredded non reusable tyres have been used, conferring to the study an ecological interest. Previous results confirmed that rubber aggregate substitution is detrimental to both compressive and tensile strengths. In turn, as expected, a cement composite containing such particles presents low deformation modulus. Four-point flexure tests show that it exhibits a high straining capacity before the peak load in accordance with the research objective. However, the presence of such deformable particles as aggregates implicitly infers that the internal restraint by the aggregate is reduced, inducing an increase of free drying shrinkage length change. Consequently, rubber aggregate substitution leads to a couple of phenomenons with opposite effects in relation with restrained shrinkage cracking. Ring tests demonstrate that the balance between the improved straining capacity and the increased shrinkage length change is beneficial.
BACKGROUNG Materials Preliminary tests have been performed in order to access the influence of rubber aggregate substitution on the basic mechanical properties of cement-based materials. The experimental setup is reported in [3]. The control material is a mortar with a CEM I 52.5 R Portland cement and natural sand. Its mix proportions are given in table 1. Modified mixes are made of the same mortar with a volume percentage of rubber aggregates replacing the same volume of natural sand. In order to reduce the bleeding and segregation prominently noticed when rubber aggregates are added (densities of sand and rubber aggregates are 2.7 and 1.2 respectively), an admixture was used as a stabiliser. Known as Underwater Concrete System (UCS), this admixture was designed to increase cohesion and to prevent cement washout. The stabiliser may affect the properties of the material. For this reason, in order to point out the actual influence of rubber aggregate substitution, the stabiliser was also used in the mix without rubber aggregates. The grading curves of sand and rubber particles are given in figure 1 and two rubber aggregates contents have been investigated: 20 and 30 % of the aggregate total volume. The different mixes studied will be designated using their rubber aggregate substitution ratio, the letters M and R referring to Mortar and Rubber respectively. For instance M30R means the mix incorporating 30 % of rubber aggregates.
Cement-based materials incorporating rubber aggregates: shrinkage length changes
36 1
100
#
E
40 20
0 0.01
0.1 1 Sieve size (mm)
10
Figure 1 - Grading curves of sand and rubber aggregates Basic mechanichal properties Whatever the particle size and shape, it is well established that rubber aggregate substitution is detrimental to tensile and compressive strengths of the cement-based composites [4-61. Our results are presented in figures 2, 3 and 4. They confirm this general trend. Figures 2 and 3 show that the maximum of rubber aggregate substitution should be limited if a minimum strength is required. For instance 30% of rubber aggregates substitution induces about 80% compressive strength loss and about 70% tensile strength loss. The variation of the deformation modulus with rubber aggregates substitution is presented in figure 4. As expected, the results show a significant decrease of the compressive deformation modulus when rubber aggregate content is increased. Eldin et al. [5] explained this trend through the low elasticity modulus of rubber aggregates, which they considered as acting as large pores. Such a view is not strictly accurate. Although rubber can undergo very high deformations, it exhibits a bulk modulus of the order of 1 GPa with the associated capacity to transfer stresses. Evaluation of the tensile deformation modulus (not presented here) shows a similar trend but with an amplitude about 1.5 times higher.
0
10
20
30
Rubber aggregate contents (Oh)
Figure 2 - Compressive strength versus rubber aggregate substitution
362
Anaclet TURATSINZE?Sandra BONNET and Jean-Louis GRANJU 41
2
E. 5m
-.--e E
3'
2.
a,
e
f
-
1.
0%
Figure 3 - Tensile strength'versusrubber aggregate substitution
25000
1
-. 0
10
20
30
Rubber aggregate contents (%)
Figure 4 - Compressive modulus of deformation versus rubber aggregate substitution STRAINING CAPACITY OF RUBBERISED MORTAR
Experimental setup The straining capacity has been evaluated through four-point flexure tests. The test setup is presented in figure 5. LVDT
c
a=
14Oinin
. - .
& :
c= S5
min
b Figure 5 - Ex:erimental
setup forevaluation of straining capacity
Cement-based materials incorporating rubber aggregates: shrinkage length changes
363
The tests were carried out at 28 days on a series of four prismatic specimens (85x50~420 mm’) that had been continuously cured at 20°C and 100% R.H. The deflection 6 of the specimen was measured with a yoke by reference to the specimen itself. The tests were controlled by this deflection 6 at the rate of 50pdmin. The load F and the deflection 6 were automatically and continuously recorded by a data acquisition system. Results and discussion Curves in figure 6 are representative of the test results. It is well known that in flexure crack is initiated largely prior to the peak load. However, as far as the post peak zone is not reached, there are grounds to believe that microcracks coalescence is not achieved. For this reason we have considered the straining capacity of the material before cracking localisation as the deflection 6 corresponding to the peak load. With regard to such a definition, results illustrated by the curves in figure 6 show that rubber aggregates significantly increase the straining capacity of cement-based mortars. For instance, it turns about three times higher when the volume fraction of rubber is increased from 0 to 30%. It is an interesting result with regard to the objective. Such a behaviour can be explained by the rubber particles capacity to absorb energy when the microcrack tips run into their interface with cement paste, denying a mechanism for further propagation and delaying the macrocrack formation. In this sense, they act as crack arresters.
‘OR
51
0
M2OR
4
I
0.1
0.2 0,3 Deflection (mm)
0.4
0,5
Figure 6 - Four-point flexure tests: load versus deflection curves, influence of rubber aggregate substitution . SHRINKAGE LENGTH CHANGES
As it has been shown, rubber aggregates substitution enhances the straining capacity of cement based composites. However such a finding is not enough to conclude that the composite is less sensitive to drying shrinkage cracking. Actually, shrinkage cracking is the result of the coupled effects of three factors: the free shrinkage, its degree of restraint [7-81 and the straining capacity of the material. Free shrinkage tests Free shrinkage tests have been carried out in accordance with NF P 15-433 recommendation. The used 40x40~160mm’ prismatic specimens were continuously exposed to drying, the
364
Anaclet TURATSINZE,Sandra BONNET and Jean-Louis GRANJU
curing conditions being 20°C and 50% relative humidity. Plots of free shrinkage versus time are presented in figure 7 where each point results from the average of three tests.
f
3000
-
1500
-
I000
-
500
0
1 & : I : : : : : : ;
0
50
i : i : : : : : : ; : : : : ;
100
150
200
i : : : ; : : : : ; : :
250
300
350
::I
400Time(days)
Figure 7 - Free shrinkage versus time, influence of rubber aggregates substitution. Higher free shrinkage is obtained with the presence of rubber particles. It is consistent with the lower restraint brought by less stiff aggregates. In order to balance the benefit due to the improved straining capacity against the higher free shrinkage, restrained shrinkage cracking tests by means of ring-tests have been performed. Results should give a good idea of the potential of rubberised cement-based composites to reduce the risk of shrinkage cracking which particularly affects large cementbased area, first of all slabs, pavements.. ... If this potential is proved, such a composite should be suitable to design more durable structures, such as cement-based repairs [9-lo], toppings and linings. Restrained shrinkage cracking tests The shrinkage restraint was obtained by the use of steel ring according to NF P15-434 recommendation. A 35-mm thick and 140-mm deep mortar ring cast around a 25-mm thick stainless steel ring was used. The external diameter of the steel ring was of 250 mm. As outer mould, we used two steel semi-cylindrical shells that can be easily dismantled and reused. The steel ring and the mould were concentrically fastened onto a stainless steel base and the free space was filled with the mortar mixture. The outer mould was removed 24 hours after casting and the specimens were immediately exposed to drying at 21°C and 50% RH. A silicone sealing was used to prevent drying from the upper face of the mortar ring. Generally, it is assumed that the shrinkage along the height of the specimens is uniform when its height is higher than four times its thickness [ 111. As detailed in figure 8, such a criterion was fulfilled.
Cenierrt-based materials incurparating rubber aggregates: skrinlnge length changes
365
Figure 8 - Ring-test setup A video microscope was used to detect cracks as soon as their initiation, to monitor their propagation and eventually, to quantify their opening. Obtained results are presented in figures 9a to 9c and summarised in table 2. For the studied mixes and using two front views (A and B) of each ring mortar, the crack network after 55 days is accurately drawn: localisation, length (L) and maximum crack opening (MCO) are indicated on the figures and details are given through micrographs. The age at each crack initiation (CI) is also given.
CI = 6 days MCO= 1.1 mm L = 140 mm
Figure 9a - Restrained shrinkage cracking: control mortar (MOR)after 55 days
3 66
Anuclet TURATSINZE.Snndru BONNET und Jean-Louis GRANJU
CI = 9 days MCO = 0.8 mm L = 140 mm
Figure 9b - Rcstrained shrinkage cracking: mortar incorporating 20 % of rubber aggregates (M20R) after 55 days
CI = 21 days MCO = 0.07 mm L=9Omm
CI = 17 days MCO = 0.1 1 mrn L=60mm
CI = 17 days MCO = 0.10 mm L=90mm
Cl = 21 days MCO = 0.08 mm L=SOrnm
Figure 9c - Restrained shrinkage cracking: mortar incorporating 30 % of rubber aggregates (M30R) after 55 days
Ratio of rubber aggregate substitution Age at the first crack initiation (days) Number of cracks after 55 days Main crack length (mm) Maximum crack opening (mm)
0% (MOR)
16 1 140 11.1
20% (M20R) 19 1, discontinuous 140, discontinuous 10.80
3% (M30R) 117
I
4
90 10.11
I
Cement-based rnaterials incorporating rubber aggregates: shrinkage length changes
367
With regard to restrained shrinkage cracking, these results clearly demonstrate the benefit of rubber aggregate substitution. On the one hand restrained shrinkage cracking is delayed, on the other hand the crack openings are significantly decreased. An other interesting benefit is the discontinuous crack path of the mortar incorporating 20% rubber aggregates (M20R) and the multiple cracking of the mortar incorporation 30% rubber aggregates (M30R). This behaviour contrasts with the one of plain mortar (MOR) exhibiting a single and wide crack cutting the specimen along its full height. However, rubber particles being detrimental to the composite tensile and compressive strengths, deriving maximum benefit from such interesting behaviour remains incompatible with high strength priority. In other respects, it is well known that fibre reinforcement is a solution to reduce the detrimental effects of restrained shrinkage cracking and combining this traditional technique with rubber aggregate incorporation is expected to lead to enhanced performance: first results now available are promising.
CONCLUSIONS Results presented here show that incorporation of rubber aggregates obtained from shredded non reusable tyres in cement-based mortars is a suitable solution to limit their brittleness. Despite some drawbacks such as high decrease of tensile and compressive strengths and an increased free shrinkage length change, tests demonstrated that rubberised mortars exhibit an interesting increase of their straining capacity. Ring-tests have been carried out to balance these opposite properties with drying shrinkage cracking. Results show a clear benefit of rubberised mortar. Ongoing investigations explore effectiveness of the combination of rubber aggregate substitution with fibre reinforcement to reduce the detrimental effect of shrinkage cracking. The first results available are highly promising. Moreover, this programme presents a second facet, the use of rubber aggregates in cimentitious materials provids an opportunity to recycle rubber tyres and by the way, to achieve an environmental goal. ACKNOWLEDGEMENT
The authors acknowledge the financial support of the (( Agence de I'Environnement et de la Maitrise de I'Energie )) (ADEME) and of the (( Manufacture Franqaise des Pneumatiques MICHELIN v . REFERENCES 1. Chanvillard, G., Aitcin, P-C., and Lupien, C., Field evaluation of steel fibre reinforced concrete overlay with various bonding mechanisms. Transportation Research Record, n"l226, 1989, pp 48-56 2. Granju, J-L., Thin bonded overlays : About the role of fibre reinforcement on the limitation of their debonding. Advanced Cement Based Materials, vol. 4, n"1, 1996, pp 21 -27 3. Bonnet, S., Turatsinze, A. Granju, J-L., Capacite de deformation des mortiers incorporant des granulats caoutchouc. Forum des Associations AFGC / AUGC / IREX., Innovation et Developpement en GBnie Civil et Urbain. Toulouse, 30 et 31 mai 2002, CD, edited by SCOM, Universite Paul SABATIER, Toulouse
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4. Toutanji, H. A., The use of rubber tire particles in concrete to replace mineral aggregates. Cement and Concrete Composites, 18, 1996, pp 135 - 139 5 . Eldin N.N., Senouci A.B, Observations on rubberized concrete behaviour. Cement, Concrete and Aggregates, vol. 15, nol, 1993, pp 74 - 84 6. Li, Z., F. Li, F and Li, J.S., Properties of concrete incorporating rubber tyre particles. Magazine of Concrete Research, vol. 50, n04, 1998, pp 297 - 304 7. Shiotani, T., Bisschop, J., Van Mier J.G.M., Temporal and spatial development of drying shrinkage cracking in cement-based materials. Engineering Fracture Mechanics, 70, 2003, pp 1509-1525 8. Hobbs, D.W., The dependence of the bulk modulus, Young's modulus, creep, shrinkage and thermal expansion of concrete upon aggregate volume concentration. Materiaux et construction, Vol. 4, n"20, 1971, pp 107-1 14 9. A. Turatsinze, A., Farhat, H. , Granju, J.-L. ,The impact of precracking on the durability of thin bonded overlays. In: Proc. Int. Conf. Infrastructure regeneration and rehabilitation Improving the quality of life through better construction. A vision for the next millennium, Sheffield, 28 june - 2 july, 1999, Ed. R. Narayan Swamy, Sheffield Academic Press, pp 861868 10. A. Turatsinze, A., Farhat, H. , Granju, J.-L. , Durability of metal-fibre reinforced concrete repairs: drying shrinkage effects. In: Proc. Symp. "Brittle matrix composites 6", A.M. Brandt, V.C. Li and I.H. Marshall eds. Warsaw 9-11 oct., 2000, Woodhead Publishing Limited, Cambridge and Warsaw, 2000, pp 296-305 11. Grzybowski, M., Shah, S. P., Shrinkage cracking of fiber reinforced concrete, ACI Materials Journal, vol. 87, no, 1990, pp 138-148
Proc. Int. Symp. ,,Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and WoodheadPubl.. Warsaw 2003
ADVANCED CONSTRUCTION MATERIALS FROM FLY ASH
Hwai-Chung WU and Peijiang SUN Advanced Infrastructure Materials Laboratory Department of Civil and Environmental Engineering Wayne State University, Detroit, MI 48202, U.S.A. e-mail: [email protected] ABSTRACT
In this paper, we will report the development of “ductile” high performance fly ash composites. These fly ash composites are made from 100% fly ash or with various amounts of chemical promoter (NaOH). An innovative process involving mixing, mechanical pressing and hydrothermal reaction is being developed. These three major steps follow a sequential order. After mixing, a fly ash mix is filled in the mold, then compressed by a press machine to specified pressures up to 20 m a . After reaching specified pressure, the mold is heated to moderate temperatures up to 3OO0C and for a period of specified times, during which hydrothermal reaction develops and solidifies the samples. In addition, a small amount of short fibers is added to the mix to hrther increase the ductility and crack resistance of the high strength fly ash composites. Both Class C and Class F fly ash have been used in this study. The differences in the types of fly ash and optimal processing conditions (pressure, temperature and time) will be discussed, together with their mechanical performance. Keywords Fly ash, masonry, high performance, hydrothermal, fiber reinforcement. INTRODUCTION Coal Combustion Byproducts Burning coal generates electrical power. This process also produces a residue material called coal combustion byproduct. Ash typically contains about 80 percent fly ash. It is collected in an air pollution control device called an electrostatic precipitator as flue gasses pass through large chambers. The remaining 20 percent, bottom ash falls into a collection hopper beneath the boiler. Fly ash produced at different power plants or at one plant with different coal sources may have different colors, particle size and shape characteristics, and chemical compositions depending on the source and uniformity of the coal, the degree of pulverization prior to burning, and the type of collection system used. Depending on how hot a coal plant is burning, the fly ash’s carbon content changes. Rapid cooling of the ash from the molten state as it leaves the flame causes fly ash to be predominantly noncrystalline (glassy) with minor
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Hwui-Chung WU and Peijiung SUN
amounts of crystalline constituents, carbon, and varying quantities of lime. Fly ash is divided into two classes based on the chemical composition of the ash [I]. Ashes from subbituminous and lignite coals are Class C ashes and may contain more than 20 percent CaO. Ashes from bituminous and anthracite coal are Class F ashes and generally contain less than 10 percent CaO. Typically, Class C ashes contain 1 to 3 percent free lime and are reactive with water. Class F ashes generally contain no free lime. In the Civil Engineering construction industry, Fiber Reinforced Cementitious (FRC) composites have been used for almost five decades. However the idea of using natural fibers such as straw in construction materials could go back to 2500 B.C. Most recently, many studies show that the uses of FRC in applications such as new construction, insulation, and repair give very promising results. Additionally lightweight materials are increasingly used to make lightweight concrete. The most important advantage of using lightweight concrete is significant weight reduction. Besides reduction of dead load, faster construction, lower transport and handling costs, and reduction of labor become dominant factors for using lightweight concrete. Low themial conductivity is another characteristic of lightweight concrete. As reducing energy or fuel consumption during operation of buildings becomes necessary, demands for lightweight concrete increase. In this project, we attempt to incorporate short fibers into lightweight cementitious matrix to achieve both lightweight and high strengthhigh ductility. Current Applications Using Fly Ash At present, roughly 60 million tons of ash is produced in the U S . each year, but just 25% finds its way into other products [ I , 21. Of that total, more than eight million tons, or fourteen percent, is used in cement and concrete applications [3]. The remaining 11% is used in all other industrial and agricultural applications [4]. Among the current uses in construction in US, fly ash is primarily used as a partial replacement for cement in the following applications: High Volume Fly Ash Concrete 1. There are several benefits resulting from the use of fly ash in concrete. Typical gains include: a. increased strength gain after the age of 28 days due to its continuing pozzolanic reaction b. improved workability due to the spherical nature of fly ash c. increased durability due to reduced permeability since additional (C-S-H) forms that block bleed channels and fill pore space reduced heat of hydration leading to lower temperature rise and reduction in thermal cracking d. reduced cost However, these advantages disappear when the amounts of fly ash exceed certain optimum values for any given concrete mix design. By careful selection of mix proportions and the use of chemical admixtures, the optimal fly ash content can reach 70% [5,6,7].Even within this limit, the Clean Air Act has resulted in fly ash containing higher carbon concentrations, and has made them unusable. Once carbon levels get above lo%, fly ash begins to interfere with the air-entrainment process, leading to unreliable pours 181. It is perhaps more important to point out that the abovementioned benefits are somewhat marginal, hence they are not regarded as high performance products. Cost saving is almost entirely obtained from the cost differences between cement and fly ash. It is true that reduction in cement
Advanced construction materialsfrom fly ash
37 1
consumption can save energy and reduce COz emission from cement production [I], however, these additional cost savings are difficult to be quantified and realized by fly ash concrete users. Because of cement hydration concern, allowable variations of fly ash compositions have to be narrowly defined and permit very little room for adjustment on each individual job site. 1. Autoclaved Cellular Concrete (ACC) ACC originated in Sweden in 1926. Its manufacture involves mixing Portland cement, lime, aluminum powder, water, and a silica-rich material. The aluminum powder reacts with the calcinated materials, forming hydrogen gas, which causes the concrete to rise due to bubble formation. The air filled concrete thus gives its lightweight, approximately one-quarter to one-fifth the normal weight of concrete. The silica in ACC is typically derived from sand. A number of other countries (e.g. Britain and China) have successhlly used fly ash [9,10]. ACC is particularly popular in Europe, where 95% of construction materials are made of masonry. The main use for non-reinforced ACC products is as blocks in loadbearing internal and external walls, for partition wall, filler walls, linings and coverings, as well as fillers in flooring construction; reinforced ACC products are used as roof and floor slabs, wall panels that are loadbearing or non-loadbearing, as well as lintels [9]. In the US, a revived effort towards development of ACC technology for the US marketplace is pursued by North American Cellular Concrete (NACC) under hnding provided by Electric Power Research Institute (EPEU). A demonstration project involving a mobile plant and tour through several utilities' service areas and producing ACC blocks from each of the utilities' fly ash was successhlly completed in late 1994. All blocks were autoclaved at 190 "C (375°F) and 1.5 atmosphere for 10 to 12 hours. Among the many exploratory uses of the ACC blocks in the EPRI project, it is perhaps most noticeable for the construction of a 1400-square-foot house in Pittsburgh. ACC blocks made with fly ash were used throughout the structure, except for the roof trusses. A traditional wood-frame house with the same dimensions was also constructed for direct comparison. The ACC-block home cost 9 percent less than its woodframe counterpart [ 101. It is also projected a 17% energy savings for the ACC house because of the superior insulation of the ACC blocks.
2. Flowable Fill Large quantities of fly ash, Fixed with a small amount of portland cement and water, can be used as backfills or road bases including foundation and embankment [ 10,11,12]. These types of applications involve large volume but typically low unit price. Hydrothermal Process (Autoclave) Hydrothermal processing also is commonly known as autoclaving. A process involves moderately high temperature and water. Silicate materials including cement, sand, and clay are typically mixed with water to produce moldable mixture that can be used to make various products with simple geometry. During molding process, low mechanical pressure may be applied to produce a more compact green material with adequate green strengths for subsequent handling. The molded but non-hardened units are then cured at a controlled environment of 38 to 150 "C (100 to 300 OF) and saturated moisture at one-to-several atmosphere pressure for a period of time ranging from 6 to 12 hours. Comparing with regular air cured products, autoclaving has advantages of high strength and more stable dimensions. This technology is a well-known industrial process, especially in the masonry industry. '
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Hydrothermal Hot Pressing In a recent study on recycling pulverized concrete waste, Sat0 et a1 [13] attempted to use hydrothermal hot-pressing technique to solidify the waste. Hydrothermal hot-pressing is a solidification method for inorganic powder. This method involves mechanical compression and hydrothermal reaction simultaneously. This solidification process is similar to ordinary sintering reaction for ceramics, possessing dissolution, precipitation and the formation of new crystalline components in the presence of an appropriate amount of water [14]. It should be noted that the compositions of the concrete wastes in Sato’s study (1996) are similar to that of fly ash, especially Class F. Atter mixing with water, the pulverized concrete waste was discharged to a pressure fixture. The applied pressure was 20 MPa, the temperature was from 120 to 300 “C,and the residence time was between 10 to 40 minutes [13]. Tensile strength of the solidified concrete waste was determined to be (4 to 5) MPa that already exceeds the strength of ordinary concrete. Sat0 et a1 also discovered that by partial replacement of the concrete waste the maximum tensile strength could reach 13 MPa under the following conditions : 30-50 wt. % Mast hrnace slag, 20 wt.% water, and 15 minutes at 230 “C. In another case, the tensile strength also reached 12.6 MPa with the following conditions: 50 wt.% Portland cement, 30 wt.% water, and 20 minutes at 230 “C. These tensile strengths represent three to four times higher than ordinary concrete. To improve the toughness and ductility of the strong but brittle material, Sat0 et al added various short fibers to the mix. With only 1 volume-percent fiber, they found an 870 times increase in fracture toughness [ 131. EXPERIMENTAL PROGRAM In this project, we intend to develop high performance construction materials from fly ash [ 151. This process under development is based on hydrothermal (autoclaving) and mechanical pressing as discussed above. The term “high performance” is defined to have compressive strength higher than 30 MPa, flexural strength higher than 10 MPa, and ductility (with fiber reinforcement) more than 1.5 % strain while possessing equal or less unit weight compared to concrete. Some preliminary results and findings are reported in this paper. The starting material used in this experiment is a mixture of fly ash (both class C and F), water, short fiber and a small amount of sodium hydroxide serving as activator. The ratio of water to fly ash is 1:3. The amounts of sodium hydroxide vary from 0 to 10Y0of fly ash by weight. Atter mixing for 5 minutes, the mixture is filled in the cylinder chamber of the mold. The mold will be mounted on a universal testing machine and will be compressed to designated pressures. The MTS machine slowly pushed the piston, permitting a pressure built-up to 20 MPa in about 20 minutes. During this period, the entire mold is heated to specified temperatures in a split tube fbmace (AVS Series 3210) that also is mounted on the MTS machine. The mold is heated to various temperatures for a range of time periods from 0.5 to 5.5 hours, during which time hydrothermal reaction develops and solidifies the samples. More details about the mold design can be found elsewhere [ 151. Preliminary Results After completely cooled, the sample is demolded. Figure 1 shows a typical sample, 1 inch diameter and 5 inch long. All the samples have very smooth surfaces. Subsequently tensile strengths of the samples are determined from splitting tensile tests. Figure 2 shows the splitting tensile test setup on the MTS test machine. The ages of all samples were two days‘ old at the time of testing.
klvunced coristruction materialsfroin,fly us11
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Figure 1: Typical fly ash sample.
Figure 2: Splitting tensile test setup on MI'S test machine
It has been identified that key factors in the process under development are: hydrothermal temperature and content of sodium hydroxide [ 151. In the following discussions, attention will be given to the effect of fibers. Process and other effects can be found elsewhere [ 15,161. Fiber Effect To improve brittleness of such fly ash products, a small amount of short fibers is added to the mix. Fiber reinforcement has been well recognized to be very effective in improving ductility and toughness of brittle cement and concrete [ 17,181. Two types of fiber are employed in this project to improve the properties of the fly ash products: PVA fiber (from Kuraray Co., Japan) and Kevlar-29 fiber (from Dupont), which properties are listed in Table 1.
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Hwai-Chung WU and Peijiang SUN
Table 1 : Fiber Properties Fiber
~i~~~~~~
Length
(pm)
(mm)
specific
Modulus of
Tensile Strength
Elongation at
Elasticity (GPa)
(GPa)
Brfakage (“h)
PVA
37
15.0
1.30
40
Kevlar-29
14.8
35.0
1.44
70.5
.
..-* -
.. 2.92
3.6
#
When short fiber is used to reinforce fly ash matrix, several properties, especially the ductility of the composites are enhanced significantly. The effects of fiber reinforcement on Class C fly ash samples are shown in Fig.3. The concentration of the NaOH solution is 10M and the liquid to solid ratio (US) ratio is 0.62 for all samples. The pressure on each sample is 20MPa. For one set of samples, set-A, 130°C of processing temperature and 5.5 hours of heating time are employed. For the other set, set-B, the parameters are 15OoC and 2.5 hours. The age of the samples is 2 days. The fiber used here is PVA fiber, and its volume ratio is 1.0%. Fig.3 shows the changes in strength and ductility when the fiber is added. For set-A, when no fiber is used, the sample is brittle, and the first crack strength, also the ultimate strength, is 5.44MPa. With the addition of 1.0% PVA fiber, the sample shows excellent ductility, and the ultimate strength (the highest load registered) is 7.68MPa, almost a 50% increase from 5.44MPa. Its first crack strength is 5.03MPa, a little less than that without fiber, and the reason for this phenomenon might be due to poorer workability of the mortar with fiber. For set-B, the first crack strengths are 5.16MPa with 1.0% PVA fiber and 5.03MPA without fiber, but both the ultimate strength and the ductility are significantly increased when fiber is employed. Fig.4a and 4b are direct comparison of the failure modes between two samples after the splitting tensile tests, one of which has no fiber and the other has 1.O% PVA fiber. It can be seen clearly the brittle failure of the sample without fiber and the ductile failure of the sample with fiber.
0
Displacement (mm) Figure 3: Fiber Effect on the Ductility of Class C2 Fly Ash Samples (Pressure: 20MPa, NaOH: IOM, US=0.62, Age: 2Day).
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Typical values of density and modulus for Class C samples produced with NaOH activation and fiber reinforcement are 2.0-2.2g/cm3 and 18-20GPa, respectively, almost the same as those without fiber.
Figure 4a: Different failure modes of Class C samples during testing [without fiber (lef?) and with 1.O% PVA fiber (right)]
Figure 4b: Class C samples after lest showing brittle failure (without fiber, left) and ductile failure (with 1.O% PVA fiber, right)
Fiber Content Effect When fiber is used, the properties of the Class C fly ash samples are largely improved. In order to further understand the effect of fiber, the parameter of fiber content is investigated, and the results are illustrated in Fig.5 and Fig.6. Four Class C fly ash samples are prepared with different fiber volume ratios of O.O%, OS%, 1.0% and 1.5%. The fiber used is PVA fiber. The process conditions are 20MPa pressure on the samples, 15OoC of heating temperature, and 2.5 hours of heating duration. The concentration of the NaOH solution is 10M and the L/S ratio is 0.62 for all samples. The age of the samples is 2 days. The sample without fiber is brittle as expected, and its first crack strength, also its ultimate strength, is 5.03MPa (Fig. 5). For other samples with fiber content from 0.5% to 1.5%, they demonstrate extensive ductility and their failure modes are ductile (Fig.6). The first crack strengths vary between 5.2MPa and 5.4MPa, a little higher than 5.03MPa. It is evident that the ultimate strengths of the samples with fiber are much higher than 5.03MPa. When the fiber content is 1.O%, the ultimate strength reaches the highest value of 6.9MPa, and the ductility is the best among the samples under investigation. As fiber content increases
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Hwai-Chung W a n d Peijiang SUN
to 1.5%, there is no further property improvement because of poor workability resulting in mixing difficulty. In other words, 1.O% is the optimum fiber volume ratio for Class C fly ash. 7.0
-2
6.0
I, 5
Be! m --
5.0
c
c"
.z 3
u)
.........
.._ .....
4.0
+First
Crack Strength
+Ultimate
Strength
3.0 0.0
OS
1.5
PVA Fiber Content (%)
Figure 5: Effect of fiber content on strength of Class C fly ash samples (Pressure: 20MPa. Temperature: 15OoC, Heating Time: 2.5Hrs, NaOH: 10M, US=0.62, Age: 2Day)
I
0
0.5
0 0% PVA Fiber
0 5% PVA Fiber
1 0% PVA Fiber
1 5% PVA Fiber
1 1.5 Displacement (mm)
2
2.5
Figure 6: Splitting tensile strength vs displacement curves (Pressure: 20MPa, Temperature: 150°C, Heating Time: 2.5Hrs, NaOH: 10M, L/S=0.62, Age: 2Day) CONCLUSIONS The preliminary data confirm that the process under development in this project can solidify fly ash. The resulting fly ash samples are very strong in tension (ranging from 1.0 to 10.0 MPa) depending on specific processing conditions. However, they are very brittle. With
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addition of (0.5%-1.5%) fibers by volume, the fly ash samples can show significant increase in ductility and toughness.
REFERENCES 1. American Coal Ash Association, Technical Brief, TB-1 I , January 1998. 2. Tamcone, P., “Fly Ash for Hire”, Civil Engineering, October 1991, p.46-49. 3. American Coal Ash Association, Coal Combustion Product (CCP) Production and Use USA, Alexandria, Virginia, 1997. 4. American Coal Ash Association, Buy Recycled Coal Fly Ash, Alexandria, Virginia. 5. Malhotra, V.M., “Superplasticized Fly Ash Concrete for Structural Concrete Application”, Concrete International, V. 8, No. 12, 1986, p.28-3 I . 6. Berry, E., Hemmings, R., Zhang, M., Cornelius, B., and Golden, D., “Hydration in HighVolume Fly Ash Concrete Binders”, ACI materials Journal, V. 91, No.4, 1994, P. 382389. 7. Jiang, L., Lin, B., and Cai, Y., “Studies on Hydration in High-Volume Fly Ash Concrete Binders”, ACI materials Journal, V. 96, No.6, 1999, P. 703-706. 8. American Society of Civil Engineering, Civil Engineering, September 1998. 9. Golden, D.M., “Ash-Derived Autoclaved Cellular Concrete Building Materials Amve in North America”, in Proc. 1Ith Inter. Symp. On Use and Management of Coal Combustion By-products, Orlando FL, American Coal Ash Association, 1995, p.35-1-9. 10. Valenti, M., “Using Fly Ash for Construction”, Mechanical Engineering, May 1995, p. 82-86. 1 I . Jalali, S., “The Effect of Compactive Efforts on the Final Strength of Lime-Fly Ash mixtures”, in Proc. 1l‘h Inter. Syrnp. On Use and Management of Coal Combustion ByProducts, Orlando FL, American Coal Ash Association, 1995, p.68-1-13. 12. Hemmings, R.T., Berry E.E., and Golden, D.M., “Investigation of No-Cement Concretes Produced from AFBC By-products and PFA”, in Proc. I l l h Inter. Symp. On Use and Management of Coal Combustion By-products, Orlando FL, American Coal Ash Association, 1995, p.79-1-10. 13. Sato, K., Hashida, T., Takahashi, H. and Yamasaki, N., “Development of a Solidification Method for Pulverized Concrete Waste by Hydrothermal Hot-Pressing and Fiber Reinforcement”, in Proc. ASCE 4Ih Materials Engineering Conference, Ed. K. Chong, 1996, p.684-693. 14. Nakane, Y . , Sato, K., Takahashi, H., Yamasaki, N. and Hashida, T., “Development of Solidification Technique for Recycle of Concrete Waste By Hydrothermal Hot-Pressing and Its mechanical Property”, J. Cer. SOC.Of Japan, Vol. 102, No.4, 1994, p.405-407. 15. Wu, H.C., and Sun, P., “High Performance Ductile Fly Ash Composites,” in CD Proc. 151hInter. American Coal Ash Association Symp. On Management & Use of Coal Combustion Products, St. Petersburg, FL, 2003. 16. Wu, H.C., and Sun, P., “High Performance Masonry Products from 100% Fly Ash”, Project Report, Department of Civil and Environmental Engineering, Wayne State University, Detroit, 2003. 17. Wu, H.C., and Li, V.C., “Trade-off Between Strength and Ductility of Random Discontinuous Fiber Reinforced Cementitious Composites”, Cement & Concrete Composites, 16, 1994, p23-29. 18. Li, V.C., Mishra, D.K., and Wu, H.C., “Matrix Design for Pseudo Strain-Hardening Fiber Reinforced Cementitious Composites”, RILEM J. of Materials arid Structures, 28, 1995, ~586-595.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C.Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
IMPLICATIONS OF MATURITY AND ULTRASONIC WAVE SPEED MEASUREMENTS IN QC/QA FOR CONCRETE Cole GRAVEEN', Jason WEISS', Jan OLEK' and Tommy NANTUNG" 'Purdue University, School of Civil Engineering .* Indiana Department of Transportation, Research Division West Lafayette, IN, United States, email: [email protected]
ABSTRACT Recently, maturity testing has become more widely used to describe the rate of concrete strength development. Maturity predictions can be used to indicate when loading can be applied to a concrete pavement or structure. While the implementation of the maturity method has numerous potential benefits, it is important that potential limitations are recognized as well. Test methods are needed to signal when the predictions made using the maturity approach are not conservative. This paper will focus on three main aspects of quality controVquality assurance (QC/QA) testing using the maturity method. First, it will illustrate that mixture proportion variations can influence the maturity predictions. Second, this paper will illustrate that the use of an ultrasonic wave velocity screening technique can indicate when the maturity-strength relationship may over-predict the strength in a structure. Finally, this paper will demonstrate that supplementing maturity predictions with the use of early-age mechanical property measurements can improve the estimate of long-term performance while providing rapid information on the acceptability of the concrete. Keywords Early-age, maturity, non-destructive testing, quality control, ultrasonics, variability
INTRODUCTION During the construction of concrete pavements and structures it is common to find that a minimum level of strength is required before specific construction operations can be performed. For example, this frequently includes the removal of formwork and shoring [ 11 or the opening of a concrete pavement to construction traffic [2]. Typically, agencies determine the acceptability of concrete by testing companion specimens cast from concrete that is sampled during construction of the concrete structure or pavement. Testing can be costly however, and the strength of these companion specimens may not necessarily represent the actual strength of the in place concrete. In addition to differences in placement and compaction procedures, the curing conditions used for the companion specimens may differ from the curing conditions of the actual structure. Although the strength-maturity relationship should be independent of curing temperature, significant differences have been
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Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tornmy NANTUNG
reported in specimens exposed to a high temperature at early ages [3]. Companion specimens may not represent changes that occur in the microstructure due to high temperature curing at early ages which may result in an over-prediction of the mechanical properties (including strength) of the in place concrete The maturity method has been proposed as one approach to estimate the in situ strength of a concrete structure [4]. In general, the maturity method is based on the concept that strength development in concrete is uniquely related to the product of the time and temperature (i.e., a maturity index). This maturity index can be measured in a concrete structure or pavement and used with a previously established strength-maturity relationship (determined from laboratory experiments) to estimate in situ strength of the concrete. It should be noted however that the use of the maturity method involves several assumptions. For example, the maturity method assumes that the concrete in the specimens and the concrete in the structure have been properly placed, compacted, and cured. If proper placement and compaction procedures are not followed, defects such as honeycombing, segregation, or excessive bleeding can occur. These defects cannot be detected by the maturity method and will result in an erroneous estimate of in-place strength. In addition, the maturity method cannot detect if the supply of moisture for hydration is not provided (i.e., improper curing). When this happens, the concrete will not continue to gain strength, however the maturity method will continue to indicate an increase in strength with time. Third, the ultimate strength of the concrete has been reported to be sensitive to the temperature of the concrete during curing. If sufficiently high or low temperatures are experienced (especially at early ages) the maturity approach may need to be adjusted [5]. Finally, the maturity method inherently assumes that the concrete for which the in-situ strength is being estimated was made using a concrete with identical constituent materials and mixture proportions as the concrete that was used in the creation of the strength-maturity relationship. If the material properties of the constituent materials change, or the concrete mixture proportions vary, an error can be introduced into the estimate of strength. It should be noted that in practice variations in the mixture proportions typically occur in large-scale concrete construction projects. For example, the variation in water-to-cement ratio (w/c, as calculated based on batch 16 weights after accounting for aggregate moisture and trim water) is presented in Figure 1 for sixty-four sublots (each sublot covers an area of approximately 2000m’) of a 350 mm thick concrete pavement. This concrete had a target w/c of 0.42 and was produced using a mobile batch plant. As the water-to-cement ratio (w/c) is potentially the most influential mixture design parameter with respect to the strength-maturity relationship, it is critical that the implications of the 0.38 0.4 0.42 0.44 0.46 variation in the w/c on the maturityWater-To-Cement Ratio strength relationship are known. In the case presented in Figure 1 the w/c was observed to vary from slightly above 0.45 Figure 1: Variation in the Water-Toto slightly below 0.40. While the extent Cement Ratio (wlc) for an Actual of variation that can be expected on any Concrete Pavement
bnplications of maturity and ultrasonic wave speed measurements in QC/QAfor concrete
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given project will differ depending on the contractor and quality control procedures implemented, some variation will allows be present. The information presented in Figure 1 was used to develop the bounds of experimental program that is discussed in this paper.
RESEARCH SIGNIFICANCE This paper presents results from a recent study in which the flexural strength of concrete was estimated using the maturity method. It will be shown that slight variations in the mixture proportions, consistent with those that may be observed during a construction project, may cause variations in the maturity predictions that may be either conservative or unconservative. An approach is presented in which the use of ultrasonic testing may signal when the predicted strength from maturity may be non-conservative. In addition, an approach is presented which uses early mechanical testing in conjunction with the maturity method to improve the maturity-strength predictions.
MIXTURE PROPORTIONS, CASTING, AND TEST PROCEDURES Testing was conducted to assess how variations in the water-to-cement ratio (w/c) influence the strength prediction made using the maturity-strength approach. This was performed to illustrate how slight variations in the mixture proportions, consistent with those that commonly occur in concrete construction, may translate into changes in the flexural strengthmaturity response. The mixture proportions used in this study are provided in Table 1. This baseline mixture is similar to the typical mixture proportions used in a concrete pavement, however it should be noted that the cement content was increased by approximately 11.8 kg/m' to facilitate laboratory mixing and placement procedures. Slight changes in water-tofrom the baseline mixture (Table 1, w/c = 0.42) to simulate construction variability. While the w/c
was the Of aggregate was maintained the same as the baseline
Material Cement Water
Type Type 1 I
Fine Aggregate Coarse Aggregate Air Water Reducer
#23 Sand
#8 Stone*' Daravair 1400 WRDA 82
Mixture Proportions* 320 134 868 972 145 2.44
kglrn3 kg/m3 kglm3 kglrn3 rnl/rn3 rnllkg
The test specimens that were prepared for this research consisted of 152 x 152 x 535 mm beam specimens. The beams were cast in steel molds in accordance with ASTM C 192. The concrete was mixed in the laboratory using a pan mixer and internal vibration was used to consolidate all of the beams. Two thermocouples were placed in one beam from each batch of concrete to record the temperature history. The temperature at each thermocouple was measured every minute and the average temperature over a ten-minute interval was recorded using a Campbell Scientific, Inc. CRlOX Measurement and Control System. After finishing, the beams were covered with wet burlap and a layer of plastic. The specimens were removed from the molds approximately twenty-four hours after casting and placed in a temperature
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Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tommy NANTUNG
controlled moist curing room (23OC +/- l0C, 95% €34) where they were kept until the time of testing. It should be noted that one series of beams with a w/c of 0.42 was exposed to high temperature during the curing process as described later in the paper. A series of tests were conducted on the beam specimens that included: the measurement of temperature history using the aforementioned thermocouples, measurement of the P-wave velocity using a pulse velocity te'st apparatus in the direct transmission mode along the length of the beam, and measurement of flexural strength testing using third-point loading in general accordance with ASTM C 78. The flexural strength and P-wave velocity were determined for the design mixture (w/c = 0.42) at ages of 1, 1.5, 3, 7, 14, and 28 days, while the flexural strength and P-wave velocity for the mixtures with the other w/c were determined at 7 and 28 days only.
EXPERIMENTAL RESULTS The Maturity-Strength Relationship for the Baseline (w/c = 0.42) Mixture The temperature-time factor (used as the maturity index (M) in this paper) was calculated using equation 1.
In equation 1 At is the time interval (ten minutes), T, is the measured average temperature in the concrete during the time interval, and To is the datum temperature which was assumed to be -10 "C based on standard Indiana Department of Transportation assumptions [2]. Once the maturity index (M) was known, a strength-maturity relationship could be created for the baseline mixture as shown in Figure 2. The points represent the average of two strength measurements and the line represents the offset hyperbolic strength-maturity relationship as described by Equation 2:
where f loo is the ultimate flexural strength (i.e., the strength as the time tends toward co), k T is the rate constant, and M, is the offset maturity (i.e., maturity at set). The three parameters (f rm, kT, and M,) were determined for the strength-maturity relationship using the procedure suggested by Knudsen [6] which has also been described by Carino [4]. The value of the ultimate flexural strength was determined using the tests at 7, 14, and 28 days while the offset maturity and rate constant were determined using early-age tests (i.e., 1, 1 %, and 3 days). The parameters computed for the baseline mixture (w/c = 0.42) were f,, = 5.76 MPa, k T = 0.004169 I/"C-hr, and M, = 498 'C-hr. It can be noticed that the hyperbolic strength function represents the data well, provided sufficient data is collected at the early ages to enable k T and Mo to be determined accurately [8].
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Once the strength-maturity relationship was ' ' ' ' ' ' developed for a given concrete (Equation 2 and 6 ' ' ""I ;ii Figure 2), this relationship can be used to estimate the strength in a structure or pavement f,s, = 5.76 MPa made using this concrete. To do this, the user would simply record the temperature that g develops in the structure or pavement, compute 2 a maturity index using this measured 2temperature, and use the relationship shown in Figure 2 to estimate the strength in the structure 3 ,M~ = 498 "C-hr for the given maturity index. As previously $ ' mentioned, this assumes that the concrete that was placed in the structure has the same 1000 10000 constituent materials and mixture proportions as Maturity, M (i.e., the TimeTemperature Factor OC-hr) those used in the development of Figure 2. To illustrate the importance of variations in the Figure 2: Maturity-Flexural mixture proportions on the predictions made Strength Relationship using the approach described above, a series of tests were performed where the w/c was varied over a range that is consistent with variation that may be expected in the field (i.e., Figure 1). The results of this investigation are described in the following section. 1 ' 1 1 1
Influence of Variation in WIC and Temperature During Curing on Predicted Strength Flexural strength was measured for the mixtures in which the w/c was varied (i.e., 0.40, 0.41, 0.43, 0.44, 0.47) at 7 and 28 days. In addition, the maturity index (time-temperature function) was computed based on the average of two thermocouples from one beam in each batch. Variations in the w/c resulted in variations in the measured flexural strength as expected, with the measured flexural strength decreasing with increasing w/c (Table 2). A lone exception occurred for the measured strength at 28 days for the specimen with a wlc equal to 0.44. It should be noted that multiple batches were required to cast the specimens For each mixture due to the size of the mixer, therefore slight variations between each mixture may have occurred and this is expected to be responsible for this lone discrepancy. It should be noted that even small changes in the w/c (0.0 1 to 0.02) can introduce error in the estimate of flexural strength. Figure 3 shows the ratio of the strength that would be predicted for each of the mixtures made using the hyperbolic strength relationship and the actual strength measured in the beams with the slight differences in the w/c. It should be noted that the strength-maturity relationship generally underestimates strength for mixtures with a w/c lower than the design ratio, which is conservative, and overestimates strength for mixtures with a w/c greater than the design, which is non-conservative. To prevent overestimating the strength of concrete (this may result in acceptance of an inferior or low strength structure or pavement) an additional screening method may be desirable.
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Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tommy NANTUNG
Table 2: Results from the P-Wave Measurements in the Beam Exposed to High Temperatures at Early Ages and the Beams Made with Various WIC's Predicted Water-toFlexural Strength Actual Measured Measured PCement Flexural Strength Wave Velocity Age (Days) Using Maturity Ratlo~(wIc) (mrs) (MPa) (MP4
Strength Predicted I Prediction Actual Flexural Considered Valid Strength After Ultrasonic Wave Testing
'High Tenperature Specimen
It should be noted that even small changes in the w/c (0.01 to 0.02) can introduce error in the estimate of strength. Figure 3 shows the ratio of the strength that would be predicted for each of' the mixtures made using the hyperbolic strength maturity relationship and the actual strength measured in the beams with the slight differences in the w/c. It should be noted that the strength-maturity relationship generally underestimates strength for mixtures with a w/c lower than the design ratio, which is conservative, and overestimates strength for mixtures with a w/c greater than the design, which is non-conservative. To prevent overestimating the strength of concrete (this may result in acceptance of an inferior or low strength pavement) an additional screening method may be desirable. Although the standard beam stored at temperature (23OC) exhibited a temperature rise that was less than 4OC above ambient temperature during hydration, thermocouples in the core of a concrete pavements show that these pavements can easily reach 43-45OC even under mild ambient temperatures (23-25'C). I.2 Testing was also conducted to assess how high temperature conditions during curing can influence the .Conservative strength estimated using the maturity Predictions method. To illustrate this effect, three additional beams were cast with the mixture proportions used in Conservative the baseline mixture (w/c = 0.42), Predictions 0.9 with one beam stored at regular temperature (w/c = 0.42, 23°C) and , , D;ig,nW,ater;-l two of' the beams were cured at Cement Ratio = 0.42 0.8 elevated temperature (w/c = 0.42, 0.40 0.42 0.44 0.46 0.40 temperature history described Water-To-Cement Ratio below). The high temperature beams were placed in an insulated box with Figure 3: Ratio of Strength Predicted heaters that were used create the Using the Hyperbolic Strength elevated temperatures which Function (wlc = 0.42) and the simulated temperatures similar to Measured Strength (Various wlc) what may be expected to occur in
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,
385
.Implications of maturity and ultrasonic wave speed measurements in QUQAfor concrete
thick concrete pavements on a hot summer day. The temperature of the beams was maintained at 23°C for approximately 2 hours before the temperature of the box was increased causing the temperature in the beam to rise (nearly linearly to a temperature of 55°C at an age of 10 hours). The beam was held at this temperature until an age of 17 hours when the temperature was reduced to ambient temperature. The strength predicted for the regular temperature beam at a maturity index of 1050 "C-hrwas 31% higher than the strength measured in the beams stored at higher temperature. This indicates that high temperature curing can introduce a significant error in the estimate of strength. Combining the Use of Ultrasonic Wave Speed Measurements and Maturity An alternative to using only maturity by itself to predict the strength of the in-place concrete is to combine maturity by with other methods of non-destructive testing. The following section describes how maturity and P-wave velocity techniques can be used jointly to indicate when maturity measurements may not be conservative. The advantage of using the maturity and P-wave velocity methods in parallel lies in the differences between the test methods [8]. The strength estimated from the maturity method is a function of time and temperature. As such the maturity index can be thought of as being related to the chemical reactions during hydration. Alternatively, the strength estimated from the P-wave velocity is a function of the structure of the material, including the density, air voids, and the aggregate contribution. Therefore, combination of these approaches may provide complimentary information. Figure 4 illustrates the strength-P-wave velocity relationship for the design mixture. It can be seen that a bi-linear relationship exists where the behavior at early-ages (1, 1.5, and 3 days) shows a greater slope than the data at later ages (7, 14, 28 days). At early ages the P-wave velocity is more sensitive to strength changes which can be attributed to the fact that at earlyages the flexural strength is dependent almost solely on the properties of the matrix since cracking occurs around the aggregate. The relationship between the P-wave velocity and the flexural strength changes as fracture paths in the beams is observed to change from a crack that primarily occurs through the mortar to a crack that propagates through the aggregate. This has recently been confirmed in subsequent testing by Barde et al. [7]. As previously described, the use of maturity-strength relationship as determined from time-temperature predictions with information from ultrasonic pulse velocity-strength relationship may provide complimentary information. For example, if the strength estimate from the strength-P-wave velocity relationship is equal to or in excess of the estimate of strength from the strength-maturity relationship, the estimate of strength from the maturity test method could be considered as conservative. However, if the estimate of strength using ultrasonic wave speed was lower than the estimate from the maturity test method, additional action may be required, such as conventional strength
x
Q U
Design Water-toCement Ratio = 0.42 4200
4400
4600
4800
P-Wave Speed (mls) Figure 4: Variation in P-Wave Speed as a Function of Strength
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Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tommy NANTUNG
testing. Table 2 provides results from the ultrasonic measurements in the mixtures with the variable w/c and the specimen that was cured at a higher temperature. It is interesting to note that when using the maturity method alone, the predicted strength was greater than the actual strength in 5 of the 9 cases. However, when both methods (P-wave velocity and maturity) are used in combination each of the five non-conservative cases would have been identified. Of the four cases where the predicted strength using the maturity method alone was less than the actual strength, only one of the cases (w/c = 0.44 at 28 days) was indicated to not be valid using the combined methods (It should be noted that in this case the predicted and actual strength were very similar to one another). While this approach is not ready to move into practice immediately and some bands may be necessary to allow for typical variability in each test, it should also be noted that the cost associated with developing the P-wave velocity vs. strength relationship may be trivial as ultrasonic wave speed can be determined at the same time the maturity strength relationship is obtained. The approach described in this paper may also be amenable to in-situ stress wave measurements using sensors placed inside the concrete during construction. Although the ultrasonic wave speed was discussed in this paper as measured using the P-wave speed from direct transmission it is easily foreseeable that the information on wave speed could be obtained using one-sided velocity, impact echo, pulse echo, or one-sided wave reflection approaches. This could enable these measurements to be made in-situ, potentially leading to a reduction in the reliance of separate testing of companion samples thereby facilitating a move to more in-situ based testing.
Using an Early-Age Test Result In Combination Maturity Prediction Another possible way to consider the influence of material variations with the maturity method is to use an early-age third-point flexural test in combination with maturity to estimate a long-term strength. Using an early-age test could provide the contractor with rapid feedback thereby facilitating changes in the construction operation during the construction process to allow the specified strengths (or other properties) to be achieved. One option would be to use the early-age test result (for example a measurement of flexural strength at 1 or 3 days) to verify that the pavement flexural strength is acceptable at an earlyage and then to use this early-age strength value in conjunction with a maturity prediction to estimate the later-age strength (28 days for example) for use in life-cycle predictions or pay determination. An equation of the following type could than be used to estimate the 28 day strength using some predetermined maturity index (M28);
where, Meartyage is the maturity measured at an early age (1 or 3 days for example), and Mzg is the maturity at 28 days. For illustrative purposes the results of this method are presented in Table 3 using the earlyage measured strength at 7 days, the measured maturity at 7 days, and the measured maturity
387
Implications of maturity and ultrasonic wave speed measurements in QC/QAfor concrete
at 28 days to predict the 28-day strength in mixtures with two different w/c’s. It can be seen that when equation 3 is used, the predicted strength is closer to the actual measured strength than the prediction made using maturity alone (i.e., equation 2). Table 3: Using Early Flexural Strength with Maturity to Predict Long-Term Strength When Variations in Mixture Proportions Exist
wlc
0.41 0.43
Predicted Actual Actual Strength At 28 Strength Strength Days Using At 7 Days At 28 Days Maturity Alone (Eqn 2) MPa 5.81 5.21
MPa 6.16 5.34
Percent Percent S t ~ ~ ~ Difference ~ ~ ~ Z Difference 8 Days Using Eqn Between Equation Between Equation 2 and the Actual 3 and the Actual 3 28 Day Strength 28 Day Strength
MPa 5.70 5.70
% 81 6.2
MPa 6.02 5.41
% 2.3 1.2
It should be noted that for curing of QCIQA beams at a constant temperature, equation 3 can be rewritten as equation 4 f’, (28duys)= f ’ , (early uge).C
where C is a strength gain coefficient (as illustrated in Figure 5) which depends on the rate of strength gain coefficient (KT), the offset maturity (Mo) (although to a lesser extent), and the age at which the specimen is tested. Equation 3 was simplified to obtain equation 4 through two assumptions: 1) it is assumed that the Mo value is similar for a series of mixtures and 2) the maturity at any given testing time and the maturity at 28 days can be approximated as the product of the time and temperature. It should be noted that if very early ages of testing are desired, specific attention should be paid to the value of Mo that is used in the development of the strength gain coefficient [8].
-
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Rate Constant, K, (l/(C-hr)) Figure 5: Strength Gain Coefficient as Determined From Maturity Concepts
SUMMARY AND CONCLUSIONS This paper has reiterated the fact that although the use of maturity shows great potential application for assessing strength gain in concrete structures and pavements, ‘it is not prudent to rely solely on measurements of in-place maturity to verify the attainment of a required level of strength” [ 11. This paper also indicates that although the same materials and mixture proportions may be specified, day to day variations in batching may result in fluctuations in the water-to-cement ratio for a given concrete mixture. Although these variations are expected, they can result in errors in the maturity based estimation of strength of +/- 10% for
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Cole GRA VEEN, K Jason WEISS, Jan OLEK and Tommy NANTUNG
variation of +/- 0.02 in the w/c for the mixtures investigated in this work. High temperature curing was also observed to result in non-conservative strength predictions. This paper suggests that the combination of maturity and ultrasonic wave speed may provide additional information to indicate cases where the maturity predictions may not be conservative. For example, combination of maturity and ultrasonic pulse velocity was able to identify all the mixtures where strength was over-predicted by the maturity method in cases with both high water-to-cement ratio and high temperatures during early age curing. In addition, the combination of early-age strength testing with maturity may make it possible to reasonably predict strength at any age while providing the contractor with feed-back very early in the construction process which ultimately could result in concrete with improved performance. ACKNOWLEDGEMENTS The authors gratefully acknowledge support received from the Indiana Department of Transportation through the Joint Transportation Research Program Project Number 6561284-0 1 15, “Performance Related Specifications for Concrete Pavements In Indiana” which is administered under the direction Dr. Tommy Nantung. The views expressed in this paper are those of the authors, and as such are not intended to represent the official views and policies of the sponsors nor do they reflect a standard, specification, or regulation. The second author also wishes to thank the National Science Foundation for support received through NSF Grant No. 0034272, a Career Grant. The authors also wish to thank J. Johnson for assistance with beams used in the high temperature testing. REFERENCES
1. 2. 3.
4. 5.
6. 7. 8.
Naik, T.R., “Concrete Strength Prediction by the Maturity Method”, ASCE Journal of Engineering Mechanics, Vol. 106, No. EM3, 1980. Indiana Department of Transportation, Standard Specijkations, 1999. Chanvillard, G. and D’Aloia, L., “Concrete Strength Estimation at Early Ages: Modification of the Method of Equivalent Age”, ACI Materials Journal, Vol. 94, No. 6, pp. 520-530, 1997. Carino, N. J., “The Maturity Method”, CRC Handbook on Nondestructive Testing of Concrete, Malhotra, V.M. and Carino, N. J., Ed., CRC Press, Florida, 1991, 101-1 46. Carasquillo, R., and Myers, J. J., “HPC Bridge Newsletter,” Knudsen, T., and Geiker, M., ‘Chemical shrinkage as an indicator of the stage of hardening,” International Conference on Concrete at Early-Ages, Vol. 2, RILEM, Paris, 1982, pp. 163-166 Barde, A., Mazzotta, G., and Weiss, W. J., “The Influence of Aggregate Behavior on Flexural Strength Development, Cracking and Maturity Predictions”, Under Development Weiss, W. J., “Experimental Determination of the ‘Time-Zero’, to,”, Early-age Cracking in Cementitious Systems, RILEM Report 25, ed. A., Bentur, 0 2003 pp. 195-206.
Pvoc. Int. Sytnp, ,,Brittle hIafri.x Composites 7” A.M. Brana‘t, V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Wooa’head Publ.. Warsaw 2003
PLENARY INVITED PAPER
ON THE DETERMINATION OF ELASTIC MODULI WITH BRITTLE MATRIX COMPOSITES Dieter LOIDL, Stephan PUCHEGGER, Herwig PETERLIK, Karl KROMP Institute of Materials Physics; University of Vienna Boltzmanngasse 5; A - 1090 Vienna, Austria e-mail: karl. [email protected]
ABSTRACT Composite materials behave in general elastically anisotropic. For the purpose of designing constructive parts under load by finite element calculations, the elastic moduli in dependence on orientation and on temperature have to be known. A short survey on practicable procedures for the determination of the elastic moduli, their applicability to composites and their extension to measurements at high temperatures are given. A new procedure, based on the Resonant Beam Technique, and its application to anisotropic composites at high temperatures is presented together with results gained from a 2,5D carbon fibre-reinforced carbon composite up to 1800 “C. Finally an outlook on a new procedure, a combination of Resonant Ultrasound Spectroscspy and Resonant Beam Technique is given. Keywords Elastic moduli, carbon fibre-reinforced carbon composite, anisotropy, high temperature
INTRODUCTION In the course of the rapid progress in e.g. aerospace and communication technologies during the last decade specific high performance materials for special applications were developed. The materials, intermetallics, high performance ceramics and ceramic composites are predominantly anisotropic. For the purpose of designing constructive parts under load by finite element calculations, the dependence of the elastic constants (the coefficients of the elastic stiffness or compliance tensor) on orientation and on temperature have to be known (the engineering “elastic moduli” can be calculated directly from these elastic constants). The knowledge of the elastic constants is also important for the investigation of thermophysical properties, in particular for phase transitions of high performance materials. Thus, there is a strong interest in practicable experimental procedures for the determination of the elastic constants in dependence on orientation and on temperature.
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Dieter LOIDL, Stephan PUCHEGGER, Henvig PETERLIK and Karl KROMP
ELASTIC PROPERTIES OF COMPOSITES In general composite materials are elastically anisotropic. Following theory of elasticity the elastic properties of composites are characterised by the stiffness tensor C or the compliance tensor S, with its coefficients (the elastic constants) Ci, and Si, , respectively. The composites generally applied for constructional purposes have independent elastic constants as listed below, from low symmetries up to highest symmetry: orthothropic (orthorhombic): 9 elastic constants, a;tb#c, a=P=y=9O0, e.g. 2,5D composite quadratic (tetragonal): 6 elastic constants, a=b#c, a=P=y=9O0, e.g. 2D composite hexagonal (transversely isotropic): 5 elastic constants, a=b*c (a=b, isotropic), e.g. UD composite (4 components for single ply quadratic) isotropic: 2 elastic constants, e.g. chopped fibre composite When anisotropy, a specific feature of composite materials, has to be taken into account, the elastic behaviour can only be h l l y characterised by the elasticity tensor with a certain number of independent coeficients (the elastic constants). This number depends on the crystallographic symmetry of the composite as shown above. Certain methods allow the determination of the elastic constants, while other the determination of the elastic engineering moduli (Young's moduli, shear moduli and Poisson's ratios, Eii , Gij , vij). From the coefficients of the elastic compliance tensor, Sij, the elastic moduli can be calculated and vice verse.
OVERVIEW OF MEASUREMENT PROCEDURES In general two main groups of procedures for the determination of elastic properties may be distinguished: quasi-static (isothermal) procedures e.g. tension (compression and torsion) tests and bending tests (3- or 4-point) dynamic (adiabatic) procedures e.g. direct measurement of sound velocities and measurement of resonant frequencies The results from isothermal and adiabatic procedures in general differ by far less than I%, depending on temperature, extension coefficient and specific heat at the given temperature and thus this difference generally is neglected. Contrary to quasi-static procedures (mechanical test methods), the determination of elastic properties by dynamic procedures (sound velocities and resonant frequencies) is not based on the evaluation of the stress-strain response over a given deformation range obtained under quasi-static loading conditions, but is based on non-destructive dynamic measurements at very small amplitudes. The values of Young's moduli, shear moduli and Poisson's ratios determined by the two kinds of procedures may not be comparable because of these reasons, particularly for ceramic matrix composites which exhibit ?on linear stress-strain behaviour. Therfore only results from dynamic procedures and values of the initial tangent moduli in the limit of zero strain from quasi-static procedures can be compared.
On the delamination of elastic constunls wifli ht-ittle matri,v composites
39 1
SPECIFIC MEASUREMENT PROCEDURES
In the following the advantages and disadavantages of specific methods of the two main groups of procedures, will be characterised shortly. Existing standards for the measurement of composites will be mentioned. The quasi-static (isothermal) procedures: The methods applied are based on the determination of stress-strain response with tension (compression and torsion) tests and bending tests (3- or 4-point). Observations for composites show that the strains, at which the measurements were performed, have considerable influence on the results. As mentioned above, a comparison to results from dynamic procedures is only in the limit of zero strain straightforward. For ceramic matrix composites the quasi-static loading methods are standardised in EN 658-1, ENV 658-2, ENV 1892, ENV 1893, ENV 12290 and ENV 12291 with EN: Euronorme, ENV: Euronorme Volontaire. The dynamic (arlinbntic)procedures: The most representative method for procedures using the determination ofsound velocities is the “Ultrasound Wave Spectroscopy” [ 1,2], standardised for ceramic matrix composites in ENV 14186. This method is based on the measurement of the time delay between ultrasonic wave pulses through materials with low attenuation (ceramics, hard metals, intermetallics, ceramic composites). The determination of the elastic constants is carried out by calculating the coefficients of the propagation equation of an elastic plane wave from a set of properly chosen velocity measurements along known directions: A thin specimen of known crystallographic orientation with planparallel faces is immersed in an acoustically coupling fluid (e.g. water or oil). The specimen is placed between an emitter and a receiver which are rigidly connected to each other and have two rotational degrees of freedom, Using appropriate signal processing, the propagation velocities of each wave in the specimen are calculated. Depending on the angle of incidence, the pulse sent by the emitter is refracted within the material in one, two or three bulk waves (one longitudinal wave, one transverse wave or two transverse waves), which propagate in the solid at different velocities and in different directions. The receiver collects one, two or three temporally delayed pulses, corresponding to each of these waves. The difference in propagation time of each of the waves and the propagation time of the emitted pulse in the coupling fluid without the specimen is measured. The great advantage of this method is that the complete elastic tensor for composites down to orthothropic symmetry can be determined. The disadvantage is that the method is restricted to room temperature or modest temperatures corresponding to the coupling h i d (oil). A frequently applied method is the “Ultrasound Pulse Propagation” (Pulse-Echo Method), standardised for monolithic ceramics in ENV 843-2 at room temperature, which can be adopted to composites too. The principle is similar to the ultrasound wave spectroscopy mentioned above. Two transducers (emitter and receiver) are acoustically coupled to the planparallel surfaces of the specimen. For longitudinal waves the ultrasound pulse is applied perpendicularly to the surface, for transverse waves parallel to the surface. The elastic constants or the elastic moduli can then be calculated from the differences of the propagation times (sound velocities) if the specimen is oriented. For the time being the method is restricted to room temperature or to moderate temperatures, because the transducers have to be coupled directly to the specimen. Another method based on the measurement of sound velocities is the “Ultrasound Phase Spectroscopy” [3]. T w o transducers of the same kind are attached to opposite sides of a specimen with planparallel faces. One trailsducer is used to transmit a continuous, harmonic longitudinal elastic wave into the specimen, the other one is used to receive the transmitted
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Dieter LOIDL, Stephan PUCHEGGER. Henvig PETERLIK and Karl KROMP
signal. The number of phase periods as well as the magnitude ratio between the input and the output signal are measured. The group velocity can be deduced from the slope of a plot of the number of phase periods against the frequency. From this group velocity the elastic constant Cii can be calculated. The method has the disadvantage that only one constant in direction of transmission can be measured. For the time being it is restricted to room temperature, because the attenuators have to be coupled directly to the specimen. The great advantage of this method is that it can be performed with highly attenuating materials, such as fibrous materials, plasma-sprayed materials with high porosity and in the thickness direction of laminates. Bodies of elastic materials have characteristic sets of natural resonant frequencies (“eigenmodes”), which are determined by the elastic constants, the crystallographic orientation, the density, the dissipation and the shape of the bodies. It is evident, to use these frequencies as a tool to determine the elastic constants (the elastic moduli). “Resonant Ultrasound Spectroscopy” (RUS) is the most general case of the methodology, where all elastic constants can be acquired from (small) rectangular parallelepiped-shaped specimens or other specific shaped specimens (discs, cylinders) [4-81. The method also was extended to higher temperatures [9]. An overview of the method and its development is given in [4]. With RUS, small rectangular parallelepiped-shaped specimens down to 2 x 2 ~ 2mm3, with the main symmetry axes oriented parallel or pkrpendicular to the sides of the specimens, can be investigated. In principle the full set of elastic constants can be determined from the measurement of one single specimen. The set of elastic constants is determined by minimising the difference between observed and calculated resonant frequencies, using a least squares method. In order to fit the calculated to the measured eigenfrequencies with the elastic constants (elastic moduli), some prior knowledge of the constants has to exist. The theory of RUS is based on a series solution of the three dimensional free body problem. The sample shape and the accuracy needed are reflected in the order of the series solution, which in turn is reflected in the size of the matrix equation, that needs to be solved. Exploitation of crystallographic symmetry can reduce the matrix sizes dramatically, but until relatively recently such computations required large computers [4]. Other methods using resonant frequencies are more or less special cases of this spectroscopic measurement, restricted to e.g. specific geometry of specimens. One of these methods in use for decades is the “Resonant Beam Technique” (RBT), [lo]. In principle this method can only be applied to isotropic materials, which includes quasi-isotropic brittle composites such as chopped fibre materials. Standards exist for monohthio ceramics e.g. ENV 843-2, I S 0 17561, ASTM C1198-01 and C1259-01, JIS R1602, extended to high temperatures in prENV 820-5, for glass and glass-ceramics ASTM C623-85 and ceramic whitewares ASTM C848-94. With this method a prismatic bar of a length to width ratio of more than ten is excited to bending vibrations. From the dimensions of the bar, its density and the resonant frequency of the fundamental mode the Young’s modulus can be calculated, in principle by solving the Euler-Bernoulli equation. Exciting torsional vibrations by specific excitation the shear modulus can be calculated. For the calculations only the frequency of the fundamental mode is used, because the higher modes exhibit a shear perturbation which is not included in the Euler-Bernoulli equation. Another frequently used method is the “Impulse Excitation Method”, [ 1 I]. In principle this method can only be applied to isotropic or quasi-isotropic materials (see last method), standards only exist for monolithic ceramics, e.g. ENV 843-2. The excitation to resonant vibrations is performed by light mechanical impact. The Young’s modulus is calculated for isotropic and regular shaped test pieces from the resonant frequency of the hndamental mode, solving the Euler- Bernoulli equation, the shear modulus from the wave equation for torsional vibration, which has to be excited separately. Additionally, the internal
On the detertnination of elastic constants with brittle matrix coniposite.s
393
friction can be determined from the exponential decay of the vibration. This method was successfully extended to high temperatures (1 750 “C), [4] and is standardised in the European pre-standard prENV 820-5.
THE RESONANT BEAM TECHNIQUE WITH ANISOTROPIC COMPOSITES IN DEPENDENCE ON TEMPERATURE The classical Resonant Beam Technique (RBT) is frequently used to determine the dynamic elastic moduli in Standardisation (examples see above). All these applications have in common that they neglect the influence of shear, which increases with the order of the mode of vibration. For the calculation of results the Euler-Bernoulli equation, valid for the basic mode only, is applied and it is combined with correction factors for higher modes (in general only the first mode i.e. the first overtone is considered additionally to the fundamental mode). The shear moduli itself are determined separately from torsional vibrations. The development of the method described below was started in our working group in 1988, following the method of Forster [lo], with the introduction of corrections for higher modes and a graphical solution of the problem for anisotropic ceramic matrix composites (Carbon fibre-reinforced Carbon, C/C), [ 121. The method developed and applied at the Institute of Materials Physics now turns around the problem: The higher modes, which show the influence of the shear deformation, are measured up to the sixth order. Timoshenko’s equation, that includes a perturbation for shear, can now be used to calculate the Young’s modulus and additionally the shear moduli. The Young‘s modulus being the longitudinal modulus in the length direction of the prismatic test piece, the shear moduli being the moduli along the height and along the width of the test piece, respectively (Poisson‘s ratios can be calculated from these moduli). Thus it is important to cut out the specimen with respect to the crystallographic orientation. For example from a 2,5D or a 3D composite (orthothropic symmetry) test pieces can be cut out perpendicular to each other in reinforcing directions x, y and z, so that the Young’s moduli E,, E,, E, and the shear moduli GxyrGyz, G,, can be obtained. As already mentioned above, contrary to mechanical test methods, the determination of elastic properties by the Resonant Beam Technique described here is not based on the evaluation of the stress-strain response over a given deformation range obtained under quasi static loading conditions, but is based on a non-destructive dynamic measurement from vibrations at very small amplitudes. Therefore the values of Young’s moduli, shear moduli and Poisson’s ratios determined by quasi static and dynamic methods may not give the same results, particularly for ceramic matrix composites which can exhibit non linear stress-strain behaviour.
Measurement of moduli by the “Resonant Beam Technique (RBT)”, measurement procedure The test piece, a long thin prismatic bar (ratio of length to width or length to height larger than ten), cut out from the composite along a specific orientation of interest is excited to bending vibrations. The mechanical excitation at continuously variable frequencies is provided by means of a transducer that transforms cyclic electrical signals to cyclic mechanical forces on the test piece. A second transducer senses the resulting mechanical vibrations of the test piece and transforms them into electrical signals. The resulting spectrum (amplitude in dependence on frequency) is measured via a network analyser. From the resonant frequencies i.e. the peaks of the spectrum (fundamental vibration and harmonics up to the sixth mode), the dimensions
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Dieter LOIDL, Stephan PUCHEGGER, Henvig PETERLIK and Karl KROMP
and the density of the test piece, the engineering elastic moduli can be calculated by numerically solving Timoshenko's equation. Starting with estimated values for Young's and shear moduli, those moduli are computed by an iterative process, which minimises the difference between the measured and the calculated eigenfrequencies. The result for every specimen is one Young's modulus and two shear moduli in directions perpendicular to each other. The specific equations and the calculation procedure are summarised in [ 131, the theoretical background was taken from [ 14-171. At the Institute of Materials Physics, University of Vienna this technique was extended for the application to temperatures up to 2000 "C [ 131. Most of other methods proposed for the measurement of elastic constants with anisotropic materials are, at least at the moment, restricted to room temperature, see e.g. [ 1,2]. Testing equipment for high temperatures Specific transducer systems (emitter-receiver) have been developed. The specimens are suspended from the transducers by loops of carbon fibre bundles (several hundred fibres each) and excited to bending vibrations via the loops. The specimen hangs between graphite heating elements in a vacuum chamber, Fig. 1, [13].
r-J
controland
evaluation unit
networkanalyser
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1; transmitter
I temperature con Ll I
I
receiver
heating element
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FIG. 1 : Scheme of the resonant frequency apparatus "ELASTOTRON 2000" (left). The prismatic specimen is excited to bending vibrations by carbdn fibre-bundle loops attached to transducers in water-cooled housings (right). Most important and decisive is the software: data acquisition and evaluation are performed online by a single software package in connection with a network analyser (HP 875 IA). The software encloses an effective user interface and operates on a standard personal computer. Meanwhile the third prototype of equipment has been built up, see Figs. 2 and 3.
011
the detmtnitiution of elastic cotzstnttts with brittle ttrutrix composites
395
FIG. 2: Resonant frequency apparatus "ELASTOTRON 2000", overview, vacuum vessel closed.
FIG. 3 : Resonant frequency apparatus "ELASTOTRON 2000": transducers in watercooled housings (top), attached carbon fibre-bundle loops with C/C specimen in graphite heating element (open). Example of measurements with a 2,5D-reinforced ceramic matrix composite In the frame of a co-operation project with Snecma Propulsion Solide, Le Haillan, Bordeaux we received specimens from needled woven 2,SD carbon-fibre reinforced carbon composites (C/C-composites) out of the hot zone of the nozzle of the booster of the Ariane 5 . The specimens were cut out in three directions perpendicular to each other. The orientation of the specimens is given in Fig. 4.
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Dieter LOIDL, Stepl~anPUCHEGGER. Henvig PETERLIK and Karl KROMP
Fig. 4: Orientation of specimens out of the nozzle of Ariane 5 From Fig. 4 it can be assumed that the specimens in direction x cannot follow the curvature, thus the reinforcement will not be homogeneous along the length of the specimen, though the inner radius of the nozzle is rather big (0,9 m). The material “Novoltex” is produced by winding a 2D carbon fibre fabric around a mandrel, finally the cylindric body is needled with chopped fibres perpendicular to the fabrics. The reinforcement in direction z thus is rather weak. The pyrocarbon matrix is deposited by chemical vapour infiltration (CVI), then the composite is heat treated. Kesults at room temperature An example of a frequency scan of a specimen cut out in direction x is given in Fig. 5. The resonant modes identified up to the sixth order are marked (the non marked ones are torsional modes). The prismatic specimens with the dimension 65x10~5mm3 exhibit resonant sites at different directions of bending vibration (flatwise, fw means vibration along thickness 5 mm and edgewise, ew along width 10 mm), denoted as f and e in Fig. 5, respectively.
-60
-
-
-00
m
-0
c
.-c0 m r’
-100 -120
Q)
E
-140
fl
el
f2
f3e2
f4 e3 f5 e4 f6 e5
e6
-160 2
3
4
5
6 7 8 9 1 0
20
30
40
50 60
frequency [ kHz ] Fig. 5: Frequency scan and resonant modes of bending vibration of composite Novoltex at room temperature, orientation x.
397
On the determination of elastic constants with brittle matrix cotnposites
By the procedure described above and using all the modes identified, the Young’s and shear moduli for the three specific orientations of specimens (x,y,z), perpendicular to each other, were computed. As mentioned above. the result for every specimen with the RBT is one Young’s modulus and two shear moduli in directions perpendicular to each other. The results at room temperature are given in Fig. 6.
1‘
E y = 17.1 GPn
3.2
= 31.3 GPa
Fig. 6 : Young’s and shear moduli for specific orientations (x, y, z) and different directions of vibration (flatwise, fw and edgewise, ew) with C/C-composite Novoltex at room temperature. Two general features should be anticipated before discussing the results: during the measurements in direction x it turned out that the values of the resonant frequencies did not follow precisely the theoretically predicted ones, this is argued to be a consequence of the fact that the straight specimens in direction x do not follow the curvature of the structure of the nozzle (see Fig. 4). On the other hand the measurements with specimens cut in direction z in general showed resonant sites less distinct and thus exhibited larger errors, because the reinforcement in this direction is rather weak. The Young’s moduli in directions (x, y, z) differ significantly from each other. As the Young‘s moduli should directly reflect the structure of reinforcement (the fibre structure) this result could be expected. The largest value, Ex is measured in direction of warp, the median value, E, in direction of weft and the smallest value, E, in direction of reinforcement by needling with chopped fibres, see Fig. 6. The shear moduli are influenced by both, matrix and reinforcement. The stronger reinforcement is in the plane (x y), i.e. warp and weft. The weaker reinforcement is in the planes (x z) and (y z) by chopped fibres. Thus the G,, are larger than the G,, and the Gyr, respectively. The G,, and the G,, should show nearly the same values, as it is the case (see Fig. 6). It is to expect that edgewise vibration in orientation x (Gxy)gives the same result as edgewise vibration in orientation y (Gxy).because the reinforcement in this plane is the same for both the directions of vibration.
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Dieter LOIDL. Stephan PUCHEGGER. Henvig PETERLIK and Karl KROMP
On the other hand the results for the G,, in the different directions of vibration (ew and fw) should be identical, the same should hold for the G,, considering the errors [13] this is the case. For reasons of weak reinforcement in z mentioned above, the results for G,, and G,, measured with the z-specimen showed the largest error, thus these values were not introduced into the high temperature graph in Fig. 7b. Results at high temperatures The measurements in dependence on temperature were performed in vacua of 3.IO4 mbar. The measurements were followed up to a maximum of 1800 "C (to go up to 2000 "C would need Argon atmosphere, to prevent damage on the graphite heating system).
__ 1000
temperature ["C]
a)
1500
.
2000
500
1000
1500
2000
temperature ['C]
b)
Fig. 7: Dependence on temperature of a) Young's moduli for specific orientations (x, y, z); b) shear moduli for specific plains (xy, xz, yz) with C/C-composite Novoltex Fig. 7a exhibits a continuous increase of Young's moduli with temperature, the same for the shear moduli in Fig. 7b. G,: means shear in the plain (xy), measured with the specimen cut out in direction y, analogous for the other notations (compare Fig. 6 ) . in the graphs the error bars are shown together with the symbols. The G,- and G,, -values measured with specimens cut out in direction z are not shown in the graphs, because of reasons mentioned above. Summarising it can be stated that all the moduli of this C/C-composite raise continuously with temperature. Polished cuts through the material and microscopic investigation exhibited a high content of pores and interlaminar, intralaminar and intrabundle microcracks. Most of the microcracks open during cooling down of the composite from heat treatment temperature to room temperature. It is argued that most of these microcracks close with raising the temperature and contribute to the stiffening of the composite. On the other hand the rather weak bonding between fibre and matrix (for C/C not much more than van der Waals) is improved by continuously raising clamping between fibre and matrix when
On the determination of elastic constants with brittle tnntrii cotnposites
3 99
temperature approaches the heat treatment temperature. Both these effects contribute and thus result in raising the moduli.
RESONANT ULTRASOUND SPECTROSCOPY (RUS) AND RESONANT BEAM TECHNIQUE (RBT)
RUS and RBT are two very successful procedures to determine the elastic properties of composites. RUS is an option for the determination of the complete set ofelastic constants of specimens with various shapes (eg. small cubes or parallelepipeds) and with the option to extend the procedure to application to high temperatures. RBT is an easy to handle technique up to high temperatures with the restriction to specific shapes of specimens (long thin bars) and the corresponding engineering moduli. The problem with RUS is that exciting an e.g. cubic specimen results in a very dense spectrum of resonant frequencies (more than 30 resonant sites). A solution of this problem only is possible, if some precise knowledge on the elastic constants already is available. The idea now is to combine these two procedures. At the Institute of Materials Physics in our working group a new software has been developed to be easily extensible and flexible. This software has been adapted to the different requirements, which are specific to the problem, e.g. the fitting of the calculated frequencies to the measured frequencies can now be optionally performed by “simulated annealing” and will thus not easily end up in a local instead of the global minimum, which would give wrong results. The number of polynomials used to approximate the true displacement function along the different axes can be better adapted to Timoshenko-beam like geometries, which results in a drastic decrease of the computational time needed at a steady level ofaccuracy. By means of this new software the complete set of eigenfrequencies of RBT-shaped specimen can be calculated. Now the procedure proposed is to gain preliminary results with RBT and then to continue with RUS by introducing these preliminary results. Results on simulation calculations for this case were already achieved [ 181. ACKNOWLEDGEMENT The financial support by the Austrian Science Foundation FWF under Project P14294 and Project P15670 is acknowledged. Many thanks to our Partner M. Bourgeon from Snecma Propulsion Solide in Le Haillan, Bordeaux and his support in the frame of the co-operative Project PPO8275LOOO.
REFERENCES 1. Baste, S., El Bouazzaoui, R., An experimental investigation of stiffness reduction and cracks geometry in an unidirectional brittle matrix composite; J. Compos. Mater., 30/3, 1996, pp 282-308 2. Castagnkde, B., Jenkins J. T., Sachse, W., Baste, S., Optimal determination of the elastic constants of composite materials from ultrasonic wavespeed measurements; J. Appl. Phys. 67, 1990, pp 2753-2761 3. Wanner, A., Elastic modulus measurements of extremely porous ceramic materials by ultrasonic phase spectroscopy; Mater. Sci. Eng. A248, 1998, pp 35-43
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Dieler LOIDL, Stepharz PUCHEGGER, Herwig PETERLIK and Karl KROMP
4. Migliori, A. M., Sarrao, J. L., Resonant ultrasound spectroscopy; John Wiley and Sons, New York, Chicester, Weinheim, Brisbane, Singapore, Toronto; 1997; ISBN 0-471- 12360-9 5. Leisure, R. G., Willis, F. A., Resonant ultrasound spectroscopy; Phys. Today, J. Phys. Condens. Matter 9, 1997, pp 600 1-6029 6. Maynard, J., Resonant ultrasound spectroscopy; Phys. Today, 4911, 1996, pp 26-3 I 7. Migliori, A., Sarrao, J. L., Visscher, W. M., Bell: T. M., Lei Ming, Fisk, Z., Leisure, R. G., Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids; Physica B 183, 1993, pp 1-24 8. Maynard, J. D., The use of piezoelectric film and ultrasound resonance to determine the complete elastic tensor in one measurement: J. Acoust. SOC.Am. 91/3, 1992, pp 1754-1762 9. Goto, T., Anderson, 0. L., Apparatus for measuring elastic constants of single crystals by a resonance technique up to 1825 K. Rev. Sci. Instrum. 59/8. 1988, pp 1405-1408 10. Forster, F., Ein neues Verfahren zur Bestimmung des Elastizitatsmoduls und der Dampfung; Z. Metallkd. 29, 1937. pp 109- I 15 11. Roebben, G., Bollen B., Brebels, A., Hurnbeeck J. Van, Biest, 0. Van der, Impulse excitation apparatus to measure resonant frequencies, elastic moduli and internal friction at room temperature and high temperature; Rev. Sci. Instrum. 68/12, 1997, pp 451 1-45 I5 12. Wanner, A., Kromp, K., Young's and shear moduli of laminated carbodcarbon composites by a resonant beam method; in: "Brittle Matrix Composites 2", ed. by A.M. Brandt and I.H. Marshall, Elsevier Appl. Sci. Publ., London-New York 1988, pp 280-289 13. Lins, W., Kaindl, G., Peterlik, H., Kromp, K., A novel resonant beam technique to determine the elastic moduli in dependence on orientation and temperature up to 2000 "C; Rev. Sci. Instrum 7017, 1999, pp 3052-3058 14. Timoshenko, S. P., On the correction for shear of the differential equation for transverse vibrations of prismatic bars; Phil. Mag. 41, 1921, pp 744-746 15. Timoshenko, S. P., On the transverse vibrations of bars of uniform cross section; Phil. Mag. 43, 1922, pp 125-131. 16. Huang, T. C., The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions; J. Appl. Mech. 28, 1961 pp 579-584 17. Kaneko, T., On Timoshenko's correction for shear vibrating beams; J. Phys. D: Appl. Phys. 8, 1975 pp 1927-1936 18. Puchegger, S., Loidl, D., Kromp, K., Peterlik, H., Elastische Moduln anisotroper Verbundwerkstoffe bei Hochtemperatur; 14. Symposium ,,Verbundwerkstoffe und Werkstoffverbunde", July 2nd-4th, 2003, Wien; Proc. by Wiley-VCH, D-69469 Weinheim, Germany, in print
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw. October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
PLENARY INVITED PAPER
A MECHANICAL STUDY OF REINFORCED-CONCRETE BEAMS REPAIRED WITH COMPOSITE SHEETS Stephane AVRIL', Alain VAUTRI", Patrice HAMELM', Yves SURREL3 'SMS/MeM, ENSMSE, 158 cours Fauriel, 42023 Saint- Etienne Cedex 2, France. email: [email protected], [email protected] 'L2MS, Universite Claude Bernard Lyon I, 43 bd du 1 1 Nov. 1918, 69622 Villeurbanne Cedex, France, email: [email protected] 1 .fr 'BNM-PJM, CNAM, 292 rue Saint Martin, 7 5 I41 Paris, France, email: [email protected]
ABSTRACT This paper deals with rehabilitation of Reinforced-Concrete infrastructures with externally bonded carbon-epoxy sheets. The flexural behaviour of repaired structures under service loads is addressed, focussing mainly on the problem of crack width prediction. Firstly, the state-of-the-art methods for crack width prediction in concrete beams are recalled. Then, they are confronted to experimental data obtained with a full-field optical method onto small scale beams. Those experiments conducted on physical models show that classical formulae are not suited for the prediction of crack widths in the repaired beams, because they do not take into account the crack bridging effect due to bonding between the composite sheet and concrete. In order to elaborate a numerical modelling, a multi-scale approach is suggested. It is based upon the definition of a relevant Representative Volume Element of beam. The assets are that input parameters have a physical meaning and that the simulated mechanical behaviour is consistent with the one characterized experimentally. Finally, the main results obtained in this study are verified in beams whose scale is representative of real infrastructures. The paper focuses mainly on the validation of the numerical model for computing crack widths in the repaired beams. The interest for the identification of bonding properties between the composite sheet and concrete is also poir.:ed out. Keywords Repair with composites, crack bridging, Reinforced-Concrete, full-field measurements. grid method, bonding.
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Stephane AVRIL. Alain VAUTRIN, Palrice HAMELIN- and Yves SURREL
INTRODUCTION The context of this work is within the rehabilitation of civil engineering infrastructures. The issue of upgrading the civil engineering infrastructures has become of great importance for over n decade [ 11. The main reasons are increasing traffic volume. lack of maintenance, environmentally induced degradation, earthquakes.. . Many experimental studies have shown that CFRP (Carbon Fibre Reinforced Plastic) sheets are mechanically effective for upgrading damaged RC structures. Especially concerning Hexure, bonding CFRP sheets can significantly increase the moment of failure of damaged beams [2, 31. For the design, both the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS) of the structure must be verified. Despite of the moment of failure increase, the experimental studies cited previously have also shown that externally bonded composites do not really enhance the serviceability. This has been confirmed by on-site investigations. Hag-Elsafi et al. [4]have applied CFRP composite laminates to strengthen an aging reinforced-concrete T-beam bridge in the USA. They have shown that rebar stresses were only moderately reduced after installation of the laminates. Actually, the structural effect of the CFRP sheet is only clear after yielding of internal steel rebars, ie. beyond the Serviceability Limit State of the structure. [ndeed, on one hand, CFRP materials have high strength and no large amount of CFRP are needed for ULS. On the other hand, the modulus of elasticity of CFRP manufactured directly onto the damaged structure can be relatively low (60 GPa). Higher amounts of CFRP may be needed to introduce sufficient stiffness for meeting the serviceability design criteria.
As both ULS and SLS must be taken into account for the design, serviceability appears more restrictive than failure for the repaired beams. Among serviceability aspects, the most critical one is often cracking. Crack widths should be limited for insuring infrastructures durability. In the absence of specific requirement and for exposure classes 2-4, Eurocode2 [S]recommends that a limit of 0.3 mm under quasi-permanent (long-term) loads should be satisfied. Wide cracks are also harmful for the durability of RC beams repaired with CFRP sheets because wide cracks may be at the origin of CFRP debonding [6, 71. Therefore, the value of 0.3 mm utilized in Eurocode2 should be kept as the SLS of repaired beams. However, the use of this limit value as a design criterion implies that sound methods are available for the assessment of crack widths in repaired beams. This problem is addressed in this paper. Firstly, the state-of-the-art methods for crack width prediction in concrete beams are recalled. Then, they are confronted to experimental data obtained with a full-field optical method onto small scale beams. It is shown that classical formulaes are not suited for the prediction of crack widths in repaired beams, because they do not take into account the crack bridging effect due to bonding between the composite sheet and concrete. For modelling numerically this effect, a multi-scale approach is suggested, using the Finite-Element-Method (EM).Finally, the paper focuses on the validation of the model for computing displacement fields, crack widths and curvatures in real scale repaired beams.
THEORETICAL BACKGROUND Concrete reinforced with steel rebars The post-cracking behaviocr of f C s t h t u r e s depends on a great number of influencing factors: the tensile strength of concrete, anchorage length of embedded rebars, concrete cover, steel
A mechanical study of reinforced-concreie beams repaired with composiie sheets
403
spacing, which are strongly related to the bond characteristics between concrete and steel. The approach which has been the most widely used for assessing crack widths in concrete reinforced with steel rebars is based on the theory of multiple cracking (Figure I ) and on bond-slip models [8,91 whose basic formulae is: AJt 1,, = rmC0 where: 0
r, is the average bond stress over a given transfer length ltr (the subscript 712 is linked to the word “average”), is the tensile strength of concrete (the subscript t is linked to the word “tensile”),
0
ft
0
Co is the bar perimeter.
Figure 1: Multiple cracking of RC elements in tension From the strain distribution, the crack width W I ; can be defined as the total difference of elongations between the reinforcement and the concrete matrix measured between two adjacent cracks, which is equivalent to the crack spacing. Structural concrete codes generally use this type of approach for computing allowable crack width. For example, the relation supplied by Eurocode 2 [ 5 ] for the design of reinforced concrete beams writes: wk = PScrmErn
(2)
where: 0
w k is the assessed crack width (the subscript k is linked to the word “crack”),
0
E,
is the average tensile strain difference between the steel and the concrete, taking into
. account bond stress, tension stiffening, shrinkage effects ... 0
s,., is the average crack spacing for the final load,
0
/3 is a design coefficient.
The use of this theory for crack widths prediction in flexure is based on a large number of simplifying assumptions. Crack width can not be assumed to be constant over the depth of the element, naturally equalling zero in zones of compressive stress for example. Moreover, tests have shown that the concrete cover can have a significant effect on surface crack widths. Attempts to apply eq. (2) have led to the development of simple empirical equations to compute E., For example, the approach adopted by CEB-FIP [ 101 is based on the average strain in the member. It has been kept by Eurocode2:
where:
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0
0
0
0
Sfkphane AVRIL, Alain VAUTRIN Patrice HAMELIN, and Yves SURREL
is the stress in the tension steel under the service conditions being considered, calculated on the basis of a cracked section (the subscript s is linked to the word “steel”);
fs
fsr is the stress in the steel rebars under the relevant conditions that just causes the tensile strength of concrete to be reached, calculated on the basis of a cracked section;
Dl is a coefficient that accounts for the bond properties of reinforcements, which are responsible for the tension stiffening effect, Pz is a coefficient that accounts for repeating stressing of the bars.
Equation (3) obviously has an empirical basis but it leads to quite good results For RC beams [lo]. Concrete reinforced with steel rebars and external FRP sheets The post-cracking behaviour of RC beams strengthened with composites is quite similar to unstrengthened ones [ 11, 121. It is still relevant to assess crack widths by using bond-slip models. However, bonding properties between concrete and the composite must be taken into account for crack width prediction in RC beams repaired with C F W sheets. Its role has already been evidenced for reinforced concrete beams st‘rengthened with steel plates [ 13, 14, 151. It has not been proved yet if the adherence of the laminate onto concrete can significantly contribute to bridge the cracks in the damaged concrete structure. Models involving tension stiffening are scarce. Some authors [16] attempted to introduce crack bridging effects in beam equations but refined experimental studies are still necessary to understand those local phenomena and their influence onto the global behaviour of the structure. Consequently, design guidelines provided presently by the task groups [7] and utilized in practice are based upon Eurocode 2 [5]. However, experiments conducted by Fenier et al. [ 171, and which are recalled in this paper (Figure 2 ) have shown that they do not lead to a good assessment of crack widths after repair. It penalizes greatly the use of composites for tackling serviceabilitydeficiencies in concrete structures. In view of that, the main objective of the study which is described below is to contribute to a more accurate prediction of crack widths after repair.
“P 4
S 300
5P 200 0
5
E
0
100
0
L 0 -crack
Load I(kN)
I
20
40
width measured after repair
60 -crack
80
100
width predlcted b y EC2
Figure 2: Comparison of the crack widths assessed with Eurocode 2 formulae and the experimentally measured crack widths in a RC beam repaired with a composite sheet
A niecliairical study ojreinforced-concrete hecims repaired with composite sheets
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EXPERIMENTAL CHARACTERIZATIONOF SMALL-SCALE BEAMS Details of the specimens For characterizingthe mechanical behaviour of cracked beams externally reinforced with CFRP sheets, tests have been carried out firstly onto a physical model of beam (Figure 3). The physical model is actually a small-scale beam. It has a cross section of 84 x 50 mm2, a total length of 770 mm, and an effective span of 667 mm. The longitudinal and shear steel reinforcements are the same for all these specimens: 2 44.5 rebars and 2 20-mm-spaced stirrup. The cover concrete is 8 mm thick. Similar mixed concrete is used for all the beams. The cement : sand : gravel proportions in the concrete mix are 1 : 2.2 : 3 by wcight. The waterkement ratio is 0.52 and 462 kg/m3 type I Portland cement (CPA 55) is used. The maximum size of the aggregate is 5 mm. The average compressivestrength of concrete is 39 MPa. The elastic modulus is 41 GPa.
\
'\i,paii~*.'uUlh,11
r
E4rr3a.l.
Figure 3: Details of the small-scale beams.
Figure 4: Photography of the experimental set-up utilized for small-scale beams. Small-scale beams were designed by applying the similitude thcory which leads to the different scale factors to be used with respect to the real-scale reference model [18]. Not only steel bars and stirrups diameter but also aggregate size and granulometry of the concrete havc
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Stkphane AYRIL, Alain YAUTRIN. Patrice HAMELIN. and Yves SURREL
been multiplied by a scale factor in order to match with the reduced dimensions of the beams. These factors are obtained on the basis of a dimensional study [ 191. The basic scale factor for lengths is 1/3. The suitability of the physical model to represent the mechanical behaviour of real-scale specimens is discussed in the last section of the paper. Five small-scale RC beams have been tested in four-point-bending before bonding the composite sheet. The main objectives of this first test are to create tensile cracks and to characterize the mechanical behaviour of cracked beams before repair. Since the maximum tensile strain is reached in concrete, several vertical cracks occur in the tensile part of the beam. The global equilibrium is kept because the internal steel rebars bear the tensile stresses. Each test is stopped once 60% of the load corresponding to the rebars yielding is reached. Afterwards, the beams are unloaded. A second bending test is carried out directly up to failure on one of the beams. This beam is used as the reference unstrengthened beam. Four, out of the five pre-cracked beams, are repaired with a composite laminate bonded onto the bottom surface. The bonded CFRP laminate is made of a unidirectional high modulus carbon fibers taffetas (330 g/m2 reference Hexcel 46320) and epoxy resin (Ciba LY 5052). It is directly polymerized on the specimen, the first epoxy resin layer working as the bonding joint. The thickness of the bonding joint is 0.4 mm and the thickness of the composite is 0.8 mm. A tensile test carried out on such a laminate provides a Young modulus of 55 GPa. After polymerization, the repaired beams are loaded in flexure up to the steel rebar yielding load. The bending test and instrumentation are the same as the one used in the case of unstrengthened beams. Each beam is instrumented with a bi-directional grid laterally over a 140 x 84 mm rectangular surface in the constant moment span. The grid is utilized as a spatial carrier to measure the displacement fields over the lateral surface of the specimen [20]. The grid is made of the superposition of horizontal and vertical black lines printed over a white surface. Such a pattern is easy to realize. It is obtained in our experiments by printing the grid over a transparent sheet and transferring it over the surface of the specimen firstly painted in white (Figure 4). The lines of the grid must be separated by the same distance p , which is called the grid period. The grid period is p = 571 p m here. A numeric BASLER A1 13 1200 x 1000 pixels CCD sensor connected to a PC is used for grabbing images. The displacement computation is performed with an in-house software called Frangyne2000, applying the principle described in the following section. The resolution of the measurement, i.e. the smallest displacement which can be detected, is about 2 or 3 pm, depending on the quality of the grid transfer. The spatial resolution is 1.2 mm [21,22].
The grid method The principle of me_asurements is quite simple: a given point hfo+of. the space is determined by its position vector R ( X ,Y )in the reference Cartesian frame (0, i, j ) . In the initial undeformed configuration, the material point M coincides with Mo.In the final deformed configuration, another material point M‘ coincides with the spatiaf point Mo. The position of M’ in the initial undeformed configuration was characterized by R’(X’, Y’)in the Cartesian reference frame (Figure 5). In the initial undeformed state, the reflected light at point A40 is the light reflected by the material point hf.Its intensity writes: I ( @ = I0 { 1 where:
+ r f r g n [27rP.ii]}
(4)
407
A mechanical study of reillforced-concrete b e a m repaired with cotnposite sheets
is the local intensity bias,
0
I0
0
y is the contrast,
0
f r g n is a 2x-periodic function,
0
Lu'denotes the dot product of both vectors G(uZ,uv)and u'(u,,
0
L.,,):
is the spatial frequency vector. It is orthogonal to the grid lines and its amplitude is the spatial frequency of the grid. If the gridlines are vertical, they are parallel to meaning that the spatial frequency vector writes F ( l / p ,0). If the grid lines are horizontal, they are parallel to meaning that the spatial frequency vector writes F ( 0 , l/p).
y,
z,
When a loading is applied, there is a deformation of the structure and the grid is also deformed. The reflected light at spatial point ibl~has become the light reflected by the material point M'. As the position of M' in the undeformed configuration is determined by @(X,Y ) , the new intensity at point A40 is actually:
T(8)= 1, { 1 + r j r g n [2nF.@]}
(6)
The deformation from the undeformed config_ura_tionto the deformed configuration is described mathematically by the displacement field U(R)= l? - d,, but also by the inverse displacement field 6-'(2)= n' - ?I (Figure 5 ) . Therefore eq. (6) writes:
[(a)= I , (1 + y j r g n [ 2 x F . (a- ~ - ' ( 8 , ) ] }
(7)
The phase of the function f r g n at the point M varies of 2xF.6-'(8) from the undeformed to the deformed state. [f the assumption of small deformations is valid, 6-'(f?) and 6(@are similar. Therefore, it can be written in the deformed state:
Z(R) = t o ( 1 + y f r g n [27rF.(a- 6(")]}
(8)
The first component U,(x, y) of the displacement is calculated from the phase of the function f r g n when the grid lines are vertical, the second component U , ( z , y ) when the grid lines are horizontal. A suitable algorithm of signal processing [22] is utilized to compute the phase of the function f r g n .
Figure 5: Displacement vector and inverse displacement vector at the pixel location
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Stepphane AVRIL, Alain VAUTRIN Patrice HAMELIN, and Yves SURREL
Figure 6: U,(rc, y) and Uy(z, y) displacement fields.
tributary
new vertical
crack
crack
Figure 7: Detection of cracks in a repaired beam from full-field measurements. Experimental characterization of cracking Examples of displacement fields measured onto the lateral surface of a repaired beam have been plotted in Figure 6. Whether the beam has been repaired or not, the V,(z,y) field is discontinuous. Discontinuities are always linked to the presence of a crack, as it was shown in a previous study [23]. Maps of these discontinuities are plotted in Figure 7, where continuous black lines represent the cracks. The smallest crack width which can be detected is 5 pm [20]. In Figure 7, the cracks are mapped out: 0
at the beginning of the test, the pre-existing cracks of the RC beam are still open because of the non-linear friction behaviour of the concrete-steel interface,
A mechanical study of reinforced-concrete b e a m repaired with composite sheets
a
409
at the end of the test, i.e. at 100%of the steel yielding load, new crack have occurred and grown.
During the four bending tests, the new cracks which appear (Figure 7) are classified in two types: a
0
most of them are oblique shear cracks : they do not propagate up to the neutral axis but they are deflected towards the neighbouring pre-existing crack at the level of the internal re-bars. They are called tributary cracks. a few are vertical and appear halfway between two pre-existing contiguous cracks. They are not deviated in their propagation towards the neutral axis. They may result of tensile stresses in the concrete induced by the action of crack bridging of the composite laminate.
The creation of new cracks, especially tributary ones, is a phenomenon specific to repaired beams. None are detected when the reference unrepaired beam is loaded up to failure. For one of the detected cracks, the motion of the left hand side lip and the motion of the right hand side lip have been plotted versus the ordinate g on the same graph (Figure 8). This motion is measured with a precision of 1 pm. It is better that the resolution of displacement measurements because data are averaged on both sides of the crack. The graph in Figure S shows that the motion of the crack lips is affected near the soffit after repair. On the other hand, beyond the height of steel re-bars, the motion depends linearly of y and it is parallel to the motion of the lips before repair. The width reduction is only induced by the stiffening effect provided by the composite sheet after repair. Finally, the essential effect observed here is the local bridging of the tensile cracks by the composite laminate. This effect is located mainly in the cover concrete where the crack opening is hindered by the bond stresses. This phenomenon is responsible for the occurrence and the growth of new cracks after repair [ 121.
Figure 8: Detection of cracks in a small-scale beam from full-field measurements before and after repair. Characterization of plane cross sections Experiments have shown that the cracking behaviour after repair is quite different of the one before repair because new cracks occur between the preexisting ones. [n order to verify if the
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Sriphane A VRIL, Alain VAUTRIN, Patrice HAMELIN, and Yves SURREL
theory of multiple cracking exposed in the Section “Theoretical background” is still relevant, it has been checked if the crack widths can still be defined as the total difference of elongations between the reinforcement and the concrete over a given length. For that, the measured displacement fields have been compared with the one predicted by the beam theory of Bernoulli. Locations where the modelled and the experimental field U,(z, y) are equal are detected (Figure 9). The following criterion is used : at one pixel, if the absolute difference between the experimental and the modelled displacement is less than 2 pm, then the pixel is black, else it is white. A cut off value of f 2 m has been chosen because it is the resolution of the grid method. In the tensile region, few locations are detected. They are mostly concentrated in narrow strips aligned perpendicularly to the length of the b e q . The cross sections located at the middle of each strip can be considered as the only ones to remain plane. It must be noticed that only the displacement of the lateral surface of the beam is measured. The internal behaviour is not addressed. Yet, the particular cross-sections identified here actually delimit lengths of beam over which Bernoulli’s theory is verified in average [12]. Finally, two consecutive plane cross sections define a length of beam containing only one vertical crack which has already grown before repair. It can also contain some new cracks occumng after repair. The existence of plane sections is directly linked to the parameter,,s, of eq. (2), i.e. the crack spacing in the RC beam before repair. The average distance separating two consecutive cross sections remaining plane is,,,s and the average distance between a crack and a cross section remaining plane is scrm/2[ 111. It means that eq. (2) is still relevant for assessing the width a vertical crack after repair, provided that the contribution of new cracks is subtracted from the expression of E., This major result is used for modelling crack opening in the repaired beam.
Figure 9: Locations where the experimental displacement field and the Bernoulli-modelled one are similar, for an unrepaired beam in picture 1 and for a repaired beam in picture 2.
t
I IP
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Stephane A V N L , Alnin VAUTRIN, Patrice HAMELIN, and Yves SURREL
[24].The bonding law between steel and concrete can be approached by an elasto-plastic model: a.
If
IT/ <
70,
Au =
(9) kS
where T is the tangential stress at the interface and Au is the steel rebar slipping. The threshold TO can be identified from experimental results and the ratio ks is given in the literature: k, = lo6 N.mm-3 [24].
I f 7 = ffi,, b. Au does not depend of tangential stresses anymore. Two constrain equations impose that slipping in the z direction only is possible; 0
because of the low thickness of the composite laminate, the composite laminate is modelled by three-dimensional, four-node shell elements, with an orthotropic elastic constitutive law; because of the low thickness of the epoxy bonding layer, it is modelled by threedimensional, two-node contact elements. The composite slipping over the bottom surface of concrete has been investigated in the literature [25, 261. The bonding law can still be approached by an elasto-plastic model. a.
If
[TI < T!,,
The threshold T~ can be identified from experimental results. The constant k , is characteristic of the elastic mechanical behaviour of the lap joint. The lap joint theory [26] gives:
where G, is the shear modulus of epoxy and e p is the thickness of the bonding layer. An experimental value found in the literature has been chosen: k , = 2500 N . n ~ m - ~ . b. If T = i~,, An does not depend of tangential stresses anymore. Because of concrete shrinkage, steel rebars are confined inside the beam [24]. The comparison of FEM and experimental results shows that this effect must be taken into account in the model. Therefore. it is assumed that spar elements representing steel rebars are initially preloaded. An initial stress QO is given. It is a uniaxial compression. A value of -100 MPa was identified for matching experimental results.
Modelling of the crack The cracked surface is assumed to be plane and belongs to the left hand side cross section of the RVE (Figure 10). It induces a non-linearity because when the material is cracked, its stiffness is zero in tension but it is unchanged when it goes in compression. This description is of course a simplified description and it is assumed that both tension and compression are uniaxial perpendicularly to the crack plane. Penetration of materials when the crack closes is prevented by the penalty method [27].
A rnechanical study ojreiizforced-concrete b e a m repaired with composite sheets
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The phenomenon of crack occurrence is not modelled: it is considered that the stiffness in tension is always zero in the crack plane. It is assumed that the crack has already occurred when the model becomes effective. It means that numerical results will only be relevant once the crack length has stabilized. The model could be improved by modelling crack occurrence and growth. However, the study described here focuses only on crack opening mechanisms because most of RC beams have already been cracked under service loads.
load SIW number
Figure 1 I: Loading program. Parametric study of bonding properties The non-linear mechanical behaviour of the model is computed using the “Newton-Raphson” approach. A computation is achieved at each step of the load history curve plotted in Figure 1 I . The purpose is to compute the crack width evolution. The beam is repaired at load step 20. This is simulated numerically: 0
0
during the twenty preceding segments of the load history curve, the stiffness of the composite material is multiplied by a very small constant and boundary conditions on the left hand side cross section are not applied to the nodes belonging to shell elements, at load step 20, the constrain u, = 0 is imposed to the node on the left hand side cross section belonging to shell elements and the stiffness of the composite is restored.
The different parameters of the model are listed in Table 1. Their numerical value is also given. The main ones (underlined) have been chosen by trial and error to match experimental results. The other ones have been chosen from experimental studies found in the literature [24, 261.
composite
Table 1: Collection of input parameters and values chosen for the example
4 14
Stkphane AVRIL, Alain VAUTRIN Patrice HAMELIN* and Yves SURREL
-E . 250
130
j
:I
I1
70
5 0 1
J
,
m
,
roo
,
rmr
,
m
, lax,
,
lm
, 14xI
, 1Mo
, Ism
applied moment (Nm)
Figure 12: Parametric study of the influence of T~ for reducing crack widths.
The effects of the bonding constitutive law between concrete and the composite have been characterized. A parametric study has been performed in order to investigate the sensitivity of the model with regard to T~ (Figure 12). The evolution of the crack width, evaluated just at the bottom of the beam, has been plotted for different value of T~ and also for different thicknesses of the composite sheet. For T~ = 20 MPa and a one-ply thickness (0.8 mm), the reduction of crack widths is higher than for rP= 0 MPa and a two-ply thickness (1.6 mm). It means that the contribution of bonding in crack bridging is at least equivalent to the contribution of a supplementary ply of composite. This is an encouraging result for taking into account the contribution of bonding in the design of a repair with composites. It contributes significantly to the reduction of crack opening, and consequently enhances the structural serviceability. A validation of this effect on real-scale specimens is now presented.
VALIDATION ON REAL SCALE BEAMS Details of beams The main results described before had to be verified in beams whose scale is representative of real infrastructures. Then, new tests have been carried out onto real-scale beams (Figure 13). Those beams are the reference beams which were considered for designing the physical model presented before. They have a cross section of 250 x 150 mm, a total length of 2300 mm, and an effective span of 2000 mm. The longitudinal and shear steel reinforcements are the same for all these specimens: 2 414 rebars and 2 40-mm-spaced stirrup. The cover concrete is 25 mm thick. The mix proportions of concrete are similar as the one used for the small-scale beams. The granulometry and the aggregate size are now representative of the concrete which is used in real civil engineering applications. The maximum size of the aggregate is now 15 mm. About twenty 160 mm x 320 mm concrete cylinders were cast and tested to determine the mechanical properties of the hardened concrete. The average compressive strength is 39 MPa and the flexural tensile strength 4.2 MPa. Concrete has an average elastic modulus of 3 1 GPa in compression. It is slightly lower than the modulus of the micro-concrete utilized in small-scale beams [ 191. However, moment-curvature diagrams lead to a good validation of the similitude theory at the structural scale [28].
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Figure 13: Details of the real-scale beams. Five real-scale RC beams have been tested in four-point-bending. The procedure is similar to the one achieved onto small-scale specimens. Each beam is loaded up to 60% of the load corresponding to the rebars yielding before bonding the composite sheet. Afterwards, the beams are unloaded. A second bending test is carried out directly up to failure on one of the beams. This beam is used as the reference unstrengthened beam. The four other beams are repaired with a composite laminate bonded onto the bottom surface. The bonded CFRP laminate is made of the same material as for small-scale beams. The thickness of the bonding joint is 0.4 mm and the thickness of the composite is 2.4 mm. After repair, the repaired beams are loaded in flexure up to the steel rebar yielding load.
Beams are laterally instrumented with bi-directional grids over the constant moment span. Two types of grids are used: 0
0
the first type of grids are such as the grid period is p = I mm. With those grids, the resolution of the measurements is 5 pm and the spatial resolution is 2 mm. They have been used to investigate the behaviour over the whole depth of the beams. The field of measurements has been a rectangular surface of 300 x 250 mm. Results have proved that the plane cross section still exist between each consecutive crack in a real scale beam repaired with a composite sheet [ 171. the second type of grids are such as the grid period is p = 57 1 pm. They are the same as the ones used for small-scale beams. They have been used to investigate sharply the mechan-
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Stbphane AVRIL, Alain VAUTNN, Patrice HAMELIN, rind Yves SURREL
ical behaviour in the vicinity of cracks which were preexisting in the unrepaired beam. The field of measurements has been a rectangular surface of 140 x 140 mm (Figure 13). Only the results obtained the the second type of grids are analysed in the following of the paper, because they relate to crack bridging. The numeric BASLER A1 13 1200 x 1000 pixels CCD sensor and Frangyne2000 are still used for grabbing images and computing displacement fields.
1630
122.3
857 48.6 11.4
25.7 623
.100,5
Figure 14: Example of Crz(x,y) displacement field obtained on a repaired real-scale beam.
I
Figure 15: Detection of cracks in a real-scale beam before and after repair. Comparison of the results with the physical model An example of U,(x, y) displacement field obtained during these tests have been plotted in Figure 14. The fields are similar to the ones obtained on the small-scale beams. They still lead to the detection of new cracks after repair (Figure 15. Most of them are oblique shear cracks : they do not propagate up to the neutral axis but they are deHected towards the neighbouring pre-existing crack at the level of the internal re-bars. Differently to the small-scale beams, new vertical cracks propagating towards the neutral axis do not occur. This difference can be related to the fact that the adherence of steel rebars was different in small-scale beams: high adherence rebars were used in real-scale beams and low adherence rebars were used in small-scale beams. Nevertheless, the creation of new tributary ones is a phenomenon specific to repaired beams. None are detected when the reference unrepaired beam is loaded up to failure. Finally, the tests achieved on real-scale beams validate what was observed on small-scale specimens for crack width reduction after repair:
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crack widths are reduced after repair when they are compared for the same given load. This reduction results from the stiffening effect due to the composite sheet. 0
the reduction of crack widths is more significant at the bottom of the beam. Slipping of the composite over concrete induces shear stresses in the bonding joint. The shear stresses are at the origin of tensile strains in the cover concrete: this phenomenon is called tension stiffening [ 13, 161. Tensile straining in the tensile part of the beam induces the occurrence of new cracks and then a more significant crack width reduction.
Figure 16: Comparison of experimental and numerical crack widths.
Comparison with the numerical model The numerical model with the parameters of Table 1 has been applied for simulating the behaviour of real scale beams. The qualitative comparison of numerical and experimental results over the lateral surface of a given RVE is successful. The crack widths predicted by the model have been compared with the experimental ones at the bottom surface of unrepaired and repaired beams (Figure 16). Both experimental and numerical results are in good agreement. The following effects are clearly evidenced: 0
the stiffening effect of the repair (the slope of the curve after repair is higher),
0
steel rebars slipping as a residual curvature exist after unloading due to this effect.
However, the correlation between experimental and numerical curves would be improved if crack occurrence and growth were modelled. Nevertheless, the agreement between experimental and numerical results proves that the elasto-plastic model for composite-concrete bonding constitutive law is relevant. It takes into account both sliding and new cracks occurrence.
CONCLUSION A study about the mechanical behaviour of RC beams repaired with composite sheets under service loads has been described, focussing mainly on the problem of crack width prediction.
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Stkphane A VIUL, AIain VAUTRIN, Patrice HAMELIN. and Yves SURREL
The first contribution of this study has shown the efficiency of a full-field optical method, the grid method, for characterizing the mechanical behaviour of BMC-based structures. All crack widths, depths and average spacing have been measured with a suitable accuracy. Secondly, the efficiency of external bonded CFRP in strengthening degraded concrete structures has been clearly shown. The essential effect under service loads is the reduction of crack widths. This reduction can be significant. The effect of bonding stresses on the crack width reduction has been characterized both experimentally and numerically. The results are original and should be introduced in design codes such as Eurocode 2 for updating the crack width predictive models. For the moment, a formulae has been suggested by Ferrier et al. [ 171 in order to take into account the stiffening effect of the composite sheet. This new relation is advised while the validation of the FEM model elaborated in this study is going on. The actual FEM model is quite novel for this type of applications. It is based upon a multi-scale approach thanks to the definition of a relevant Representative Volume Element. It was shown that the numerical results obtained with this model are in good agreement with experimental data obtained with the grid method. Parameters of the model were only adjusted by trial and error and the study is still on-going to identify accurately unknown parameters from experimental displacement fields. Nevertheless, the effects governing the mechanical behaviour of a cracked beam repaired with composites are now well characterized. Once quantified, it is envisaged to integrate them in design rules for improving the efficiency of repairs with composites. Perspectives are quite attractive. For example, the multi-scale approach would permit to consider damaged zones in the concrete beam, which is not possible in classical models and which tends however to a more representative modelling. The multi-scale approach employed here has only been verified for pure bending. An extension to elements subjected to combined flexure and shear is envisaged.
ACKNOWLEDGEMENTS The authors are grateful to the Region RH6NE-ALPES for its financial support to our research work concerning the project: “rehabilitation of civil engineering structures with composite materials : modelling of repaired cracked beams”.
REFERENCES 1. Hamelin, P., AFGC recommendations concerning strengthening and repairing of concrete structures with composite materials. AFGC/RILEM Seminar on Advances in Materials and Structures, Bagneux, France, 2002 2. Triantafillou, T.C., Plevris, N., Strengthening of RC beams with epoxy-bonded fibercomposite materials. Materials and Structures. 25, 1992, pp 201-21 I 3. EIMihilmy, M.T., Tedesco, J.W., Analysis of reinforced concrete beams strengthened with FRP laminates. I. of Struct. Engng., 126(6), 2000, pp 684-691 4. Hag-ElsaH, 0.. Alampalli, S . , Kunin, J., Application of FRP laminates for strengthening a reinforced-concrete T-beam bridge structure. Composite Structures, 52,2001, pp 4 5 3 4 6 6
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5. Eurocode 2 Editorial Group, Design of concrete structures. Technical report, Eurocode Editorial Group, 1991. pp 4-77 6. Swamy, R.N., Mukhopadhyaya, P.. Debonding of carbon-fiber-reinforced polymer plate from concrete beams. Proc. Inst. Civ. Engrs., Structs. and Bldgs, 134, 1999, pp 301-317 7. fib (FkdCration International Du Btton), Externally bonded FRP reinforcement for RC structures. Technical Report 14, fib, 2001 8. Kwak, H.-G., Song, J.-Y, Cracking analysis of RC members using polynomial strain distribuion function. Engineering Structures. 21, 2002,455-468 9. Bentur, A., Mindess, S., Fiber-reinforced cementitious composites. Elsevier Applied Science, 1990 10. CEB-FIP, Comite euro-national du beton, CEB design inaririnl on crucking a i d deforinations, &ole Polytechnique Ftdtrale de Lausanne, Switzerland, 1985 1 I . Avril. S., Vautrin. A., Hamelin, P., Surrel, Y., Local and global analysis of cracked reinforced concrete beams repaired with CFRP laminates. proceedings of ECCMIO, Brugge, Belgium, 2002 12. Avril, S., Hamelin, P., Vautrin, A., lMechanical behavior of cracked beams strengthened with composites: application of a full-field optical method. Materials and Structures, in press 13. Swamy, R.N., Jones, R., Bloxham, J.W., Structural behavior of reinforced concrete beams strengthened by epoxy-bonded steel plates. Structural Engineer, 66(5), 1998, pp 85-94 14. Swamy, R.N., Jones, R., Charif, A,, The effect of external plate reinforcement on the strengthening of structurally damaged rc beams. Structural Engineer, 67(3), 1989, pp 4556 15. Garden, H.N., Hollaway, L.C.. A preliminary evaluation of carbon fiber reinforced polymer plates for strengthening reinforced concrete members. Proc. Inst. Civ. Engrs., Structs. and Bldgs., 123(2), 1997. pp 127-142 16. Aiello, M.A., Ombres, L., Analysis of the deformability of concrete beams strengthened with FRP sheets. CICE 200 I , International Conference on Composites in Construction, Ed. J.G. Teng, Elsevier, Hong-Kong, 1, 200 I,pp 449-456 17. Ferrier, E.,Avril, S., Hamelin, P., Vautrin, A., Mechanical behavior of RC beams externally reinForced with CFRP sheets. Materials arid Structures, in press 18. Tuset, J., Physical modelling of Reinforced-Concrete. PhD thesis, INSA, Lyon, France, 1973 19. Ovigne, P.A., Dynamic behavior of cracked RC beams strengthened with composite sheets. PhD thesis, University Claude Bernard of Lyon, France. 2001 20. Avril. S., Ferrier, E., Hamelin, P., Surrel, Y.. Vautrin, A., Flexural repair of reinforced concretc beams by composite materials : Op1ical method for evaluation. CICE 2001. International Conference on Composites in Construction, Ed. J.G. Teng, Elsevier, Hong-Kong, I , 2001, pp 112-120 21. Surrel, Y., Moirt and grid methods in optics : a signal-processing approach. Proceedings of SPIE, 2342, 1994, pp 213-220 22. Surrel, Y., Fringe analysis. in: Rastogi, P.K. (ed), Photomechanics, Topics Appl. Phys., 77, 2000, pp 55-102 23. Avril, S., Surrel, Y., Vautrin, A. Grid method: Application to the characterization of cracks. Experimental Mechanics, in press 24. Clement, J.L., Steel-Concrete interface and mechanical behavior of RC structures : characterization and modeling. PhD thesis, University Pierre et Marie Curie of Paris. France, 1987 25. Chajes, M.J., Finch, W.W., Januszka, T.F., Thomson, T.A., Bond and force transfer of composite material plates bonded to concrete. ACI Structural Journal, 93(2), 1996. pp 208-217
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26. Ferrier, E., Fatigue and creep behavior of the composite-concrete interface. Application to the design of RC structures strengthened with externally bonded FRP sheets. PhD thesis, University Claude Bernard of Lyon, France, 1999 27. ANSYS, User manual, version 5.7,2001 28. Avril. S., Application of full-field optical methods to the mechanical characterization of concrete beams repaired with composites. PhD thesis, University Jean Monnet of Saint-Etienne, France, 2003
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt. V.C.Li and I. H.Marshall, eds. Warsaw, October 13-15, 2003 ZTLJREK RSI and Woodhead PLihl., Warsaw 2003
PROGRESS IN ULTRASONIC TESTING OF CONCRETE Sandor Popovics Dept. of Civil, Architectural and Environmental Engineering, Drexel University Philadelphia, PA 19104 USA e-mail: [email protected]
ABSTRACT This paper represents the subjective view of the writer on three topics: - ultrasonic determination of the water-cement ratio in a fresh concrete, - nondestructive estimation of concrete strength in structures, and - split spectrum processing (SSP) to use high-frequency ultrasound for defect detection and characterization, thickness measurements, and location and characterization of steel as well as nonmetallic reinforcement embedded in concrete. In each case, the problem is described, the present state of the art is given, technical and economical importance of these topics is presented along with recent progress in these areas.
Keywords Defect detection, fresh concrete, hardened concrete, nondestructive testing, signal processing, strength, ultrasound, water-cement ratio. INTRODUCTION This paper represents a subjective view of certain aspects of ultrasonic testing of concrete. It is not a general state-of-the art report but rather is restricted to three features in which this writer is interested at this time because he feels that they are important. Therefore he hopes that there will be more progress in these directions in the future. Pertinent Properties of Concrete Concrete is a mixture of four materials: portland cement, mineral aggregate(s), water, and air, that is porous cement paste and aggregate. One can model concrete as a four-phase composite material but this model is still a simplification. This complex structure results in complex properties. Hardened concrete: (a) is brittle in some respects and ductile in others; (b) is elastic in some respects and inelastic in others, and the elasticity is not linear; (c) has some of the properties of a liquid (flow, for instance), and some of the properties of a solid (shear strength, for instance); (d) shrinks to a significant extent during drying; (e) is full of pores and small cracks that may be filled with liquid or air or both; (f) has properties (strength, for instance) that change with time; (g) has properties that can be affected greatly by environmental conditions. This complexity makes the behavior of ultrasonic waves in concrete highly irregular which, in turn, hinders the nondestructive testing. Some of the obstacles are: (a) the attenuation of ultrasonic waves in concrete is higher than in most other solids [ I ] . Thus, it is difficult, in many cases even impossible, to produce satisfactory wave penetration; (b) the signal-to-noise ratio of the received signals frequently is so low that the noise masks the meaninghi signals. In most
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cases the signal-to-noise ratio cannot be enhanced adequately by time averaging because the major portion of the noise is coherent; (c) the present methods for ultrasonic testing of concrete require direct contact between the concrete surface and the transducers. Since the contact is not perfect in the real life, the air entrapped in between causes variable errors in the measurements. The problems with testing concrete with ultrasound are even more serious when there is no access to two opposing sides of the concrete for testing.
The Infrastructure Problem If further reseaech in nondestructive testing of concrete will be successful, this will contribute to the solution of the inficistructure problem, the poor condition of highways, mass transit, airports, bridges, buildings, dams, waste disposal units, ports, military structures, etc. The magnitude of the problem is demonstrated in a recent survey of the American Society of Civil Engineers [2] reporting quantitatively the huge extent of deterioration. National security, economy, safety, the every-day life are all based directly on a sound infrastructure, thus upgrading the infrastructure and keeping it in satisfactory condition are essential. Once a specijk conclusion as to the cause and extent of damage in the concrete has been reached, then and only then can a rational selection be made among alternative maintenance and repair strutegies. Thus, dozens of attempts have been made during the past 70 - 80 years to develop reliable test methods. Unfortunately all these traditional attempts have failed, as of today no satisfactory test method exists because of the complexity of the problem. The size of the cost related to the infrastructure problem reflects the significance. According to the ASCE Report [ 2 ] ,the cost of upgrading the infrastructure in the US. to the safe level is $1.3 trillion. So, if the proposed method is successful and reduces the cost of upgrading only by a modest I%, this means 213 billion in savings. INSTANTANEOUS DETERMINATION OF THE WATER-CEMENT RATIO IN FRESH CONCRETE Background If the water-cement ratio in a fresh concrete is high, the concrete cannot be anything else but poor in the structure with serious technical and economical consequences [3]. Therefore the deficiency must be detected and corrected before the concrete is placed in the form. Yet, none of the available test methods for the direct instantaneous determination of the water-cement ratio is satisfactory. For instance, a higher than specified slump is assumed to indicate excessive water content but the obtained information cannot provide information about the strength potential. Other rudimental mechanical tests cannot provide either the results soon enough (accompanying strength tests, maturity), or are inaccurate (determination of the cement content and water content separately), or unsafe (nuclear tests). They are used only because there is nothing better available despite 50 years of research effort [4]. Another weakness is that these tests do not provide direct information about the quality of the concrete affer placement. For instance, the degree of consolidation cannot be determined. Therefore, further research in this direction is clearly needed. It is believed that advanced ultrasonic methods provide the best promise for the success of such new tests. That is, there is no acceptable practical method at present, all attempts have failed due to the complexity of the problem. The savings from the elimination of these consequences are highly significant since the construction industry is a large industry in the USA. Concrete is considered "fresh" while it is still workable, that is before setting. In case of portland cement concrete, this period lasts three four hours under normal circumstances.
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A decisive difficulty with testing ftesh concrete ultrasonically is the high attenuation of the paste portion. With special arrangement used earlier, the penetration could be improved but this still was not good enough for the satisfactory estimation of the w/c [ 5 ] .
The Problem Attempts to test concrete with ultrasound while it is still in the plastic state, that is, before setting, go back to almost 50 years [ 3 ] . It does mean, however, that all such efforts have been largely unsuccessful. Nobody could receive any signal passing through the fresh concrete earlier than about three hours after mixing [6]. The main reasons for this failure are: (a) high ultrasonic wave attenuation which restricts the penetration of conventional pulses; (b) intensive noise levels that inask the meaningful ultrasonic signals; and (c) concrete testing has relied solely on the longitudinal pulse velocity (ASTM C 597) which is not sensitive enough for testing concrete. No traditional method has succeeded in overcoming these obstacles. Concrete researchers have not taken advantage of new developments in ultrasonics [7,8]. So, innovative tests are needed for testing fresh concrete ultrasonically. Innovations The objectives are innovative because a thorough search of the literature revealed no previous attempts for testing the coniposifion of fresh concrete ultrasonically. Specifically, the innovative objectives are: (a) to develop test method(s) that can force ultrasonic pulses through fresh concrete; (b) to produce a numerical method that calculates the water-cement ratio and/or air content from the features of the received ultrasonic waves; (c) to make these methods suitable for testing the concrete not only before placement, but also after placement and compaction in the field; (d) to adjust the methods so that the measurements can be performed not only in through-transmission mode (which requires access to two different surfaces on the specimen) but also in pitch-catch or pulse-echo modes where only one surface is needed; (e) to make these tests fast and relatively simple to perform with portable equipment and cost-effective procedure; and, (t) to create the potential for these for automation. The development of a reliable test method for the instantaneous determination of the water-cement ratio will not only lead to the correct acceptance/rejection decisions within a few minutes after the completion of mixing, or before placement, but, also, after placement, compaction and finishing. The simplicity and rapidity of ultrasonic tests are also pertinent here because the test must be finished before the concrete starts hardening. A case in point is a lock project on the Ohio River where 3,000 cu yd of substandard concrete had to be removed despite the careful proportioning and batching [4]. The obtained results may pave the way for fhture research on ultrasonic testing of fresh concrete. A topic could be the nondestructive determination of pavement thickness immediately after compaction, that is, when it is still relatively easy to correct any deficiency. The automation of such measurements is also a possibility. NONDESTRUCTIVE DETERMINATION OF CONCRETE STRENGTH IN STRUCTURES The Present Concrete is unique in that it is the only engineering material in which strength determination is attempted from ultrasonic measurements. The reason for this unusual attempt is the need created by the acute infrastructure problem. Without reliable evaluation of the concrete strength within the structure, there is no rational rehabilitation. Traditionally, the concrete strength has been determined in a structure by testing concrete cores drilled from the structure
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(ASTM C 42). This, however, is not a desirable procedure because it is cumbersome, slow, expensive, may damage the structure, and can leave an unsightly spot on the concrete surface. Nondestructive test is needed. Despite this need, past research could produce no better solution to the problem of nondestructive strength determination than unreliable empirical formulas. The most popular such formula for the calculation of strengthf from the standard longitudinal pulse velocity V , is the simplistic single-variable exponential formula
where a and b are empirical parameters determined for a given concrete by elementary curve fitting from corresponding experimental f and V I results. Eq. 1 provides the concrete strength with the accuracy of +20% under laboratory conditions, the potential error in the field is even higher [9,10]. This is not good enough! Other similar methods have been equally unreliable. The well known multi-variable formula for the calculation of the dynamic modulus of elasticity from the combination of longitudinal pulse velocity, density and Poisson's ratio is theoretically correct but no successful such formula exists for strength [ 11,121. For instance, it has been shown that the combination of the standard ultrasonic method (ASTM C 597) with the Schmidt hammer test (ASTM C 805), logical as it may seem, has not proved better than Eq. 1 [9]. The same negative conclusion can be drawn from the combination of the longitudinal pulse velocity with pullout test or attenuation [lo]. The impact-echo method (ASTM C 1383) is for thickness measurements and defect detection; it is not applicable for strength determination. Very little, if any, research has been done for testing concrete strength with shear, surface or other guided waves. Thus. it is clear that there is nothing available, as of today, for the reliable nondestructive assessment of concrete strength in structures.
The Difficulties This does not mean necessarily that it is impossible to estimate concrete strength adequately from longitudinal wave measurements so that further research is useless; it does mean that either inappropriate approaches have been used, or potentially good approaches have been misused. An example for the latter is the ultrasonic longitudinal pulse velocity test. It has been popular, nevertheless, there are intrinsic and practical factors that disrupt the determination of concrete strength by longitudinal waves. Some of these are: (a) lack of a theoretically justifiable relationship between strength and wave velocity; (b) the complexity of the internal structure of concrete; (c) differences in the extent how certain factors affect the strength and how the pulse velocity [S]; (d) insensitivity of the longitudinal pulse velocity to small but important changes in the internal structure of concrete [13]. The Goals The desirable strength tests and the related equipment should be: (a) nondestructive; (b) more accurate for the in-situ assessment of concrete strength than the present methods; (c) simple and rugged enough to be used in the field by a trained technician; (d) able to monitor the changes in concrete condition; (e) suitable for both young concrete for testing form removal and checking the adequacy of retrofitting, as well as for mature concrete for condition evaluation; and (0 applicable for one-sided testing when only one surface is accessible. The economical objective is to produce a method that is cost effective, that is, both the price of the equipment and the operation cost are reasonable. Another way to show the significance of the project is that if it is successful, the method will improve the following applications: (a) collection of information on current structure conditions; (b) monitoring the condition of the structure for prioritizing alternative preservation,
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maintenance, reconstruction, and rehabilitation strategies, timely replacement and safe operation of civilian and military infrastructure; (c) forecasting fiiture conditions; (d) warning of functional or physical failure; and (e) checking the adequacy of retrofitting. Another significant application is the nondestructive strength estimation of concrete during the construction phase. Examples are the determination of: (a) the safe time of form removal; (b) the end of wet curing procedure; (c) the time of release in post-tensioning; (d) the progress in slip form construction. Up to this point, the most widely used pertinent test has been the compressive test of accompanying concrete cylinders. However, the cylinder test does not provide adequate information about the condition of the concrete in the structure, even when the maturity method is used. This uncertainty slows down unnecessarily the construction process and makes it more expensive. A reliable nondestructive strength test would eliminate this delay, and would save millions of dollars yearly to the construction industry.
USE OF HIGH-FREQUENCY ULTRASOUND WITH SPLIT SPECTRUM PROCESSING History It has been common knowledge that the ultrasonic testing of concrete is lagging way behind the application of ultrasound in other engineering and medical areas. The reason for this is also known, concrete technologists have been using low-frequency ultrasound, meaning typically ultrasound of 100 kHz or lower frequency. The methods that have been successful in the inspection of materials other than concrete use ultrasonic waves with frequency contents ranging between 1 through 15 MHz because the higher the frequency the better the resolution and beam directivity; thus they are superior to detect and characterize small flaws (defects of mm size). After all, the wave length at 100 kHz in concrete is about 40 mm. Unfortunately, the complex, heterogeneous nature of concrete has made the efforts to apply high-frequency ultrasound unsuccessful because at high frequencies wave attenuation is very intensive due to absorption and scattering losses. Furthermore, even when sufficient penetration is achieved, the backscattered noise level from the microstructure in the received signal is so high that the signal components of the target of interest are masked., Since Drexel researchers have contributed significantly to the development of highfrequency ultrasound in bio-engineering and metal testing, (Joseph. L Rose, John M. Reid, Vernon L. Newhouse, Nihat M. Bilgutay, etc. are internationally known), it was natural that they were asked to use their experience for extending the high-frequency method for testing concrete. The first attempt, around 1990, was to overcome the intensive attenuation by using high-energy ultrasound techniques, such as tone burst system, lithotripter, and laser generation, to increase the penetration of the waves. Although the obtained results were better than any such attempt by others, the project was only partially successful. Interesting side results were obtained but the signal-to-noise ratio in the captured ultrasonic signals was too low, the noise masked the echoes from the targets of interest (defects, boundaries, etc.) [ 141. Since higher intensiveness was not a solution of the high-frequency problem, noise reduction was tried subsequently with signal processing. The Split Spectrum Processing (SSP) is such a technique. This was developed about twenty years ago for ultrasonic testing by Bilgutay [I51 and refined by his associates, who are past or present members of Drexel University. Therefore, and for the sake of brevity, the combination of high-frequency ultrasound with SSP for concrete testing is called the Drexel method. SSP has been successfully used to distinguish meaningful target signals from the background microstructure (scatterer) noise in nondestructive testing of stainless steel and other metals. So it seems to have the potential to improve ultrasonic testing of concrete as well. However, its application to concrete is not automatic. An SSP protocol, proved successful with
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Sandor POPOVICS
testing steel, is not necessarily applicable to concrete without modification because (a) the internal structure of concrete varies within much wider limits than that of metals or polymers. Concrete can contain many more scatterer types (aggregate particles. voids, cracks, filled with air andor water) present in varying quantities; and (b) the scatterers in concrete vary in size to a much greater extent than in metals or polymers.
Signal Processing The most frequently used signal processing method for noise reduction is rime averaging but it can reduce only the incoherent content of the signal noise. This is not enough for testing concrete because the remaining noise, the coherent (or scattering) noise caused by back-scatter of the propagating ultrasound, is still overwhelming. The reduction of the scattering noise content requires more advanced technique, for instance one that utilizes the frequency dependence of the coherent noise. A scatterer in the concrete retlects different echoes from different frequencies in the form of coherent noise. That is, the scattering noise content is highly sensitive to shifts in the operating frequency whereas the echoes froin defects and boundaries are not. For instance, when an ultrasonic measurement is repeated in a location with several narrowband transducers of different frequencies, the combination of these received narrow-band signals tends to suppress the frequency-dependent noise whereas the signals reflected by targets of interest remain unchanged. The net result is an increase in the signal-to-noise ratio for echoes from targets. Reportedly arrays of 7, I6 and 19 transducers have been used successfully for such tests by Cambridge Ultrasonics [ 161. Note that one-sided tests are preferred in practice because of their wider applicability and because they are suitable for localization of the targets. The Cambridge method and the pulseecho test with SSP are one-sided tests. Here a transducer, capable of operating both as a pulser and a receiver launches a short ultrasound beam into the concrete and subsequently receives the echoes reflected by the target(s) of interest. This is called A-scan which can provide onedimensional spatial information about the targets. Split Spectrum Processing Protocol The hdamental principle of SSP is the same as that of the Cambridge method above, namely, reduction of the coherent noise by combining narrow-band signals of different frequencies obtained from the same scatterer(s). The difference is in the splitting technique. SSP achieves the same result with one, broad band transducer as the Cambridge method with many transducers with associated experimental complexities because in the SSP the splitting is done by the computer from a single ultrasonic measurement. An ultrasonic signal with broad frequency content is captured after passing through concrete and stored in an appropriate data acquisition unit. It is then time-averaged and its spectrum is obtained in the frequency domain by the Fourier transform. Subsequently, the spectrum is led through a Gaussian filter bank that splits the original signal into n different frequency bands (windows). These spectral decomposition components together comprise the frequency content of the original signal. If the number of filters is high enough, the splitting decorrelates the individual components after which the bands of different frequencies are reassembled non-linearly by the computer to form again a single output signal. The reassembly can cancel out the scatterer noise by the use of one of several noise suppression algorithm. The result, that is, the processed signal, is obtained by the return to the time domain by inverse Fourier transform. The main factors affecting SSP performance are the spectral region selected for processing; the frequency increment between adjacent bands; and the width of each band. The present form of reassembly is a trial-and-error process. The starting parameters for the reassembly are chosen arbitrarily, thus the first attempt at noise reduction is usually insufficient. However, it can be improved gradually by changing the parameters of the assembly (bandpass
427
Progress in ultrasonic testing of concrete
window shape, bandwidth, spacing, and operating spectral range). Fortunately, the entire SSP process is performed digitally by the computer; so one captured signal may be repeatedly processed without additional measurement, until an appropriate scheme for a particular problem is obtained. On the other hand, it is unfortunate that the present form of this iteration process is clumsy and time consuming. Thus, the optimization of the iteration process will be the focus of future work on SSP. The reassembly may follow a variety of algorithms, including minimization and polririty threshholding. The split-spectrum processing technique was also generalized for twodimensional applications to improve imaging of materials [ 171. Previous Work on SSP with Concrete Numerous examples can be found in the literature both for successful layer thickness determination and for defect detection and characterization with SSP in various inhomogeneous materials [15, 17, 19-23] but non with concrete. The first application of SSP to concrete was probably performed by Drexel researchers in 1990-9 1. Some of the results were reported in a research proposal submitted to NSF in March 1991 [24]. The experimental work, although preliminary in nature, support the view that Split Spectrum Processing has the potential to improve nondestructive testing of concrete by making possible the use of ultrasound of MHz frequency [IS]. Despite the presence of significant scatterer noise in the captured signal, the method reduces the noise level, thereby it helps identify the ultrasonic signals reflected from the targets of interest. This, in turn, helps locate the target(s) within the concrete and characterize them in one-dimensional data. Properties of the Drexel Method The properties of the Drexel method can be summarized, as follows: (a) it is nondestructive; (b) the measurement is simple because only a single transducer and standard ultrasonic pulser are needed; (c) it is one-sided test so the measurement can be performed when there is access only to one side of the concrete element; (d) it can use ultrasound in the MHz range for testing concrete. This enables the detection of smaller defects (in the mm range) and more precise interpretation of the results; (e) it uses ultrasonic waves that are exclusively longitudinal. These are better than the waves created by mechanical impact because impact creates longitudinal, surface, and shear waves simultaneously that travel at different speeds, and interact differently with boundaries and defects making the interpretation of the received waves complicated and uncertain; (0 it can control the content of the ultrasound input which makes the interpretation of the captured signals more precise whereas the input by mechanical impact is far less controllable; (9) it is local, that is, it provides information about the existing condition in a specific spot of the concrete rather than about the average condition between two spots (global); and (h) it is simple and cost effective because the field equipment is planned to consist ofoff-theshelf components, and the field operation to be performed by a trained technician. There are test methods that have some of these features but there is none that can do all. Thus, the Drexel method seems better than any other available method for condition evaluation of concrete structures. CONCLUSIONS,,,,
The topics discussed in this paper are: (a) instantaneous determination of the watercement ratio in fresh concrete; (b) nondestructive measurement of concretre strength in structures; and (c) use of high-frequency ultrasound in testing concrete. Although there has been
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progress in these areas, hrther research is still desirable because if it is successful, they contribute to the solution of the infrastructure problem.
REFERENCES 1. Carleton, H. R. and Muratore J. F., "Ultrasonic Evaluation of Concrete," Proceedings of the 1986 IEEE Ultrasonic Symposium, pp. 1017-1020. 2. ASCE, "Report Card for America's Infrastructure," American Society of Civil Engineers, March 200 1. 3. Whitehurst, E.A., "Use of the Soniscope for Measuring Setting Time of Concrete," Proceedings, ASTM, Vol. 5 1, 195I , pp. I 166-1 176. 4. Mather, B., "How Soon is soon Enough?", ACI Journal, V. 73, No.3, 1976, pp. 147-150. 5. Popovics, S., Silva-Rodrigez, R., Popovics, J.S., "Behavior of Ultrasonic Pulses in Fresh Concrete", New Experimental Techniques for Evaluating Concrete Material and Structure Performance, ACI Publication SP 143, 1994, pp.207-225. 6. Pessiki, S.P., and Carino, N.J., "Setting Time and Strength of Concrete Using the Impact-Echo Method", ACI Materials Journal, Vol. 85, No. 5, Sept. - Oct. 1988, pp. 389-399. 7. Popovics, S., Fundamentals of Portland Cement Concrete: A Quantitative Approach - Fresh Concrete, John Wiley & Sons, New York, etc., 1982,477 p. 8. Popovics, S., "Present State of the Determination of Concrete Strength by Pulse Velocity in America," I1 Cemento, Anno 830, No. 3, July - September 1986, pp. 117-128. 9. Malhotra, V. M. and Carette, G. G., "In-Situ Testing - A Review," Progress in Concrete Technology, V. M. Malhotra, editor. Energy, Mines and Resources, Canada, MOP/MEL 80-89 (TR), 1980, pp. 749-796. 10. Popovics, S., Strength and Related Properties of Concrete - A Quantitative Approach, John Wiley and Sons, Inc., New York, etc., 1998, 535 p. 11. Pohl, E., Nondestructive Test and Measurement Methods for Concrete (in german), 2. ed., VEB Verlag fur Bauwesen, Berlin, 1969. 200 p. 12. Galan, A., Combined Ultrasound Methods of Concrete Testing, Elsevier, Amsterdam, etc., 1990,344 p. 13. Popovics, S., "Effect of Porosity on the Strength of Concrete," Journal of Materials, JMLSA, Vol. 4, No. 2, June 1969, pp. 356-371. 14. Popovics, S., Newhouse, V. L., Rose, J. L., and Popovics, J. S., Final Report for the Project "Condition Evaluation of Concrete Structures Using High-Frequency Ultrasound," Submitted to the National Science Foundation, Project #9114238, June 1995. 15. Bilgutay, N.M., "Split Spectrum Processing for Flaw-to-Grain Echo Enhancement in Ultrasonic Detection," Ph. D. Thesis, Purdue University, 198I . 16. Cambridge Ultrasonics, "High performance transducers for concrete," Innovation News, Issue 3, September 1997. 17. Bilgutay, N.M., and Sweeney, J., "The Effect of Grain Size on Flaw Visibility Enhancement Using Split-Spectrum Processing", Materials Evaluation, Volume 42, May 1984, pp.808-8 14. 18. Karaoguz, M., Bilgutay, N. M., Akgul, T., Popovics, S., "Defect Detection in Concrete Using Split Spectrum Processing", IEEE International Ultrasonic Symposium, Sunday, Miyagi, Japan, 1998. 19. Bilgutay, N.M., Bankrupt, U.,Murphy, R., Sweeney, J., "Analysis of a non-linear frequency diverse clutter suppression algorithm", Ultrasonic, Vol. 28, March 1990, pp. 90-96. 20. Rose, J.L., Corpora, P., and Newhouse, V.L., "Utility of Split-Spectrum Processing in Ultrasonic Non-Destructive Evaluation", Material Evaluation, Volume 46, January 1988, pp. 114-122. 21. Bilgutay, N.M., Murphy, R., Bankrupt, U., and Sweeney, J., "Spatial processing for coherent
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noise reduction in ultrasonic imaging", Journal of the Acoustical Society of America Volume 87, 1990. pp. 728-736. 22. Bilgutay, N.M., Bankrupt, U., and Sweeney, J., "Nonlinear spectral processing techniques for ultrasonic imaging", Review of Progress in Quantitative NDE, Vol. 7A, Plenum Press, New York, 1988, pp.757-767. 23. Murphy, R., Bilgutay, N.M. and Lo, X., "Temporal and Spatial Spectral Features of B-Scan Images", Proc. 1991 IEEE Ultrasonic Symposium, Orlando, Dec. 199 I , pp.799-802. 24. Popovics, S., Bilgutay, N.M., Newhouse, V., and Rose, J., "Condition Evaluation of Concrete Structures Using High-Frequency Ultrasound", research proposal submitted to NSF on March 1991.
Proc. Int. Svtnp. Brittle iMatrix Composites 7 ” A.M. Brandt. V.C. Li and 1. H. Marshall, rds. Warsaw, October 13- 15. 2003 ZTUREK RSI and Woodliead Publ., Warsnw 2003 I,
INTERNAL STRUCTURE OF CONCRETE WITH ARTIFICIAL AGGREGATE Elsadeg A. ABDALLA, Wojciech RADOMSKI Institute of Roads and Bridges Warsaw University of Technology Al. Arniii Ludowej 16,OO-637 Warszawa, Poland e-mail: [email protected]; [email protected]
ABSTRACT The paper presents a laboratory study of lightweight concrete with the standard compressive strength at least 50 MPa. Aggregate ”Pollytag” with density of I .28 g/cm3 and grains up to 12 mm produced from fly-ash from electric power station burning bituminous coal with addition of about 1 YOof bentonite has been used for the tested concrete. Its mechanical and physical properties such as compressive and tensile strengths, modulus of elasticity, thawing-freezing resistance, water absorbability as well as shrinkage and creep, are determined according to the relevant Polish standards. However, the main part of the paper is devoted to the structural investigation of the lightweight aggregate itself and concrete made with the use this aggregate. The relevant investigations have been performed by means of the scanning electron microscope LEO 1430. Keywords ktificial aggregate, concrete, internal structure, microscope tests
INTRODUCTION In recent years, a growth of interests concerning lightweight concretes can be observed, in particular for production of lightweight high strength concrete that can be used for bridge construction and other special applications such as off-shore structures [ 1-31. For the production of such high quality concretes there is a need to better understand the mechanisms by which the high strength of the material is generated. This is necessary for making the proper choice of aggregates. Studies of the internal structure of such concretes suggest that the interaction of the paste matrix and the aggregate can be quite complex [4-71 and is different from that of natural aggregate concretes Since 1980, several investigations [S-1 I ] on high-performance lightweight concrete have been reported and there are, of course, world environmental, economic and technical impetuses to encourage the structural use of this material.
432
EIsadeg A. ABDALLA and Wojciech RADOMSKI
CONCRETE MATEKAL Mix proportion of lightweight concrete Mix proportions are listed in Table 1. Table 1.Mix proportion of lightweight concrete per m3of the mixture
I No 1,
'I 21
Concretecomponents
I
Unit
I
Amount of components
Used in amounts relative to the mass o f cement - the amount of 1YOwas used Volumetric density of the fresh mass of concrete
Properties of lightweight concrete Average properties of hardened lightweight concrete are given in Table 2.The properties have been determined by the tests performed according to the relevant Polish standards.
(fJMPa 53.7
1 (f,)' MPa 1 (fr)' MPa I (EtJ4MPa I (Abs)' % I ( P ) ~kg/m3 I (AG)' % I 3.48 3.58 I 23500 I 8.57 I 1945 I 1.28
433
Internal struclure of concrete with artificial aggregate Summary of test results
The average properties of hardened lightweight concrete are summarized in Table 2. The 28 day compressive strength and density varied from 52.20 to 54.70 MPa and from1901 to 1991 kg/m3, respectively. Tensile strength (splitting) and flexure tensile strength varied from 3.25 to 3.90 MPa and from 3.50 to 3.70 MPa respectively. The modules of elasticity varied from 22800 to 24000 MPa, water absorbability and mass loss of thawing-freezing resistance varied From 8.05 to 9.0% and 0.75 to 1.91%, respectively. Maximum shrinkage and creep, strains are 0,503 and 0.526 %O respectively
- - - Sample1 .-..-Sample2 Sample3
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MICROSCOPE TESTS Scope
The tests have been performed on sintered fly-ash “Pollytag” aggregate with four chosen fractions of grains and concrete made with the use of this aggregate. The structural features of above both materials have been investigated to try to determine the following problems: - degree of compaction and vitrification of dust particles during the sintering process, - differentiation of the types of characteristic structures of aggregate grains, - crystallization forms of the hydration products from the cement paste,
434
Elscideg A. ABDALLA arid Wojciech RADOMSKI
- character of the interface zone between the aggregate grains and the concrete paste,
- effect of time and storage conditions on the structure of the cement paste in the concrete tested,
- relationship between microscope observation and the laboratory strength and other tests. The tests were carried out with the use of an electronic scanning microscope of LEO company, type 1430 with a digital image notation. A detector of secondary electrons was used during observations. An X-ray EDX detector was also selectively used to obtain some informatioii about the chemical composition of the materials tested.
Materials and samples “Pollytag” aggregate with four various fractions and five samples of concrete taken from the previous laboratory tests were used for the structural microscope investigations. The samples for the tests were glued on a microscopic stand and latcr sprinkled with gold powder to obtain a conductive layer. The samples were subjected to microscopic observation to determine their structural properties. The magnitude of observation for the grains of each fraction changed from 64 to 8000. Observation results for aggregate grains Aggregate grains (0.5-2.0 mm) show a structure of low compactness with conserved, in fragments weakly connected globules (granules) of ash (Fig 3,4). A part of the brown and black grains have a pumice structure characteristic of the formed agglomerate (Fig 5 ) . Some of the grains have a distinct vitrified coating on the surface (Fig 6). The degree of vitrification is relatively low and highly developed specific surface is predominant. Aggregate grain (2.0-4.0 mni) shows the colors of a grain have not any reflection on the degree of its vitrification or porosity. All aggregate grains are formed of a highly developed specific surface, presenting a sub-microporous sinter of pumice structure in a large scale (Fig.7). The grains are often built from glaze micro-globules glued together on the pumice surface of the sinter (Fig.8). Aggregate fraction (4.0-8.0 mm) is characterized by the presence of grains of a higher vitrification in relation to the fraction described above. The sub-microporous and small globular phases are present in the surroundings of the black centers (Fig.9), but are glued together on the external surfaces of the sinters. A phase of vitrified material of non-uniformly distributed pores (Fig. lo), The vitrified surfaces contain attached glaze globules, as well as pumice sinters (Fig. 1 l), anyhow no crystallizing calcium oxides or hydroxides (hydrates) are observed with them as it took place in the case of aggregate grain 2.0-4.0 mm. Recrystallized build up plaques of ferrous oxides can be found on the surfaces of red and brownish color that are part of the enveloping section of the particles (Fig. 12). This is a typical component of the fly-ash which presence is fairly common. The degree of vitrifcation is higher on the surface of the grains, which gives structures of higher and seldom distributed pores in many places (Fig. 10 and 13) Aggregate grains (6.0-12.0 mm) are characterized by the presence of highly sintered and vitrified fragments on the external surfaces of most of the tested aggregate grains and small globules or granules and very porous packs visible in the central parts ol‘the grains. Structural differences in the central and border (external) parts can be observed (Fig.14 and 15). Despite of the larger sizes of the grains, the structural features are close to the grains 4-8 mm. Considerable expansions of the surface caused by both the presence of the glued ash globules of glaze and the developed system of pores in the pumice parts of the sinters are observed (Fig. 16).
435
Internal strircttire of concrete with artificial aggregate
Fig.3 A low sintered and porous grain (magnification 54x)
Fig. 4 Low sintered globules ofglazc (magnification 471x)
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Pig. 8 Globular grains o f ash covering the surfacc of the sinter (magnification 572x)
436
Elsadeg A . ABDALLA and Wojciech RADOMSKI
Fig9 Low sintered centers of aggregate grains of a very high porous granules (magnification 600x)
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Fig. I 3 A vitrified fragment of a grain with large and irregularly distribute pores (magnification600x)
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Summary of the structural characteristics of fly-ash aggregates In aggregate grains 0.5-2.0 mm. grains of a granular structure and low degree of sintering were dominated. A similar situation takes place in aggregate grain 2.0-4.0 mm. It seems that both the two grains are formed from fragments of low sintered, easily crumbling off in the process of breaking up large pieces of fly ash material. In the aggregate grain 4.0-8.0 mm and 6.0-12.0 mm the number of vitrified on the aggregate grains clearly increases. These envelopes have porous pumice structure with seldom and larger distributed pores; however
lnteniul structure of coticrete with urtijicial uggregute
437
the centers of grains belonging to the larger fractions are still fine granular and show a lower degree of sinter. Observed structural characteristics of the aggregates are reflected in their physical parameters, which are shown by a very small though systematic increase in the value
sinlering (niagnilic;itiirn JOOx)
I:ig. I6 /\ dcvclopstl structtirc of pores and sititered aegregalr grain (m:ignilicntion I2OOs)
Observations results for lightweight concrete The area of penetration, each time covered about 5 cm2 of the area of the paste and the observations were carried out by gradually increasing the magnifications in order to make analysis both of the structure of the pastes and contact zones of the paste with the fly-ash aggregate. Sample ( I ) , taken from absorbability tests, shows the bond between the cement paste and the aggregate grains is almost ideal (Fig. 17). Silicate phases of the paste distinctly adhere to the ash, forming a relatively tight and thick prismatic cladding around the aggregate grains (Fig.18). Storage in water of the hydration processes that took place as time elapsed distinctly favored the increase of crystal sizes in the silicate phases of the cement paste and enabled its ideal adhesion to the aggregate. The rosette texture of the thick prismatic crystals (Fig. 19) of the formed cement paste components due to the increased hydration process should lead in effect to an increase of compressive strength relative to the samples stored in dry air conditions. The cohesion of the concrete and bondage of fly-ash aggregate are so high that in many places the aggregate grains are almost unidentifiable. The aggregate grains are most often set in the binding material of the paste. At times they are only differentiated from the cement due to the vitrified envelopes. As far as the paste is not thick prismatic, it forms granular micro-pore groups penetrating the interior boundary regions of the fly ash grains. Most of the micro-pores of the paste are closed and their system doesn't show any possibility of communication with the others, which is expressed by the relatively low absorbability. Sample (2), taken from freeze resistance tests, shows that the structure of concrete is very dense and cryptocrystalline (Fig.20) only in a few places it was possible to observe the existence of fiber forms forming rosette textures (Fig.2 1). The forms of crystallizing calcium hydro silicates in this way are probably quite numerous, however in a microscopic image they are rarely seen which can undoubtedly be attributed to the filling of the pore spaces of the crystalline paste framework with microcrystalline and gel phases of C-S-H (I). The structure of concrete is remarkably sealed; the communication between the pores is closed and leads to the attainment of its higher freeze resistance. The bondage of the aggregate grains to the paste is very good. These particles don't only adhere in a reactive way but also make their boundary pores available to the adhering fiber crystals of C-S-H (11) (Fig.22).
439
Internal structure of concrete with artificial aggregate
powdery which could testify about the amount of water needed for the hydration of the paste. In these places the part of micro-pores considerably increases (Fig.25and 26). Despite of the existence of areas of the paste with micro granular structure and porous texture, the compressive strength is high, which is probably the effect of a perfect bondage of the cement paste to the aggregate as well as the long period of curing of concrete which took place before carrying out the tests for strength.
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Fig.23 Micro granular structure of the paste adhering to the aggregate grains (magnification 6760x)
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Fig.25 Cement paste zones of micro-granular shape and increased porosity (magnification 7900x)
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Sample (4), taken from shrinkage tests, shows the short prisms and needle-like forms of the C-S-H (I and 11) crystals penetrating in all directions and laminar groups. Moreover, fine needles (Fig.27) in all directions are visualized between which amorphous filler also belonging to the C-S-H is found. The feature of the directional increase and needle-like splicing in a “basket” structure of grains is seen well (Fig.28). Aggregate covering by the silicates of the paste is in particular well exhibited (Fig.29), and filling of the framework with the calcium fiber silicates through the microcrystalline phases makes the pastes tight. Sample (5), taken from creep tests, shows long needle-like packets of C-S-H (I and 11) crystals changing in a basket form (Fig. 30). Similarly to the sample “4”, the needle-like silicates are very long and the spaces between the framework are filled with crypto crystalline C-S-H. In some places, the forms of a short needle-like texture are also seen. Similarly to the samples described above the bondage of the aggregate grains with the paste is very good what is seen both in the adhesion with glazed perimeters and in the silicate adhesion
440
Elsacleg A. ABDALLA and Wojciech RADOMSKI
laminar way (magnification 3070x)
adhering aggiegate surface (magnification 6850x)
.Li.
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silicates of C-S-H(I) on a glazed aggregate surface (magnification 4950x)
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CONCLUSIONS AND FINAL REMARKS Aggregate grains show different degrees of sintering depending on the type of the tested grain. Finer fractions contain a majority of weakly sintered grains; thicker ones strongly sintered grains contain glazed envelopes. The color of the grains doesn’t express its degree of sinter. A slight increase of bulk density in the case of thicker fractions is a reflection of an increased degree of sinter. The surface of the sintering, as well as un-sintered grains are very expansive what favors the improvement of bonding to the cement paste that strongly penetrates into all its accessible edge pores. This also favors chemical affinity of the ashes in relation to the components of the cement paste to the aggregate. The bondage of the flyash aggregate to the cement paste for all the tested samples is very good which [avors the attainment of high strength. The slight fall in strength relative to the samples of a micro-granular and short prismatic structure may confirm the theory that an increase in the sizes of the crystalline calcium silicates above stipulated sizes causes a double reduction in the strength of the concrete. The structure of concrete tested for freeze resistance is also thick crystalline, rosette and very tight. In effect, this type of structure reflects on a small fall of strength of these concrete samples relative to the samples stored in dry air conditions. The samples taken from absorbability and freeze resistance tests show a clear effect of a second hydration
Internal structiire of concrete with artifciul aggregate
44 1
process on the sealing of the paste and crystallization of the rosette and thick prismatic phases of C-S-H. They are completely different in respect of the thickness and shape than those that are observed in the samples stored under dry air conditions. The structure of the pastes in the samples of concrete stored in dry air conditions is small crystalline and even powdery in some places. A fibrous or prismatic framework of crystalline phases of C-S-H is seen. In spite of this, their strength is considerable showing the important role of filling the framework with amorphous phases, which though weak and porous they improve. The contact between all the components and increase of the concrete strength can be observed. The structure of the paste in the samples of concrete prepared for the shrinkage and creep tests show certain reciprocal similarity. They show a lot of fibrous forms building up in layers or intertwined i n the so-called “basket” structure. Small shrinkage shown by the tested concrete is assumed to be the result of the accumulation of the make-up water in the fly- ash aggregate and its gradual given-up during the curing of concrete to the phases of C-S-H being crystallized. In this way, the shrinkage arising from the drying up is compensated by the increase in volume or the hydrated silicates phases.
ACKNOWLEDGEMENTS The authors are indebted to express their thanks to Mrs. Ewa Starnawska from the State Institute of Geology for her help in the microscope experiments reported above.
REFERENCES 1. M.H. Zhang and O.E. Gjorv, Amer. Concr. Inst. Materials .I., 88(2), 150- I58,I 991. 2. G.C. Hoff, Proc, 2nd. International Symposium on High Strength Concrete, Berkeley, California, 1990,ACI SP- I2 I , 6 19-644, 1990. . 3. A. Short and W. Kinniburgh, Lightweight Concrete, 3rd edition, Applied Science Publishers, London, 1978. 4. M.H. Zhang and O.E. G j ~ r v Cement , and Concrete Research, 20(4) 610-618,1990, 5 . M.H. Zhang and O.E. G j ~ r vCement , and Concrete Research, 20(6), 884-890, 1990. 6. N.K. Khokorin, The durability of lightweight aggregate concrete structural members, Kuibyhev, USSR, 1973. 7. G. Fagerlund, Frost resistance of concrete with porous aggregate, Research Report 2/78, Cement and Concrete Research Institute, Sweden, 1978. 8. M.P. Elinson, The slag and fly ash caking products structure and composition, Lightweight aggregates for lightweight concretes, NIIST, Moscow. 95- 108, 1954. 9. Zhang MH, G j ~ r vO.E., Mechanical properties of high-strength lightweight concrete. ACI Materials J. 88(3) 199 1 : 240-7. 10. Holm TA, Bremner TW. High strength lightweight aggregate concrete. In: Shah SPand Ahniad SH, editors, High performance concrete: properties and applications. New York: McGraw-Hill; 1994.p.341-74. 1 1. Malhotra, V.M., CANMET investigations in the developmeni of high-strength concrete. In: Proceedings of the Symposium on the Utilization of High Strength Concrete, June 1518,1987, Stavanger, Norway; TAPIR, Trondhein, Norway.
Proc. Int. Sytnp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSIand Woodhead Publ., Warsaw 2003
INFLUENCE OF A GAS INFLOW SURFACE ON MEASURED PERMEABILITY OF CONCRETE Jacek SLIWINSKI Tomasz TRACZ Aleksander KOZAK Cracow University of Technology Warszawska 24, 3 1-155 Krakow, Poland, e-mail:[email protected] ABSTRACT The permeability of concrete to a steady flow of a gas is assessed according to RILEM requirements under the conditions under which the volume gas flow enters through a surface (Fi) equal to the total cross-section area of the sample (A). The paper describes the tests results, the aim of which was to determine quantitatively the influence of the FJA ratio (I 1) on the measured value of the permeability. The results showed that a decrease in the FJA ratio is associated with the lower measured permeability. On the basis of the tests performed it was found that the change in the Fi/A ratio causes similar relative changes of the permeability of different concretes. Relationship which made it possible to determine the nominal value of the permeability (k) assessed at Fi = A on the basis of the values determined at Fi/A < 1 is given. Keywords Concrete, gas permeability, Cembureau method, test conditions. INTRODUCTION The permeability is one of the characteristics that make it possible to assess the degree of accessibility in porous materials to gaseous and liquid media. Hence, the permeability allows us to judge the durability of materials. It is possible to estimate this characteristic, at least theoretically, on the basis of the measurement of parameters of the flow of any medium through the material. So far water has usually been used to assess the permeability of concrete. In connection with the progress in cement technology and the possibility of making concretes which have very tight structure ( High-Performance Concrete), water turned out to be both too dense and too viscous. Now, in order to assess the permeability of such concretes gases are often used. One of the most popular methods of determining the permeability by means of the flow of a gas is the RILEM-Cembureau method [1,2]. The paper describes the influence of one experimental variable on the assessment of the permeability.
444
Jacek SLZWIAbKI. Tornasz TMCZ and AIeksander KOZAK
PERMEABILITY AND ITS UNITS The permeability (k)is determined by means of the measurement of parameters, which characterise the flow of a gaseous medium through concrete. For gases, (compressible media) the permeability is described by the following equation (1) [I]:
where:
Q=V/t - the measured gas flow intensity [m3/s], P - applied pressure (absolute) [Pa], Pa - atmospheric pressure [ 1 bar = 10’ Pa], q - dynamic viscosity of the gas [Pas], A - cross-section area of the sample [m‘], L - thickness of the sample [m].
The permeability (k) defmed above may be treated as material constant, independent of the kind of gas used. It is also possible to use another measure of permeability for specified gas. So-called permeability coeflcient (K) can be used. The relationship between permeability coeflcient (K) and permeability @) is expressed by the following equation (2).
Pg K = k-[mls] rl where:
k p g q
(2)
- permeability [m’],
- density of the medium [kg/m’],
- gravitational acceleration [m/s*], - dynamic viscosity of the medium [Pas] THE AIM AND SCOPE OF THE PRESENT STUDY
The aim of the study In accordance with the RILEM-Cembureau method [I], the surface of gas inflow (Fi) should be the same as the cross-section area of the sample (A) during measurements. The aim of the studies was to assess the influence on the permeability fi) of the surface of gas inflow (Fi), which is less than the cross-section area of the sample (A). Materials and methods Three concretes were tested: ordinary concrete of class C 20 and two highperformance concretes (HPC) of classes C 55 and C 75. The composition of concretes tested and their basic properties are summarised in Table 1. The measurements were carried out using the apparatus shown in Fig .3. The inert gas used was nitrogen. Cylindrical samples were used in all tests. The specimens were 150 mm in diameter with thickness of 50 mm. Each of the concretes tested was represented by 3 samples put into the test chamber shown in Fig. 1. Before the permeability was measured the
lnjluence of gas injlow sioface
011
Ineusured perrneahility of concrete
Lateral seal (inner-tube)
Measurement Q
?
/
. .
445
Samole b=150 I h=50 m m
,
Gas inflow
Steel housing
Fig. 1. Chamber used for testing the sample, ensuring gas inflow on the surface (A) according to RILEM-Cembureau requirements cross-section area A (gas outflow surface)
Table. 1. The composition of concretes tested and their basic properties
gas inflow surface Fi
water-cement or water-binder ratio slump [mm] bulk density [kg/m3] water absorption [%I compressive strength [MPa] after: - 28 days - 90 days
0.70
0.40
0.301
170 50 2220 2340 5.5 4.8 I
25.2 29.4
61.5 70.4
Fig.2 Scheme of the specimen at Fi/A < 1
specimens were dried to constant mass at 105’C. According to RILEM requirements, the mean value of the permeability was calculated as the arithmetic mean of the test results at three different absolute pressures (P), i.e. 0.15, 0.20 and 0.30 MPa. For each series of specimens seven measurements of the permeability were made. In the fust one the surface of gas inflow (Fi) was equal to the cross-section area of the sample (A). The remaining determinations of the permeability were carried out for Fi/A ratio equal to 0.8; 0.6; 0.4; 0.2; 0.1 and 0.05. The decrease of the surface of gas inflow (Fi) was obtained through coating part of the sample surface facing the gas flow with a layer of epoxy resin (Fig.2). The layer of the epoxy resin was completely tight against nitrogen for the pressure used. The permeability was calculated on the basis of equation ( l ) , in which the total cross-section area (A) of the sample was included for each time.
446
Jmek SLIWINSKI, Tomasz TRACZ atrd Aleksander KOZAK
/
Two-stage Dressure reducer
Bubble meters
r,
measuring gas
/j
Fig. 3 Scheme of the apparatus for testing the permeability by mcans of Cembureau method [1,2] RESULTS The tests results ofthe permeability ofthe concretes determined for different values of the FiIA ratio are given in Fig. 4.
Fig. 4 The relationship between the absolute value of the permeability (k) of the concretes tested and the Fi/A ratio
It can be seen that, the lower FJA ratio the lower permeability (k). However, the permeability (k) does not decrease in direct proportion to the reduction of the surface of gas inflow (Fi).. Fig. 5 shows the relative changes of the permeability (k) of the individual concretes depending on the F,IA ratio.
F,lA ratio
Fig. 5 The relationship between the relative changes of the permeability (k) of the individual concretes tested and the F,/A ratio On the basis of diagrams in Fig. 5 it was found that relative changes produced by varying the Fi/A ratio are very similar, regardless of the type of concrete and its absolute permeability (k). Hence, the tests results can be generalised. The relationship for all concretes tested is reasonably precisely described by the linear hnction (r = 0.97; rz = 0.94) shown in Fig. 6. The hnction is expressed by the following equation: I
k
= 0.349
+ 0.729-Fi
A
(3)
or
k=
kF,/A
Fi 0.349 + 0.729 A
(3a)
where:
k - the permeability [m'] determined under the conditions, when Fi/A = 1, kFi,*- the permeability [m'] determined under the conditions, when Fi/A < 1.
448
Jacek SLIWINSm, Tomasz TRACZ and Aleksander KOZAK
y=0,349+0,729*x; r = 0.97; r
0 1 ...............; ...... .... ........ .......;_ .
..... ....
.......; .
......................
= 0.94
'.....................
... ....
........
,
...._. 1_...._.
FilA ratio
Fig. 6 The relationship between the relative changes of the permeability (k) and the Fi/A ratio, common to all concretes tested CONCLUSION On the basis of the results obtained it was found that the measured value of the permeability (k) of concretes depends strongly on the ratio of the surface of gas inflow (Fi) to the total cross-section area of the sample (A). In case of carrying out research on the permeability of concretes under the conditions in which the surface of gas inflow is only a part of the total cross-section area of sample the equation developed can be used, ACKNOWLEDGEMENTS The research reported in this paper was carried out in the Institute of Building Materials and Structures at Cracow University of Technology, as a part of project L-l/245/DS/2003. REFERENCES 1. RILEM Technical Recomendation: Tests for gas permeability of concrete TC 1 16-PCD: Permeability of concrete as criterion of its durability, Materials and Structures, ~01.32,1999, 174- 179 2. Kollek J.J., The determination of the permeability of concrete to oxygen by the Cembureau method - a recommendation, Materials and Structures, v01.22, 1989, 25-30 3. Sliwinski J., Tracz T., Concrete gas pemeability - theoretical background, methods and test results (in Polish), Proc. of Conf.: Dni betonu - tradycja i nowoczesnosc, Stowarzyszenie Producentow Cementu i Wapna, Polski Cement, Szczyrk, 2002,327-34 1
Proc. Int. S v t p . ,,Brittle Matrix Composites 7 A.M. Brandt. V.C. Li and I. H. Marshall. rds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsuw 2003 'I
INFLUENCE OF COARSE AGGREGATE SIZE AND CEMENT MATRIX STRENGTH ON STRESS-CRACK WIDTH RELATIONSHIP OF CONCRETE
Jun ZHANG, Qian LIU and Lin WANG Department of Civil Engineering, Tsinghua University, Beijing, 100084, P.R.China ABSTRACT In this paper, the effect of coarse aggregate size (single grade of 5-10 mm and 16-20 mm) and matrix strength (concrete compressive strength of 40 and 80 MPa respectively) on stress-crack width ( 0 - w ) relationship is studied. The investigation is based on three point bending tests implemented by fictitious crack analyses. The result shows that coarse aggregate size and cement matrix strength significantly influence the shape of 0-w curve. For the same total aggregate content, in the case of compressive strength is equal to 40 MPa, small size aggregate leads to a high tensile strength and a sharp stress dropping after the peak stress. As concrete compressive strength increases to 80 m a , the effect of aggregate size on 0-w relationship almost vanishes. Coarse aggregate size and matrix strength are both important parameters which influence the crack bridging law of concrete. In addition, a four-linear function is accurate enough to reflect the characteristics of the stress-crack width relationship of concrete. Keywords Coarse aggregate size, bending test, stress-crack width relationship CNTRODUCTION It has been recognized that because of the heterogeneity inherent in the microstructure of concrete, strain softening, microcracking and larger scale fracture process zone, linear elastic fracture mechanics is only applicable to large-scale initially cracked structures and ultrabrittle concrete in which the effect ofthe process zone can be neglected [ 1,2]. In all other cases, i.e., for normal-sized concrete structures, the influence of fracture process zone has to be taken consideration when using the classic linear elastic concepts of fracture mechanics to predict crack propagation. An well-accepted model, called fictitious crack model (FCM) proposed by Hillerborg et al. [3], which is used to describe the behavior of the Fracture process zone of concrete has been developed. The fundamental idea of the FCM can be demonstrated by means of a hypothetical uniaxial tensile test on a concrete specimen, as shown in Fig 1. The test is assumed to be deformation controlled and stable. The complete stress-deformation curve consists of an ascending part and a descending part. In the pre-peak stage, at beginning, the stress-deformation response is almost linear elastic and the deformation is uniformly distributed along the whole specimen. In this stage,
450
Jltn ZHANG, Qiaii LIUcind Liri WANG
\ process zone
t
Deformation
A1
Fig. I Defoniiatioii behavior of coiicrcte under tensile load
the behaviour ofconcrete can be well described by the stress-strain relation As microcracks which are distributed randomly within the concrete volume start to grow, the stress-deformation curve begin to become non-linear. In the mean time, the formation o f microcracks starts to localise in a narrow zone called the process zone. With increase of deformation i n the zone, the loading capacity of the specimen first increases then decreases after passing a peak load. As a result, the part outside the process zone unloads after the peak load. The fracture zone is concentrated within a very thin band and can be considered as a discrete crack, called the fictitious crack. The loading capacity of specimen is governed by the degree of deformation in the fracture zone, normally called the fictitious crack width, simplified as the crack width. Finally, the specimen is broken into two halves along the fracture zone and the bridging force vanishes. In the fracture zone, a relation, called the stress-crack width ( F W ) relationship must be used while the rest can be still described by a stress-strain (0-E)relation with the initial tangent modulus. Therefore, the following material parameters are hndamental in the constitutive relations of concrete in tension. the Young's and the stress-crack width ( 0 - w ) modulus E, the cracking strength or, tensile strength relationship (see Fig. 2 ) .
t
t
stress crack \wdth (a-W)relationship
stress strain (u-E)relationship
0
D
I
' Erc
I
Strain
E
Crackwidth
Fig.2 Basic constitutive relations of CoilCrete in teilsioti
w
45 I
lnjluence of course aggregute size and cemeiit matrix strength on stress-crack width _..
The addition of aggregates, in the form of sand and stone, reducing shrinkage strain, and at the same time enhances the tensile strength and fracture energy ofthe resulting mortar and concrete [4, 51. In the microstructure point of view, the improvement ofcoarse aggregate on the macro fracture behavior should be due to the enhancement to crack bridging, which provides closing pressure in the fracture process zone. However, in the view of fundamental material constitutive relation, the investigations on the influence of coarse aggregate on the (T-M’ relationship are still limited. These investigations are required in both numerical predictions of structural responds of concrete structures using fracture mechanics tool and material microstructure tailoring for enhancing fracture and cracking resistance of concrete. In this paper, a reverse analysis based method [6] to determine the CFW relationship from a three point bending test is used to evaluate the effect of coarse aggregate size and cement matrix strength. DETERh3INATION OF
0-wRELATIONSHIP
FROM A BENDING TEST
A three-point bending test is adopted to determine the 0-w relationship of concrete. A pre-notched beam is used in the test. A standard Toni linear variable differential transducer (LVDT) is used for measuring the deflection. The crack mouth opening displacement (CMOD) is measured by an extensometer with lOmm gauge length mounted across the 10 mm deep and 3 mm width notch. The test set-up and the geometry of the test specimen are shown in Fig. 3 . The bending test is conducted as a prescribed deformation rate of 0.05 mm per minute using the signal from the LVDT used for deflection measurement as feedback. All tests are carried out on a Toni testing machine equipped for close-loop testing. The determination procedures of ( F W relationship are described in the follow section. Load
(b)
Fig 3 Schematic \ien of experimental set-up (a) and the geometry of test specinien (b),
uiiit
(mm)
Cracking strength, ofc In the present investigation, cracking strength is defined as the stress level at which crack starts to propagate. From above three-point bending test, as the pre-induced notch, starts to grow, the
452
Jun ZHANG. Qinn LIUand Lin WANG
value of CMOD will exhibit jump compared with the elastic crack mouth opening stage. The transition point from the linear elastic stage to the nonlinear elastic stage (with fictitious crack developed) will be detectable by the extensometer mounted at the mouth of pre-notch as long as the sensitivity of the extensometer is sufficient high. In the current experiments, the cracking load was successfully detected by the extensometer mounted at the notch mouth. A typical test result is shown in Fig. 4 in terms of load-time and CMOD-time diagrams. The cracking strength qcis then calculated by a finite element method from the cracking load Pfi.
4
6000
0 15
0.12
[0.09 0
m
4000
-E
E
0
0 -I
0.06 2000
0
5
0.03
0
0.00 0
200
400
600
800
1000
1200
1400
Time (s)
Fig.4 Experiniental detenuination of cracking load
Stress-crack width relationship Based on the cohesive crack model, a reversed analysis method to determine the stress crack opening relationship from bending test is adopted. Firstly, consider a central pre-notched concrete beam under a three point bending load. The direction of crack propagation should be perpendicular to the maximum principal stress. Therefore the crack propagation path in this load configuration can be predicted in advance, i.e. parallel to the load, tiom the notch tip upwards to the beam top. Here the fictitious crack tip is defined as the point where the principal tensile stress attains the cracking strength af,and the crack opening at this point is equal to zero. The material in the process zone is still be able to transfer stress, which is governed by the crack opening displacement w. The relationship between cohesive stress and crack opening can be expressed by a multiple-linear equation, i.e.: o , , = k , w + o o , for
w,_, I w ~ w , ( ~ = 1 , 2,.._nrnax)
Where k, is the slope for WE [ w , . ~ w,]. , ool= o@,oOn =
(1)
zr-'
[(k, - k,+lb y , ] + olb. Our target is
to solve the individual values of k, from each experimentally determined load-CMOD diagram. Fig. 5 shows a cracked beam section with crack length, n and external load P. The fictitious bridging stress acting on the crack surface along the cracking section is ob(w(x)). According to the principle of superposition shown in Fig.5, the crack opening along the crack length can be obtained by summing the contributions of the external load and the bridging force, i.e.
Similarly, the stress at the crack tip can be obtained by
Influeiice of coarse aggregate s i x and cerneizl matrix strength 011 stress-crack width ...
45 3
P
P
1
Fig.5 Superposition principle of cracked beam with fictitious force
on,= K,P - B[ K , ( x , y)o,(y)dy for
0 <_ x < LI
(3)
As equilibrium is achieved, we haveo,, = of=. The load point deflectionf can then be given by
f = K,P
-
BSd' K , ( Y b b Q)&
(4)
where Kp and Kfare the influence factors of external load and fictitious force. It is noted that for each parameter, such as to crack opening displacement or crack tip stress, the factors Kpand K , are different. From equation (I), ebb) can be expressed as a hnction of w as:
'
( y ) = knw(y)
oOn
(5)
Replacing ebb) by ( S ) , equation ( 2 ) becomes: w ( x ) = K , ( ~ ) P - R ~ K ~ ( x , y ) [ k , , ~ ( y ) + o ~, f, ~, j/ 'dOy < X < U
(6)
Instead of solving the above equation by integration during iteration towards self-consistency to w(x), the problem can be solved in matrix form, greatly reducing the computational load, especially when many applied loads are needed to be scanned over. With reference to the bending specimen shown in Fig. 5 , nodes are distributed along the potential fracture line. The closing stresses acting on the crack surface are replaced by node forces that depend on the crack opening displacement according to the cr-+v relationship of the material. When the cracking strength is achieved at the crack tip, a node is then spilt into two nodes and a pair of opposite node forces starts to act on these two nodes. The fictitious crack tip then moves to the next node. Let vector IW(W,, w2, w 3 , .. .w,,,), K/=(Ko, Kc, Kt3, ...K,j,,) and Kp =(Kpl,Kpz, Kp3,. . . K,,,,,), F=(FI,F2, F3, . . .F,,,),and assume the node for the crack tip ism+ 1, then the equation
454
Jun ZHANG. Qian LIUand Lin WANG
of (2) and (3) can be expressed in matrix form as: n,
W~
=2Kp,P-2CK,E
( i = U ... m)
(7)
,=I
"I
D~
= KPP-CKJl;l
(i=1,2,..nt)
,=I
F, can be related to w, by
F, =(k,w, +D,,)BAI, (i=1,2,. . , m )
(9)
where B is the specimen width and AI, is the calculating length at node i. Generally Al, =A1 except for i=l where A4 =0.5AI. Here A1 is the distance between two adjacent nodes. The influence factors for node openings, crack tip principal stresses and load point deflection are obtained by a finite element analysis, where the cracked beam is subjected to m+l (P, F,, . . .F,,,=l) different loading conditions. For a given fictitious crack length n (rr=.mAL),equations (7),( 8 ) and (9) constitute a linear algebraic system of (>?+I) equations and (2ni+l) unknowns, i.e. =(P, w,, w2, w3, . ..w,, F,, F2, F3, . ..El,).The crack mouth opening displacement wo can be related with P and Fi by m
wo = 2 K p P - 2 C K p F ,
(i=l,2,..m)
1 4
Thus, for a given crack length, CI (not including the initial unbridged crack no) and stress crack width relation, by solving equations (7),(8) and (9), the critical external load capacity P, fictitious force F, and crack profile w ( x ) can be obtained. The CMOD can then be calculated from equation (10). Our target is to solve 5 w relation from experimental determined Load-CMOD result. In order to do so, a numerical procedure is implemented to simulate a loading process where the incremental parameter step by step is the fictitious crack length. The minimum crack length is A1 and may increase up to the maximum value m,luxAlby step A1 or multiples of this value and where m,,,, is an integer which depends on the maximum node number. The number of node along the potential cracking line depends on the node density. In each crack propagation step, by optimizing the model calculated load and the experimental determined load, corresponded 5 w relationship can be determined. The detailed procedures can be found in [7]. EXPERIMENTAL PROGRAM
In the present investigation, a total of four series of bending tests with two different concrete grades according to designed concrete compressive strength and two coarse aggregate size were carried out. The bending test results are used as input to solve the D-w relationship of each type of concrete. Ordinary Portland cement, nature sand and crashed stone with maximum particle size of 5-10mm and 15-20mm were used respectively. The concrete mix proportions are list in Table 1. The mixing procedure can be described as follows. First, the tine and coarse aggregates and cement were mixed together for 2 minutes. Next. the water was gradually added with the supperplasticizermixed in and the mixing was continued for another 3 minutes. Prism specimens
45 5
Iiijluertcc of coarse aggregate size and cement rnntrix slretigtli on stress-cruck width .,.
Table I . Mix DroDortions of concrete h h
Cement
Water
Sand
Stone
SF'
FA'
AS'
(kg/1n3)
(kg/ni3)
(kg/ii?)
(kg/m3)
(kg/m3)
(kg/iii3)
(m4
1
397.0
205.0
532.4
1064.8
-
70.0
5-10
2
397.0
205.0
532.4
1064.8
-
70.0
16-20 5-10 16-20
NO
3
450
150
572. I
1144.2
50
-
4
450
150
572.1
1144.2
50
-
* SF-Silica
fume; FA-Fly ash; AS-Coarse aggegate size. Note: Supperplasticizer was used to niaintaiii the of Gesh concrete to be 45-55 i i m . s1~11ip
with size of 1OOx1OOx4OO mm were cast for each mix. The specimens were cast horizontally in three layers and the concrete was well compacted on a vibrating table. The specimens were cured for 24 hours at room temperature. Then the specimens were removed from their moulds and put into a temperature and humidity controlled room where temperature of 20°C and a relative humidity above 90% were maintained for 28 days. Afterwards, a 10 mm deep notch was cut with a water-cooled concrete cutting saw. All notched beams were stored in air for another two months before testing.
RESULTS AND DISCUSSIONS Typical bending test results in the form of Load-CMOD curves are shown in Fig. 6 a to d. All the Load-CMOD curves of different series with various coarse aggregate size and matrix strength combinations show similar pattern. The Load-CMOD curve can be divided into three sections: (1) elastic stage up to the stress at the tip of notch achieves the cracking strength qc with a constant stiffness; ( 2 ) crack developing stage one, load increases with a gradually reduction on the stiffness of beam until the peak load; (3) crack developing stage two, load decreases with a negative stiffness. However, significant differences in both the maximum bending load and the stiffness in each stage, especially in the post peak section can be observed. These differences must related to their 0-w relationship. According to the procedures described in last section, the 0-iv relationship of each type of concrete is determined. The parameters needed in determining the 0-w relationship are listed in Table 2 . It is noted that the cracking strength is determined from the bending tests by method described in last section. Figure 7 a to dshows the deduced 0-w relationship ofthe four series ofconcrete. Fig.8 shows typical comparison between model predictions using above deduced 0-w relation as inputted constitutive law and experimental results in terms of Load-CMOD curves. First from Fig.8, it can be seen that a very good agreement between model predictions and test results is found. Therefor, the four-linear function, shown in Fig.7, is accurate enough to reflect the characteristics of the 0 - w relationship of concrete. Second, the general characteristic of the 0-w relationship of concrete can be described as an ascending portion with a very large stiffness (dddw) and a descending portion with a gradually increased negative stiffness. The ascending portion may principally due to aggregatdmatrix interfacial debonding. The descending portion may correspond to the aggregate pull-out. Third, the coarse aggregate size and cement matrix
456
Jcin ZHANG, Qian LIUand Liri WANG
Mix No.
fC* (GPa)
I
30
1.38
39.55
4.43
5.23
2
30
1.18
39.23
2.14
3.66
(MPa)
0 , ' (MPa)
(MPa)
4.
oj' (MPa)
3
35
1.64
85.97
4.95
6.32
4
35
1.64
82.28
4.78
6.09
12oOo
,
,
,
,
,
, , , - cm.biomm
,
-t V
3
OW
020
0.40
060
OW
1W
OW
040
020
l2wo
lzOO0 C(o.510 m m
060
080
1W
CMOD (mm)
CMOD (rnrn)
~,
,
,
,
, , , cw1e-wmm
,
loo00
Bwo
E
gx)o
U
A 0
4wo
2 x 0
OW
020
040
060
CMOD (rnrn)
(c)
080
100
0 OW
020
040
OBO
060
103
CMOD (rnrn)
(4
Fig.6 Load-CMOD diagram of four typcs of concrete strength significantly intluence the shape of 0-w curve. In general, for the same total aggregate content, in the case of compressive strength is equal to 40 MPa, small size aggregate leads to a high tensile strength and a sharp stress dropping after the peak stress. This characteristic leads to the difference in the Load-CMOD curves shown in Fig.6 a. However, as concrete compressive strength increases to 80 MPa, the effect of aggregate size on e w relationship almost vanishes. The two types of concrete with different size of coarse aggregate respectively ~ (see Fig.6 h). This indicates that the number of aggregate have a similar o-1,~relationship particles can not intluence the magnitude of the crack bridging force of concrete. The reasons
45 7
Influence of coarse aggregate size and cetiienl matrix strengtli on slmvi-crack width ... I
600
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0 30
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Fig.7 Deduced u-w relationship based on thee point betiding results
8000
6000 7J m _I 0
4000
2000
0.00
0.05
0.10
0.15
0.20
0 25
0.30
CMOD (mm)
Fig.8 Comparison of model predictions and experimental results in ternis of Load-CMOD diagranis
for above results may be summarized as follow. The number of aggregate which across a crack and the matridaggregate bond strength are the two principle parameters, which control the magnitude of crack bridging force in concrete. First, with coarse aggregate size reduction, the number of aggregate which across a crack increase. This will increase the bridging force even though the reduction on the aggregate size
458
Jim %HANG. Qian LIUancl Lin WANG
may decrease the bond length of matridaggregate interface. However, high matridaggregate bond strength may lead aggregate breakage [8], which in turn reduces the contribution of aggregate to the crack bridging force. Therefore, a similar CT-I.Y curve is obtained in the series of concrete with compressive strength of 80MPa even different size of aggregate were used, see Fig.7 c and d. CONCLUSIONS In the present investigation, the effect of coarse aggregate size (particle size of 5-10 mm and 16-20 mm) and cement matrix strength (concrete compressive strength from 40 to 80 MPa) on the stress crack width relationship (a-w)are evaluated by three point bending test. The results show that the influence of coarse aggregate size on shape of CT-w curve is significant. For the same total aggregate content, in the case of compressive strength is equal to 40 MPa, small coarse aggregate size leads to increase in tensile strength and a sharp stress dropping after the peak stress. As concrete compressive strength increases to 80 MPa, the effect of the size of coarse aggregate on the CT-w relationship almost vanishes. In addition, a four-linear fhnction is accurate enough to reflect the characteristics of the stress-crack width relationship of concrete. ACKNOWLEDGMENTS This work has been supported by a grant from the National Science Foundation of China (No, 50 178043) to Tsinghua University.
REFERENCES 1. Kaplan, F. M., Crack propagation and fracture of concrete. Journal ofthe American of Concrete Institute, Proceedings, 58(5), 1961, pp.591-610. 2. Strange, P.C. and Bryant, A.H.,Experimental tests on concrete fracture. ASCE Proc, Journal of the Engineering Mechanics Division, 105, 1979, pp.337-342. 3. Hillerborg, A,, Modeer, M. and Peterson, P-E., Analysis of crack formation and crack growth by means of fracture mechanics and finite elements. Cement Concrete Res., 6, 1976, pp.773-782. 4. Chang, TP., Taso, KL. and Lin, BR., Effect of aggregate on fracture properties of high-performance concrete. In: Proc. of FRAMCOS-3. Mihashi, H. and Rokugo, K., eds, D-79 104 Freiburg: Aedificatio Publishers, 1998, pp. 15 1- 160. 5. Hassanzadeh, M., The influence of the type of coarse aggregates on the fracture mechanical properties of high performance concrete. In: Proc. of FRAMCOS-3. Mihashi, H. and Rokugo, K., eds, D-79 104 Freiburg: Aedificatio Publishers, 1998, pp. 161 - 170. 6. Kitsutaka, Y.,Fracture parameters by polylinear tension-softening analysis. J. of Engineering Mechanics, 123(5), 1997, pp. 444-450. 7. Zhang, J. and Liu, Q., Determination of Fracture Parameters of Concrete from a Three-Point Bending Test. Will appear in Tsinghua Science and Technology, 2003. 8 . Buyukozturk 0. and Hearing, B., Crack propagation in concrete composites influenced by interface fracture parameters. Int. J. Solids Struct., 35(3 1-32), 1998, pp.4055-4066.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
PREDICTION OF NON-UNIFORM MULTIPLE CRACKING IN POLYMER COMPOSITES USING AN ENERGY-BASED PROBABILISTIC MODEL
K. P. HERRMANN' and Junqian ZHANG' 'Laboratory for Technical Mechanics, University of Paderborn, 33098 Paderborn, Germany, email: jherrl @Itm.uni-paderborn.de *Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China, email: [email protected] ABSTRACT A probabilistic model is developed to predict the evolution of a transverse ply cracking in a composite laminate as a function of the underlying statistical fracture toughness and the applied load. The instantaneous formation of a matrix crack spanning both the ply thickness and the ply width is assumed to be governed by an energy criterion associated with the material fracture toughness, r, at the ply-level. Assume multiple matrix fractures occur quasistatically and sequentially such that the ply cracks form one after another under the constant external load that is imposed on the specimen. The number of cracks, n, within the gauge length, 2L, is a discrete random variable for a given applied load, cr, because the fracture toughness varies with the location of fracture in a given specimen as well as from specimen to specimen. The probability function f ( n , a , L ) of the discrete random variable, n, is determined from the fracture toughness distribution and the solution for the potential energy release rate. Consequently the distribution of the crack density, d , - n / 2 L , is obtained. Finally the mean crack density is formulated as a function of the applied load. Keywords Composites, multiple cracks, thickness effect, probabilistic model, fracture toughness.
INTRODUCTION Fiber reinforced composites have at least two different scales of hierarchical microstructures, say the multi-plies mesostructure and the fibedmatrix microstructure for composite laminates. Since the composite laminates have a layered structure at the mesolevel a ply crack cannot extend into the neighboring plies, and it will be arrested at the interlaminar interface. This permits that the multiple fractures at the ply-level can be caused by an increase of the applied load without a catastrophic failure of the laminate [I-51. In order to predict the formation of the first ply-crack and the accumulation of the number of cracks against the applied laminate stress one may assume that the multiple ply-cracks form one after another without simultaneous occurrence of two or more cracks. The instantaneous formation of an intralaminar crack spanning both the ply thickness and the ply width is assumed to be governed by an energy criterion associated with the material fracture toughness, r, at the ply-level, i.e.
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K. P. HERRMANN and Junqian ZHANG
G(o,T)=((',,,o+C,T)'glr, where o and T are a mechanical loading parameter and the temperature difference, respectively; g is the normalized energy release rate; r denotes the surface energy of the material, called the fracture toughness. which may depend upon the mode-mixity. The potential energy release rate, G, varies with the location of the new cracking, having a maximum at the mid-point of a segment bounded by two previous cracks. This leads to a simultaneous occurrence of cracks at the midpoints of all segments, provided the fracture toughness has a unique value. Then a multiple-crack configuration with a uniform crack spacing, 2s, is produced. The relationship between the applied stress and the crack spacing can be established by substituting the expression for the potential energy release rate into the fracture criterion (I), that is
where the crack density, d, and the crack spacing obey the relationship of d = 1/ 2s, the normalized energy release rate, g, derived from the shear-lag analysis [ I ] for the cross-ply laminates takes up the form of g(d) =
(3)
h
the other parameters are laminate constants which were explicitly given in [ 6 ] . Such a deterministic model predicts that the crack density vs the applied stress curve increases always sharply at the initial stage, no matter how accurate the local stress fields can be computed. The sharp accumulation of the cracks does not agree with the experimental data which shown a gradually increasing tendency. Such a discrepancy may be reduced by taking statistical aspects of the cracking into account.
DISTRIBUTION OF A NUMBER OF CRACKS The experimental results have shown that the number of cracks varies from specimen to specimen and the location of a crack cannot be well defined although the laminate configuration and the load are given. Such uncertainties are believed coming from the statistical distribution of the fracture toughness r. The variation o f the fracture toughness from specimen to specimen could be characterized by the probability density function p ( T ) . We specialize to the case where the fracture toughness is of the Weibuli form, but the theory is by no means restricted to this special case. The Weibull distribution of the fracture toughness r is defined by
where rs and j3 are the scale parameter and the Weibull modulus. The uncertainty of the cracking location seems connected directly with the variation of l- along the length of a single specimen which is totally random. The statistical nature of the fracture toughness has origins
Prediction of non-uniform multiple cracking in polymer composites using an energy-based ...
46 1
in the microstructure level factors, such as the fracture morphology. the curved profilc 01’ :I crack and the microstress fluctuation at the fibedmatrix level. It is assumed that multiple matrix fractures occur quasi-statically and seqiicnrial I! . ;I> shown in Fig.1. In the first step, the thermomechanical load is imposed on thc coliipositc laminate, without causing any cracking. In the following steps, the multiple p l y - c r x k s timi one after another without simultaneous occurrence of two or more cracks under the unchanged external load that has been imposed on the specimen. Given an applied laminare stress the number of cracks is a discrete random variable, N , which takes on a non-negati\.e number, n, (n=O, I, 2 , , ..,a). The probability hnction of the random variable, N , denoted by f ( n , o , 2 L ) , represents the failure probability that the exact n-cracks appear sequentially within the gauge length, 2L, under the constant load, u .
L
<
I
I-
2L
-->
-I
Cracks appear one aRer another under unchanged load
Z
< 1
T
I-
2L
-
Figure. 1 A quasi-static and sequential process model for multiple fractures in composite laminates.
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K. P. HERRMANN and Junqian ZHANG
The first crack will appear at a location where the composite material toughness is smaller than the potential energy release rate for the first cracking, i.e. 5 GI (o,L,cI). Since the variation of the lamina fracture toughness with the location is totally random the crack could be with an equal chance at any location among those locations where the fracture criterion holds true. Because it has been assumed that the fracture takes place one after another under the constant applied load, 0 ,the satisfaction of l- I GI (cr,L,cI) ensures the appearance of the first crack, but does not exclude any other events of more fractures after the first cracking under an unchanging stress. Therefore, the probability that ply cracks, regardless of the number of cracks, appear in a composite laminate under a constant load can be expressed by
The probability of an uncracking ( n = 0 ) can be derived from equation (5) as follows
Let us consider the second ply cracking within the gauge length under the constant load after the first crack has been fomied. By using the fracture criterion given by equation (1) the second ply cracking could occur at a location where r I G?(G,L,c?,c, ) holds true. By noting the fact that the variation of r with the location is totally random, the probability that the second ply cracking takes place (N22) can be expressed by
The probability of a single crack in the laminate is then given by f ( n = I , o , L ) = P ( N 1 I,o, L ) - P ( N 2 2 , 0 , L )
The probability analyses of the third cracking, the fourth cracking and so on can be conducted by a similar procedure which has been just discussed for the second ply-cracking. By repeating the procedure (n-])-cracks can be formed sequentially under constant load. A new cracking, the n-th ply cracking, is controlled by the fracture criterion r I G,,(G,L, D,,) . Again, among locations where the fracture criterion holds true there is not a preferential location where the new cracking occurs. Therefore, the probability of the n-th cracking within the laminate takes on the form of
463
Prediction of non-uniform multiple cracking in polymer composites using an energy-based .. .
It is implied that the multidimensional integral in this equation has the physical meaning of the failure probability that the number of cracks is less than 11. i.c.
Consequently the probability that exact @])-cracks appear sequentially is expressible as , f ( n - I,o, L ) = P( N 2 n - I,o,L ) - P( N 2 n,o, L ) ,
(1 1)
for n 2 l . Now the probability function, f ( n ,CT, L ) , has been expressed as a function of the potential energy release rates as well as the Weibull parameters of the fracture toughness. Knowing the potential energy release rate the multidimensional integral, P ( N < n,o, L ) given by equation (lo), can be evaluated numerically. The probability function , f ( n , a ,L ) can then be easily calculated from equation (1 I). A simplified expression for P ( N < n.o. L ) has been obtained in [6], which involves only three-dimensional integrals regardless of the number of cracks. i.r.
for n>2 and where
$,I’
=
Q:? (1 + x) 2 tanh(hL(l - c)) + tanh(2ALc) - tanh(2hLl) h
g,’,’) = Q?”? (I + h
(1 3a)
2
(tanh(hLc) + tanh(hL(/ - c)) - tanh(hLf))
.
By introducing the crack density. d,, = n / 2 L , the average crack density, determined via the mean number of cracks. E , as follows
2,
can be
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K. P. HERRMANN and Junqian ZHANG
where the probability function of the crack density, d,,, is
It is implied that the crack density is a complex function of the applied stress and the fracture toughness distribution.
RESULTS In order to illustrate the predictability of the model we consider the [+8/904], glass fiber composite laminates. The laminates were tested by Joffe et a1 (2001) subject to uniaxial tension. The experimental data of the average crack density versus the laminate stress were reported there. The material properties used in the analyses are El=44.73 GPa, Ez=E3=12.76 GPa, GI2=GI3=5.8GPa, G23=4.49 GPa, 1' C , ~12=~13=0.297, V 2 ~ ~ 0 . 4 2ct:, = 8 . 6 ~ I" C , cty = ct: = 22.1 x ply thickness = 0.144 mm, temperature difference, T, = -105°C. In figure 2 the curves of the averaged crack density versus the laminate stress, which are generated from the experimental data and from the prediction of the deterministic model, are plotted together in order to show a comparison. For the same reason the experimental data and the present probabilistic model are putted together in figure 3. From both figures it can be seen that both the deterministic and the probabilistic models are able to predict the thickness effect on the multiple cracking in the laminates, namely, the thicker the laminate is, the smaller the stress that produces the same number of cracks. Figure 2 suggests that the deterministic model predicts a very rapid accumulation of ply cracks succeeding the first ply-
Fig. 2 Comparison of the deterministic model predictions (lines) with experiincntal data (discrete symbols ) in terms of the crack density in the 903 ply in the glass fiberlepoxy composite [fW90,,,lT(lJ laminates as a function ofthe applied stress.
Fig. 3 Comparison of the probabilistic model predictions (r,= 750 J/m', p = 10. lines) with experimental data (discrete symbols ) iii terms o f the crack density i n the 905 -ply in the glass fiherlepxy composite [M902mMl]laminates as a function of the applied stress
Prediction of non-uniformmultiple cracking in polymer composites iising an energy-based ...
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cracking. In contrast Figure 3 shows that the probabilistic model presents a smooth increase of the crack density with applied stress. The latter one is closer to the observed values in the experiments.
CONCLUSIONS We have presented an energy based probabilistic theory to predict the evolution of transverse ply cracking in a composite laminate as a function of the underlying statistical fracture toughness and the applied load. The variation of the ply-level fracture toughness was characterized by a probability density function, p ( r ) . The probability function ,fi, (d,,,o,L) of the crack density, a discrete random variable, was determined from the fracture toughness distribution and the solution for the potential energy release rate. The mean crack density was formulated as a function of the applied load. In contrast to the deterministic models which predict a very rapid accumulation of the number of cracks the probabilistic model shows a smooth increase of the crack density against the applied load.
ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support by the Alexander von HumboldtFoundation of Germany and the National Science Foundation of China under grant number 19972076.
REFERENCES Zhang, J., Fan, J. and Soutis, C. (1992), Analysis of multiple matrix cracking in [+€I m/9On]s composite laminates: part 11, development of transverse ply cracks. Composites 23,299-304. 2. Joffe, R., Krasnikovs, A., Varna, J., (200 I ) , COD-based simulation of transverse cracking and stiffness reduction in [S/90,], laminates, Composites Science & Technology, 61, 637656. 3. Kashtalyan, M and Soutis, C (2000), Modelling stiffness degradation due to matrix cracking in angle ply composite laminates, Plastics Rubber and Composites, 29 (9), 482488. 4. Liu, S and Nairn, J. A. (1992), The formation and propagation of matrix microcracks in cross-ply laminates during static loading, J. Reinjorced Plustics and Composites, 11, 158178. 5. McCartney, L.N., (2000), Model to predict effects of triaxial loading on ply cracking in general symmetric laminates, Composites Science & Technology, 60, 2255-2279. 6. Herrmann, K. P., Zhang, J. and Fan. J. (2002). An energy-based statistical model for multiple fractures in composite laminates, subniifted to J. of Multiscale Compututiorial Eng. 1.
Proc. Int. Synip. Brittle Matrix Coinposites 7” A M Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003 I,
FRACTURE MECHANICS AND PLASTICITY MODELLING OF THE SPLIT CYLINDERTEST John Forbes OLESEN, Lennart BSTERGAARD and Henrik STANG Department of Civil Engineering, Technical University of Denmark Brovej, Building 1 18, DK-2800 Kgs. Lyngby, Denmark, e-mail: j foO,bvg.dtu.dk
ABSTRACT The split cylinder test is subjected to an analysis combining nonlinear fracture mechanics and plasticity. The fictitious crack model is applied for the analysis of splitting tensile fiacture, and the Mohr-Coulomb yield criterion is adopted for modelling the compressive crushing/sliding failure. Two models are presented, a simple semi-analytical model based on analytical solutions for the crack propagation in a rectangular prismatic body, and a finite element model including plasticity in bulk material as well as crack propagation in interface elements. A numerical study applying these models demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive properties. This implies that the linear elastic interpretation of the ultimate splitting force in term of the uniaxial tensile strength of the material is only valid for special situations, e.g. for very large cylinders. Furthermore, the numerical analysis suggests that the split cylinder test is not well suited for determining the tensile strength of early age or fibre reinforced concrete.
Keywords Fictitious crack model, hinge model, concrete, fibre reinforced concrete, size effect. INTRODUCTION The split cylinder test, also known as the Brazilian split test, has been accepted in many countries as a standard test method for assessing the uniaxial tensile strength of concrete and similar materials. This test is performed by loading a cylindrical specimen along diametrically opposed generators of the cylinder until failure. The diametrically loading of the cylinder induces an almost uniform tensile stress normal to the plane of loading, and the failure load is interpreted as the load at which these tensile stresses reach the uniaxial tensile strength of the material. The tensile strength based on this interpretation is known as the splitting tensile strength. For a perfectly brittle material the splitting tensile strength would coincide with the uniaxial tensile strength. However, concrete is not a perfectly brittle material but a so-called quasi-brittle
30s
.John Forbes OLESEN, Lennari OSTERGAARD and Henrik STANG
material, and it is well-known that for noiinal strength concrete the splitting tensile strength overestimates the true uniaxial tensile strength. Thus, the splitting tensile strength is normally reduced by an empirical factor in the range of 0.6-0.9 when estimating the uniaxial strength. D The overestimation of the concrete tensile strength when based on the result of a split cylinder test is due to the quasi-brittle nature of concrete fracture. Here we adopt the fictitious crack model, a model first proposed by Hillerborg et al. [ I ] for modelling crack propagation in concrete and similar quasi-brittle Figure 1: Yield lines of the assumed plastic failure mode. materials. In this model a linear elastic pre-crack behaviour is assumed and crack initiation and localization is assumed to take place when the tensile stress reaches the uniaxial tensile strength of the material,&. This is followed by a crack opening phase where aggregate bridging is responsible for crack bridging stresses. The bridging stress. as,, is related to the width of the crack, w, through the tension softening curve or stresscrack opening relationship, which is a curve descending from the peak stressf;. The stress-crack opening relationship must be established experimentally e.g. by performing a uniaxial tension test in closed loop control or by some indirect method such as the wedge splitting test in combination with an inverse analysis method, see [ 2 ] . Originally, Hillerborg et al. [ I ] assumed a linear tension softening behaviour for concrete, however, a bilinear representation of the stress-crack opening relationship gives a more precise description of the behaviour of concrete and fibre reinforced concrete. Thus, a bilinear relationship is applied here, and it is given by the following expression:
""={ f;
I-a,w,
05w<w,
b2-a,w,
w,Iw<w,
The stresscrack opening relationship may be seen as a constitutive relationship for a crack and as such it may be implemented in a finite element model, e.g. through interface elements as done by Bstergaard et al. [3] and described below. The simple bilinear representation of the stress-crack opening relationship allows for an analytical solution to the problem of crack propagation in simplified situations such as flexural cracking of a straight beam o f rectangular cross-section. This is demonstrated by Olesen [4] who developed a so-called nonlinear hinge element incorporating the effects of crack propagation due to moment and normal force loads. Later it will be shown how this hinge element may be applied to the split cylinder test configuration to produce a semi-analytical model. The failure of the split cylinder specimen is characterized by a splitting crack beginning at the centerline and propagating towards the loading points. If the material is sufficiently brittle the splitting will proceed until the specimen is divided into two halves. In this case the ultimate load is governed by the tensile strength as well as the tension softening behavior of the material. However, if the material is not sufficiently brittle the splitting process will not be completed before a compressive crushingkliding failure develops, which then governs the ultimate load. In compressive failure concrete may be modelled as a rigid-plastic material with a Mohr-Coulomb
friction yield criterion, cf. [ 5 ] . Upper-bound solutions exist for the rigid-plastic failure of the split cylinder test and will be given later. These solutions are characterized by the formation ofwedgelike regions under the loading strips, simultaneously splitting the rest of the specimen. The compressive failure of concrete in the form of the Coulomb friction hypothesis may also be implemented in a finite element model as will be demonstrated. In the present paper it will be shown how the split cylinder test may be modelled to cope with materials ranging from perfectly brittle to ideal plastic, thus nonlinear fracture mechanics as well as plasticity is modelled. A finite element modcl will be presented, together with a simple semi-analytical model based on the hinge element in combination with a simple plastic solution.
LINEAR ELASTIC SOLUTION
A circular disk with a diameter D acted upon by two equal and diametrically opposite forces P is a classical problem in elasticity. The state of stress in the plane of loading is uniform tension perpendicular to this plane [6], and the magnitude of these tensile stresses is c =2P/(nD). In the split cylinder test the loads are applied over a certain width (2a) as shown in Figure 1. This will affect the state of stress, and if it is assumed that the loads are distributed evenly over the loading strips, the tensile stress at the centre of the disk should be modified according to the following expression [ 7 ] :
In the case of the split cylinder test we have that P = PJL, where P, is the total load on the cylinder and L is the length of the cylinder. For a perfectly brittle material - disregarding the risk of a compressive failure - the ultimate load of the split cylinder is given by ( 2 ) with c =A, the uniaxial tensile strength. This load, PE , is referred to as the linear elastic splitting load.
IDEAL PLASTIC SOLUTION
An ideal rigid-plastic solution to the problem of the split cylinder test is presented by Nielsen [ 5 ] . Here concrete is modelled as a so-called modified Coulomb material with a sliding failure condition given by the angle of Friction 4 and the cohesion c. The sliding failure condition is overruled by a separation failure condition stating failure when the tensile stress reaches the uniaxial tensile strength. The solution is based on a failure mechanism with yield lines as shown in Figure I , Based on this mechanism and introducing the uniaxial compressive strengthh, the following optimal upper-bound solution to the load-carrying capacity of the cylinder is found:
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John Forbes OLESEN, Lennart 0STERGAARD and Henrik STANG
Figure 2: (a): Finite element mesh, 0=100 mm, a=5 mm. (b): Deformation plot. FEM IMPLEMENTATION One quarter of a cylinder is modelled by finite elements in a commercial programme environment, DIANA [S]. The elements are three-node triangular isoparametric plain strain elements (type T6EPS), and the mesh is shown in Figure 2a. It is assumed that a crack may develop in the vertical plane of symmetry; thus, interface elements (type LSF) are attached at the vertical face of the quarter cylinder. Symmetry boundary conditions are specified along the vertical and horizontal sections defining the quarter cylinder, i.e. deformations normal to these sections are suppressed. All vertical displacements of the nodes on the loaded horizontal surface of the loading strip are tied together to ensure synchrony. For concrete in solid elements the constitutive behaviour is described by a linear elastic model in combination with a Mohr-Coulomb yield criterion. The angle of friction for concrete is set to 37", and the cohesion is given by c =,fJ4, wheref, is the compressive strength. After crack initiation the normal relative deformation is governed by a bilinear stress-crack opening relationship as described by ( I ) . The FEM formulation of the split cylinder test constitutes a highly nonlinear problem with snap-back effects. The iterative scheme applied is based on the tangent stiffness matrix and the arc length method. The problem is solved under an adaptive load step control, and the convergence criterion is based on an energy norm. Figure 3a shows the results of a number of FE-calculations of the split cylinder test. The figure depicts load versus deformation. The load is noniialized with respect to the linear elastic load at crack initiation PE, and the deformation is the total compression of the specimen. Different materials are represented differing only by the value of the tension softening parameter a l . The remaining material parameters were kept constant at values representing a normal strength concrete:f; = 2 MPa, E = 30 GPa, a? = 0.2 mm-', b2 = 0.1. The softening parameter al describes the initial toughness ofthe material, and a value o f a l = 20 mm-' would apply to normal strength concrete. For large values of a i , i.e. al > 5 mm'l we observe snap back of the load deformation curve, for smaller values of a , , however, there is no snap back behaviour. All curves
47 1
Fracture mechariics and plasticity modelling of the split cylinder test
2.0
--1
P P , Iu
1 !, l
05
I
'
i
1
i !' I '
on i 11 0
no
~
02
U I
u [mm]
I1 1
-i no
-02
0.6
0-1 1:
08
10
[mm]
Figure 3: FE-results for normalized load versus specimen compression 11. shown in Figure 3a exhibit a behaviour where the first part is linear until a crack is initiated in the centre of the cylinder. This crack propagates towards the loading points as the load is increased, however, the crack also opens and as a consequence the crack bridging stresses decrease according to the stress-crack opening relationship, especially the a1 parameter. At some point the load reaches a maximum and subsequently drops while the crack opening continues. During crack opening redistribution of stresses in the whole specimen takes place, and at large crack openings the load is primarily canied through compression and bending of the almost separated semi-cylinders. The load carrying capacity at this stage is governed by the Mohr-Coulomb yield criterion, which is responsible for the second part of the load defomiation curve. After the load has dropped to this curve it increases again as the deformation increases. In the end the load approaches a constant yield level. The finite element load deformation curves are obtained by controlling the crack opening. However, split cylinder tests are normally performed in load control, thus only the ascending part of the curve may be obtained, i.e. only the first peak load is found from the test. On the other hand, if the test were deformation controlled with the compression 11 as the controlling parameter, the full load deformation curve could be obtained only for materials with a sufficiently low value ofthe softening parameter a t , ruling out the risk of snap-back. In Figure 2b the deformed finite element mesh is plotted at an extreme load step with extreme deformations for a1 = 20 nim-'. The figure illustrates the almost plane opening of the splitting crack, which, however, is prevented from penetrating all the way through the cylinder due to compressive stresses below the loading strip. Furthermore, it illustrates the plastic deformations in a region near the loading point. In Figure 3b finite element results for load deformation curves are shown for different values of the tensile softening parameter 62. The remaining material parameters have been kept constant atf;= 2 MPa, E = 30 GPa, a1 = 20 mm-' and a2 = 0.2 mm-I. The softening parameter b2 defines the level of the second part of the stress-crack opening curve, and is the one parameter, which is most directly influenced by the addition of fibres to concrete. The curve representing b2 = 0.1 is identical to the curve shown in Figure 3a representing CII = 20 mm-'. We note that bZ= 0.35 marks the point of transition kom a situation with a distinct peak preceding the plastic
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John Forbes OLESEN, Lennart 0STERGAARD and Henrik STANG
Figure 4: Geometry and loading of WST-specimen. Strut and tie model and hinge element. behaviour. Thus, for values of b2 < 0.35 the caRacity of the split cylinder test in load control is determined by the peak governed by the magnitude of a , , whereas the capacity for larger values of b2 is determined by the plastic yield capacity. SEMI-ANALYTICAL MODEL
A simple model has been developed for the analysis of the splitting of a cylinder. The model is based on the so-called nonlinear hinge model [4], which is an analytical solution to the crack propagation in a rectangular prismatic body due to moment and normal force loads. The model is based on the fictitious crack model with a bilinear tension softening curve. Another hndamental assumption of the hinge model is that it is modelled as independent incremental layers, thus neglecting the shear stiffiess of the hinge. The hinge solution is expressed in terms of the normalized angle of rotation B = $~hE/(:fi),where $O is the angle of rotation of the rigid boundary lines of the hinge, see Figure 4c, and where h is the height of the hinge, E is the elastic modulus and s is the length of the hinge. The hinge solution may be found in [4] and it furnishes the relative crack depth a =d/h and the normalized moment p = 6M&h2t) as functions of the relative normal force p = Nh/V;ht), where Mh and Nh are the hinge moment and normal forces, respectively, and d is the depth of the crack and I is the width of the hinge. The solution comprises four distinct phases, the elastic pre-crack phase and three cracked phases differing in how much ofthe softening curve that has been activated. The simple split cylinder model assumes that the state of stress in the cylinder caused by the diametrically opposite loads may be replaced by the strut and tie model shown in Figure 4a, where w denotes the strut inclination angle and z denotes the distance of the horizontal tie from the centre of the cylinder. Now the hinge element is incorporated in place of the horizontal tie, and the tie force is referred to the mid-height of the hinge producing a moment loading of the hinge. The loads are thus given by N = % f t a n q and M = N(%h-z). So far the simple split cylinder model has only considered one half of the cylinder. In order to model the cooperation of the two halves, an elastic interaction is ensured by a rotational spring counteracting the rotational deformation p o f the hinge. Equilibrium of the hinge and spring system requires that = M,,($o,N ) + K<$o
(4)
473
Fracture mechanics and plasticity modelling of the split cylinder test
where K, is the stiffness of the rotational spring. In nonnalized terms (4) reads
The value of k, may be established by comparison with FEM results. The strut inclination w is tuned such that crack initiation in the simple model coincides with the elastic solution, i.e. the load at which the elastic stress in the most stresses fibre of the hinge equalsf;, coincides with the load at which the elastic solution (2) produces o=J.Thus, the strut inclination wis given by
n Due to the coupling between the loads M and N and the nonlinearity of the hinge solution the equilibrium equation (5) must be solved iteratively. The parameters of the hinge model have been calibrated against finite element predictions of the peak load for different values of the softening parameter a1 ranging from 7.5 mm-l to 320 mm-l; all other parameters were kept constant at the following values:f; = 2 MPa, E = 30 GPa, a l =0.2 --I, 62 = 0.1, D = 100 mm, L = 200 mm and a = 5 mm. This calibration hmished the following values: z = 0, k,= 0.44 and s = 2 . 6 2 0 . In Figure 5a, results obtained with the simple hinge based model are compared with finite element results. The finite element results are equivalent to the results shown in Figure 3a except that the normalized load has been plotted versus the CMOD, i.e. the opening of the crack at the center of the cylinder. The hinge model does not take into account the limited compressive strength of the material, and the ideal plastic solution may be exceeded. However, later the
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---
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--- Plastic
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0.4
0.5
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0.1
0.2
0.3
0.4
CMOD [mm]
Figure 5: Split load vs. CMOD. Hinge solution with markers, compared with FE-solutions.
0.5
474
John Forbes OLESEN, Letinart 0STERGAARD and Henrik STANG
V
H I.o I
10
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*.
~~
I000
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, . ._ 0.2
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0.6
0.4
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Figure 6: Model results for the split load versus softening parameters a1 and b2, respectively. simple model is combined with the ideal plastic model, truncating the hinge solution by the plastic solution when appropriate. The comparison between the finite element and the simple model results show remarkable agreement considering the simplifications made. The simple model captures the initial behaviour and gives a good prediction of the peak load, however, the solution is truncated due to break down ofthe analytical expressions. In Figure 5b results obtained with the simple hinge based model are again compared with finite element results. In this case the finite element results are equivalent to the results shown in Figure 3b except that the normalized load has been plotted versus the crack opening at the center, CMOD. The same comments as given above apply here. The hinge model predicts the same initial behavior, however, it predicts a higher value of the b2 parameter corresponding to transition point mentioned in the previous section, namely a value of approximately 0.6. NUMERICAL STUDY A numerical study of the expected outcome of the split cylinder test has been performed applying the different methods covered in this paper. It has been assumed that the test is performed in load control, thus the expected maximum load P,,,,is taken as the first peak of the load deformation curve if a peak is predicted; if no peak is predicted then the ultimate load in the plastic region is taken. The influence of the material parameters al and bz is studied, as well as the influence of the cylinder diameter D and the width of the loading strip a. For this study the modulus of elasticity has been calculated from the empiric expression: E = lS,OOOJ, and the compressive strength has been calculated from the empiric expression:& = V; /0.35)2 with strength units in MPa. Figures 6 and 7 show the results of this study, with figure legends given by: Plastic refers to ideal rigid-plastic upper-bound limit given in (3), Hinge refers to the semi-analytical hinge based model, however, cut off by the ideal rigid-plastic upper-bound limit, Rocco et al. refers to the solution given in [9], note that this solution has limited range of applicability characterized by 0.4 2 2alDf;/E I 10, Tang refers to the solution given in [7], and FEM refers to the finite element model presented here. In Figure 6a the influence of n~ IS presented. High values of a1 correspond to brittle materials, low values to plastic materials, and intermediate values correspond to quasi-brittle materials. It is obvious &om the figure that the elastic solution only applies for high values of a , , and that the ideal plastic solution only applies for low values. The finite element results
475
Fracture mechanics and plasficity modelling of the split cylirrder fesf
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Figure 7: Model results for split load vs. D and rel. width of loading strip a/D, respectively. demonstrate the transition from brittle to plastic behaviour. The hinge model reproduces this transition nicely. Normal strength concrete is quasi-brittle material, and a1 = 20 nun-' is a representative value. From the results shown here it is obvious that the split cylinder test will overestimate the tensile strength of normal strength concrete. Figure 6b shows the influence of the sofening parameter b2. As mentioned earlier large values of bZ could be obtained if fibres are added to the concrete; the more fibres the larger the b2-value. We observe that for small values of b? there is no influence of this parameter. The reason for this is that the first peak of the load deformation curve has been reached before the second part of the bilinear stress-crack openins relationship is activated. For larger values of b2 the finite element load deformation curve does not exhibit a peak, see Figures 3b and 5b. In such cases the maximum load is given by the plastic yield level, which is affected by the magnitude of b2, therefore we observe a sudden jump From a constant level to an almost linear dependency. The FEM results exceed the upper-bound ideal rigid-plastic level, which is attributed to the fact that the FE-model includes the elastic deformations. The hinge based results exhibit a jump from the constant non-plastic level to the ideal rigid-plastic level, since, in the actual case, if the hinge solution does not exhibit a peak it will exceed the plastic level as may be seen from the load deformation curves. The size effect is demonstrated in Figure 7a for material parameters corresponding to normal strength concrete. We observe a transition from plastic behaviour to brittle as the size increases from small to large values. It is worth noting that the simple model is in good agreement with the FEM predictions. Finally, the influence of the width of the loading strip is presented in Figure 7b. The FEM results exhibit a transition from brittle behaviour to plastic behaviour as the relative strip width is increased from narrow to wide. For wide loading strips the FEM results exceed the ideal rigidplastic solution. Apart from the effects o f including the elastic deformations in the FE-model, this is attributed to the possible interaction between the stress fields in the two wedge-like regions below the loading points. The linear elastic influence given by Tang [7] is also shown, and it is seen to be negligible for the present material and geometry. The simple hinge model does not capture the effect o f strip width as predicted by the finite element model, this is due to the fact that the loads on the cylinder are modelled as point loads, although the effect by Tang [7] is incorporated.
476
fohn Forbes OLESEN, Lennart 0STERGAARD and Henrik STANG
CONCLUSION Two models have been developed for the analysis of the split cylinder test, a simple semianalytical and a finite element model. The simple model has been calibrated against FE-results, and it is demonstrated that this model captures the characteristic features of the behaviour of split cylinder tests. The failure of the split cylinder has been analysed by the two models. The failure is characterized by either being brittle, quasi-brittle or tough depending on material or geometrical parameters. When the failure is interpreted under the presumption that the test is executed in load control, then the brittle and quasi-brittle failure loads are fracture mechanics dominated, whereas the tough failure load is plasticity dominated. For tests in load control the failure mode exhibits a transition fkom plasticity dominated to fracture mechanics dominated when the tensile softening parameter a1 increases, the tensile softening parameter bz decreases, the cylinder diameter increases, or the width of the loading strip decreases, and all other parameters are kept at constant values. This transition is associated with a decrease in the peak load leading to a decrease of the apparent tensile strength based on the linear elastic stress distribution. The implications of this is that the split cylinder test may not predict the same tensile strength if one or more of the above parameters are changed, even though the true tensile strength has not been changed. However, for extreme values of the parameters the peak load is independent to changes in the magnitude, e.g. for large values of the diameter the peak load is independent of the magnitude of the diameter. In view of the above remarks the split cylinder test should be applied with great caution. Thus, the split cylinder test cannot be applied for the determination of the development of the tensile strength of early age concrete, since at early ages all material properties of concrete undergo significant changes. Also the split cylinder test cannot be applied directly for determining the tensile strength of fibre reinforced concrete, since the fibres will affect the tensile softening parameters. REFERENCES 1. Hillerborg, A., ModCer, M. & Peterson, P., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Res. 6(6), 1976, pp 773-782 2. Bstergaard, L., Olesen, J. F., Stang, H. & Lange, D. A., A simple and fast method for interpretation and inverse analysis of the wedge splitting test, J. Eng. Mech. Accepted, 2003 3. 0stergaard, L., Olesen, J. F. & Stang, H., Modelling Simultaneous Tensile and Compressive Failure Modes of the Split Cylinder Test, Proc. 14th Nordic Seminar on Comp. Mech., eds. L. Beldie, 0. Dahlblom, A. Olsson, N. S. Ottosen, G. Sandberg, Lund Univ. 2001, pp 193-196 4. Olesen, J. F., Fictitious Crack Propagation in Fiber-Reinforced Concrete Beams, Journal of Engineering Mechanics 127(3), 2001, pp 272-280 5 . Nielsen, M. P., Limit Analysis and Concrete Plasticity, 2"d edn, CRC Press, 1.999 6. Timoshenko, S. P. & Goodier, J. N., Theory of-Elasticity, 3rd edn, 1970 7. Tang, T., Effects of Load-Distributed Width on Split Tension of Unnotched and Notched Cylindrical Specimens, Journal of Testing and Evaluation, 22(5), 1994, pp 401-409 8. DIANA, DIANA Manual, 8'h edn, TNO Building and Construction Research, P.O.Box 49, 2600 AA Delft, The Netherlands, 2000 9. Rocco, C., Guinea, G. V., Planas, J. & Elices, M., Size effect and boundary conditions in the . Brazilian test: theoretical analysis, Materials and Structures, 32, 1999, pp 437-444
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H.Marshall, eds. Warsaw, October 13- 15. 2003 ZTWREK RSI and Woodhead Publ., Warsaw 2003
FATIGUE SENSITIVITY ANALYSIS FOR THE CURVED LAYERED COMPOSITE BEAM L. FIGIEL,M. K A M ~ ~ ~ S K I Institute of Polymer Research Dresden e.V. Hohe Strasse 6, 0 1069, Dresden, Germany, e-mail: [email protected] Faculty of Civil Engineering, Architecture and Environmental Engineering Technical University of t o d z Al. Politechniki 6, 93-590, todz, Poland, e-mail: [email protected] ABSTRACT Brittle layered materials and structures are used in many fields of engineering. The long-term behaviour of these materials and structures depend not only on service conditions but also material properties of layered components. The sensitivity analysis introduces a new aspect into optimisation of layered materials and structures against fatigue failure with respect to components’ material properties. Numerical sensitivity analysis of the fatigue life is performed here using the Finite Element Method (FEM) program and adopting such design parameters as Young’s moduli and the Poisson’s ratios of composite constituents as well as the interface friction coefficient. Keywords Brittle layered composites, fatigue interface crack propagation, parameter sensitivity of fatigue life, Finite Element Method
INTRODUCTION Layered composite materials and structures are used for many applications in, for example, microelectronics [ I ] , bioengineering [2] or structural engineering [3]. Fatigue interface cracking is the most frequent mode of fatigue failure in layered materials and structures resulting from long-term cyclic, quasi-static or dynamic, loading. At the same time, the initial interface defects can be the reason of fatigue failure of laminated or fiber-reinforced structures. The long-term structural integrity and durability, termed as fatigue performance. of brittle layered materials and structures depend on the service conditions such as cyclic mechanical loads, temperature, humidity etc. The material properties of layered components, such as, for example, the elastic constants, also influence a fatigue performance of the layered materials and structures. To the best knowledge of the authors, there has not been done much to understand the role of layered components’ material properties in fatigue performance of the layered materials and structures. Such an analysis can help to optimise layered composites against fatigue phenomenon by a modification of material properties as design variables. Thus, the sensitivity analysis [4,5] can introduce a new aspect in the understanding and
478
Lukusz FIGIEL und M. KrlMINSKI
preventing from fatigue phenomena - it can reveal the component material properties, which the most and least affect the long-term performance of layered materials or structures. The various numerical methods as for example the finite element method (FEM) [6] or boundary element method (BEM) [7] can be used for sensitivity studies to analyse the influence of material properties of layered components on the fatigue, in cases where no analytical solutions have yet been found or exist. That is why, the main objective of the present study is the numerical sensitivity analysis of the fatigue life with respect to the material properties of two component layered composite beam subjected to cyclic shear loading. The material properties as the Young's modulus and the Poisson's ratio of a single layer are considered as design parameters. Moreover, the fact that the shear loading is applied makes it possible to account for another design parameter as the interface friction coefficient. A combination of the FEM and the linear elastic fracture mechanics (LEFM) theory for interface cracks [8] is adopted in numerical studies. The nonlinear FEM analysis is carried out with the finite contact elements, implemented in program ANSYS [ 9 ] , to prevent crack surfaces overlapping and account for sliding dry friction between crack surfaces [LO]. It is assumed that delamination (or interface crack) propagation is the main mode of failure for analysed composite. Thus, the composite life span is identified through a loading cycles number necessary to reach a delamination size, at which fatigue failure takes place. Cycles number for a given delamination growth rate is calculated from the energy relation in terms of a power function. This procedure is repeated for different increments of studied material properties (Young's modulus, Poisson's ratio, friction coefficient) and then, the sensitivity gradients are calculated externally using the finite difference scheme [ S ] .
COMPUTATIONAL MODEL OF THE COMPOSITE The deformation of two-layer composite under plane stress is considered here in the framework of the finite elasticity theory. The body forces and inertia effects are neglected in this work. Each layer is linear elastic and isotropic and described by the Young's modulus E(") and the Poisson's ratio d"), where 'n' denotes the n-th layered component. Classical Dirichlet and Neumann boundary conditions hold on external edges of the composite. The minimum applied load is crm'n(aPP)=O, then the range of applied load is A~(aPP)=~mdx(aPP), and thus cycle asymmetry ratio is R=gmin(aPP)/crmax(app)=O. Two different conditions can occur behind the crack-tip along crack surfaces. These are (1) traction-free crack surfaces and ( 2 ) crack surfaces in sliding contact described by the classical Coulomb's law of dry friction as [ 101
where p is the sliding friction coefficient, that represents constant roughness along entire crack surfaces; ZT is the frictional stress, PN denotes the contact normal pressure; g stands here for the relative sliding velocity between contacting surfaces. It is assumed that the stress distribution at the interface ahead of the crack-tip at delamination length follows the oscillatory singularity [8]
Fatigue sensitivity analysis for the curved layered composite beam
479
where K"'" is the maximum complex stress intensity factor, which describes the magnitude of near-tip stresses; E is the elastic mismatch; r denotes the distance from the crack-tip; r, is the characteristic length [81. Analogously, the near tip displacements of crack surfaces behind the crack-tip are described as
where urnax =u?
+iuy
Then, the total maximum energy release rate is assumed to describe the fracture process at the interface. It is derived from the real and imaginary parts of the complex stress intensity factor as follows:
Furthermore, the classical exponential Paris-Erdogan law is adopted to describe the rate of fatigue delamination growth as
where a and p are the fatigue constant and exponent, respectively. These two variables are regarded as material constants that depend on many factors (e.g. material properties, temperature andor stress ratio, etc.) and their numerical values can vary on the experiments. The fatigue life is described as the cycles' number necessary for composite delamination with the interface crack propagating from its initial to the final length as follows:
where the initial length is identified here with the pre-crack length, aA, while the final is the total length of the interface, aT. The sensitivity gradients of fatigue cycles number with respect to design parameter p denoted by dN/dp are determined through the finite difference scheme from the following numerical scheme:
with aN&p denoting the sensitivity gradient of the entire composite fatigue life with respect to the design parameter p; Ap stands here for the design parameter perturbation. The following variational inequality is used to determine the FEM solution for the contact problem between two isotropic and linear elastic deformable bodies Q(") defined by the elasticity tensors C(")=C(")(En,Vn):
where 6v is the admissible virtual displacement; t denotes tractions on boundary r,. . As it can be expected, the final sensitivity gradients should strongly depend on the fatigue law adopted in the model. The application of Palmgren-Miner rule, for instance, eliminates any material dependent coefficients from the fatigue model. As a result, computational analysis analogous to that presented here would be quite sufficient for final conclusions whether fatigue cycles number does depend on some material characteristics of a specific composite component or it does not.
480
trrkasz FIGIEL and hf. KAMINSKI
NUMERICAL ANALYSIS AND RESULTS Curved boron/epoxy-7075 T6 composite specimen, which consists of two layers is shown in Fig. 1 and is the subject of computational analysis. One curved layer is made of boron-epoxy and is joined to an aluminium alloy layer 7075 T6, along a curved interface of constant curvature described by interface radius RO=5.25x102m. The mode of fatigue failure is by delamination propagation, thus initial edge interface crack of length a ~ = 5 . 5 x l 0 % -is1 introduced between layers. The total interface length is equal to a ~ = 1 . 8 3 ~ 1 0 - ~Both m . layered components are of the same thickness hl=hz=2.5~1O'~rn. Both materials are regarded as linear elastic and isotropic with properties collected in Table 1. The interface is a zero thickness layer with no assigned material properties. The initial interface friction coefficient is equal to p=O.O5. The fatigue exponent, p= LO, and the total energy release rate threshold, GT.,I,=IOOJ/~~, are taken from the literature [ 111. Then, the fatigue constant is calculated as a=1 ~ 1 0using . ~ ~the model reported in [ 121.
Figure I Curved layered composite beam Table 1 Input material properties in FEA [ l l ] Property BaronlEpoxy (BIEp) Aluminum 7075-T6 (Al) Young's modulus E [GPa] 207.0 70.8 Poisson's ratio Kirchoffs modulus
V
G [GPa]
0.21
0.33
85.5
26.6
Young's modulus and the Poisson's ratio of the boronlepoxy layer as well as the friction coefficient of crack surfaces are adopted here as the design variables. Their values from Table I are initial or original values. Three ranges of increments for design variables are considered in this work - the promiles, percents and tenths. It should be noted that although fatigue constant and the exponent in Eq ( 5 ) are material property dependent, however herein they are assumed not to change along with increment of design variables. This assumption is made due to the lack of relation between material properties and fatigue constant and exponent, which should be determined experimentally. Boundary conditions and loading profile are presented in Table 2 and Fig. 2, respectively. The circumferential edges AB and FG of the composite specimen (cf. Fig. 1) are supported in the radial direction, while AC is supported in the angular direction. The fatigue load omax(aPP) is applied to the specimen edge EG. This kind of shear loading configuration brings an opened zone close to the crack-tip and enables usage of the classical interface to the ~ edge ( ~ BE and ~ angular ~ ) supports to CF, LEFM theory. However, an application of o ~ ~
Fatigue sensitivit.v analysis for the curved layered composile beam
48 1
gives a closure of entire crack surfaces and requires non-classical LEFM theory, accounting for the friction dependent stress singularity to calculate a fracture parameter. Table 2 Boundaty conditions for FEM analysis Line Boundary conditions uR=O for Oe(OO,Or) and R=Ro+hl AB FG
uR=Ofor O ~ ( 0 0OT) , and R=Ro-h2
EG
Oe=$'ax(app' for O=O"
AC
ue=O for @=QT and RE( Ro, Ro+hl )
and R€(Ro, Ro-hz)
4
Cycles number N
Figure 2 Loading profile The FEM model of the composite consists of two different types of finite elements, as it is shown in Fig. 3. PLANE82 is eight node solid structural element that discretises the domains of both layers. The crack surfaces are discretized using three node finite contact elements' pairs: CONTA172 and TARGE169 that discretise lower and upper crack surfaces, respectively. Contact element pairs prevent overlapping of crack surfaces and make it possible simulation of sliding friction between crack surfaces. The finite element mesh is designed in such a way that the number of contact elements' pairs exhibits a variability from 42 (aA=5.5x10'3m)to 94 (a=1.74xlO"m). The total number of solid elements is equal to 2224, while the node number is 17760. Special attention is focused on the design of the crack-tip mesh to simulate singular stress behaviour. The first row of finite elements around the cracktip consists of sixteen PLANES2 elements modified to the triangular shapes with quarterpoint rnidside nodes. Solid finite elements: PLANE82
Figure 3 The,finite e l c m c r i r model of the layered c'otiiposite Numerical problem is nonlinear due to contact with friction. since the contact or contact-free zones are not known a priori. That is why, the Newton-Iiaphson iterative and incremental technique implemented in ANSYS is used. Then, the penalty combined with
482
tukasz FlGlEL and M.KAMlfiSKI
Lagrangian multipliers algorithm is used here, to compute contact constraints, to prevent crack surfaces overlapping. Additional numerical tools as predictor-corrector or line-search options are used to enhance solution convergence. The integration of the constitutive friction law is carried out through the radial return algorithm, implemented in the program ANSYS. The problem of fatigue life calculation is a series of static solutions for stresses, displacements for each delamination length and value of design variable. Then, the energy release rate is calculated, as a function of delamination length, from the near-tip stress fields through the extrapolation of the real and imaginary parts of the complex stress intensity factor. The nodal stresses directly at the crack-tip are not accounted for the calculation of C T ! due to two main reasons - they are infinite at the crack-tip and they exhibit oscillatory behavior close to the crack-tip. Outside of this oscillation zone, the stresses obtained from the FEM and analytical solution show good agreement, as it is reported in [13], that makes possible calculation of the total interface energy release rate. The analytical and the FEM stresses diverge from each other at the position, where contact occurs between crack surfaces. Then, it is possible to calculate number of cycles Ni,, corresponding to the total ~ delamination growth Aa=&+l-q.The cumulative number interface energy release rate G T and of cycles and delamination growth results in fatigue delamination growth curves for different increments of design parameters. The sensitivity gradients of cumulative number of cycles are calculated from Eq (7) with respect to three different design variables’ increments, and are shown in Figs. 4-6. The numerous experiments result from the Fact that, particular values of sensitivity gradients of the fatigue life depend on the perturbation of a given parameter.
Figure 4 Sensitiviv coefficients of,fatigue cycles number w. r.t. the friction coefficient As it is presented in Figs. 4-6, the sensitivity gradients smoothly converge through the entire delamination growth to the constant values denoting the sensitivity coefficients of the composite fatigue life with respect to the particular design parameter. The best numerical stability is obtained in case of partial derivatives with respect to the interface friction coefficient - for various perturbation orders the results are closed each other. Different situation takes place in case of the sensitivity coefficients related to composite material parameters - perturbation order has some influence on the gradients computed final values, cf. Figs. 5-6, which needs further computational verification. Observing particular results of the computational analysis it can be noticed that sensitivity gradients resulting from the Young’s modulus and the Poisson’s ratio are negative, which means that an increase of elastic constant characteristics of the borodepoxy results in the decrease of the fatigue life. Contrarily, the positive sign of the fatigue life sensitivity gradient with respect to the friction coefficient is equivalent to an increase of the fatigue life.
483
Fatigue sensitivity analysisfor the curved layered composite beam
2
6
4
10
8
12
Delamination growth, a[m]x102
Figure 5 Sensitivity coeficients of fatigue cycles number w.r.t. Young modulus Ei r--
---
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Figure 6 Sensitivity coeficients of fatigue cycles number w.r.t. the Poisson ratio V I It is necessary to undertake analogous study for the elastic constants of aluminum component to fully assess the fatigue life sensitivity to components’ material properties. The main drawback of the analysis is an assumption of the lack of correlation between fatigue constants and components’ material properties - such a relation can be only chacked through the experimental tests. However, it is still possible and necessary to analyse computationally the fatigue life sensitivity with respect to fatigue constant a and fatigue exponent p having no correlation with the elastic constants. As it was mentioned above, this problem is strongly connected with the fatigue law describing the composite behavior - in case of the PalmgrenMiner rule for instance, this problem does not appear in the analysis.
CONCLUSIONS 1. The present study dealt with the sensitivity analysis of the fatigue delamination growth in a two-component layered composite beam (borodepoxy-aluminum) under cyclic shear loading. The sensitivity gradients were calculated and analysed with respect to the Young’s modulus and Poisson’s ratio of the borodepoxy component as well as the interface friction coefficient. The results show that the fatigue life can be reduced by an increase of the boron/epoxy (stronger) layer elastic characteristics, while it becomes longer together with increasing friction coefficient. Thus, if one considers maximisation of the fatigue life of analysed
484
Lukusz FIGIEL and 121. KAMINSU
composite, then the contrast between the Young’s moduli of both layers should tend to 1. On the other hand, if one considers statistical scatter effects from specimen-to-specimen, then the Young’s modulus should be chosen as random variable or process for further numerical probabilistic analysis [ 141. 2. From the physical point of view, the main drawback of the present approach is lack of correlation between elastic constants, friction coefficient and the fatigue constant and exponent from the law of fatigue delamination growth. This can be only corrected experimentally or by highly reliable simulation of the fatigue delamination growth. Further research should focus on the computation of the fatigue life sensitivity gradients with respect to the elastic constants of aluminum and with respect to the fatigue theory constant and exponent. 3. The present approach can be relatively easily extended to include anisotropic properties of layers, and calculate the sensitivity gradients with respect to more than two elastic constants. Another interesting extension could perhaps be the incorporation of thermal effects generated by the friction phenomena as well as the contacting surfaces wetting and/or lubrication into the computational model. This could also bring new design variables, such as for example the coefficient of thermal expansion, to study the fatigue life sensitivity. REFERENCES
1. Kook, S.Y., Snodgrass, J.M., Kirtikar, A., Dauskardt, R.H., Adhesion and Reliability of Polyrner/Inorganic Interfaces. Trans. ASME 120, 1998, pp 328-335. 2. Ramakrishna, S., Mayer, J., Wintermantel, E., Leong, K.M., Biomedical applications of polymer-composite materials: a review. Composites Science and Technology 6 I, 2001, pp 1 189- 1224. 3. Reifsnider, K.L., editor. Fatigue of Composite Materials. Elsevier Publishers, 199I. 4. Haug H.J., Choi K.K., Komkov V., Design sensitivity analysis of structural systems. Orlando, Academic Press, 1986. 5. Karninski, M., Sensitivity analysis of homogenized characteristics for some elastic composites. Comp Meth Appl Mech Eng 192(16-18), 2003, pp 1973-2005. 6. Zienkiewicz, O.C., Taylor, R.L., The finite element method. McGraw-Hill, 5th edition. 2000. 7. Brebbia, C., Telles, J.C.F., Wrobel, L.C., Boundary element techniques. Berlin: SpringerVerlag; 1984. 8. Hutchinson, J.W.. Suo, Z., Mixed Mode Cracking in Layered Materials. Advances of Applied Mechanics 29, 1990, pp 63-191. 9. ANSYS User’sManual. ANSYS, Inc., Southpointe, Canonsburg, 2002. 10. Wriggers, P., Computational Contact Mechanics. Wiley & Sons, 2002. 11. Johnson, W.S., Butkus, L.M., Valentin, R.V., Applications of fracture mechanics to the durability of bonded composite joints. Report DOT/FANAR-97/56. NTIS Springfield, Virginia, 1998. 12. SchOn, J., A model of fatigue delamination in composites. Comp Sci Techn 60, 2000, pp 553-558. 13. Figiel, t.,Kamihski, M., Lauke, B., Analysis of a compressive shear fracture test for curved interfaces in layered composites. Eng Fract Mech, in press. 14. Kaminski, M., On probabilistic fatigue models for composite materials. Int J Fatigue 24(2-4), 2002, pp 477-495.
Proc. Int. S y i p . ,,Brittle Matrix Composites 7" A.M. Brandt. V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodliead Publ.. Warsaw 2003
DURABILITY OF NEW POLYMER MORTAR USING WASTE EXPANDED POLYSTYRENE SOLUTION Nakwoon CHOI Research Center of Industrial Technology Chonbuk National University Deokjin Jeonju 561-756, Korea, e-mail: [email protected] Yoshihiko OHAMA College of Engineering, Nihon University Koriyama, Fukushima-ken, 963-8642 Japan, e-mail: [email protected]
ABSTRACT New polymer mortar using waste expanded polystyrene (EPS) solution-based binders has been developed as an effective recycling method of EPS. The polymer mortar has almost the same properties as conventional polyester mortar or polymethyl methacrylate mortar in working life and mechanical properties such as flexural and compressive strengths, and elastic modulus. In the present study, the durability of a polymer mortar using an EPS solution based-binder is investigated. A styrene solution of EPS is prepared by dissolving EPS in styrene at an EPS concentration of 40%. The binder for the polymer mortar is made by mixing the EPS solution with a crosslinking agent, a coupling agent, a promoter and an initiator. The polymer mortar using the EPS solution-based binder is prepared with the selected mix proportion of the binder: filler (ground calcium carbonate): silica sand=l8.0: 16.4:65.6 (by mass), and tested for temperature dependence of compressive strength, water resistance, hot water (60, 80 and 100°C) resistance and chemical resistance. As a result, the compressive strength of the polymer mortar is linearly decreased with raising test temperature within the test temperature range of 0 to 100°C. The polymer mortar has excellent water resistance, hot water resistance and chemical resistance excepting organic solvent. Keywords Waste expanded polystyrene, styrene, polymer mortar, durability.
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A! CHOland Y. OHAMA
INTRODUCTION Expanded polystyrene is currently used as a popular packaging or insulating material in various industrial fields in the world'). A large quantity of expanded polystyrene is consumed, and is disposed as a waste. the effective recycling countemeasures against the waste expanded polystyrene are strongly requested2).In this paper, a new polymer mortar3)using the styrene solution of the waste expanded polystyrene as an effective recycling system for the waste expanded polystyrene is prepared, and the durability of the polymer mortar is investigated.
MATERIALS Materials for binder systems The expanded polystyrene (EPS) (density, 17kg/m3), specified in JIS A 951 1 (Preformed cellular plastics thermal insulation materials), was used as a model of waste EPS. The properties of EPS for a binder are given in Table 1. The styrene for industrial use, specified in JIS K 6727 (Styrene), was employed not only as a solvent to dissolve EPS but also as a binder for a polymer mortar. Trimethylolpropane himethacrylate (TMPTMA) and ymethacryloxypropyl- trimethoxy silane (silane) were used as a crosslinking agent and a coupling agent, respectively. Fifty% dicyclohexyl phthalate powder of benzoyl peroxide (BPO) was used as an initiator, and N,N-dimethyl-p-toluidine(DMT) done as a promoter. The properties of the monomers for the binder are shown in Table 2.
Molecular weight (g)
ca. 300000
Table 1 Physical properties of EPS. Density Thermal conductivity Compressive strength (kdm3) [ W m . K)1 V/cm2) 17 0.040 10
Table 2 Properties of monomers for binder. Molecular weight Density Type of monomer (~OOC, g/dm3) (g, Styrene 104.1 0.91 TMPTMA 338.4 1.06
Purity (%j
99.8 97.3
Filler and fine aggregates Commercially available ground calcium carbonate (size; 2.5pm or finer) was used as a filler, and commercial silica sands No.26 (size; 425-850pm) and No. 100 (size; 106-121pm) prescribed in JIS G 5901 (Molding silica sand) were done as fine aggregates. The water contents of the filler and fine aggregates were controlled to be less than 0.1% by heat drying at 105°C for 48h. The properties of the filler and fine aggregates are shown in Table 3.
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Durability of new polymer mortar using waste expanded polystyrene solution
Table 3 Properties of filler and fine aggregates. Size Density Water content Organic Type of filler or fine aggregate (pm) (~OOC g/cm’) , impurities Ground calcium carbonate < 2.5 2.10 < 0.1 Nil < 0.1 Nil Silica sand No26 425-850 2.63 < 0.1 Nil Silica sand No.100 106-121 2.61 TESTING PROCEDURES Preparation of liquid resin and binder A waste EPS solution with a waste EPS concentration of 40% was prepared by dissolving EPS in styrene at about 70°C in a stainless steel vessel. A liquid resin for a polymer mortar was prepared by mixing TMPTMA with the waste EPS solution. The binder for the polymer mortar was prepared by mixing a coupling agent, an initiator and a promoter with the liquid resin according to the binder formulations given in Table 4.
EPS
Table 4 Formulations of binder for polymer mortar. Formulations (YO) Liauid resin Silane BPO Styrene TMPTMA Inhr*\
32 4s 20 Note, *: parts per hundred parts of resin.
0.50
2.00
DMT lnhrl
0.25
Preparation of polymer mortar A polymer mortar using the binder as shown in Table 4 was mixed with the mix proportions as given in Table 5 at 20°C and 60% (RH) according to JIS A 1181 (Method of making polyester resin concrete specimens). Table 5 Mix proportions of polymer mortar. Mix proportions (YO) Filler: Silica sand No.26: Filler Silica sand Silica sand No.100 Binder (by mass) Ground calcium carbonate No.26 No. 100 18.0 16.4 49.2 16.4 1:3:1
Preparation of specimens Cylindrical specimens +SOXlOOmm for temperature dependence (of compressive strength), water resistance, hot water resistance and chemical resistance tests were molded with a fresh polymer mortar in accordance with JIS A 1 l S l . After molding, the cylindrical specimens were subjected to a 24h-2OoC-60Yo (RH)-dry+l Sh-70°C-heat cure. Fig. 1 represents the process for making specimens from the polymer mortar using the EPS solution-based binder.
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Test on temperature dependence of compressive strength The compressive strength test of the cylindrical specimens conditioned at constant temperatures of 0, 20,40, 60 and 100°C was performed according to JIS A 1182 (Method of test for compressive strength of polyester resin concrete). The relative
YYY LLLL-0 Filler
aggre-
aggre-
1
Dry mixing
n Fig.1 Process for making specimens of polymer mortar using waste EPS solution-based binder. compressive strength of the specimens was calculated by the following equation (1): Relative compressive strength ('YO) = (aJa20) x 100
(1)
where a, is compressive strength (MPa) of the specimens at the respective temperatures, and a20 is compressive strength (MPa) of the specimens at a temperature of 20°C. Water and hot water resistance tests Cylindrical specimens were immersed in water at 20, 60, 80 and 100°C for 28d. The water absorption or mass change of the specimens at water immersion periods of 7, 14, 21 and 28d was measured, and the compressive strength tests of the specimens before and after 28-d water immersion were carried out at a test temperature of 2OOC. The mass change and relative compressive strength of the specimens were calculated by the following equations (2) and (3): Water absorption or mass change ('YO) = ((Mn-Mo)/Mo} x 100 (2)
489
Durability of new pdvmer mortar using waste espanded polystyrene solution
where Mo is mass (8) of the specimens before water or hot water immersion, and M is mass (9) of the specimens after water or hot water immersion. Relative compressive strength (“h) =
(o28/Uo) x
100
(3)
where o0 is compressive strength (MPa) of the specimens before water or hot water immersion, and u28 is compressive strength (MPa) of the specimens after 28-d water or hot water immersion. At the same time, the visual inspection of the specimens before and after 28-d water and hot water immersion was carried out. Chemical resistance test Cylindrical specimens were immersed in chemical agents of 20%HCI, 20%H~S04, 20%CH3COOH, 45%NaOH, Sat. NaCI, acetone and kerosene for 28d. The mass change of the specimens at water immersion periods of 7, 14, 21 and 28d were measured, and the compressive strength tests of the specimens before and after 28-d chemical agent immersion were conducted at a test temperature of 20°C. The mass change and relative compressive strength of the specimens were calculated by the following equations (4) and (5):
Mass change (%) = ((Xl-&)/Xo}
x
100
(4)
where & is mass (g) of the specimens before chemical agent immersion, and X I is mass (9) of the specimens after chemical agent immersion. Relative compressive strength (“h)= (ul/ao)
x 100
(5)
where uo is compressive strength (MPa) of the specimens before water and hot water immersion, and U Iis compressive strength (MPa) of the specimens after 28-d chemical agent immersion.
TEST RESULTS AND DISCUSSION Fig.2 illustrates the test temperature vs. compressive strength of a polymer mortar using a waste EPS solution-based binder. The polymer mortar has temperature dependence that the compressive strength is linearly decreased with increasing test temperature. There are reliable relationships between the test temperature and compressive strength, and between the test temperature and relative compressive strength of the polymer mortar. The empirical equations of the correlations are also expressed in Fig. 2. Fig.3 shows the water immersion vs. water absorption of a polymer mortar using a waste EPS solution-based binder. The water absorption of the polymer mortar increases with increasing water immersion peirod, and becomes nearly constant at a water immersion period of 14d. The water absorption at 14d is 0.23%. There are no swelling, discoloration or any other appearance change of the polymer mortar after 28-d water immersion.
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N. CHOI and Y. OHAMA
I
0 50 100 Test temperature (“C), T
3
Fig.2 Test temperature vs. compressive strength and relative compressive strength of polymer mortar using waste EPS solution-based binder. Note, y: correlation coefficient. Fig.4 gives the compressive strength and relative compressive strength of a polymer mortar using a waste EPS solution-based binder before and after 28-d water immersion at 2OoC. The relative compressive strength of the polymer mortar after 28-d water immersion is about 98%, and the strength reduction of the polymer mortar is hardly recognized. Fig.5 represents the hot water immersion period vs. mass change of a polymer mortar using a waste EPS solution-based binder. In spite of the hot water temperature, the mass change of the polymer mortar increases with additional hot water immersion period, and becomes nearly constant at a hot water immersion period of 7d. The 7-d mass change is approximately 0.10%. Their appearance changes such as surface-cracking, pitting and softening, excepting a little discoloration were hardly recognized. Fig.6 exihibits the compressive strength and relative compressive strength of a polymer mortar using a waste EPS solution-based binder before and after 28-d hot water immersion at temperatures of 60, 80 and 100°C. The relative compressive strengths of the polymer mortar after 28-d hot water immersion at temperatures of 60, 80 and 100°C are 105, 99 and 98%, respectively. The polymer mortar using the waste EPS solution-based binder has excellent hot water resistance because the polystyrene has no ester linkage and the matrix of the polymer mortar is crosslinked by TMPTMA. The hot water resistance of the polymer mortar is superior to that of conventional polyester mortar and polymethyl methacrylate mortar4’. Fig.7 shows the mass change of a polymer mortar using a waste EPS solution-based binder during immersion in various test solutions. The mass loss of the polymer mortar after immersion in 20% HCI and 20% CH3COOH solutions is decreased with increasing immersion period. It is observed that the
49 1
Durability of new polymer mortar using waste expanded polystyrene solution
-2
100.0
z
100
;
5 70.0 60.0 2 50.0
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;.
g
40.0
;
30.0 20.0
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0
10.0 0.0
'Beforewater I After water' immersion immersion
10 15 20 25 30
Water immersion period (d)
8
90 9 80 70 $, 60 50
90.0 80.0
40
g
30 20 10
:.
8
= Ad CI
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Fig.3 Water immersion period vs. Fig.4 Compressive strength and relative water absorption of polymer compressive strength of polymer mortar using waste EPS mortar using waste EPS solutionsoluton-based binder. based binder before and after 28-d water immersion at 20Oc.
OSO 0.40
... :........... ;.... ........
;;;IOO.O 90.0 80.0 70.0
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$ 40.0 & 30.0 20.0
0
10.0 0.0 ..
Hot water immersion period (d)
-
'ater
Fig.5 Hot water immersion period Fig.6 Compressive strength and relative vs. mass change of polymer compressive strength of polymer mortar using waste EPS EPS mortar using waste solution-based binder. solution-based binder before and after 28-d hot water immersion.
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N. CHOlancl Y. OHAMA
Immersion period (d)
h
s
v
0.00
% I
s s
'
3 -0.50
h
s
1
20%HCI
-1.00
L 2 0 % CH3COOH
0.50 r I
v
0.00
5
I 10 I S 20 25 30 Immersion period (d)
5
m
-c
10 15 20 25 30 Immersion period (d)
2 -0.50 d
-1.00 L45%NaOH
s
o.50
0
2 -0.50
2
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-
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t
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_D
F
5
10 15 20 25 30 Immersion period (d)
-$ 2
Immersion period (d) -0.50
Sat. NaCl ___
5
10 15 20 25 30 Immersion period (d)
Fig.7 Mass change of polymer mortar using waste EPS solution-based binder during immersion in various test solutions.
ground calcium carbonate in the polymer mortar is transformed into water-soluble calcium chloride and calcium acetate, respectively by the reactions with HCI and CH3COOH. The
493
Dtirability of new polymer. inortar using waste expanded polystyrene solution
mass gain of the polymer mortar after immersion in 20% HzS04, 45% NaOH, Sat. NaCl solutions and kerosene is increased with increasing immersion period. Fig.8 illustrates the compressive strength and relative compressive strength of a polymer mortar using a waste EPS solution-based binder after immersion in test solutions for 28d. Except for acetone, the strength reduction of the polymer mortar by 28-d immersion in any test solutions is within 5.0%. and the polymer mortar has excellent chemical resistance.
90 80
8
%
70
60
,g k Y)
50
y,
40 u
30 .$
-2 m
20 10
0 .O% LO% 45% rosene Before r S 0 4 CHCOOH NaOH NaCl immersion Fig.8 Compressive strength of polymer mortar with waste EPS solution-based binder after immersion in test solutions for 28d. '
CONCLUSIONS ( I ) A polymer mortar using a waste EPS solution-based binder has a temperature dependence that the compressive strength is almost linearly decreased with increasing test temperature in the range of 0 to 100°C. A reliable emprical equation of the correlation between the test temperature and compressive strength can be proposed. (2) The water absorption and relative compressive strength of a polymer mortar using a waste EPS solution-based binder after 28-d 20°C water immersion are 0.23% and 98%, respectively. (3) The relative compressive strengths of a polymer mortar using a waste EPS solution-based binder after 28-d hot water immersion at temperatures of 60, 80 and 100°C are 105, 99 and 98%, respectively. The polymer mortar has excellent hot water resistance, and it is one of superior points compared with conventional polyester mortar and polymethyl methacrylate mortar. (4) Except for acetone, the strength reduction of a polymer mortar using a waste EPS solution-based binder by 28-d immersion in 20% HCI, 20% HzS04,20% CH,COOH, 45%
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NaOH, Sat. NaCl solutions and kerosene is within 5.0%, and the polymer mortar has excellent chemical resistance.
REFERENCES 1. EPS International Web Site, Recycle, Available at: http://www.epsrecycling.org/recycling/index. hhnl, Accessed Jan. 15, 2003 2. Noguchi, T., Inagaki, Y . , Miyashita, H., A New Recycling System for Expanded Polystyrene Using a Natural Solvent. Part 2. Development of a Prototype Production System, Journal of Packaging Technology and Science, Vol.11, No.29, 1998, pp.29-37 3. Ohama, Y . , Choi, N.W., Properties of Polymer Mortars Using Waste Expanded Polystyrene Solutions, Proceedings of the International Conference on Polymer Concretes, Mortars and Asphalts, University of Porto, Porto, Portugal, Oct. 2002, pp. 161-173 4. Kukacka, L.E., Polymer Concrete Materials for Use in Geothermal Energy Process, Proceedings of the Second International Congress on Polymers in Concrete, The University of Texas at Austin, Austin, U.S.A., Oct. 1978, pp.152-172
Proc. Int. Symp. Brittle Matrix Composites 7 *’ A.M. Brandt. KC. Li and I. H.Marshall. edr. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003 ))
APPLICATION OF EXPERIMENTAL-STATISTICAL MODELING TO EVALUATE [NFLUENCE OF AMOUNT AND GRADING OF SAND AND REGIMES OF BURNING UPON COMPRESSIVE STRENGTH AND WATER ABSORBABILITY OF BUILDING CERAMICS Beata BACKIEL-BRZOZOWSKA Chair of Building Engineering and Prefabrication Bialystok Technical University Wiejska 45E Street, 15-351 Bialystok, Poland, e-mail: [email protected]
ABSTRACT Procedure of formulating two experimental-statistical models of high level of complexity is discussed in this work. Their multiplicative form has been developed. These models allow to determinate the amount and grain size of weakening admixture in the form of sand and they also allow to determinate parameters of thermal treatment of ceramic mix for which required values of compressive strength and water absorbability are obtained. Original combined experimental design has been chosen to evaluate parameters of these models. Evaluation of experimental error which is necessary to evaluate adequacy of models and statistical significance of input parameters (coefficients) is discussed in this paper. Building ceramics is characterized by different features which depend on components of ceramic mix and ways of its mechanical and thermal treatment. This treatment decides of stone - like features of ceramics. High level of complexity of dependent physical, chemical and physic0 -chemical phenomena which occur in ceramic mix during burning makes it difficult to construct proper analytical theory which would enable to determine components of ceramic mix and parameters of thermal treatment in order to obtain product of required characteristics. In the given case there is a need to obtain calculation dependence of empiric or quasiempiric character. As a results of experiments the known effects of temperature and components, and the effects not described in literature have been obtained as well. Among these unknown, combined effects of grain size of wakening admixture, its amount in ceramic mix and burning temperature upon considered features should be mentioned. Keywords Building ceramics, experimental-statistical models, compressive strength, water absorbability.
INTRODUCTION The final and most important parameter in ceramic technology is burning. As a result of burning the structure and properties of ceramic material, which decide of possibility to apply the material to particular products, are formed. The main technological features of ceramic products depend to great extent on composition of ceramic mix and parameters of burning. Quantitative description of these dependencies would allow to solve in easy way problems related to production of goods with desired properties. Because of the great degree of complexity of physical, chemical and physico-chemical processes occurring in ceramic mix
496
Beata BACKIEL-BRZOZOWSKA
during burning in high-temperature high-conducting furnace aggregates, the level of mathematical description of accumulated knowledge is low. It results in very complex hypothesis about character of searched dependencies formed during solving the specific problem on the base o f existing physico-chemical knowledge. Experimental data are used in order to evaluate unknown parameters of dependencies. In technological investigation it is usehi to present these dependencies in the form of polynomial models. The coefficients of these models are determined on the base of specially planned test results. Deep knowledge not only about the tested object but mathematical theory of experimental design as well is required in order to formulate such models. This paper reports development of polynomial models which allow to evaluate quantitatively the influence of quartz sand in ceramic mix (amount and grading) interacting with parameters of burning upon compressive strength and water absorption of wall ceramics. The aim of the first investigation was to determine the influence of sand grading upon tested ceramic features. Nevertheless that sand has been used in ceramic technology for thousands of years, the proper attention has not been paid to it.
CHARACTERISTIC OF TESTED OBJECT The test was conducted in laboratory conditions on cubic specimens (125 cm') wet-moulded from plastic mix using press. The moulding mix consisted of plastic clay from Ceramic Factory "Lewkowo" and local river sand. It was fusible clay of melting point (fusion temperature) about 1200°C and sintering range 50-60°C. It is used for wall ceramics production. It mostly contains the finest fraction - grains smaller than 10 pm make up 88% of its total mass and grains smaller than 2 pm 50 to 60%. The specific surface of dry clay is 128 m2/g. The main clay mineral is illite (hydromica), which is accompanied by minerals belonging to chlorite and montmorillonite group or laminar minerals (illite-montmorillonite). The chemical composition of clay in the form of percentage of oxides is following: Si02 - 4648%; A1203 - 14-17%; Fez03 +FeO - 6,l-7,4%;CaO - 9-10%; MgO - 3,6-4,1%;K20+ Na20 - 3,8-4,6%.Roasting weight loss is 12.5-13.1%.Amount of free quartz (SiOz) is about 10%. The clay should be susceptible to swelling during burning according to [ 1,2] because the main clay mineral is hydromica, the finest grains make up majority in grain size distribution, there is high content of Fe203+FeO and K20+Na20 and low content of free Si02 and high roasting weight loss. During heating of hydromica clay, at the end of dehydration process, when incomplete burning of organic intrusions at 700°C takes place, small stains of liquid phase are formed between illite laminas. Formation of liquid phase in crystal lattice of hydromica is explained by presence of potassium, magnesium and ferric ions. Illite-like structure preserves its feature during heating up to 1000°C temperature and then when temperature reaches I1OO"C ferric and magnesium spinels are formed and further precipitation of liquid phase (or liquid-like phase) takes place [1,3].With increase of temperature up to 1200°C spinel may disappear or pass to mullite. This description presents the character of main changes occurring in clay and hydromica during burning. The correcting admixture in the form of quartz sand (containing approximately 0.3% of very small marl grains) has been introduced in order to regulate technical properties of clay. The majority (96%) of sand grains is in the range from 0.06 to Imm. The shape of grains is spherical. Approximately 67% of these grains is in the range from 0.25 to lmm. This sand is qualified as medium-graded sand according to [4].Unfortunately, there is no unity of options about desired grain size distribution of sand in literature. According to Awgustnik [ I ] it is advisable to apply medium-graded sand (0.25-0.5mm), but according to Rogowy [2] - coarsegraded sand (0.5-2mm). However, both authors agree that dusty sands can not be used in building ceramics.
Application of experiinental - statistical inodeling to evaluate influence of ainount and ...
497
CHOICE OF MATHEMATICAL MODEL AND EXPERIMENTAL DESIGN The main features of ceramic materials are determined to great extent by phase composition and porous structure, which is formed as a result of complex and often unidentified processes occurring in ceramic mix during burning. Quartz sand plays particular role in all these processes. It has been stated in [j] that coarse quartz grains can not react during heating and after burning quartz is partially not changed. Very fine quartz grains react in whole and they are a part of liquid phase. The author of work [6] also noticed that crystalline silica grains do not take part in forming liquid phase and they only undergo polymorphic transformation. According to [3] shrinkage of quartz related to volume changes during phase transition is so great that quartz grains remain separated from liquid phase. Probably that is the reason why decrease ofs compressive strength and increase of porosity of ceramic products are observed. Such unclear description of effects of above phenomena allows to formulate only some of premise, which should be considered while selecting mathematical models connecting in a quantitative way material features with amount and grading of sand in interaction with burning parameters. The number of input quantities (independent quantities) and scale (the level of variation of tested factors), which are the base of experimental design, should be established before selection of mathematical model. It has been assumed that the burning process is characterized by two factors: X I maximum burning temperature, Xz - duration of burning in the maximum temperature. As it is known, relation between ceramic properties and burning regimes is not linear. That is why parabolic dependency has been used. Factors XI and X2 varied on three levels (lower, medium and upper): 900, 990, 1090°C (XI); 1; 2; 3 hours (Xz).At the same time the rate of increasing and decreasing the temperature was constant (3"C/min). The total duration of burning was 10.8; 12.5 and 14.2 hours respectively. The third variable was the content of sand in ceramic mix: 5; 10; 15% (by weight). Sand was composed from three fractions: fine-graded Z I (grains up to 0.25 mm), medium-graded (0.25-O.5mm) and coarse-graded (0.5-1 .Omin). The condition CZ,= I was satisfied at variation of grain-size (mass) factors ZI, ZZand Z3. Dependency of each of two tested features f k , k=1,2 on technological factors X I , Xz and X3 was described by second order polynomial: 2x IXZ+ b 1 3I ~~ 3 bz,xzx3+bl + Ix iZ+ bzzx;+ fk=bo+blx 1+bzxz+b3~3+bl
X -990 L x I 90 ; X 2 = x l - 2 where:
X)
b33~3~,
(1)
X,-15
=-
. 10 are coded (non dimension) factors, which have equal levels in experimental design: -1 (lower), 0 (medium), 1 (upper); XI is a natural value of input quantity. All coefficients of polynomial ( I ) are functions dependent on grain-size factors Z, and they are described by reduced (incomplete) third order polynomial: b(0. ,,
,,,, , , = P I ~ IPzZZ+ + P ~ Z ~ + P I Z Z I PZ IZ~+Z I Z ~ +
PZ3zZz3+
PIZ~ZIZZZ (i,j=1, ~ , 2,3; b,, i<j). (2)
It was expected that the accepted model (I), (2) should reflect all complex interactions between grain-size factors Z, and technological factors XI. In [7] that type of model was used to describe sorption humidity (water content) in ceramic brick and hardened cement mortar containing three types of salts. Literature gives also other examples of application of this model [8]. Composition and symmetrical experimental design containing 14 samples with different coded values of input quantity X, [9] was used in order to obtain experimental data necessary
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t?eata BACKIEL-BRZOZOWSKA
to evaluate coefficients of polynomial (1). Each point of this design was repeated seven times at different proportions of three sand fractions Z,. These proportions were prepared according to simplex Scheffe’s design, which is commonly used at experimental design of “composition-feature’’ type [9] and to analyze material technology problems. The clearest picture of the chosen experimental design can be obtained after consideration of data presented in the Table. According to this design, at possibly maximum randomization, N=14.7=98 samples were made. For each sample two specimens were prepared.
ANALYSIS OF EXPERIMENTAL RESULTS Compressive strength (yl, MPa) Experimental design and the values of compressive strength are given in Table. When analyzing rows in the Table it can be easily noticed that grain-size distribution of sand introduced into ceramic mix can change compressive strength of ceramic specimens approximately two times. Experimental data in each column vary in even wider range (up to 6 times). It may be then concluded that at least some effects of technological factors Xi have significant meaning from statistical point of view. Unfortunately repeated tests of compressive strength were not made so it was not 7
possible to evaluate dispersion of experimental error, the variance ’ Y I , which is necessary for further statistical analysis of experimental results. Results of previous test were used for this purpose. This test was conducted at different level of input quantities. The values of input quantities were within the variation interval of the present experiment. As a result variance -
valueSyt-’ - 24’4 was obtained at 12 degrees of freedom. Standard deviation was
= 4,94
Table: Experimental design and experimental results of compressive strength of ceramic
Each column of experimental data presented in the Table was analyzed. Each column contains results of compressive strength tests of specimens with the same grain-size
Application of experimental - statistical modeling to evaluate influence of amount and ...
499
distribution of sand and prepared at different levels of factors X I , X2 and X3. Regression equations in the form of second order polynomial were determined for each column and than they were analyzed and interpreted. As an example the analysis of data in the first column of the Table is conducted. Only fine-graded (Z,) sand was added to these specimens. At the beginning all evaluations of regression model (1) coefficients were calculated. Than, at the selected significance level = 24.4 a=O.O5 and dispersion of experimental error based on 12 degrees of freedom according to Student’s t-test criterion (to,oj:12=2,18), statistically significant regression coefficients were determined. Only six in ten coefficients of equation (1) bo, bl, b3, b13, bll, b33 turned out to be statistically significant. Repeated analysis of significance of regression model coefficients was made after elimination of insignificant ones. Then the model was formulated as follows:
’
91=40.44-10.39~1+3.99~3+6.3~1~3+7.79~1~-11.~3Xj~.
(3)
Fisher’s criterion was used for evaluation of model adequacy. The criterion was determined as a ratio of variance of random deviation to dispersion of experimental error:
F=
%= 1.43,
s, wh -p=8 degrees of freedom. Calculated value F is lower than the critical value Fo.oj:8:,2=2,85-evaluatedfrom statistical tables. It confirms adequacy of regression function to the tested object. A
\
The difference between the experimental results and the values of compressive strength calculated from regression equation (3) for single specimen of “u” sample is called residual of “u” sample and it is noted as e,. Degree of freedom of random deviation variance was determined as a difference between number of samples N=14 and number of coefficients of model (3) p=6. Model (3) is characterized by very high significance of criterion y (forecasting ability) which was determined as a ratio of dispersion 6’ (which shows spread of data in relation to the average value) to random deviation variance s,,~.According to demands described in (10) a model can be considered as useful when the value of this dispersion ratio is in the range from 3 to 5 and more. In the present study y= h2/ s o r ~ =1.1. l Statistical procedures recommended by scientific literature prove that the model (3) can be considered as a useful one. It is purposeful to analyze the whole set of 14 residuals e,. Residuals of equation (3) were determined basing on Daniel’s method in the form of empiric distribution function (Fig. I), which should be close to theoretical distribution function of normal distribution. In this case the values of residuals lie close to straight line. The line should cross zero level in the point lying between vertical lines of 7‘h and 8‘h residuals. For determining an angle of line inclination higher significance is ascribed to points for 3rd and 12” residuals. These points are located close to vertical broken lines which limit 2 0 range (ostandard deviation) in normal distribution. As it is shown in Fig. 1, the residuals are approximately in accordance with normal distribution and standard deviation is equal 4.0 (8 degrees of freedom), slightly less than the previously determined value equal to 4.94 (12 degrees of freedom). Fig. 7- shows Enskomb-Tiuka diagram [ I 11. All 14 residuals are here presented in dependence on 91.No evident dependency between e,, and 91 can be noticed in this diagram, In this way another two conditions of regression analysis were satisfied. Other conditions were
500
Beata BACKIEL-BRZOZOWSM
satisfied on the stage of experimental design and examinations. It proves high quality of the model (3).
Fig. 1 Empirical cumulative distribution function of equation (3) residuals
-2
0
20
10
.
-4
-6
-a -10
40
30
50
60
"
91
b
b
. Fig. 2 Dependency between residual e, and calculated values 31
Bifactor model (3) has linear and quadratic responscs of factors, which can be easily physically interpreted. Additionally, the model has the effect of mutual interactions of factors which express internal contradiction of considered process. It changes significance of linear effects. Negative linear response X I because of mutual interactions can change its value without change of its sign but positive linear effect o f factor x3 can change the sign (becomes negative). Different problems can be solved using the model (3). In the discussed case the authors were interested in maximization of compressive strength 4'1. The problem was solved using stepwise method [ 121. In the considered esperinient specimens have the highest compressive strength at thc ti)llowing vducs of coded factors: sl=-L,x;--O.l. It means that the maxiniiitii
Application of experimental - statistical inodeling to evulrrale influence of atnount and ...
50 1
temperature of burning is 900°C and fine-graded fraction of sand reaches 14%. Statistical analysis of experimental data in the first column (based on Student's t-test) proves that effects of factor Xz(duration of keeping in the maximum temperature) can be regarded as statistically insignificant. Its value can be then established on the average level x2=0 (2 hours). Experimental data from the next six columns of the Table were analyzed according to the scheme described above. As a result 6 bifactor regression models (3) were formulated. They described in the adequate way values of experimental results. It has been proven that s, . factor X2 does not give statistically significant effects. I S a good estimator of standard deviation and with high probability covers values of the unknown standard deviation of the whole population. Values of equivalent factors of all families of bifactor models were approximated by polynomial (2). As a result the final model for defining compressive strength of specimens was defined: I
7 I =40.4421+27.4222+2323-47.442 IZZ-19.142IZ3+20.662223+329.821Z2Z3-( I O.39Zl+5.67Z2+4.44Z3-12.2ZlZ2-15.5ZlZ3-3.58Z2Z3+5 1.6ZIZ2Z3)xl+
+(3 .99ZI- 1.1422I22+23.14Z123+9.962223-48.42 IZ ? Z ~ ) X ~ + +(6.3Z 1+3 .2 122+4.7723-3.46Z 122-3.6621Z3- I 5.96Z?Zj+1822 I ZzZ3)x I x3f +(7.972~+2.52~+2.642~+14.32Z~Z~-23.82Z~Z~-23Z~Z~+45.1 ZIZ~Z~)XI~-(I 1.2321-0.822-3I . l Z ~ Z 2 - 1 6 . 6 6 Z ~ Z 3 + 1 1 . 7 6 2 ~ Z ~ + 2 6 6 . 7 2 ~ Z ~ Z ~ ) ~ 3 ~ .
(4)
It results from the model (4) that changes in grain size distribution of sand introduced to ceramic mix can significantly change all effects of factors X I and Xj. It would not be possible to come to such a conclusion using traditional single factor dependencies for complex burning processes. Adequacy of the model (4) turned out to be positive basing on experimental data of one test realized beyond experiment. 7 samples were prepared from ceramic mix containing 3% of sand (granulation Z1=22=23=1/3). Maximum temperature of burning was 930 "C. The average - compressive strength was yl=32.6 MFa. The value calculated from equation (4) after 930-990 - _ 2_ x, =-=I25-15 x, = substitution of values Zi and coded coefficients 90 3 ; 10 was f1=29.8 MPa. From the statistical point of view convergence of calculated and experimental value of compressive strength is satisfying. Optimal conditions according to bifactor model (3), which is a part of model (4). are when the value of coded factor X I always equals - 1 (x1=900"C) and x3 is in the range from 0.5 to 0. It may be accepted x3=-0.25 (X3=12.5%). After substitution xl=-l and x3=-0.25 to the equation (4) we obtain: f I(iill,l,=58.7ZI +3 6.4Z2+31.323-44.02I 22-64, I Z I Z3- I 3.1ZrZ3+467.5Zl ZzZ3.
(5)
Equation ( 5 ) allows to calculate the maximum value of compressive strength (optimum condition) for the specific grain-size distribution of sand. Geometrical picture of dependency ( 5 ) i n the form of isolines of compressive strength is presented in Fig. 3 on tricomponent diagram. This diagram allows determining grain-size distribution at which specimens achieve the highest compressive strength. Fig. 3 shows that the highest compressive strength of ceramic material can be achieved when sand contains only tine grains (Zl approaches I and Z2, Zi approach 0). The area of compressive strength not lower than the required value can be separated on this diagram. Other problems can also be solved like finding the compromise between compressive strength and other features of building ceramics.
502
Beata BACKIEL-BRZOZOWSKA
Fig. 3: Isolines of compressive strength on tricomponent diagram of grain-size distribution of sand for optimum conditions (temperature of burning 900 "C and sand content 12.5% by weight) Water absorption (yz, %)
Each test of water absorption was repeated twice in 98 samples of experimental design. The -
7
average value y2tfl and its dispersion S~~~ were determined. Homogeneity of dispersion of these samples was proven using G-criterion at significance level a=O.O5. As a result ' = 1.337 sufficiently reliable evaluation of experimental error dispersion was determined at 98 degrees of freedom. After analysis (as in the case of compressive strength) a model of water absorption, forecasting in the considered area of variability of factors, was built: sj2n
32=12.821+13.2Z2+13.5Z~+6.4Z~Z2-0.6Z123+1 Z2Z3+58.8 Z12223-4.12~1+ +(0.2421+0.5822+1.02Z3+l.362122+1.52Z123-47.1212223) ~ 1 x 3 -(2Z I +2. I 22+2.1Z3+5.4Z122-2.22123-0.42223+60 212223) x I '.
(6)
Sufficient accuracy of approximation of the average tested values was proven after evaluation of adequacy of bifactor models which have linear and quadratic responses of factor xI and the response of mutual interactions of X I and x3. The last effect can change by 30% the value of linear response of factor X I . Thus dependency of water absorption on factors X I and x3 has fully traditional character. When grain-size distribution of sand varies, responses of factors x I and x3 (without linear responses of factor X I )can be changed significantly. Experimental results of one test realized beyond experiment were taken for evaluation of forecasting power of the model (6). The average value of family of repeated tests was 72 = These specimens were prepared under the following conditions: x1=-2/3 (930°C), x3=l (25% of sand), 21=22=23=1/3. After substitution of these values to the equation
Application of experimental - statistical modeling to evaluate influence of amount and
...
303
(6) we obtain 92=16.4%. Residuals of the model e=0.7 for calculated value of water absorption in relation to experimental value turned out to be lower than standard deviation
c
sg, = S- =1.156
. It proves correctness of the model (6) and its usefulness for forecasting calculations. Forecasting calculations may be applied to choose optimum conditions in order to achieve the required compressive strength. In the case of wall ceramics there is a need to explain if at required compressive strength water absorption does not drop below the threshold value. As the water absorption characterizes to a great extent the porous structure of material, numerical experiments on the model (6) can be applied to evaluate material durability and insulation properties.
CONCLUSIONS The experiment proved that not only parameters of burning process and sand content influence compressive strength and water absorption of wall ceramics. Also grain-size distribution of sand influences ceramics performance. Formulated statistical-experimental models describe with sufficient accuracy results of very complex mutual interaction between considered factors and they allow to solve different engineering problems.
ACKNOWLEDGEMENTS The experiment was carried on in Bialystok Technical University in the frame of Dean's Project supported by State Committee for Scientific Research.
REFERENCES 1. Avgustinik A. I., Ceramics (in Polish), Arkady, Warszawa 1980, pp 452 2. Pogovoj M. I., Technology of artificial pore aggregates and ceramics (in Russian), Strojizdat, Moskva 1974, pp 3 15 3. Pavlov V. F., Physico-chemical grounds of building ceramics burning (in Russian), Strojizdat, Moskva 1977, pp 240 4. Rohvargera E. L., Building ceramics (in Russian), (spravoenik), Strojizdat, Moskwa 1976, pp 493. 5. Worrall W., Clays and ceramic raw materials, London 1980, pp 238 6. Peregudov V. V., Pogovoj M. I., Heating processes and installation in building articles and details technology, Strojizdat, Moskva 1983, pp 416 7. Nikitin V., Guriev V., Lapko A., Modeling of sandwich concrete building structures production and exploitation processes (in Polisch), Bialystok Technical University, Bialystok 1999, pp 244 8. Voznesenskij V. A., Vyrovoj V. N., KerS V., Ja., LjaSenko T. V., Modern methods of composite materials optimization (in Russion), Budivel'nik, Kiev 1983, pp 144 9. Nalimova V. V., Experimental designs tables for factor and polynomial models (in Russian), Metallurgija , Moskwa 1982, pp 752 10. Ruzinov L. P., Slobodiekova R. I., Experimental design in chemistry and chemical technology (in Russian) Himija, Moskwa 1980 pp 287 11. Daniel K., Statistics in industrial experiment (in Russian), Mir, Moskva 1979, pp 300 12. Voznenski V. A., Statistical methods of experimental design in technical-economical examinations (in Russion), Finansy i statistika, Moskva 1981, pp 263
Proc. Int. Symp. ,)BrittleMatrix Composites 7" A.M. Brandt. V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE PULTRUSION TECHNOLOGY FOR THE PRODUCTION OF FABRICCEMENT COMPOSITES (a'Alva PELED and (b)BarzinMOBASHER (a) Structural Engineering Department, Ben Gurion University, Beer Sheva, Israel, e-mail:[email protected] (b) Department of Civil and Environmental Engineering, Arizona State University, Tempe, AZ, USA, e-mail:[email protected]
ABSTRACT Use of reinforcement in thin cement based elements is essential in order to improve the tensile and flexural performance. The reinforcements can be either short fibers or continuous reinforcement, in a fabric form. Practical use of fabric-cement composites requires an industrial cost-effective production process. The objective of this study was to develop the pultrusion technique as a novel industrial cost-effective method for the production of prefabricated high performance thin-sheet fabric-reinforced cement composites. Woven fabrics made from low modulus polyethylene and glass meshes were used to produce the pultruded cement composites. The influence of fabric cell opening, application of pressure during the process, and cement-based matrix modification were examined. The mechanical behavior of the pultruded fabric-cement components was found to be relatively high obtaining strain hardening behavior even for fabrics with low modulus of elasticity. The best performance was achieved for glass fabric composites when high content of fly ash replacing the cement. The intensity of the applying pressure significantly affects the mechanical behavior of the pultruded composite. The promising combination of fabric reinforcement in cement composite products and the pultrusion process is expected to lead to an effective novel technique to produce a new class of high performance fabric-cement composite materials.
Keywords Fabric, cement, composite, glass fiber, polyethylene fiber, pultrusion, processing
INTRODUCTION The past decade has seen an increased use of prefabricated cement-bonded fiberboard around the world. Such elements are used for wall panels, exterior siding, pressure pipes, and roofing and flooring tiles. Use of reinforcement in these elements is essential in order to improve the tensile and flexural performance. The reinforcements can be either as short fibers or as continuous reinforcements, in a fabric form. Recently, several researchers began to examine the potential of thin sheet cement-based products reinforced with hand lay-up of fabrics, showing very promising results [I-61. In addition to ease of manufacturing, fabrics provide benefits such as excellent anchorage and bond development. Peled et a1 [3] found that the flexural strength of cement-based composite products with low modulus polyethylene fabrics
506
Alva PELED and Barzin MOBASHER
is almost two times higher than the strength of composites reinforced with straight continuous polyethylene yams. The main explanation for the improved performance of fabric reinforced cement composites is the enhanced matrix-reinforcement bond due to mechanical anchoring. The mechanical anchoring is provided by the non-linear geametry of the individual yams within the fabric, induced by the fabric structure [4,7]. These results for cement-based composites differ from the behavior of polymer composites, where straight yams lead to optimal results while non-linear yams reduce the reinforcing effectiveness [8]. Practical use of fabric-cement composites requires an industrial cost-effective production process, which has not been developed yet. The pultrusion process is a natural candidate for this purpose, as it is based on a relatively simple set up using low cost equipment while assuring uniform production. Pultrusion has been examined to produce cement composites with continuous filaments (filament winding technique) by several researchers, exhibiting significantly improved performance. Cement composites containing 5% (AR) unidirectional glass fibers produced by pultrusion achieved tensile strength of 50 MPa [9], compared to an average tensile strength of about 6-10 MPa of conventional GFRC (Glass Fiber Reinforced Cement) composites. Pultrusion products reinforced with PAN-based carbon continuous filaments achieve superior flexural strength of about 600 MPa with 16% content by volume [ 101 and 800 MPa with 23% content by volume [ 1 I]. The challenge in developing an industrial production method to produce thin sheet cement elements with fabrics is not only technological, but also scientific, as it has been demonstrated in numerous circumstances that the production method can have substantial impact on the properties of the final product. It was reported that even when keeping the same matrix and fibers, changing the process could significantly affect the properties of the composite [ 12-14]. The objective of this study was to develop a novel industrial cost-effective method, the pultrusion technique, for the production of prefabricated high performance thin-sheet fabricreinforced cement composites. Woven fabrics made from low modulus polyethylene as well as glass meshes were used to produce the pultruded cement composites in this study. The influence of the opening of the fabric as well as the applying pressure during the pultrusion process was studied. Also, various mixtures containing superplasticizer and fly ash as replacement for cement were examined in order to find the appropriate rheology for the pultrusion process. A microstructural analysis was conducted and correlated with the mechanical performance of the composite. EXPERIMENTAL
Two types of fabrics were used for this study: bound fabric and woven fabric (plain weave). In bounded fabrics a perpendicular set of yams (warp and weft) are glued together at the junction points. In woven fabrics the warp and the fill (weft) yams pass over and under each other. The bounded fabric was made from multifilament AR with 2 yams per cm, in both directions of the fabric. The woven fabric was made from monofilament polyethylene (PE) with 22 yarns per cm in the reinforcimg direction (warp yams) and 5 yams per cm in the perpendicuar direction (fill yams). The AR glass fibers were with tensile strength of 12702450 MPa, elasticity modulus of 78,000 MPa and filament diameter of 13.5 microns. The PE. fibers were with tensile strength of 260 MPa, 1760 MPa modulus of elasticity and 0.25 mm diameter. The pultrusion process was used to produce the fabric-cement specimens in this work. In this process the fabrics were passed through a sluny infiltration chamber, and then pulled through a set of rollers to squeeze the paste in the openings of the fabric, removed excessive paste, and formed composite laminates. The pultrusion set up is presented in Figure I. By using this method fabric-cement sheets with width of 20 cm, length of 33 cm and thickness of
The pultrusion technologyfor the production offabric-cement composites
507
about 1 cm were produced. Each cement board was made with 7 layers of fabrics, giving reinforcement content of about 4.5% and 9.5% by volume of AR glass fibers and PE fibers, respectively. After forming the sample through the rollers, a pressure was applied on top of the Fabric cement laminates to improve penetration of the matrix in between the opening of the fabrics. A constant pressure of 15 KPa due to a 900 N load applied on the surface of the fabric-cement sheet was applied for both fabric types. Most of this pressure wad removed 1 hour after the pultrusion process, with a 100 N load up to 24 hours (1.7 KPa) from the pultrusion process. In the case of the AR glass fabric a load of 100 N was studied to examine the effect of the applying pressure on the mechanical performance of the composite. Note that the intensity of this applied pressure is limited and cannot reach high levels, as the matrix is still fresh at this point and elevated pressures can remove most of the matrix in between the fabric laminates. This results in an insufficient matrix content to help bind the laminates. In this study, 900 N was the highest pressure examined which still kept the cement matrix in between the laminates of the fabric.
Figure I: Set-up of the pultrusion process Controlling the rheological properties of the cement mixture is an important factor during the pultrusion process. The mixture should be sufficiently fluid to enable the fabric to transfer through the cement slurry but dense enough so that it will remain on the fabric when it leaves the cement bath. In order to develop a mixture with optimal rheology for the pultrusion process addition of fly ash as well as superplasticizer were used to produce the fabric cement laminates. The mix designs used in this study are presented in Table 1. In all cases the waterhinder ratio by weight was 0.4. The rheology properties of the fresh mixtures were measured by shear rheometery 10 minutes after starting mixing. This was the average time required to produce the pultruded sheet. Table 2 presents the experimental program for all tested systems. Table I: Ingredients of the pultruded mixtures Volume Fraction % Batch # Cement Silica Fume Flv Ash Superplasticizer
#1
I
42 5 I
---
I 0.1
#2
I
42 5
I
I
_-_
0.2
I
I
#3 19 5 24 0.05
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Alva PELED and Barzin MOBASHER
After 24 hours from the pultrusion process the remaining 100 N loads were removed and then the fabric-cement laminates were cut to specimens having width of 250 mm and length of 180 mm. There after all specimens were cured for 3 days in 80°C steam and then stored in room environment until testing in tension, 7 days after the pultrusion process. For studying the mechanical performance of the pultruded laminates closed loop control direct tensile tests were performed on a MTS testing machine with a rate of 0.5 mdmin. The composite laminates were examined along the pultrusion process. The tensile stress versus strain was recorded. Typical stress-strain curves representing the tensile behavior of individual composites were chosen for comparison. Attention was given to formation of distributed cracks throughout the tensile testing. The microstructure of tQe pultruded specimens was studied by Scanning Electron Microscopy (SEM) and correlated with the mechanical performance. Fragments of specimens obtained after tensile tests were dried at 60°C and gold-coated for observation under the SEM. Table 2: Experimental program of the different fabric systems Fabric t e AR-Glass AR-Glass AR-Glass AR-Glass Pol eth lene
Batch #
PressureN
900
2
900
RESULTS AND DISCUSSION Influences of processing technology The pultrusion process was successfully used in this study and several fabric-cement sheets were produced with relative ease. Figure 2 shows an example of such pultruded specimen reinforced with AR glass fabric. The smooth surface and aesthetically appealing of this pultruded specimen is clearly seen in this figure. This smooth surface would only require painting when these elements are assembled in practice.
Figure 2: Specimen of cement composite with glass fabrics produced by the pultrusion process. Comparison of the tensile behavior of AR glass fabric produced with the pultrusion method compares with the conventional GFRC produced by the spray process containing short glass fibers is presented in Figure 3. The benefit of using the pultruded fabric laminates is obvious in this figure. A significant superior tensile behavior in both, strength and
509
The pultrusion technology for the production offabric-cement composites
toughness is seen for the pultruded specimen compares with much poorer response of the conventional GFRC. This improvement in tensile behavior of the pultruded composite is greater than four folds, indicating the advantages of using fabrics with the pultrusion process. Effects of fabric types Two fabrics were used in this study with low and high modulus of elasticity, PE and glass, respectively. The spacing between the yams in the fabric was much smaller for the polyethylene fabrics as compared to the glass fabrics, i.e., the polyethylene fabrics were relatively dense having less then 1 mm opening between the yarns in the fabric. A good penetration of the cement matrix was obtained even for the PE fabric with the finest opening (less than I mm), as presented in Figure 4. This figure presents SEM micrographs of the fabrics embedded in the cement matrix, indicating that the pultrusion process can successfully be used for relatively dense fabrics, which can open the use of fabric for wide range of fabric structures and products. The tensile behavior of both fabric systems is shown in Figure 5 . A strain hardening behavior is clearly seen for both fabrics although the polyethylene fabric is made kom low modulus fibers. Greatest tensile strength is observed for the AR glass fabric, a tensile strength of above 20 MPa is seen compared to only 12 MPa for the PE fabric. The increased tensile performance of the AR glass fabric composites can be attributed to the high modulus of elasticity of this glass fabric. The ductile behavior of the PE fabrics is clear in this figure. 20 .s
I6
9 12
_ _
I
.
Fabrics
/
L
4.0
n
---
----.--
Short fibers Spray process Vp5% .- .- ... . ~
l__l
__ - .
O f 0.01
0
0.02
0.03
Strain mmlmm
Figure 3: Tensile behavior of AR glass fabric produced with the pultrusion method compares with GFRC produced by the spray process containing short glass fibers
PE
AR-glass
Figure 4: SEM micrograph of PE and AR glass fabrics embedded in the cement matrix
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A h a PELED and Barzin MOBASHER
- - ....-./----PE
0
0.03
0.06
0.09
0.12
Strain, mmlmm
Figure 5: Tensile responses of cement composites with AR glass fabric and PE fabric
Effect of pressure After forming the fabric-cement composite with the pultrusion process an additional pressure was applied on top of the laminates to improve penetration of the matrix in between the opening of the fabrics. In order to understand the effects induced by applying pressure on the mechanical behavior of the pultruded fabric-cement laminates, two different pressures were examined for AR glass fabric composite at 100 N and 900 N. Figure 6 shows the effect of pressure on the cement penetration, and the difference in the penetration of the cement matrix is clearly observed. In Figure 6a no pressure was applied, whereas in Figure 6b the applied pressure was 15 KPa. It is observed that the matrix did not penetrate fidly to the opening of the fabric when no pressure was applied. However, a good penetration is seen in between the opening of the fabric when 15 KPa pressures (900 N) were applied. This indicates that nominal pressure is needed after the pultrusion process in order to help with the penetration of the cement matrix in between the gaps of the fabric and fill up the mesh opening.
Figure 6: Effect of pressure on the cement penetration: (a) no pressure was applied, (b) 900 N (1 5 KPa) pressure was applied Figure 7 clearly shows that the intensity of the pressure significantly influences the tensile response of the composite. Increasing the pressure from 100 N to 900 N improves the tensile strength of the element by about 80%. However, the ductility of the low pressure composite is much greater than that of the high pressure composite.
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The pultrusion technologyfor the production offabric-cement Composites
0
0.01
0.02
0.03
0.04
0.05
0.06
Strain, mm/mm
Figure 7: The effect of the intensity of the pressure on the tensile behavior of AR glass fabric composites Such differences in the mechanical behavior of the two composites can occur due to poorer penetration of the matrix in between the opening of the fabric of the low pressed composite, leading to reduction in the bond strength between the fabric and the cement matrix. This difference in bonding was observed by SEM, as shown in Figure 8, which presents the AR glass fabric embedded in the cement matrix for specimens loaded with 100 N (Figure 8a) and 900 N (Figure 8b) pressures. The observations focused on the corner of the mesh, where the perpendicular yams are connecting together to form the fabric. A larger gap between the fabric and matrix is observed for the composite with the lower pressure, indicating poorer bonding of this laminate composite (Figure 8a). Much smaller gap between the matrix and the fabric is seen for the high intensity pressure (Figure 8b), indicating improved bonding with this system.
100 N
(b) 900 N
Figure 8: SEM micrographs at the fabric-matrix interface near the corner of the fabric opening for the different pressures: (a) 100 N and (b) 900 N (XSOO). During the tensile tests successive cracks were developed along the width of the specimen, as expected. The spacing between the cracks can give indication on the bonding between the fabric and the cement, the finer the spacing the greater the bonding. Such differences in crack spacing were observed for the different pultruded specimens with the high and the low pressure, applied after the pultrusion process (Figure 9). The crack spacing of the high pressure specimen is much smaller, only 10.2 mm, than that of the low pressure specimen, which is 16.8 mm, suggesting better bond between the fabric and the cement
5 13
.Ilva PELED und Barzin MOBASHER
matrix when the pressure is increased. This correlates with the SEM observations (Figure 8) and can explain the improved mechanical behavior of the composite with the higher pressure (Figure 7).
100 N
900 N
t,'igure 9: Fabric-cement composites produced with different pressures after tensile test k1atri.x modification Controlling the rheological properties of the cement mixture is an important factor during the piillrusion process. In order to develop a mixture with optimal rheology, addition of superplasticizer (SP) and fly ash were evaluated (Table 1). AR glass fabric composites with 0. I % and 0.2% SP were produced by the pultrusion process. The tensile results indicated that the composite with the increased content of SP performed better than that with the lower content of SP, the tensile strength of the specimen with the high content SP was about 21 MPa compared with only 16 MPa of the low content SP specimen. This improvement is in about 25% and can be due to improved rheological properties with the increased SP content. Measurement of the viscosity of the fresh cement mixtures with various SP contents indicated a reduction in shear stress from 3672 N/m' to 856 N/m2 when the SP content decreased from 0.2% to 0. I % by volume. Better fluidity of the fresh matrix can lead to better penetration of the cement in between the fabric opening. Cement laminate composites with AR glass fabrics and high content of fly ash were also produced by the pultrusion process and examined in tension. In this case, 60% by volume of cement was replaced by fly ash. The results clearly indicate an improvement in the mechanical behavior of the cement composite compared to similar composites without fly ash, as clearly presented in Figure 10. This suggests that the use of fly ash as replacement for cement can be uniquely beneficial for the pultrusion process, when glass fabrics are used. A tensile strength of about 25 MPa at a strain capacity of about 5% is observed with these fly ash materials. This represents a tensile strength of more than eight times, and a strain capacity more than 400 times the plain cement based materials. Compared to GFRC, these materials are as much as five times stronger and have about six times more strain capacity (Figure 3). The ductility is therefore more than an order of magnitude increased as compared to GFRC containing 5% AR glass fibers. Such improvement by the fly ash can be attributed to the improved rheology properties of the fresh mixture and improvement in the durability of the glass fabric due to t y presence of fly ash. The rheology of the fresh mixture indicated a shear stresses of 586 N/m' with the fly ash in comparison with shear stresses of 3672 N/m' of the control mixture without fly ash.
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The pultrusion technology for the prodzictiort of:fabric-cenrenfcornposites
B$
2015 -
h
; ; Q) .C( 1
s
10
t - 5
-
Figure 10: Effect of fly ash addition on the tensile behavioi
III
iliz tiihric-cement composites
CONCLUSIONS The pultrusion technique for the production of fabric-cement products requires relatively simple set up using low cost equipment while allowing good control of laminates alignment and giving relatively smooth surface. The tensile behavior of the pultruded composite with glass fabrics was significantly improved compares with conventional GFRC made with the spray process. An improvement greater than 4 folds in tensile strength ofthe pultruded composite was observed. The mechanical behavior of the pultruded fabric-cement components was impressive with a relatively high strength and exhibiting strain hardening behavior even for fabrics with low modulus of elasticity. The best performance wiis x h i e v e d for glass fabric composites when high content of fly ash was replaced with the cement at the rate of 60% by volume. This observation suggests that the use of fly ash as replacement for cement can be uniquely beneficial for the pultrusion process, when glass fabrics ;ire used. A pressure is required on top of the fabric-cement laminates after the pultrusion process in order to enable penetration of the cement in between the opening of the fabric. The intensity of this pressure was found to significantly affect the mechanical behavior of the pultruded composites. lncreasing the pressure significantly improves the tensile strength due to improvement in bond strength between the fabric and the cement matrix. The promising combination of fabric reinforcement in cement composite products and the pultrusion process is expected to lead to an effective novel technique to produce a new class of high performance fabric-cenient composite ni:itcrials. Such breakthrough may open the way for a multitude o f n e w products and application\
The authors \\oulJ like to thank Sippon Elcciric Glah\ C'o., Ltd. for their cooperation and for the effort t l i q iiiadc to provide the $ass f;ibrics used i n this study.
5 14
AIvu PELED and Burzin MOBASHER
REFERENCES Swamy, R. N., Hussin, M. W., Continuous woven polypropylene mat reinforced cement composites for applications in building construction, In: “Textile Composites in Building Construction”, P. Hamelin and G. Verchery eds. Part 1, 1990, pp 57-67. Perez-Pena, M., Mobasher, B., and Alfrejd, M.A., Influence of Pozzolans on the 2. Tensile Behavior of Reinforced Lightweight Concrete, In: Materials Research Society “Innovations in the Development and Characterization of Materials for Infrastructure”, Dec. 199 1, Boston, MA. Peled, A., Bentur, A., Yankelevsky, D., Flexural performance of cementitious 3. composites reinforced by woven fabrics, J. Materials in Civil Engineering (ASCE), November, 1999, pp 325-330. Peled, A., Bentur, A., Yankelevsky D., Effects of woven fabrics geometry on the 4. bonding performance of cementitious composites: mechanical performance, J. Advanced Cement Based Materials, 7, 1998, pp 20-27. Peled, A., Bentur, A., Geometrical characteristics and efficiency of textile 5. fabrics for reinforcing composites, J. Cement and Concrete Research, 30, 2000, pp 78 1-790. Reinhardt, H.W. Kruger, M. and Grosse, C.U., Thin Plates Prestressed with 6. Textile Reinforcement, ACI SP206-14,2002, pp 355-372. Bentur, A., Peled, A, Yankelevsky, D., Enhanced bonding of low modulus 7. polymer fibers-cement matrix by means of crimped geometry, J. Cement & Concrete Research, 27(7), 1997, pp 1099- 1 1 1 1. Zweben, C. in: Zweben C, Hahn H.T, Chou T, eds. Mechanical Behavior and 8. Properties of Composite Materials. Delaware Composites Design Encyclopedia 1. Lancaster: Technonic, 1989, pp 3-45. Mobasher, B., Pivacek, A., and Haupt, G.J., Cement based cross-ply laminates, 9. J. Advanced Cement Based Materials, 6 , 1997, pp 144-152. 10. Kazuhisa, S., Noayoshi, K., Yasuo, K., Development of carbon fiber reinforced cement, Advanced Materials: The big Payoff National SAMPE Technical Conference, Pub1 by SAMPE, Covina, CA, USA, Vol. 21, 1998, pp 789-802. 11. Nishigaki, T., Suzuki, K., Matuhashi, T., and Sasaki, H., High strength continuous carbon fiber reinforced cement composite (CFRC), In: Proc.Int.Symp. “Brittle Matrix Composites I”, A.M., Brandt, and I.H., Marshall eds. Warsaw, Poland, 1991, Elsevier Applied Science, London 1991, pp 344355. 12. Delvasto S., Naaman A.E., and Throne J.L., Effect of pressure after casting on high strength fiber reinforced mortar, Int. J. Cement Composites Lightweight Concrete, 8(3), 1986, pp 181- 190. 13. Igarashi, S., Bentur, A., and Mindess, S. The effect of processing on the bond and interfaces in steel fiber reinforced cement composites, J., Cement and Concrete Composites, 18, 1996, pp 3 13-322. 14. A. Peled and S.P. Shah, 2003, “Processing Effects in Cementitious Composites: Extrusion and Casting”, Journal of Materials and Civil Engineering, ASCE, March-Apri I, pp. 192- 199. I.
Proc. Int. Symp. Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I.H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSIand Woodhead Publ., Warsaw 2003 )I
METHOD OF DETERMINATION OF CREEP AND SHRINKAGE OF SFRC
DuSan SpSra, Jan VodiEka, Jiii Kratky Department of Concrete Structures and Bridges Faculty of Civil Engineering, Czech Technical University in Prague Thakurova 7, 166 29 Praha 6, Czech Republic Marian Abramowicz Warsaw Technical University Armii Ludowej 16, 00-66 1 Warsaw, Poland ABSTRACT
The determination of volume changes (shrinkage, creep) of concrete is difficult and there is no reliable method that can be applied for different kinds of concretes (ordinary plain concrete, high performance concrete, fibre reinforced concrete, etc. For ordinary concretes the prediction model was indicated in EC2 [I]. It would be very usefd to develop that model for fibre concretes, where another component of composite - dispersed fibres - should be taken into account. The aim of the paper is the prediction model of volume changes of FRC based on the hypothesis that creep develops proportionally to the ratio of the compressive strength of FRC to the compressive strength of plain concrete with the same composition. A similar hypothesis is proposed for shrinkage: it is to be proportional to the ratio of the splitting tensile strength of FRC to that of the plain concrete. These hypotheses are supported by the results of volume changes measurements of FRC with steel fibres (SFRC) and of plain concrete. There measurements were initiated in 1988 and continued during several years. The obtained results show that these simple hypotheses can be to some extent accepted by the designers of concrete structures. It should be, however, expected that in the future another model will be worked-up, which will approximate better the volume changes of FRC. Keywords Strain, creep, shrinkage, compressive strength, splitting tensile strength.
[NTRO D UCTION
The volume changes of concrete: creep and shrinkage, are in many situations considered as negative properties of concretes. In all cases their values should be taken into account in design of concrete structures. Numerical expression of these properties is needed in design not only to improve the accuracy of the calculation models, but also because of their increased
5 16
DuSan SPfiRA. Jan VODICk.4. Jifi KRA’TKYand Marian ABRAMOWICZ
complexity. That is why a method for calculation strain development due to creep and shrinkage is indicated in EC2 [ 11. The increased development of application of Fibre Reinforced Concretes (FRC), and particularly that of SFRC with steel fibres in the load carrying concrete structures is observed in many countries. It is therefore important to study also the volume changes of these composites. The problem is difficult because an inert component - fibres - is added to the material structure of the concrete composite. Furthermore, this component is dispersed in the concrete matrix at random, which further contributes to the complexity of the problem. It should be also considered that a large variety of fibres are used: fibres made of different materials, with different shapes and dimensions; which still increases considerably the complexity of the problem. Database from the measurements is used as a basis for the calculation model proposed. It is expected that in the future not only the models for creep and shrinkage calculations of the plain concrete will be gradually improved, but also those for SFRC, for the calculation of strain generated by creep and shrinkage will be improved. However, it is believed that this first simple calculation model may be used to design the SFRC structures easier and that it will allow a broader application of this structural material. EXPERIMENTAL PART
The results of the measurements were published in papers presented at the International Symposia BRITTLE MATRIX COMPOSITES, organized in Warsaw [2-41. Here only a general overview of these tests is provided and the conclusions are proposed. The series of specimens were designated as follows: 3/95, 1/96, 1/97, 1/98, 1/00 (plain concrete) 6/95, 2/96, 3/97, 3/98 and 6/00 (SFRC). In SFRC specimens two different types of steel fibres were used: Bohumin long, straight with Vd = 63/0,63 mm, Dramix long type RC - 80/60 - BN. In the database taken into account were series of the same composition and designation. of the tested concretes are presented in the table 2a. Compressive strength (Gn) In Fig. 1 the creep and shrinkage curves of the series 1/00 in hnction of time are shown as examples. 0
100
too
xx)
400
m
Fig. I Creep and shrinkage curves of series 1/00,
600
700
517
Fig. 2 : The specimens tested under long-term compression load.
Figs. 3 and 4 View on one series of the specimens and 2 broken specimens
MODEL AND HYPOTHESIS FOR DETERMINATION OF VOLUME CHANGES
The models were created on the basis of a hypothesis that the volume deformation of SFRC can be derived from these deformations in plain concrete. As a basis for this hypothesis served a broad database of the records of strain (Ecreep, Erh) measurements and the database of the corresponding values of strength of studied SFRCs, i.e. the compressive strength and the tensile splitting strength.
5 18
Duiun SPfiRA. Jan VODICKA. JiJi KRkTKYanriiMariart ABRAMOWICZ
By the detailed analysis of the both databases of the test results a correlation between the reduction of volume changes and increase of the basic strength due to the added fibre reinforcement were discovered. For the change of strain caused by the creep a close correlation was discovered with the increase of compressive strength measured on 150 mm cubes and for the change of strain caused by shrinkage - with a change of splitting tensile strength, also determined on 150 mm cubes. The set of following relations is proposed:
here:
Ec.creep
.............strain - creep of plain concrete
- creep of SFRC strain - shrinkage of plain concrete
Excreep .............strain c,sh ........ EJsh .........
strain - shrinkage of SFRC
f cc .............
compressive strength of plain concrete
fJ2 .............
compressive strength of SFRC
f ct.sp1 .........
splitting tensile strength of plain concrete
fPspl
splitting tensile strength of SFRC
.........
Kxcreep ...... K J s h ..........
correction coeefficient for the measured and calculated values of strain due to creep correction coe6cient for the measured and calculated values strain due to shrinkage
EXAMPLES OF THE CALCULATCON OF STRAIN OF SFRC The results of calculation of the strain for several selected SFRC series of specimens are given in Table 1 for shrinkage and in Table 2 for creep. The tables include also the ratio between ‘the calculated and measured strain for the evaluation of the accuracy of the calculation. As one can see from the above mentioned relations for the calculation of strain this relation will be hrther corrected by factors K, which may express also possible differences in the fibres used. The values of K factors will be the subject of hrther discussion based on the hture results of new experiments.
Method of determination of creep and shrinkage of SFRC
5 19
,336
Notes: 1) Values in the Table were determined as average of 3 measured values. 2) Values shadowed were calculated from formulae for plain concrete in EC2 [ 11. 3) Young's modulus was calculated from formula: E,,, = 4734.G JoS5 (ACI 209 Model Code - [5]). 4) ,E - average Young's modulus, f,, - average compressive strength. 5 ) Values of average humidity and temperature for all series as in Table 1
Table 2 Results of measurements and calculations of strain due to creep
I
1.457
I
I
1.599
I
I
Method of determination of creep and shrinkage of SFRC
52 1
In Table 1 for shrinkage and in Table 2 for creep the values of factors K are proposed, based on the assumption that the values of relative strain measured for each analysed series of SFRC specimens were introduced into the relations. The calculated values then allow the evaluation of the correctness of the relations and accuracy of the calculation on the basis of the hypothesis. CONCLUSION The presented method of computation of strain values &,, and &sh gives acceptable results, which are to a large extent comparable with the experimental results of volume changes ( K J s h - Table 1, K L - Table ~ ~ 2). ~For the ~ model ~ calculations the recommendations for plain concrete from EC2 are h l l y utilized. The basic strengths reflect the most influences of the mixture proportions of the composite and of the method of production and processing. Also the influence of fibres, e.g. their variability that may be significant, is reflected. From the above it can be concluded that this method of calculation could be accepted and hlly utilized for the design of structures until this calculation model will hrther enhanced or a new model will be developed. It is necessary to realize that a more complex calculation model will require very extensive and time consuming experiments. The volume changes of the SFRC (Steel Fibre Reinforced Concrete) became a subject of cooperative research of the Faculty of Civil Engineering of the Czech Technical University in Prague and Polytechnic in Warsaw more than ten years ago. The results of the long term experimental measurements, recorded in both laboratories represent a database allowing the creation of the calculation model for the volume changes for several kinds SFRCs of various compositions. ACKNOWLEDGEMENT This investigation was supported by Grant Agency of the Czech Republic No. 103/03/0837 and by the Research Programme J04/98:2 10000004 - Experimental research structural material and technology. REFERENCES I. European standard - EN 1992-1 (2nddraft) (Eurocode 2: Design of concrete structures - Part 1 : General rules and rules for buildings), September 200 1
2. Abramowicz, M., Kratky, J., Trtik, K. and VodiEka, J., ,,Strains of Steel Fibre reinforced Concrete under a Long-Term Load". Proceedings of the Fourth International Symposium on Brittle Matrix Composites (BMC4), Warsaw, Poland, September. 1994, pp 408-4 14. 3. Abramowicz, M.. Kratky, J., Trtik, K. and VodiEka, J., ,,Strains of Steel Fibre reinforced Concrete under a Long-Term Load". Proceedings of the Fifth International Symposium on Brittle Matrix Composites (BMCS), Warsaw, Poland, October. 1997, pp 164171. 4. Kratky, J., Trtik, K., VodiEka, J.. Spdra D., Abramowicz, M. ,,Determination of Creep and Shrinkage of Steel Fibre Reinforced Concrete". Proceedings of the Fifth International Symposium on Brittle Matrix Composites (BMC6), Warsaw, Poland, October. 2000, pp 352356. 5. ACI 209, "Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures," Manual of Concrete Practice, ACI, 1994, pp. 209R-1 to 209R-47.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I, H.Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
LIME MORTARS WITH NATURAL FIBRES Milo5 F. DRDACKY Institute of Theoretical and Applied Mechanics - ARCCHIP Centre of Excellence Academy of Sciences of the Czech Republic Prosecka 76, 19000 Praha 9, Czech Republic, e-mail: drdacky0,itam.cas.cz Dagmar MICHOINOVA National Institute for Cultural Heritage ValdStejnsk6 n h t s t i 3, 11801 Praha 1, Czech Republic, e-mail: michoinova@,sum.cz
ABSTRACT Paper presents selected results of recent investigations [l] into behaviour of lime mortars modified with natural fibres or fibrous particles. It summarizes technical data of fibre reinforced mixtures made of lime matrix, sand and natural fibres (goat's and horses' hair) or fibrous particles (saw dust, husk), polypropylene fibres and sand. In addition to a short description of some experiments, the contribution is rather focused on explanation of the observed performance, the consequences for practical use of the composite and the questions for further research. Keywords Lime mortar, natural fibres, synthetic fibres, physical properties, experimental research.
INTRODUCTION During surveys and restoration of historic objects all over Europe we find mortars and renders modified with fibres or natural fibrous particles. The fibres were added into mixtures on the basis of a long term experience and the constructor was able to estimate the necessary dose according to the desired or expected effects. However, there has not been available any scientific knowledge about the behaviour of natural fibres in mortars with purely lime based matrix. The research in the field has been for decades mainly concentrated on mortars with cement based binders and several mortar producers introduced such mixtures modified with synthetic fibres on the building materials market. Their advantages are explained mostly in relation to improvements concerning reduction of shrinkage cracks in the early phases of mortar setting and hardening. No attention has been paid to the characteristics necessary for the use of such mortars in the conservation practice as well as to other than synthetic fibres. It is not possible to simply transfer a very rich knowledge about cement matrix mortars filled with fibres (or dispersed steel reinforcing needles) into the field of lime mortars. Therefore, a quite thorough pilot research programme has been launched with the aim to discover basic mechanisms of action of natural fibres in lime mortars and their influence on
524
MiloS F. DRDACKYund Dagmur MICHOINOVA
different characteristics of such composites. This paper is concentrated on the carried out experimental work and its results. Some approaches to numerical modelling of selected problems have already been published elsewhere [2], [3].
EXPERIMENTAL RESEARCH Experimental programme The programme was focused on study of the influence of fibre addition to lime mortars on different composite parameters and characteristics, namely: volumetric stability, volumetric gravity, overall porosity, water absorptivity, closed porosity, ratio of open to closed porosity, carbonation rate, structural effects, modulus of elasticity, energy to fracture characteristics, strength in compression (cubes) and tension (flexural), durability. It was further necessary to investigate material characteristics of natural fibres for which a special optical method has been developed [4]. Composite components Selection of fibres has been strongly influenced by the final goal to provide conservators and restores with conclusions applicable in their practice. Two kinds of animal hair were utilized horse's and goat's, two fibrous lamellar particles - saw dust and husks and one synthetic fibre from polypropylene were tested, too. For the sake of comparison, all fibres had the same length of 12 mm. Even though the aspect ration parameter would be for this purpose more suitable, it is impossible to maintain it constant because of the variety of equivalent diameters of individual animal hairs. The typical characteristics of the fibres used are presented in the Table 1. Table 1 IS
I I
E
lures ur iiuruus
particles vuiyurc3pylene
fibre
CKSTOP
I I 1 Abbrev
PP
(mm)
diameter (w)
12
18
1
I
strength (MW 70-200
I
elasticity
1
, IcpI, ,---, I
3 s
Elongation at failure ("0) 5-40
I I
Moisture ("!)
negligible
The matrix is based on a very pure calcium hydrate of the following average chemical composition: CaO - 72 YO;MgO - 0,6 YO;C02 - 2,5 YO;Si02 + non-soluble particles 0,85 %; hydrate water - 22 YO. The basic mixture is filled with a natural siliceous sand of the following granulometric data: above 2,5 mm - 0 YO; 2 mm - 7 YO;1 mm - 23 YO; 0,5 mm - 31 YO; 0,25 mm - 17 YO; under 0,25 mm - 5 %. Humidity max 1 %, specific gravity 1480 kg/m3. Drinking water from the public distribution net was used in amounts from 0,30 (in most cases) to 0,43 Ikg.
5 25
Lime mortars with naturalfibres
Tests specimens There were manufactured two types of test specimens. The first group imitated rendering and was tested for durability under exposition to severe natural weathering. The second group was prepared for laboratory physical and chemical testing. All specimens were made from the identical basic dry mixture which was then modified with the addition of fibres. The basic mixture was composed from the binder and the sand in the volumetric ratio 1:1, which ensures creation of cracks in early stages of mortar setting. The specific gravity of the dry mixture was 1000 kg/m3. Dose of fibres varied according to the Table 2 and was measured in percentage of mass. The Table 2 further summarizes marking of the test specimens. Table 2 Fibres or fibrous particles
~~
PP polypropylene fibres KO goat’s hair K horse hair Pi husk Pi saw dust plain mortar C * optimum dose recommended by producer
Dose of fibres in mass %
0,l 0,l 0,l 2,O 2,O
0,3 0,2 0,2 4,O 4,O 0,o
0,5* 0,4 0,4 6,O 6,O
Test series marking PP0,I PP0,3 PP0,S Ko0,l Ko0,2 Ko0,4 KO,I K0,2 K0,4 PI2 PI4 PI6 Pi2 Pi4 Pi6 C (Eista)
Technology of preparation of fibre modified mortars needs to maintain carefully some rules, in order to avoid damaging or uneven distribution of the fibres in the final product. Generally, manual processes are preferred to mechanical ones, especially mixing. The mortar after mixing and about one hour of maturing was placed on a wet ceramic porous roof tile and the surface was tightened with a plaster’s trowel. The specimens hardened in laboratory conditions and when they were dry, (approximately after a week), they were exposed to exterior climatic action for a year. Prismatic specimens of standard dimensions of 40 mm x 40 mm x 200 mm were made from the same mixtures as the specimens above. Minimally 5 specimens for each series of material composition or sample dimension were prepared. The samples were cast in moulds with sides provided with a separator, they were consolidated by means of percussion and the abundant mortar was removed - cut off with a plaster’s trowel. The specimens were cured in laboratory conditions for 2 days, then taken out from the form and cured for another 90 days before the first tests started.
Tests and selected results It is not possible to deal in detail with all tests performed during the research under discussion. Let us concentrate on selected items, rather oriented to mechanical or structural issues and present very shortly the data. The flexural (tension) strength tests were carried out on standard beams in a four point bending configuration which enabled to determine during one test also the deformability (modulus of elasticity). The cumulative results are presented in Figure 1 for the strength and Figure 2 for deformability. Fracture characteristics have been measured on the test specimens with a notch according to the RILEM recommendation. The samples were made from the remaining parts of the specimens tested for the tension strength and their necessary length has been achieved
526
Milo? F,DRDACKY and Dagmar MICHOINOVA
using wooden prostheses glued to the mortar prisms, Figure 3. The methodology has been verified during pilot tests and proved to give satisfactory results.
Figure 1. Results of four-point bending tests - average flexural strength values.
Figure 2. Results of four-point bending tests - average values of modulus of elasticity. The compression tests were carried out on cubes 40 mm x 40 mm x 40 mm. They were obviously influenced by the incomplete carbonation, which is possible to see on the Figure 4, where the samples denoted A were tested after previous water absorption tests and therefore were older and cured in another way than the remaining samples of this series.
527
Lime mortars with natrcrdfibres
Fikpre 3. Three-point bending fracture “toughness” tests. - .
Compression strength 4.5 _.
-.
.......
.
.
.
.......
...
.
.
....
................
..................... .........
............
.......
Figure 4. . Results of compression tests on cubes 40 x 40 x 40 mm.
DISCUSSION OF THE TEST RESULTS Summary of experimental observations Several new observations on behaviour of lime mortars modified by fibrous additives have been achieved. The problem is quite complex and influenced by a wide set of parameters. Therefore, not all theoretical as well as experimental results can be generalized beyond limits and boundary conditions applied during tests. On the other hand, the achieved knowledge enables to correct some empirical “rules” as well as to formulate new hypotheses. Let us summarize first the data from individual special tests. The addition of fibrous components into particulate lime composite has, at given boundary conditions of dosing, undoubtedly the following consequences:
528
Mil& F. DRDACKYand Dagniar MICHOINOVA
1. It improves remarkably the volumetric stability of lime mortars during setting and hardening, because it decreases dilatation to a value equal nearly a half of that of the plain lime mortar. The fibres of a high aspect ration, i.e. with a dominant length, and low adhesion surface characteristics exhibit a decrease of dilatation proportionally to an increase of dose. Lamellar fibrous particles, having an excellent adhesion to matrix parameters, have a reverse effect and their increase in volume increases the dilatation, (Figure 5). I
Volumetric stability
I
1
$ .-
5 4!5 4 3,5
-
c 3 .O 2 3 3 2 m ; 1,5 1
Figure 5. Results of dilatation measurements during mortars’ setting and hardening. 2. Volumetric gravity is influenced only by higher amounts of saw dust, (more than 4 %), and it decreases significantly with an increase of dose. 3. The specific gravity is influenced negligibly. 4. The absorptivity of the fibre reinforced mortar is affected by structural phenomena and physical and chemical characteristics. An increase in the overall porosity of mortar with the saw dust increases its absorptivity. A higher addition of naturally hydrophobic fibres, (e.g. goat’s hair), decreases the water absorption. This is generally valid for fibres-animal hair of a high aspect ratio. 5. It seems that the addition of fibres slightly increases the ratio of the closed porosity above 50% of the overall porosity, which is in accordance with the observed microstructure of the material which changes significantly in comparison to the plain lime mortar. (The accuracy of the porosity measurements is influenced by the chosen methodology for volumetric mass measurement, therefore, it should be considered as informative only). 6 . Fibres have observable influence on propagation of carbonation in thick layers of lime fibre modified mortars. An acceleration of carbonation has been observed in mortars with higher content of polypropylene fibres which are very fine and create fibre bundles in the mortar. The bundles support an easy penetration of COz into the mixture. (It is interesting that in the case of dose of 0,5% PP fibres it was not possible to disperse them evenly in the lime mixture and that the fibre bundles, sufficiently open for the gas, did not increase water absorption). On the other hand, the goat’s hair with a high content of lanolin significantly retarded carbonation of the matrix,
5 29
Lime mortars with naturalfibres
see Figure 6. The increase of saw dust improved carbonation only in the starting phases of hardening, regardless increased porosity.
Figure 6 As far as the mechanical characteristics are concerned, the fibres remarkably increase the flexural (tension) strength from bending tests. This parameter is nearly as much as two times higher in case of a lime mortar with gross animal fibres compared to the plain mortar. This ameliorative effect has been observed only for small dose of animal hair (under 1 'YO of volume), but the same influence has been found in modulus of elasticity. Nevertheless, also polypropylene or even saw dust in small concentrations (2 'YO) increases this strength almost by 50 'YO. The result with lamellar additives corresponds to the theoretically derived requirement which recommend the use of fibres with cross-sections of a high ratio of the perimeter to the cross-section area, i.e. non circular profiles. The fibres influence very remarkably the fracture behaviour of the lime composite when measured by the energy to fracture. Here higher volumes of fibres are more effective, because more fibres result in a higher work during their pulling out from the matrix, which is the basic assumption for an efficient behaviour of fibres in the composite. Fracture characteristics are improved by higher friction coefficients on the interface between fibres and the matrix. Therefore, the goat's hair give worse results compared to horse's ones which are more rough and without so much lanolin. The compression strength of lime mortars with fibres is lower than for the reference plain mortar. However, the fibres improve the unloading branch of the stress-strain curve and enable to achieve a higher residual strength. 10. The fibres improve homogeneity of the deformation behaviour of mortars under compression and in an optimum case they can even raise the modulus of elasticity in compression. 11. Animal hair exhibit very good strength, between 110 and 230 MPa and sufficiently high modulus of elasticity (between 3,9 and 7,7 GPa) for a reasonable functioning in the lime composite as a dispersed reinforcement in both the setting and hardening stage as well as in the matured mortar.
530
Milo? F.DRDACKYand Dagmar MICHOINOVA
12. The influence of fibres on durability of lime mortars exposed to weathering is very high and promising, too. Except of husks and polypropylene fibres, all other additives in higher concentrations protected thin renders against macroscopic cracks, spalling and frost damages. Behaviour and role of fibres in lime mortars Consequences of presence of fibrous particles in the lime composite concerning its structure and the associated macroscopic behaviour yield two important conclusions. The addition of natural (as well as synthetic) fibres enables in the stages of setting and hardening to originate a dense net of micro-cracks and closed pores which compensates technological volumetric changes and prevents occurrence of macro-cracks. It is difficult to distinguish how important role and part the fibres play in the plastic mixture as barriers against propagation of cracks, as crack bridging reinforcement or even as initiators of micro-defects around which the cracks open. The behaviour is very complex and further research is needed. Moreover, from the results achieved, it follows that a certain composition of the lime composite influences positively only some of its characteristics and it can at the same time to worsen another one. Only the addition of a small percentage of natural fibres significantly increases the tension strength of the lime composite. A larger amount of fibres seriously damages the lime matrix that it is then not capable to function as a binding link in the chain of non-continuous fibres and sufficiently high tension strength cannot be attained. On the other hand, the increase of volume of fibres in the lime composite improves its fracture characteristics and the composite “toughness” is significantly increased even by additional fibres which are not properly anchored into the matrix, but only into a bundle of other fibres, (e.g. in the case of polypropylene fibres). This phenomenon can be compared to the effect of the so called “dry zipper”. Nevertheless, the residual strength is then much lower than in the case of bending strength. Natural fibres of the strength of an order higher than the lime matrix can positively influence the tension strength as well as the modulus of elasticity. Because the strength of lime binder is much lower than the cement binder, the so called low-modulus fibres are capable to resist in the lime composite tension forces because they are stronger than the matrix and at same time much stiffer. The tested natural fibres seldom break or rupture in the lime composite, they are mostly pulled out from the matrix. The lime fibre reinforced mortar resists weathering very well, even repeatedly. Thanks to the retarded carbonation inside thicker layers of the composite, it can accommodate additional plastic deformations without stress initiation for quite a long time. The effect of “internal hydrophobic surfaces”, which influences the carbonation as well as water absorption, has not been fully explained so far. Nevertheless, the fibres with a waxy or fatty surface layers better initiate micro-cracks around their surface, which probably plays a very important role at reduction of the mortar’s dilatation during its shrinkage, Figure 7. The observed direct dependence between number of fibres and the decrease of dilatation in the case of goat’s hair supports this hypothesis. Negligible width of those cracks and their hydrophobic characteristics explain that they behave as closed pores and do not increase the water absorption of the composite. Even in the case of larger percentages of goat’s fibres the increase in number of cracks does not create problems. They have little tendency to join or connect because they propagate along the fibres. In contradiction, the number of saw dust particles has a reverse effect and the higher the volume is, the higher dilatation occurs. In this case the micro-cracks do not develop along the particle surface because it has very high adhesion properties. The cracks here initiate and propagate in a closer or remoter distance from the inclusion and separate in the composite micro-volumes having diameter more or less equal to the longest dimension of the particle,
Lime mortars with natural fibres
53 1
Figure 8. Matrix is able absorb in such a case some 5 % to 20 YOof saw dust. The initiated cracks have a higher thickness and may be easily interconnected, which explains the dilatation as well as the water absorption increase.
Figure 7. Horse hair pulled out from the matrix, there are apparent holes as well as cracks around the fibres, (magnification 48x).
Figure 8. A saw dust particle and an apparent crack separating a micro-volume of mortar, (magnification 18x).
532
Milo3 F. DRDACKYand Dagmar MICHOINOVA
CONCLUSION The fibre modified lime mortars are quite complicated composites, namely in cases where natural fibres are applied. Research into this problem has not been carried out even though such materials have proved excellent performance for several hundreds of years. This paper is a modest contribution to this problem. Nevertheless, it brings about useful results for scientifically justified use of fibre reinforced mortars in conservation as well as other technical practice and some inputs for firther research.
ACKNOWLEDGEMENTS The research has been supported from the Grant No.PKOO-PO4-OPPI 5 of the Czech Ministry of Culture and the 5* FP of the EC Gran: No.ICA1-2000-700013 (ARCCHIP Centre of Excellence - Advanced Research Centre for Cultural Heritage Interdisciplinary Projects).
REFERENCES 1. Drdacky, M.F., Michoinovti, D., Prochbka, P.P., Lime mixtures reinforced with fibres for conservation and restoration of cultural monuments (in Czech), ITAM Research Report, Prague 2002, p. 146 2. Drdackjr, M., Vhlek, M., Prochkka, P., Spalling of historic mortars: Numerical model. In Proc. Int. RILEM Workshop ,,Historic Mortars: Characteristics and Tests“, P. Bartos, C. Groot and J.J. Hughes eds. Paisley 12-14 May 1999, RILEM Publications s.a.r.l., PRO 12, Cachan 2000, pp. 261-270 3. Prochbka, P., Optimal shape design of structures by inverse variational principles. In OPTI’99, C.A.Brebbia ed., WIT Press, Southampton, 1999, pp. 95-104 4. Vavfik, D., Drdacky, M., Experimental determination of stress-strain dependence of nonstandard materials. In Book of Extended Abstracts Nat.Conf. “Engineering Mechanics 2003”, J. Naprstek and C. Fischer eds. Svratka 12-15 May 2003, ITAM, Prague 2003, pp.364-365.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 " A.M. Brandt, KC. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodliead Publ.. Warsaw 2003
EFFECTS OF ACCELERATED CURING CONDITIONS ON STRENGTH PROPERTIES O F EPOXY-MODIFIED IMORTARSWITHOUT HARDENER Yoshihiko OHAMA Professor of Architecture, College of Engineering, Shinobu TAKAHASHI Graduate Student, Graduate School of Engineering Nihon University Koriyama, Fukushima-ken, 963-8642 Japan e-mail: [email protected]; [email protected]
ABSTRACT Epoxy resin without any hardener can harden in the presence of hydroxide ions in cement mortars and concretes at ambient temperature. However, the hardening rate of the epoxy resin at ambient temperature is slow, and the acceleration of the hardening reaction of the epoxy resin is requested for the manufacture of precast products. Epoxy-modified mortars without any hardener are prepared with polymer-cement ratios of 0 to 20%, subjected to an autoclaving or steam curing after a I-d moist curing, followed by a 1-d heat curing, and tested for flexural and compressive strengths. As a result, the optimal curing conditions for the epoxy-modified mortars without any hardener are recommended as follows: ( I ) I-d moist[20'C, 90%(RH)] + autoclaving(90 or 120"C, 3h) + 1-d heat(l20'C) cure, and (2) 1-d moist[20'C, 90%(RH)] + I-d steam(90"C) + 1-d heat(l20'C) cure. Their flexural and compressive strengths can be predicted by the general equation expressed as a function of maturity. Keywords Epoxy-modified mortars, polymer-cement ratio, accelerated curing, strength, maturity.
INTRODUCTION It is evident that epoxy resin without any hardener in epoxy-modified mortars and concretes can harden in the presence of alkalis or hydroxide ions (OH) from calcium hydroxide [Ca(OH)z] as one of cement hydrates'). The epoxy-modified mortars and concretes without any hardener have a disadvantage that at ambient temperature the hardening rate of the epoxy resin in the mortars and concretes is low and the strength development of the mortars and concretes is inferior. The acceleration of the hardening reaction of the epoxy resin is requested for the manufacture of precast products using the epoxy-modified mortars and concretes. The authors made clear the strength properties of the epoxy-modified mortars subjected to a heat cure for 90d". At present, an autoclave cure (or autoclaving) and steam cure are generally applied to the manufacture of precast products for their early strength development. The authors reported the superior strength properties of the SBR-modified concretes subjected to
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Y. OHAMAandS. TAKAHASHI
the autoclave cure3). However, the application of the autoclave cure and steam cure to the epoxy-modified mortars and concretes has not been examined in detail yet. The purpose of this investigation is to find out the effective accelerated curing conditions for the early strength development of the epoxy-modified mortars without any hardener. In this paper, epoxy-modified mortars without any hardener are prepared with polymer-cement ratios of 0 to 20%, subjected to an autoclave cure, steam cure and combined autoclave or steam cure + heat cure, and the effects of such accelerated curing conditions on their flexural and compressive strengths are examined in order to obtain effective information about the application of accelerated cures to the precast products using epoxy-modified mortars and concretes.
iMATERIALS Cement
Ordinary portland cement as specified in JIS (Japanese Industrial Standard) R 5210 (Portland cement) was used as a cement. The physical properties and chemical compositions of the cement are given in Table 1. Table 1 Physical properties and chemical compositions of cement. Compressive strength of mortar Setting time Density Blaine specific surface (h-min) (MPa) (dcm3) (cm2/g) 3d 7d 28d Initial set Final set 3.16 3370 2-10 3-30 28.8 43.6 61.2 Chemical compositions (%) M g O so3 1.48 2.12 1.90 Fine aggregate Toyoura standard sand as specified in ex-JIS R 5201 (Physical testing methods for cement) was used as a fine aggregate. The properties of the fine aggregate are listed in Table 2.
Type of fine aggregate
Size (mm)
TO YOU^
0.3000.106
standard sand
Table 2 Properties of fine aggregate. Fineness Bulk density Density modulus (kdl) (20°C. g/cm3)
-
1.521.36
1.52
2.63
Water absorption
("/.) 0.11
Epoxy Resin Diglycidyl ether of bisphenol A was used as an epoxy resin. The properties of the epoxy resin are shown in Table 3. Epoxide e uivalent 184
Table 3 Properties of bisphenol A epoxy resin. Molecular weight Density Viscosity 380
Flash point
'C)
)
1.16
38000
264
Effects of accelerated curing conditions on strength properties of epoxy-modified ...
535
TESTING PROCEDURES Preparation of specimens According to JIS A 1 17 1 (Test methods for polymer-modified mortar), epoxy-modified mortars were mixed with a mass ratio of cement to fine aggregate 1 : 3, polymer-cement ratios (P/C)of 0, 5, 10, 15 and 20%, and their flows were adjusted to be constant at 170f5 in the water-cement ratio range of 77.0 to 78.0%. Beam specimens 4 0 x 4 0 X 160mm were molded, and subjected to the following accelerated cures. (1) Autoclave + heat cure 1-d moist [20'C, 90% (RH)]
+ autoclaving (60, 90 and 120'C, 3h) + 0-d and I-d heat (120'C) cure (2)Steam +heat cure I-d moist [20"C,90% (RH)] + 1-d steam (60, 75 and 90'C) + 0-d and 1-d heat (120°C) cure Flexural and compressive strength tests Beam specimens were tested for flexural and compressive strengths in accordance with JIS A 1171.
TEST RESULTS AND DISCUSSION Figs. 1 and 2 illustrate the maximum temperature for autoclaving vs. flexural and compressive strengths of autoclave- and autoclave + heat-cured epoxy-modified mortars without any hardener. Figs. 3 and 4 give the polymer-cement ratio vs. flexural and compressive strengths of the autoclave- and autoclave + heat-cured epoxy-modified mortars without any hardener. In spite of the polymer-cement ratio, the flexural and compressive strengths of the autoclaved epoxy-modified mortars without any hardener tend to increase with increasing maximum temperature for autoclaving. The effect of the polymer-cement ratio on the flexural and compressive strengths of the autoclaved epoxy-modi tied mortars is hardly recognized. The flexural and compressive strengths of the mortars autoclaved at a maximum temperature of 18072 are smaller than or almost the same as those of the autoclaved unmodified mortars (PIC,0%). However, the application of heat cure to the autoclave-cured epoxy-modified mortars causes a marked improvement in their flexural and compressive strengths. The flexural and compressive strengths of the autoclave + heat-cured epoxy-modified mortars without any hardener are increased with an increase in the polymer-cement ratio regardless of the maximum temperature. The flexural and compressive strengths of the autoclave + heat-cured epoxy-modified mortars without any hardener and with polymer-cement ratios of 10, 15 and 20% are reduced at a maximum temperature of 150°C for autoclaving. At a maximum temperature of 180°C for autoclaving, the flexural and compressive strengths of the autoclave+ heat-cured epoxy-modified mortars without any hardener are lower than those of the autoclaved unmodified mortars. This is attributed to the flowing out of the epoxy resin from the mortars due to a marked reduction in the viscosity of the epoxy resin in them during autoclaving at maximum temperatures of 120'C or higher. The effective modification by the epoxy resin is not expected under autoclaving at the maximum temperatures of 12O'C or higher.
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Curing conditions Autoclave cure Autoclave+heat cure
20.0
Polymer-cement ratio (%)
Maximum temperature vs. flexural strength of autoclave- and autoclave+heat-cured epoxy-modified mortars without hardener.
Fig. 1
Curing conditions Autoclave cure Autoclave+heat cure 3 60.0
Polymer-cement ratio (%)
a
3 50.0 -
5 40.0
30.0 >
’2 20.0 E
g 10.0 0
0
Fig.2
0 *
-
0 5
43-10
b v-
60 90 120150180 0 60 90 120150180
Maximum temperature (“c) Maximum temperature vs. compressive strength of autoclave- and autoclave+heat-cured epoxy-modified mortars without hardener.
-Curing conditions Autoclave cure Autoclave+heat cure
20.0
2
9 15.0
0
Fig.3
[
Maximum temperature (“c) 0 60
5
10 15 20 0
5
10 15 20
Polymer-cement ratio (%)
Polymer-cement ratio vs. flexural strength of autoclave- and autoclave+heat-cured epoxy-modified mortars without hardener.
--
Effects of accelerated curing conditions on strength properties of epoxy-modified ...
537
Curing conditions ,4utoclave cure Autoclave+heat cure
h / A n
0
5
10 15 20 0
5
10 15 20
Polymer-cement ratio (YO) Fig.4 Polymer-cement ratio vs. compressive strength of autoclave- and autoclave+heat-cured epoxy-modified mortars without hardener. Figs. 5 and 6 show the steam curing temperature vs. flexural and compressive strengths of steam- and steam + heat-cured epoxy-modified mortars without any hardener. Figs. 7 and 8 exhibit the polymer-cement ratio vs. flexural and compressive strengths of the steam- and steam + heat-cured epoxy-modified mortars without any hardener. The effects of the steam temperature and polymer-cement ratio on the flexural and compressive strengths of the steam-cured epoxy-modified mortars without any hardener are hardly recognized. However, the application of the heat cure to the steam-cured epoxy-modified mortars causes a remarkable improvement in their flexural and compressive strengths. The flexural and compressive strengths of the steam + heat-cured epoxy-modified mortars without any hardener are increased with an increase in the polymer-cement ratio regardless of the steam curing temperature. Irrespective of the polymer-cement ratio and curing temperature, the flexural and compressive strengths of the autoclave + heat- and steam + heat-cured epoxy-modified mortars without any hardener are markedly larger than those of the autoclaveand steam-cured ones. This is the result of the application of the heat cure to the autoclaveand steam-cured epoxy-modified mortars. The reasons for this are as follows: In the application of the autoclaving and steam cure to the epoxy-modified mortars without any hardener, the hydration of cement is accelerated to form cement hydrates and their matrixes are densified, the epoxy resin flowing out because of the lowered viscosity due to such high temperature and filling the pores in the mortars. In the application of the heat cure to the autoclave- and steam-cured epoxy-modified mortars, the epoxy resin without any hardener in the mortars can harden by the acceleration of its hardening reaction due to the heat cure in the presence of alkalis or hydroxide ions (OH-) from the calcium hydroxide [Ca(OH)*] as one of cement hydrates, and contribute to the strength development of the mortars. The hardening reaction of the epoxy resin in the presence of the hydroxide ions in the mortars can be expressed by the following formula'):
O-CH2-CH-CHl I OH hydration
Hardened epoxy resin
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Y. OHAMA and S. TAKAHASHI
Curing conditions Steam cure Steam+heat cure
* 5
-D- 10
10.0
-z3
5.0
60
0
Fig.5
75
,
90 0
60
75
Steam cunng temperature (“c)
90
--
Steam curing temperature vs. flexural strength of steam- and steam+heat-cured epoxy-modified mortars without hardener. Curing conditions Steam cure Steam+heat cure 9 60.0 r & 50.0 Polymer-cement ratio (%)
-
3
a
940.0
,
[> 30.0
I
.d
g 20.0 t!
g 10.0 n
4 60- 759 90 70
0
Fig.6
60 75 90 Steam curing temperature (“c ) Steam curing temperature vs. compressive strength of steam- and steam+heat-cured epoxy-modified mortars without hardener.
Curing conditions Steam cure Steam+heat cure
temperature (“c)
--
lo 15 20 0 5 lo 15 20 Polymer-cement ratio (%) Fig.7 Polymer-cement ratio vs. flexural strength of steam- and steam+heat-cured epoxy-modified mortars without hardener. 0
5
-
Effects of accelerated curing conditions on strength properties of epoxy-modified ...
-
539
Curine conditions Steam cure Steam+heat cure
0
5
10 15 20 0
5
10 15 20
Polymer-cement ratio (%) Fig.8 Polymer-cement ratio vs. compressive strength of steam- and steam+heat-cured epoxy-modified mortars without hardener. As stated above, the flexural and compressive strengths of autoclave + heat- and steam + heat-cured epoxy-modi tied mortars without any hardener are greatly improved with increasing curing temperature and period for accelerated cures, and polymer-cement ratio. This is ascribed to .the acceleration of both cement hydration and epoxy resin hardening reactions by the application of the accelerated cures. Accordingly, it is considered that the maturity method for the strength prediction of cement concrete can be applied to the autoclave + heat- and steam + heat-cured epoxy-modified mortars without any hardener. In the maturity method, the strength development of the cement concrete is expressed as a function of an integral of its curing temperature and period. Figs. 9 and 10 represent the product of the polymer-cement ratio and maturity vs. flexural and compressive strengths of the autoclave + heat- and steam + heat-cured epoxy-modified mortars without any hardener. The maturity is calculated by the following equation with a datum temperature of -10°C which is the same as that for ordinary cement concrete'). No compressive strength gain of the cement concrete takes place below the datum temperature".
M=C(T - To) t"*
(1)
where M is maturity ( V d l R ) of the epoxy-modified mortars without any hardener at any curing period, T is curing temperature ("C), TOis datum temperature (-lO'C), and t is curing period (d). The flexural and compressive strengths of the autoclave + heat- and steam + heat-cured epoxy-modified mortars without any hardener can be expressed as a logarithmic function of the product of the polymer-cement ratio and maturity as shown in Figs. 9 and 10. There is a reliable correlation between the product of the polymer-cement ratio and maturity and the flexural and compressive strengths. The general form of the equation for estimating the flexural and compressive strengths of the autoclave + heat- and steam + heat-cured epoxy-modified mortars without any hardener by the maturity method is expressed as follows: F=a+b log[(P/C)*M]
(2)
where F is flexural and compressive strengths (MPa) of the epoxy-modified mortars without any hardener at any curing period, PIC is polymer-cement ratio (%) of the epoxy-modified mortars without any hardener, M is maturity of the epoxy-modified mortars without any hardener at any curing pedod, and a and b are empirical constants.
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Y. OHAMA and S. TAUHASHI Steam+heat cure
3.03.1 3.23.3 3.43.5 3.6 3.73.83.94.0 log [(PIC).MI,x Fig.9 P/C*maturity vs. flexural strength of autoclave+ and steam+ heat-cured epoxy-modified mortars without hardener. Note, R : coeficient of correlation. 0
h
Steam+heat cure
[R = 0.94) $30.0
8
;20.0 e,
> 10.0 .z v)
Fc=-44.77 + 2 1 . 6 3 ~ (R = 0.92)
3.03.1 3.23.3 3.43.5 3.6 3.7 3.8 3.94.0 log [(P/C)-M], x Fig. 10 P/C*maturity vs. compressive strength of autoclave+ and s tea m+hea t -c ured epoxy-modified mortars without hardener. Note, R : coefficient of correlation.
8
CONCLUSIONS
The conclusions obtained from the above test results are summarized as follows: (1) The flexural and compressive strengths of autoclaved epoxy-modified mortars without any hardener tend to increase with increasing maximum temperature for autoclaving. The eRect of polymer-cement ratio on the flexural and compressive strengths is hardly recognized. The application of the autoclaving at maximum temperatures of 120°C or higher is not recommended for the epoxy-modified mortars because of the flowing out of the epoxy resin from the mortars due to a marked reduction in its viscosity. (2) The effects of steam temperature and polymer-cement ratio on the flexural and compressive strengths of steam-cured epoxy-modified mortars without any hardener are hardly recognized. (3) The flexural and compressive strengths of autoclave + heat- and steam + heat-cured epoxy-modified mortars are about twice to four times higher than those before the heat cure, and tend to increase with an increase in the polymer-cement ratio. The strengths of the autoclave + heat-cured epoxy-modified mortars are somewhat lower than those of the
Effects of accelerated curing conditions on strerigth properties of epoxy-niodfied ...
54 1
steam + heat-cured ones. (4) From the above results, the optimal curing conditions for epoxy-modified mortars without any hardener can be recommended as follows: (1) I-d moist[20'C, 9O%(RH)]+ autoclaving(90 or 120'C, 3h) + I-d heat(l20"C) cure, and (2) I-d moist[20'C, 90%(RH)]+ I-d steam(90'C) + I-d heat(l20-C) cure. The epoxy-modified mortars subjected to under the optimal curing conditions develop about twice or higher flexural and compressive strengths than unmodified mortars (PIC, 0%). ( 5 ) The flexural and compressive strengths of autoclave + heat- and steam + heat-cured epoxy-modified mortars can be predicted as a logarithmic function of the product of the polymer-cement ratio and maturity by equation (2):
REFERENCES 1. Ohama, Y., Demura, K., Uchikawa, H., Strength Development of Heat-Cured Epoxy-Modified Mortars without Hardener (in Japanese), Japan Cement Association Proceedings of Cement & Concrete, No.49, Dec. 1995, pp. 252-257 2. Ohama, Y., Katsuhata, T., Effects of Curing Conditions on Strength Properties of Epoxy-Modified Mortars without Hardener (in Japanese), Cement Science and Concrete Technology, No.56, July 2002, pp. 156-162 3. Joo, M., Ohama, Y., Demura, K., Strength Properties of Autoclaved SBR-Modified Concretes Using Ground Granulated Blast-Furnace Slag (in Japanese), Journal of Structural and Construction Engineering, No.545, July 2001, pp. 1-6 4. Carino, N.J., The Maturity Method: Theory and Application, Cement, Concrete, and Aggregates, Vo1.6, No.2, Dec. 1984, pp. 6 1-73 5 . Bergstrom, S.G., Curing Temperature, Age and Strength of Concrete, Magazine of Concrete Research, Vo1.5, No.14, Dec. 1953, pp. 61-66
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt. K C. Li and I. H. Marshall. eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ,. Warsaw 2003
FRP DEBONDING FROM A CONCRETE SUBSTRATE: CONVENTIONALBELIEF AND NEW FINDINGS Christopher K.Y. LEUNG Department of Civil Engineering Hong Kong University of Science and Technology Clear Water Bay, Kowloon HONG KONG
ABSTRACT Concrete beams and slabs can be effectively strengthened with the bonding of fiber reinforced plastic (FRP) plates. For the strengthened member, failure often occurs through the debonding (or separation) of the plate from the concrete member. The investigation of debonding mechanism has therefore been a major research topic for many years. Various theories on debonding failure have been established, but most of them have not been fully validated with experimental results. Results from an extensive testing program in our laboratory indicate that many existing theories and concepts are in contradiction to experimental observations. For debonding failure near the end of the plate, most existing failure criteria are based on interfacial stresses computed from elastic analyses that neglect the presence of discrete cracks. However, cracking at the plate end can be clearly observed before ultimate failure, and both experimental measurement and numerical modelling indicate that the interfacial stresses change significantly once cracking occurs. Predicted values from existing elastic models are therefore not applicable. For debonding initiated from a flexural crack near mid-span, fracture mechanics based models proposed by many investigators indicate that the plate stress at debonding failure is inversely proportional to the square root of the thickness. Test results from beams of various sizes and retrofitted with plates of different thickness show a different trend. To delay debonding failure, U-shape FRP ‘stirrups’ can be applied on top of the bonded strip. While it is commonly believed that the U-shape ‘stirrup’ should be placed at the end of the FRP plate, test results indicate that ‘stirrups’ applied away from the plate end can indeed be more effective.
Keywords composite, retrofitting, concrete beam, debonding
INTRODUCTION After years in service, many concrete structures have degraded and need to be repaired. In some cases, the structure has to be strengthened to accommodate the present load demand, which can be much higher than that when it was first constructed. For concrete beams and slabs, both laboratory and site investigations have demonstrated the bonding of fiber
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Christopher K.Y. LEUNG
reinforced plastic (FRP) plates to be an effective strengthening technique. For the strengthened beam (or slab), depending on the combination of parameters (such as beam size, steel reinforcement ratio, FRP properties and dimensions, etc), failure may occur in different modes [ 1-31. When failure is due to concrete crushing (with or without yielding of the steel), or rupture of the FRP plate, the failure load can be obtained from conventional section analysis for reinforced concrete members [4,5]. However, more commonly, failure is found to result from the debonding (or separation) of the plate from the concrete [6.7]. According to a wide range of experimental observations, debonding may either initiate at the end (or cutoff point) of the FRP plate and propagates inwards, or at the bottom of a flexural or shear/flexural crack of the concrete member and propagates towards the plate end. In the former case, failure usually involves the separation of the whole concrete cover from the rest of the member [8,9]. In the latter case, the debonded FRP usually carries with it a thin layer of concrete, indicating that failure is occurring inside the concrete substrate [7,10]. However, the layer attached to the FRP is only a small fraction of the cover. To predict debonding failure at the plate end, both the Coulomb criterion, involving the interfacial shear and normal stresses [ I 1,121, as well as the biaxial principal stress criterion, involving the interfacial stresses and the longitudinal stress in concrete adjacent to the interface [ 13,141, have been employed. To find the interfacial stresses, different equations have been derived in various investigations [ 15,16,17,18,19], based on elastic analysis of the strengthened member. In some cases, the reduced moment of inertia of the concrete member is employed to account for the effect of craclung. However, the ‘cracked’ concrete is still taken to be elastic (with reduced modulus) and the effect of discrete cracks near the plate end has never been studied. It appears that many researchers believe that failure is indeed governed by the elastic stresses, as many recent papers [ 16-19] are still attempting to develop better approaches to perform the elastic analysis. In the next section of this paper, we will present experiment results to show that cracking at the plate end occurs well before the load capacity of the strengthened member is reached. Once plate end cracking occurs, the interfacial stress distribution changes significantly from the elastic case. Implications to failure prediction are discussed. When debonding failure initiates from the bottom of a flexural or shear/flexural crack, the problem is often analyzed as the propagation of an interfacial crack when the FRP plate is pulled below the flexural crack. Various investigators [20,21,22,23] have proposed fracture mechanics based models for the analysis of crack-induced debonding. Despite the difference in details of the various models, they all predict the maximum debonding stress to decrease with the square root of the plate thickness. Such a theoretical trend has never been systematically assessed with experimental results. In the third section of this paper, we will describe a testing program to study the effect of FRP plate thickness on crack-induced debonding in members of various sizes. The trend of the experimental results will be compared to the prediction from existing theoretical models. To improve the resistance against debonding failure, U-shape FRP ‘stirrups’ can be applied. In Section 7.2.1.3 of the fib report on “Externally bonded FRP reinforcement for Reinforced Concrete Structures”[24], the following statement was made: “Anchoring of externally bonded reinforcement can be ensured by applying bonded FRP ‘stirrups’ that enclose the longitudinal strips at their ends these stirrups are not considered to be part of the shear reinforcement but are responsible to keep the longitudinal strips in their position and to prevent peeling-off.” According to this recommendation, FRP ‘stirrup’ should be applied at the plate end. To see if the plate end is indeed the optimal position for the FRP ‘stirrup’, experiments are performed with FRP ’stirrups’ applied at different locations along the plate. Results are presented in the fourth section of the paper.
FRP debonriingfiotn a concrete substrate: conventional belief and new findings
545
EFFECT OF CRACKING ON STRESSES NEAR THE PLATE END In this section, we will focus on debonding failure at the end of the FRP plate. To illustrate this failure mode, the photograph of a typical specimen is shown in Fig. I . For this particular specimen, the FRP plate was terminated close to the support. However, since the maximum shear force near the support was quite high relative to the maximum moment at mid-span, failure occurs by plate end debonding. In this case, the ultimate failure load is 341kN. At a load of 260kN (slightly over three quarters of the failure load), an inclined crack can be clearly observed to propagate upwards from the termination point of the FRP plate. Simple calculation shows that the bending moment at the section is not high enough to cause flexural cracking. The crack is initiated by high local stresses at the plate end, and propagates under the effect of shear force near the support. On further loading, the shear crack will continue to propagate (see Fig.1). When the failure load is approached (at 332kN). a fine horizontal crack is found at the level of the steel reinforcements. At failure, the unstable propagation of this crack causes the concrete cover to separate from the rest of the member.
Figure 1 Debonding Failure at the Plate End
In the experiment, strain gauges were placed along the bottom of the FRP plate. Knowing the variation of strain (E) with position (x) along the EXP plate, the interfacial shear stress (T)can be calculated from the following equilibrium equation: d&
r=t E yc?!x
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Christopher K. Y. LEUNG
where tp and E, are respectively the thickness and Young’s modulus of the FRP plate. As strain values are only available at a finite number of gauge points, z has to be obtained with a numerical approach. Noting that the strain has to be zero right at the end of the plate, the central difference method is employed to calculate the interfacial shear strain at each gauge point. For the specimen shown in Fig.1, the computed shear stress distribution is shown in Fig.2. While numerical differentiation may introduce errors to the stress values, the overall trend of the results should still be correct. From Fig.2, for a load value up to 260kN, the interfacial shear stress is found to increase rapidly when the plate end is approached. This observation is consistent with the results of elastic analysis [15-19]. However, with further increase in loading (P=270 kN onwards), a completely different shear stress distribution can be observed. The stress near the plate is significantly reduced. This can be explained by the formation of a major crack at the plate end, which causes unloading of longitudinal tension in the concrete, and reduction in interfacial shear stress. The transfer of loading from the concrete to the plate then becomes much more gradual. Instead of having concentrated shear stresses at the plate end. the shear stress is distributed over a much larger distance along the plate, with maximum value occurring at a distance from the end. The experimental results indicate that once cracking occurs at the plate end, the shear stress distribution obtained from an elastic analysis is no longer applicable. Note that we have deliberately shown the results for a specimen with the plate terminated close to the support. Even for this case, plate end cracking occurs at around 75% of the ultimate load. When the plate is terminated farther away from the support, plate end cracking will occur earlier, making the applicability of elastic analysis even more limited.
Figure 2 Variation of Interfacial Shear Stress obtained from Numerical Differentiation of Experimental Data To confirm the above experimental observation, finite element analysis has also been performed to study the effect of plate end cracking on the stress distribution along the interface. Two cases, one with no crack in the concrete member and one with a discrete crack extending from the end of the FRP plate into the concrete. are analysed with the same mesh refinement. In the analysis, material and geometric parameters are chosen to be within reasonable ranges. For t h e second case, an inclined crack with its tip at half of the beam depth is put in the model. Through the analysis, the effect of plate end cracking on both the
FRP debonding from a concrete substrate: conventional belief and newfindings
547
interfacial shear stress and interfacial normal stress can be obtained. The results are shown i n Fig.3. From Fig.3(a), the interfacial shear stress for the uncracked case is found to exhibit a concentration at the plate end, and decreases rapidly with distance from it. However, once cracking occurs, the stress concentration at the plate end disappears, and the shear stresses at locations away from t h e plate end are increased. This theoretical trend is in agreement with the experimental results in Fig2 above. Also, as shown in Fig.3(b), high interfacial normal stress occurs at the plate end when there is no cracking. However, once cracking occurs, the normal stress concentration is no longer present. Indeed, the normal stress decreases to very small values along the interface. Since stresses of such small magnitudes are unlikely to have significant effect on the ultimate failure of the strengthened member, they can probably be neglected in the analysis of debonding failure at the plate end.
(b) I (
-0 9 20.8 &7 * GO 6
-t o LI
5
804
g0.3
30.2 20.1
k
Y O 9 0I -0 2
Distance from plate end (mm)
Distance from plate end (mm)
Figure 3 Interfacial Shear and Normal Stresses from Finite Element Analysis In summary, experimental observations indicate that plate end debonding failure is always preceded by the formation of a crack at the plate end. Once the crack is formed, the shear and normal stress concentrations predicted by elastic analysis will both disappear. Indeed, the stress transfer mechanism is completely different, and the post-cracking stress distribution has no resemblance to the elastic distribution before cracking occurs. There is hence no theoretical ground to predict the failure load from stresses obtained by elastic analysis. For the proper modelling of debonding failure at the plate end, the actual failure mechanism needs to be considered.
EFFECT OF PLATE THICKNESS ON CRACK-INDUCED DEBONDING When a flexural or shear/flexural crack tends to open at the bottom of the beam, high interfacial shear stress will be induced along the interface to initiate debonding (Fig.4(a)). Once debonding has started, the pulling force on the plate will provide the driving force for the debonded zone to grow in size. Based on experimental observations from beams specimens under four-point loading (which is the most commonly adopted testing configuration), debonding always initiates under the crack closest to the loading point, where the moment is highest. To model crack-induced debonding, a common approach is to construct a simple model for the part of the member beyond the major crack (Fig.4(b)). A force is applied to the plate, and the debonding process is analyzed as the propagation of a
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Christopher K.Y. LEUNG
crack along the concreteFRP interface. In most existing models. bending of the concrete specimen is neglected. Debonding initiates at bottom of crack and propagates towards the plate end
Figure 4 Crack-induced Debonding and the Corresponding NIodel for Analysis One of the first models for FRP debonding was developed by Taljstan [20] with a LEFM approach. The force Fdbto cause debonding failure was derived as:
where b, t, and E, are respectively the width, thickness and Young’s modulus of the FRP plate. GIIis the interfacial fracture energy for mode II crack propagation. Also,
where E, and k are the Young’s modulus and thickness of the concrete member. a is hence the relative stiffness between the FRP plate and the concrete member (assuming the plate and the member to have the same width). In the same paper by Taljstan [20], assuming linear decrease of shear stress with interfacial sliding, the variation of debonding force with plate length was also derived. For this case, eqn (2) is also applicable to the prediction of debonding failure as long as the FRP plate is beyond the critical length (LJ for full development of the softening zone. Since most models ([ZO], [21], [23]) indicate that L, is only several hundred times the plate thickness, the plate length L (beyond the critical crack) in most strengthened members is beyond k. [n the following discussions, we’ll therefore focus on the case with L>L. For this case, Neubauer and Rostasy [21] showed that:
where fct, is the surface tensile strength of the concrete determined in a pull-off test. Also, k, is a factor accounting for the width ratio between the plate and the beam. In Neubauer and Rostasy’s model, the interfacial fracture energy is assumed to be proportional to fct,,,. Also, since the stiffness of the FRP plate is usually very small compared to the beam stiffness, the factor a is neglected. The constant 0.64 is determined from the fitting of experimental data. A similar model has also been proposed by Chen and Teng [23]. With the theoretical solution for FXP debonding derived by Yuan and Wu [ZZ], fitting of experimental data gives the following expression for the maximum debonding force (L > L):
FRP debonding from a concrete substrate: conventional belief and new findings
549
where fc is the concrete compressive strength obtained from a cylinder. Note that Pp is a width correction factor, slightly different in form to that given by Neubauer and Rostasy [21]. An important point to note from all the above models is that the maximum FRP stress (or strain) for debonding to occur, which is given by Fddbt, (Fdt,/Epbtp),is inversely proportional to the square root of the plate thickness. (Note: since a is usually small compared to one, it can be neglected in eqn(2).) Such a drastic reduction i n debonding stress will significantly affect the strengthening effect of the bonded plate. While small laboratory specimens can be effectively strengthened with thin plates, the repair method may not be effective for large members employed in real structures, where much thicker plates are required. Despite the important implication of this theoretical prediction to beam strengthening in practice, no systematic tests have been performed to verify its validity. We have therefore decided to perform a series of tests to study the effect of plate thickness on debonding in beams of various sizes. In the testing program, geometrically similar concrete beams of three different sizes are employed. These include small beams of 75mm (W) x 200mm (D) x 1S00mm (L), mediumsize beams of 150 x 400 x 3600mm and large beams of 300 x SO0 x 7200mm. The steel reinforcement ratio is essentially the same (around 1%) in all the beams. L is the span between supports, and all the members are subjected to four-point loading, with equal force applied at the one-third positions along the span. To study the size effect on plate strengthening, the small, medium-size and large beams are strengthened with geometrically similar FRP plates to achieve the same FRP volume fraction in all members. Also, to see how debonding is affected by plate thickness when the beam size is constant, medium-size beams are strengthened with plates of different thicknesses. In all the retrofitted beams, the FRP width is the same as the beam width, and the plates are terminated very close (at a distance of U120) to the supports. The test parameters and results are summarized in Table 1. TABLE I Fiber Strain at Debonding Failure of Various Beam Specimens
In the table, each specimen is notated by its size (S, M, L) and number of FRP plies (Note: thickness of each ply is 0.1 lmm). In each test, strain gauges are placed along the FRP plate, and the maximum strain (which occurs within the constant moment region) is given in the table. Also shown are computed values obtained in the following manner. Based on the point on the load vs displacement curve corresponding to steel yielding, the effective yield strength of the steel reinforcement is obtained from a conventional section analysis. Knowing the steel yield strength and the Failure load, the maximum FRP strain at debonding
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Christopher K. Y. LEUNG
is calculated. The good agreement between experimental and computed values indicates that the strain measurement is quite reliable. To study the effect of FRP thickness on maximum debonding strain, geometrically similar specimens (S2, M4, LS, or S4, M8 and L16) are first considered. For these two sets of tests, when the FRP thickness increases by four times from the small to the large specimen, the debonding strain reduces by only about 20%. Also, the rate of reduction from the small to medium-size specimens is much more significant than that from from the medium size to large members. Looking at the various medium-size beams (M2, M4, M6, M8), the EXP debonding strain does show a continuous decrease with plate thickness. However, for a fourfold increase in ply thickness, the debonding strain decreases by about one-third, rather than one-half. The inverse proportionality of debonding strain (or stress) to the square root of plate thickness, predicted by existing models, is clearly not supported by the test results. One common problem with the models described above is that only the major crack that initiates debonding has been considered. Other cracks along the beam (as shown in FigA(a)) are neglected in the model (Fig.4(b)). Since additional cracks along the span can modify the interfacial shear strain distribution, the neglecting of such cracks may lead to erroneous prediction of the debonding force (which is in equilibrium with the interfacial stresses). A recent model by Niedermeier [25] considers the presence of multiple cracks along the beam. We have compared the predictions from this model with the experimental results. The trend obtained for geometrically similar specimens is in better agreement with test results than the single crack models. However, for the medium-sized specimens strengthened with plates of different thickness, the predicted trend still differs significantly from experimental results. There is certainly a need to develop a better model for debonding failure in the future.
OF’TIMAL LOCATION OF FRP ‘STIRRUP’ ALONG THE BONDED PLATE To improve the resistance against debonding failure, one plausible approach is to apply an Ushaped FRP ‘stirrup’ (Fig.S(a)) on top of the bonded plate. As mentioned in the Introduction, according to the recommendations in afib technical report [24], the U-shaped ‘stirrup’ should be placed at the end of the bonded plate. However, it is not obvious to us that the plate end is always the optimal location for the FRP ‘stirrup’. We have therefore conducted a series of tests with the U-shaped ‘stirrup’ applied at various locations along the bonded plate. A typical specimen is shown in Fig.S(b). The size and steel reinforcement detail is exactly the same as that for the medium-size beam described in the last section. Four plies (0.44mm) of CFRP was bonded on the bottom of the beam before two U-shaped ‘stirrups’ (150mm wide,
Concrete Bonded FRP
Bonded FRP
X
(Distance of FRP ‘Stirrup’ from plate end)
Figure 5 (a) the FRP ‘Stirrup’, (b) A Typical Specimen with FRP ‘Stirrup’ along the Plate
FRP debonding from a concrete substrate: conventional belief and newjndings
55 1
0.22mm thickness) are applied symmetrically on both sides of the beam. The shear span in the beam is 1.2 m, and the plate is terminated at 50mm from each support. For various ‘stirrup’ locations, the results are summarized in Table 2. TABLE 2 Effect of ‘Stirrup’ Location on FRP Debonding Failure Specimen Control
u1 u2 u3
Location of ‘Stirrup’ from plate end (mm) N/A, No ‘Stirrup’ for the Control 0
530 750
Failure Load (kN) 263.35 263.92 783.74 299.24
The results in Table 2 indicate that the load capacity of the retrofitted beam increases when the FRP ‘stirrup’ is moved away from the plate end. Indeed, by placing the ‘stirrup’ right at the plate end, there is n o increase in load capacity. The explanation is as follows. In all the tested specimens, debonding failure is initiated by a crack near the loading point. The debonded zone has to reach the ‘stirrup’ before its resistance can be activated. If the ‘stirrup’ is far away from the middle of the beam, the contribution of the ‘stirrup’ to the total bond force is compromised by the decreasing load carrying capacity along the debonded interface due to shear softening. To maximize the total load carrying capacity, the ‘stirrup’ should be placed close to the initiation point of debonding, so the stirrup’s resistance is activated before significant debonding (and interfacial softening) has occurred. The results show that the recommended practice of putting the ‘stirrup’ at the plate end may not be appropriate.
CONCLUSION In this paper, experimental results are presented to show that many common believes related to debonding failure in FRP strengthened concrete beams are incorrect. Specifically, for plate end debonding, a physically sound failure criterion should not be based on elastic stresses. When debonding initiates from a crack at the middle of the beam, the drastic decrease of debonding stress with plate thickness, predicted by existing models, is not found in real specimens. Also, when FRP ‘stirrups’ are used to increase resistance to debonding, the recommended practice to apply the ‘stirrup’ at the plate end is not necessarily appropriate.
REFERENCES 1. Meier, U., Strengthening of Structures using Carbon FibreEpoxy Composites. Construction & Building Materials, 9, 1995, pp 341-353 2. Arduini, M., Di Tommaso, A. and Nanni, A., Brittle Failure in FRP Plate and Sheet Bonded Beams. ACI Structures Journal, 94, 1997. pp 363-370. 3. Buyukozturk, O., Leung, C., Hearing, B. and Gunes, O., Delamination Criterion for Concrete Beams Retrofitted with FRP Laminates. In “Fracture Mechanics of Concrete Structures”, H. Mihashi and K. Rokugo eds, 1998, AEDIFICATIO, pp 1771-1782. 4. Wei, A., Saadatmanesh, H. and Ehsani, M.R., RC Beams Strengthened with FRP Plates 11: Analysis and Parametric Study. i n ASCE J. of Structural Engineering, 117, 199 1, pp 34343455 5. Triantafillou, T.C. and Plevns, N., Strengthenmg of R/C Beams with Epoxy-Bonded Fiber Composite Materials. Materials & Structures, RLLEM, 25, 1992, pp 201-21 1
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6. Meier, U., Deuring, M., Meier, H. and Schwegler. G., Strengthening of Structures with CFRP Laminates: Research and Applications in Switzerland. tn “Advanced Composite Materials in Bridges and Structures”, Canadian Society for Civil Engineering, 1992, pp 24351.
Saadatmanesh, H. and Ehsani, M.R., RC Beams Strengthened with FRP Plates I: Experimental Study. ASCE J. of Structural Engineering, 117, 1991, pp 3417-3433 3. Sharif, A., Al-Sulaimani, G.J., Basunbul, I.A., Baluch, M.H. and Ghaleb, B.N., Strengthening of Initially Loaded Reinforced Concrete Beams using FRP Plates, ACI Structural Journal, 91, 1994, pp 160-168 9. Nguyen, D.M.. Chan, T.K. and Cheong, H.K., Brittle Failure and Bond Development Length of CFRP-Concrete Beams, ASCE J. of Composites for Construction, 5 , 2001, pp 1217 LO. Rahami, H. and Hutchinson, A., Concrete Beams Strengthened with Externally Bonded FRP Plates, ASCE I. of Composites for Construction, 5,2001, pp 44-56 11. Ziraba, Y.N., Baluch. M.H., Basunbul, LA., Azad, A.K., Al-Sulaimani, G.J. and Sharif, A.M.. Guidelines towards the Design of Reinforced Concrete Beams with External Plates, XCI Structural Journal, 91, 1994, pp 639-646 12. Varastehpour, H. and Hamelin, P., Strengthening of Concrete Beams using FiberReinforced’Plastics, Materials and Structures, 30, 1997, 160-166 13. Saadatmanesh, H. and Malek, A.M., Design Guidelines for Flexural Strengthening of RC Beams with FRP Plates, ASCE J. of Composites for Construction, 2, pp 158-164 14. El-Mihilrny, M. and Tedesco, J.W., Prediction of Anchorage Failure for Reinforced Concrete Beams Strengthened with Fiber-Reinforced Polymer Plates, ACI Structural Journal, 98,2001, pp 301-314 15. Roberts, T.M., Approximate Analysis of Shear and Normal Stress Concentrations in the Adhesive Layer of Plated RC Beams, The Structural Engineer, 67, 1989. pp 229-233 16. Taljsten, B., Strengthening of Beams by Plate Bonding. ASCE J. of Materials in Civil Engineering, 9, 1997, pp 206-212 17. Malik, A.M., Saadatmanesh, H. and Ehsani, M.R., Prediction of Failure Load of WC Beams Strengthened with FRP Plate due to Stress Concentration at the Plate End. ACI Structures Journal, 95, 1997, pp142-152 18. Rabinovich, 0. and Frostig, Y., Closed-form Higher-order Analysis of RC Beams Strengthened with FRP Strips, ASCE J. of Composites for Construction, 4,2000, pp 65-74 19. Shen, H.S., Teng, J.G. and Yang, I.. Interfacial Stresses in Beams and Slabs Bonded with Thin Plate, ASCE J. of Engineering Mechanics, 127,2001, pp 399-406 10. Taljsten, B., Strengthening of Concrete Prism using the Plate-bonding Technique. Int. J. of Fract., 82, 1996, pp 253-266 2 1. Neubauer, U., and Rostasy, F.S. Design Aspects of Concrete Structures Strengthened with Externally Bonded CFRP Plates.” Structural Faults and Repairs - 97, M.C. Forde, editor, 1997, pp 109-118 72. Yuan, H. and Wu, Z., Interfacial Fracture Theory in Structures Strengthened with Composite of Continuous Fiber”, Proceedings of Symposium of China and Japan, Science and Technology of 2 1” Century, Tokyo, Japan, 1999, pp 142-155 23. Chen, J.F. and Teng, J.G., Anchorage Strength Models for FRP and Steel Plates attached to Concrete, ASCE J. of Structural Engineering, 127, 2001, pp 784-791 24. Externally Bonded FRP Reinforcement for RC Structures, Technical Report prepared by fib Task Group 9.3 on FRP Reinforcement for Concrete Structures, 200 1 25. Niedermeier, R., Zugkraftdeckung bei klebearmierten bauteilen, Doctoral Dissertation. TU Munich (in German), 2000 7.
Proc. Int. Symp. ,,Brittle Matri.~Cotnposites 7 " A . M Brandt. V.C. Li and 1. H. Marshall. eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
PERFORMANCE CHARACTERISTICS OF BASALT REBAR REINFORCED CONCRETE BEAMS V. RAMAKRtSHNAN' and Ramesh K. PANCHALAN' South Dakota School of Mines & Technology, Rapid City, SD-5770 I USA, e-mail: [email protected], [email protected]'
ABSTRACT This paper presents the results of an experimental investigation that was carried out to evaluate the strength of the bond between basalt rebars (plain and modified) and concrete, and to compare the experimentally determined ultimate moment capacity of basalt rebar reinforced concrete beams and their calculated ultimate moment capacities according to ACI-3 18 Building Code recommended design procedures. It was found that the actual ultimate moments of beams reinforced with plain basalt bars were much less than the calculated ultimate moments due to bar pullout failure. The modified basalt rehars. which were provided with slots, corrugations and anchors, did not slip and the actual ultimate moments matched or exceeded the calculated moments. This paper also presents the results of the bond tests (ASTM C 234) performed on modified basalt rebars (4 slot and 8 slot), plain basalt rebars, single, double and triple cables. Keywords
Basalt rebars, basalt fibers, basalt cables, bond, ultimate moment capacity
INTRODUCTION Basalt fibers are manufactured in a single-stage process by melting pure raw material. They are environmentally safe, non-toxic, non-corrosive, non-magnetic, possess high heat stability and insulating characteristics. The tensile strength of continuous basalt fibers is about twice that of Eglass fibers and the modulus of elasticity is about 15-30% higher. Basalt fibers in an amorphous state exhibit higher chemical stability than glass fibers. When exposed to water at 70' C (158' F), basalt fibers maintain their strength for I200 hours, whereas the glass fibers do so only for 200 hours [ I ] . The innovative aspect of this research is the detailed study of non-corrosive, basalt fiber composite rebar. This rebar consists of 80% fibers and has a tensile strength three times that of the steel rebar normally used in building construction. It is made, by utilizing a resin (epoxy) binder [ I ] . Basalt fiber composite rebars have the potential to replace steel in reinforced
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V. RAMAKRISHNANand Ramesh K. PANCHALAN
concrete, wherever the corrosion problem exists. Currently there are many FRP rebar companies that market their products. Most of them ea! made of E-glass fiber and thermosetting resin. However these bars lack sufficient durability under extreme environments. These bars are costly, and are also non-resistant to alkalis [2-31. Basalt rebars do not possess these disadvantages and can be effectively used in various applications such as highway barriers, offshore structures and bridge decks. These advantages alone could warrant a sufficient argument for substitution of the basalt rebars in place of steel on a large scale. Other advantages of the basalt rebar are that its weight is one-third of the weight of steel and the thermal expansion coefficient is very close to that of concrete, The high mechanical performance/price ratio of basalt fiber composite rebar, combined with corrosion resistance to alkaline attack are further reasons, for replacing steel in concrete by basalt fiber composite rebars. There was no published information available on the behavior of the basalt fiber composite rebar and therefore there was a need for this research.
OBJECTIVE This investigation was undertaken to evaluate the performance of concrete beams reinforced with basalt fiber composite rebars. The following were the objectives of the research. To determine the ultimate failing load of the beams. To observe the bond strength between the rebar and concrete. To study the modes of failure of the beams subjected to flexural loading. 0 To compare the calculated and actual cracking and ultimate moments.
TENSION TEST O N BASALT BARS The tension test was done on basalt bars, with 14.25mm (0.56in.) and 6mm (0.24in.) in diameters and also on a cable, 6mm (0.24in.) in diameter, and the ultimate tensile strength was found to be 1458 MPa (21 1,382 psi), 707.5 MPa (102,595 psi) and 308 MPa (44,640 psi) respectively. The modulus of elasticity values for the rods and cables were 103.5 GPa and I10 GPa respectively. The bars experienced a brittle type of failure. The cable broke into two pieces without any splintering of the fibers, unlike both the bars.
PHASE I - FLEXURE TEST ON PLAIN BASALT BAR REINFORCED CONCRETE BEAMS A total of six beams designed and cast in the lab, reinforced with basalt rebars were tested. Research & Technology Inc, Madison, USA, supplied the basalt bars. The beams were designed by AC[-3 18 Building Code [4] recommended design procedures. The beams that were designed and cast in the lab are referred to as BRC-A to F in the discussion, and the details of the beams are given in Table I . The beams were tested in flexure after a 14-day curing period. The beams failed with a single crack instead of multiple cracking, which indicated slip of the reinforcing bars. All. the actual ultimate moments were much less than the calculated ultimate moments due to bar pullout failure (Table 2).
555
Performance characteristics of basalt rebar reinforced concrete beams
Table I - Details of Beams Designed and Cast in the Lab
I
I BRC-8
I
BRC-C
BRC-D
BRC-E
BRC-F
I
land length 1219.2 mm (48in). The cover was maintained at 125.4 mm (lin). Development length was 114.3 mm (4.511) on each side. 254mm x 254mm x 1295.4mni lTwo basalt rebars with a diameter of 14.2 mm (O.56in) (loin x loin x j l i n ) and length 1219.2 mm (48in). The cover was maintained at 25.4 mm ( I in). Development length IYBS 114.3 mni (&Sin) on each side. 304.8mm x 304.8mm x I295.4mm Two basalt rebars with a diameter of 14.2 mm (0.56in) (12inx 1 2 i n x j l i n ) and length 1219.2 mm (48in). The cover was maintained at 188.9 mm (3.5 in).Developnient length was 114.3 mm (4.511) on each side 2j4mm x 254mm Y 1295.4mm lTwo basalt rebars with a diameter of 14.2 mm (0.56in) (loins lOinx5lin) and length 1219.2 mm (48in). Thc cover was maintained at 82.5 mm (3.2 in).Development length was 114.3 inm (4.5in) on each side. l52.4mm x I52.4mm s 1295.4mni Two basalt rebars with a diameter of 14.2 mm (0.56in) (6in x 6in x j Iin) and length 1219.2 mm (48in). 'The cover was maintained at 15.4 min ( I in).Development length was 304.8 mm (1 2in) on each side. 152.4mm x 152.4mm x 1676.4mm Two basalt rebdrs with adiameter o f 5 . l mm (0.2in) and length 1 524 mm (60in). The cover was maintained at 25.4mm ( I in). (6in x 6in x 66in) Development length was 381 mm ( I j i n ) on each side. (12in x 12in x 5lin)
Table 2 - Comparison of Calculated & Actual Moments (Beams Cast in the Lab: BRC-A to F) Beam
No. BRC-A
Actual Moments Ultimate Cracking Ultimate Cracking Load Load kN(lbs) kN(lbs) kN.m(k-ft.) kN.m(k-ft.)
71.20 ( 16000)
BRC-B BRC-C BRC-D BRC-E BRC-F
44.50 (10000) 68.50 (1 5400) 43.00 (9700) 45.00 (10100) 12.20 (2750)
66.00 ( I 5000) 37.80 (8500) 57.80 (1 3000) 35.60 (8000) 40.00 (9000) 11.10
(2500)
19.04 (14.04)
11.90 (8.77) 18.30 (13.5 I ) 11.50 (8.50) 8.50 (6.32) 3.26 (2.60)
17.65 ( I 3.00) 10.11 (7.45) 15.50 (1 1.40) 9.50 (7.02) 7.62 (5.60) 2.96 (2.20)
Calculated Moments Ultimate Cracking kN.m(k-ft.) kN.m(k-ft.)
I 1 8.90 (87.70) 102.02 (75.23) 89.40 (659.00) 65.52 (48.30) 35.90 (26.50) 3.50 (2.60)
17.00 ( I 3.90) 9.49 (7.00) 17.00 (13.90) 9.50 (7.00) 2.20 (1.62) 2.20 (1.62)
After the testing was done the beam edges were cut using a diamond tipped saw. The slip
of the basalt bar was clearly visible at both the ends with a distinct mark left in the concrete at the original placing of the reinforcement. The actual slips were accurately measured. The overall test results indicate that there was insufficient bond strength and the bars slipped gradually before the ultimate load was reached. Two beams, BRC-E & F, were tested with increased
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development lengths. The spans for the beams were 0.75m (30in) and 0.9m (36in) respectively. Beam BRC-E failed in flexure, but at a higher load than beams BRC-A to D, due to the increased development length, whereas beam BRC-F, failed suddenly with the breaking of the reinforcement. It was a sudden and brittle failure. The measured and calculated cracking moments are also compared in Table 2. It was found from the investigation that the bond between the basalt rebar and the concrete matrix should be increased by roughening the bar or having modulations on the surface to increase the actual ultimate load carrying capacity of the beam.
PHASE 11 - BOND TEST ON BASALT REBARS AND CABLES (ASTM C 234) The results obtained from Phase I revealed that the actual ultimate moments of basalt rebar reinforced concrete beams were less than the theoretically calculated ultimate moments. This was due to bond failure between rebars and concrete. To avoid this type of failure the Principal author and Research & Technology Inc, had developed basalt cables with corrugations, rods with slots, barriers and anchors, for improving the bond between the bars and the concrete. The primary task in this phase was to study the bond between modified basalt rebars and concrete. There are several tests that can determine the bond quality of reinforcing element. One of these is the pullout test. In this test, the concrete is subjected to compression and the reinforcing bar is subjected to tension, and both the bar and the surrounding concrete are subjected to the same stress. The pull out test was done according to ASTM C234 [5].
Results First the plain basalt rebar reinforced specimens were tested for the bond strength at an age of 2 I days. As the load was applied the plain basalt rebars started slipping and there was no bond between the reinforcement and the concrete. It was also found that the grip of the testing machine was slipping i.e., it was not holding the bar properly as the basalt fibers in the bar were crushed and powdered. There was also a slip in the anchoring end leaving a scratch mark on the bar. Therefore, the anchorage was done using a chuck, which held the specimen in its place at the anchoring end. The specimen was then tested and the plain basalt bar slipped and the marks on concrete were distinctly seen on the bar. Then the 4-slot basalt bar was tested with both the lower and upper horizontal position of the reinforcement. The 4-slot basalt bar did not slip and hence there was no bond failure. But the basalt bar itself failed due to tension failure. The failure was brittle. The 8-slot basalt bar also failed in a similar manner to that of 4-slot basalt bar. The 2mm (0.08 in.) cables were also tested for the bond strength. At first a single cable was tested for the bond strength. The single cable failed in tension and there was no bond failure. The failure of the cable was brittle in nature. Similarly two cables were twisted together and were also tested for bond. The results were similar to that of the single cable test. The cables failed due to tension and not due to lack of bond. When three cables twisted together were tested, the failure mode was the same as described above for the single and two cables. All the modified basalt reinforced bars and cables except the plain basalt bar had good bond with concrete. The failure was due to the tensile failure of the rebars and the cables and not due to bond slip.
Performance characteristics of basalt rebar reitforced concrete beams
557
PHASE I11 - DETERMINATION OF CRACKING AND ULTIMATE LOADS FOR EXTREMELY UNDER-REINFORCED BEAMS Two extremely under reinforced beams (152.4 x 228.6 x 1 I 17.6 mm [6 x 9 x 44 in.], and 228.6 x 457.2 x 1320.8 mm [9 x 18 x 52 in.]), reinforced with modified basalt rebars were tested to see whether adequate bond was developed between the rebar and concrete. Research & Technology Inc supplied the rebars. The reinforcement details of the beams BRC-I and 2 are given in Table 3. The beams were designed and cast in the lab, and are referred to as BRC-I and BRC-2. The average cylinder compressive strength of the mix was 47 MPa (6816 psi). The reinforcement provided for one beam was less than the minimum required according to ACI code 318. Another beam was provided with the ACI recommended minimum reinforcement. Both beams were tested in flexure after the 28-day curing period. A development length of 203.2 mm (8 in.) was provided for both beams. The length between the two-point loading was 304.8 mm (12 inch). Beam BRC-I was reinforced with basalt cables (3.25 mm [O. 128 in. dia.]). The first crack occurred at the calculated cracking moment (Table 4). After first crack, the beam failed suddenly breaking into two pieces, because the beam was extremely under reinforced. The rebar broke without slipping, which indicated that there was good bond between the rebar and the concrete. Beam BRC-2 was under reinforced with the minimum ACI 318 recommended reinforcement. The beam first had a flexural crack at 85% of the calculated cracking moment (Table 4), but ultimately the beam failed in shear. This was attributed to the fact that the beam was very deep. Even though the beam failed in shear, it took 88% of the calculated ultimate moment (Table 4). The beam did not fail due to slip of the rebar, which indicated that there was a good bond between the 4-slot rebar and the concrete. If the beam had failed in flexure rather than in shear the beam would have definitely carried more ultimate moment than the calculated moment. The overall test results indicated that there was sufficient bond strength and the bars did not slip even after the ultimate load was reached. The measured and calculated ultimate and cracking moments are compared in Table 4. The tests indicated that it is possible to make concrete beams reinforced with basalt composite rebars. This testing gave adequate information to plan for testing other beams.
PHASE IV -TO DETERMINE CRACKING AND ULTIMATE LOADS FOR FIVE UNDER-REINFORCED BEAMS A total of five beams of dimensions, 127 x 203.2 x 1346.2 mm (5 x 8 x 53 in.), 127 x 203.2 x 1625.6 mm ( 5 x 8 x 64 in.), 76.2 x 101.6 x I143 mm (3x 4 x 45 in.), 152.4 x 254 x 1320.8 mm (6x 10 x 52 in.) [Fe-Mn-Ni anchors], and 152.4 x 254 x 1320.8 mm (6x 10 x 52 in) [Ti-Ni anchors], reinforced with basalt rebars were tested. Research 8c Technology Corp supplied the rebars and the five beams were designed and cast in the Rama Materials Laboratory at SDSM&T. The beams referred to as BRC-3 to BRC-7 in the discussion, were designed according to ACI-3 18 Building Code recommended design procedures. The reinforcement details of the beams BRC-3 to 7 are given in Table 3. All the beams were designed as underreinforced beams with the normal range used in construction. The average cylinder compressive strength of the concrete was 34.2 MPa (4959 psi). All beams were tested in flexure after a 28-day curing period. A development length of 203.2 mm (8 in.) was provided for all beams. The span between the two-point loading was 152.4 mm (6 in.) for all beams.
558
V. RAMAKlUSHNANana' Ramesh K. PANCHALAN
Table 3 - Details of Basalt Rods Used for Reinforcing the Concrete Beams ~~
No.
Size of Beam mm (Inches)
of
Description of bars
Bars
152.4 x 228.6 x I 117.6 mm BRC- I (6 x 9 x 44 in.)
Two basalt cables of 1016 mm (40 in.) length and 3.25 mm (0.128 in.) in diameter. Two basalt wires were sprirally wound to form a cable and were supplied by the manufacturer.
228.6 x 457.2 x 1320.8 mm (9 x 18 x 52 in.)
Two basalt rods of 1219 mm (48 in.) length and 10.4 r nn 2 . (0.41 in.) in diameter. Each rebar was provided with 4 slots for improving the bond.
BRC-2
I
One basalt rod of 1245 mm (49 in.) length and 8.6 mm (0.34 in.) diameter. The basalt rod had a corrugated surface. This ribbed or corrugated surface was obtained (by pultrusion. lTwo basalt strands of 1524 mm (60 in.) length and 8 mrr (0.3 I5 in.) diameter. Each strand was made by twisting three individual basalt wires of4.8 mm (0.19 in.) in diameter in the laboratory. Three basalt cables of 1041 mm (41 in.) length and 3.45 mm (0.136 in.) in diameter. Two basalt wires were spirally wound to form a cable and were supplied by the ,
BRC-4
127 x 203.2 x 1625.6 mm (5 x 8 x 64 in.)
BRC-5
7 6 . 2 ~1 0 1 . 6 ~1143mm (3 x 4 x 45 in.)
2
3RC-7
152.4 x 254 x 1320.8 mm (6 x 10 x 52 in.)
2
-
Two basalt rods of I2 I9 mm (48 in.) length and 9.65 mn (0.38 in.) in diameter. Each rebar was provided with 2 slots for improving the bond. The rods were also provided with I Fe-Mn-Ni anchors (smart alloys) on each end of the bar to prevent slip. Two basalt rods of I245 mm (49 in.) length and 10. I mn (0.399 in.) in diameter. Each rebar was provided with 2 slots for improving the bond. The rods were also provided with 2 TiNi (50/50) anchors (smart alloys) on each end of the bar to prevent slip.
Beam BRC-3 was designed as a lightly under reinforced beam with one corrugated basalt rod 8.6 mm (0.34 in. dia). The first crack occurred at 95% of the calculated cracking moment (Table 4). After first crack the beam took 2.7 times more moment than the cracking moment (Table 4) indicating very good bond strength between the rebar and the concrete. The beam failed at 98% of the calculated ultimate moment (Table 4). The beam failed primarily in flexure and secondarily in shear. Beam BRC-4 was also under reinforced. Two cables of 1524 mm (60 in.) length and 8 mm (0.315 in.) diameter were used as rebars. These cables were made in the laboratory by twisting three individual basalt wires into one. The beam first had a flexural crack at 76% of the calculated cracking moment (Table 4). After first crack the beam took 4.9 times more moment than the cracking moment (Table 4) indicating very good bond strength between the rebar and the concrete. The beam failed at 97% of the calculated ultimate moment (Table 4). The beam
559
Performance characteristics of basalt rebar reiiforced concrete beams
failed purely in flexure. Overall the performance of the beam was good and the wires split partially at failure indicating good bond strength. The cables did not slip even after the ultimate load was reached. Table 4 - Comparison of Calculated and Actual Moments
* Beam No.
BRC-I
Actual Moments Ultimate Cracking N-m (Ib-in) N-m (lb-in.)
I
5038 (44588)
4992 (441 80)
Calculated Moments Ultimate Cracking N-m (lb-in.) N-m (lb-in.)
4997 (44218)
Type of Failure
Flexural failure. Beam failed by splitting into two 4997 (44218) pieces due to the complete fracture of the rebars. First flexural cracking 28116 (248815) followed by failure in shear. Primary flexural failure 3260 (28852) and secondary shear failure. Typical flexural failure 3376 (29879) with partial fracture of strands
+ I t BRC-2 63457 (561570) 23691 (209658) 72340 (640179)
BRC-3
8407 (74400)
3107 (27497)
BRC-4 12577 ( I 1 1300) 255 I (22575)
BRC-5
I137(10063)
481 (4261)
BRC-6 33 I84 (293663)
6475 (57300)
BRC-7 38724 (342690)
6610 (58500)
8619 (76273)
12983(114895)
Beam failed primarily in flexure by splitting into 765 (6772) 505 (4471) two pieces aker fracture rebar Primary flexural failure 29685 (262701) 6199 (54855) and secondary shear failure. Primary flexural failure 32047 (283605) 6160 (545 13) and secondary shear failure.
Note: In all the beams, the rebars did not slip or pull out, and there was no bond failure.
Beam BRC-5 was made of three basalt cables of 1041.4 mm (41 in.) length and 3.45 mm (0.136 in.) diameter (Table 3). The beam was under-reinforced. The cables were supplied by the manufacturer, unlike the one used in beam BRC-4 which was made in the laboratory. The beam first had a flexural crack at 95% of the calculated cracking moment (Table 4). After the first crack the beam took 2.4 times more moment (less than the other beams because it was underreinforced, and the tensile strength of the bar was also less) than the cracking moment (Table 4) indicating very good bond strength between the rebar and the concrete. The beam took 49% more than the calculated ultimate moment (Table 4). The beam failed primarily in flexure and secondarily in shear. Overall the performance of the beam was good and the cables completely fractured at failure, indicating good bond strength. The cables did not slip even alter the ultimate load was reached. Beam BRC-6 was made with two basalt rods of 1219.2 mm (48 in.) length and 9.65 mm (0.38 in.) diameter (Table 3). The beam was lightly under-reinforced. The rods were supplied by
560
V. R4MAKlUSHiVAN and Ramesli K. PANCHALAN
the manufacturer and were provided with I Fe-Mn-Ni anchors (smart alloys) on each end of the bar to prevent slip. The first flexural crack occurred at 4.5% more than the calculated cracking moment (Table 4). After first crack the beam took 5.1 times more moment than the cracking moment (Table 4) indicating very good bond strength between the rebar and the concrete. The beam took 12% more than the calculated ultimate moment (Table 4). The beam failed primarily in flexure and secondarily in shear. Overall the performance of the beam was very good and the rods did not slip even at failure because of the anchors provided at the ends. Beam BRC-7 was made with two basalt rods of 1219.2 mm (48 in.) length and 10. I mm (0.399 in.) diameter (Table 3). The beam was lightly under-reinforced. The rods were supplied by the manufacturer and were provided with 2 Ti-Ni ( S O / S O ) anchors (smart alloys) at each end of the bar to prevent slip. A strain gauge was placed on the compression side of the beam, and another strain gauge was also placed on the rebar in the slot to measure the strain in the rebar. The first flexural crack occurred at 7.3% more than the calculated cracking moment (Table 4). After the first crack the beam took 5.9 times more moment than the cracking moment (Table 4) indicating very good bond strength between the rebar and the concrete. The beam took 21% more than the calculated ultimate moment (Table 4). Of all the beams, this beam performed very well basically because of the anchors and the slots that were provided on the rebar. The beam failed primarily in flexure and secondarily in shear. Overall the performance of the beam was very good because of the anchors at the ends. The rods did not slip even after the ultimate load was reached. A typical load vs. deflection, load vs. concrete strain and load vs. basalt rebar strain for beams reinforced with modiJied basalt rebars are shown in Figures I , 2 and 3 respectively.
Fig. I: Load Vs. Deflection.
Performance characteristics
45000
-
__ _ _ _
40000 --
'
-
.
3 5 m --
4
h
v
U
2
-1
2j000 30wO
---- -
20000 .. --- 15wO .-
.
_
_
_
-Slrain gduge located at 0 25 from the top(comfression - side) at the center ofthe beam
-
/ T i : i/.
__
-
__
_-
__
.
-
- -_ _ .
1000
500
0
~
in
~
-
--
56 1
of basalt rehar reirrforced concrete beams
I500
-
2500
2000
3000
Compressive Micro Strain
Fig. 2: Load Vs. Concrete Strain. 45m 40000
35000 30000 h
4
25000
Y
W
2
-1
20m
I jooa
1oooc SON
C 0
1000
2000
3000
4000
5000
6000
7000
Tensile Micro Strain
Fig. 3: Load Vs. Basalt Rebar Strain.
8000
9000
loo00
562
V. RrlMAKRISHNANand Ramesh K. PANCHALAN
CONCLUSIONS Phase I The beams reinforced with plain basalt composite bars failed in flexure, due to inadequate bond between the rod and the concrete. All the actual ultimate moments were much less than the calculated ultimate moments due to the bar pullout failure. Phase 11 to IV The bond between all the modified basalt rebars and concrete was extremely good. The experimental ultimate moment was much higher than the first crack moment in all the beams tested, indicating a good bond between rebar and concrete. The deflections were considerable indicating adequate ductility. All the beams had primary flexural failures and a few beams had secondary shear failures. There was no slip of the rebars in any of the beams tested and there was no evidence of bond failure between the concrete and the modified basalt rebars and twisted cables. 0 In general, the basalt rebars are suitable for use in reinforced concrete structures.
REFERENCES I . Vladimir Brik, V. Ramakrishnan and Neeraj Tolmare, “Performance Evaluation of 3-D Basalt Fiber Reinforced Concrete & Basalt Rod Reinforced Concrete”, IDEA Program Final Report, Contract No. NCHRP-45, November 1998. 2. Ramakrishnan, V., “Recent Advancements in Concrete Fiber Composites”, Concrete Lecture- 1993, American Concrete Institute, Singapore Chapter, Singapore. 3 . Ramakrishnan, V., ‘‘ Performance characteristics and Application of High-Performance Polyolefin Fiber Reinforced Concretes”, SP-17 I , Proceedings of the third CANMET/ACI. International conference ‘Advances in Concrete Technology’, American Concrete Institute, Detroit, 1997, pp. 67 1-692. 4. ACI Committee 3 18, “Building Code Requirements for Structural Concrete and Commentary”, ACI 3 18 R-99 American Concrete Institute, Detroit, 2000, pp. 1-65. 5. ASTM C234-91a, “Standard Test Method for Comparing Concretes on the Basis of the Bond Developed with Reinforcing Steel”, American Society of Testing of Materials, 1998. 6. ASTM C 293-94, “Standard Test Method for Flexural Strength of Concrete (Using Simple Beam With Center-Point Loading)”, American Society of Testing of Materials, 1998. 7. ACI Committee 440, “Guide for the Design and Construction of Concrete Reinforced with FRP Bars”, ACI Report 440.1 R-0 I American Concrete Institute, Detroit, 200 I , pp. 1-41. 8. ACI Committee 440, “State-of-the-Art Report on Fiber Reinforced Plastic Reinforcement for Concrete Structures”, ACI Report 440 R-96 American Concrete Institute, Detroit, 1996, pp. 1-65.
INDEX OF CONTRIBUTORS Elsadeg A. ABDALLA, Libya 431 Marian ABRAMOWICZ, Poland 515 Hiroshi AKITA, Japan 263 F. AKOPOV, Russia 75 U. ANTONS, Germany 233 Sttphane AVRIL, France 401 Beata BACKIEL-BRZOZOWSKA, Poland 495 I. BANJAD-PECUR, Croatia 173 Ben. BARR, UK 201 Peter J.M. BARTOS, UK 31 1 Vlastimil BiLEK, Czech Republic 269 Sarah L. BILLINGTON, USA 47 Benolt BISSONNETTE, Canada 181 S . BOIKO, Israel 351 Sandra BONNET, France 359 A. M. BRAGOV, Russia 67,754 91 F. BUYLE-BODIN, France 153 N. CHOI, Korea 485 Heidi. CUYPERS, Belgium 163 Michele F.CYR, USA 243 P. DEMENKO, Russia 91 Tejal DESAI, USA 223 Milog F. DRDACK?, Czech Republic 523 David DUPONT, Belgium 253 Liberato FERRARA, Italy 287 Lukasz FIGIEL, Germany 477 Gregor FISCHER, USA 29 A. FNINE, France 153 Jure GALIC, Croatia 173 Niels JGrgen GIMSING, Denmark 191 Michal A. GLINICKI, Poland 101 Jacek GOUSZEWSKI, Poland 339, M. GOUEYGOU, France 153 Jean-Louis GRANJU, France 181,359 Cole GRAVEN, USA 379
Michael HAIST, Germany 301 Patrice HAMELIN, France 401 K. P. HERRMANN, Germany 459 Jing HU, The Netherlands 143 Marcin KAMfiSKI, Poland 477 Maria KASZfiSKA, Poland 331 Zbynek KERSNER. Czech Republic 269 Christoph KESSLER-KRAMER, Germany 277 Janusz R. KLEPACZKO, France 1 Hideo KOIDE, Japan 263 Aleksander KOZAK, Poland 443 Jiri KRATKv, Czech Republic 515 Karl KROMP, Austria 389 Leopold KRUSZKA, Poland 67,75,91 Ming Ken LEE, UK 201 Michael LEPECH. USA 57 Christopher K.Y. LEUNG, Hong-Kong 543 Victor C. LI, USA 29,37,57 Agnieszka LITOROWICZ, Poland 101 Qian LIU, P.R. China 449 Dieter LOIDL, Austria 389 A. K. LOMUNOV, Russia 67,75,91 Tatiana LYASHENKO, Ukraine 35 1 Viktor MECHTCHERINE, G e m n y 277, 301 Dagmar MICHOINOVA, Czech Republic 523 V. MINEEV, Russia 75 Banin MOBASHER, USA 223,505 Harald S. MULLER, Germany 277,301 Tommy NANTUNG, USA 379 A. NEUBRAND, Germany 81 Y. OHAMA. Japan 485,533 Mitsuo OJIMA, Japan 263 Jan OLEK, USA 379 John Forbes OLESEN, Denmark 191.459
564 Jeanette ORLOWSKY, Germany 163,233 S. OULD-NAFFA, France 153 Chengsheng OUYANG, USA 243 Lennart OSTERGAARD, Denmark 467
Tomasz TRACZ, Poland 443 Anaclet TURATSINZE, France 181,359
Ramesh K. PANCHALAN, USA 553 A h a PELED, Israel 223,505 Herwig PETERLIK, Austria 389 B. PIWAKOWSKI, France 153 Tomasz PONIKIEWSKI, Poland 321 Sandor POPOVICS, USA 421 Stephan PUCHEGGER, Austria 389 Sunil PURI, USA 1 1 1
Lucie VANDEWALLE, Belgium 253 Alain VAUTRIN, France 401 Jan VODICKA, Czech Republic 515 V. VOZNESENSKY, Ukraine 351
Wojciech RADOMSKI, Poland 43 1 Venkataswamy RAMAKRISHNAN, USA 553 M. RAUPACH, Belgium and Germany 163,233 R. REKUCKI, Poland 91 J. Matt ROUSE, USA 47 Vincent SABATHIER, France and Canada 181 Tomasz SADOWSKI, Poland 81 Pave1 SCHMID, Czech Republic 269 I.V. SERGEICHEV, Russia 75 Rimpal SHAH, USA and Israel 223 Surendra P. SHAH, USA 243 D. SHTAKELBERG, Israel 351 Mohammed SONEBI, UK 31 1 DuSan SPfiRA, Czech Republic 515 Lothar STAERK, Germany 301 Henrik STANG, Denmark 191,467 Piet STROEVEN, The Netherlands 121, 129,143 Peijiang SUN, USA 369 Yves SURREL, France 401 Lucie SVERMOVA, Czech Republic 3 11 R.N. SWAMY, UK 211 Janusz SZWABOWSKI, Poland 321,339 Jacek SLIWINSKI, Poland 443 N. STIRMER, Croatia 173 S. TAKAHASHI, Japan 533 Basile TAMTSIA, Canada 181 D. THEDOROKOPOULOS, Greece 21 1
V. UKRAINCZYK, Croatia 173
Rasmus WALTER, Denmark 191 Shuxin WANG, USA 29 Lin WANG, P.R.China 449 J. WASTIELS, Belgium 163 Martin B. WEIMANN, USA 37 W. Jason WEISS, USA 11 1,379 Hwai-Chung WU, USA 369 Jun ZHANG, P.R. China 449 Junqian ZHANG, P.R.China 459
BRITTLE MATRIX COMPOSITES 7
Proceedings of the Seventh International Symposium on Brittle Matrix Composites BMC7, held in Staszic Palace, Warsaw, Poland, 13-15 October 2003
Also published previously: Brittle Matrix Composites 1 Proceedings of the 1'' International Symposium and EUROMECH Colloquium 204, Elsevier Science Publishers, 1985 Brittle Matrix Composites 2 Proceedings of the 2"dInternational Symposium, Elsevier Science Publishers, 1988 Brittle Matrix Composites 3 Proceedings of the 3rdInternational Symposium, Elsevier Science Publishers, 1991 Brittle Matrix Composites 4 Proceedings of the 4" International Symposium, Woodhead Publ. Ltd. (Cambridge) and Inst. of Economic Education (Warsaw), 1994 Brittle Matrix Composites 5 Proceedings of the 5" International Symposium, Woodhead Publ. Ltd. (Cambridge) and BIGRAF (Warsaw), 1997 Brittle Matrix Composites 6 Proceedings of the 6' International Symposium, Woodhead Publ. Ltd. (Cambridge) and ZTUREK Research-Scientific Institute (Warsaw), 2000
INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH POLISH ACADEh4Y OF SCIENCES
BRITTLE MATRIX COMPOSITES
7 Edited by
A.M. BRANDT Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, Poland
V.C. LI Department of Civil and Environmental Engineering University of Michigan, Ann Arbor, USA
I.H. MARSHALL Monash University, Melbourne, Australia
WOODHEAD PUBLISHING LIMITED ZTUREK RESEARCH-SCIENTIFIC INSTITUTE CAMBRIDGE and WARSAW 2003
@ 2003 Institute of Fundamental Technological Research, Warsaw
WOODHEAD PUBLISHING LIMITED Abington Hall, Abington, Cambridge, England
ZTUREK RESEARCH-SCIENTIFIC INSTITUTE Warsaw, Poland
ISBN 1-85573-769-8 ISBN 83-917926-6-8
Conditions of sale: All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. British Library Cataloguing in Publication Data. A catalogue record for this book is available from the British Library.
The selection and presentation of material and the opinion expressed in this publication are the sole responsibility of the authors concerned. No responsibility is assumed by the Publishers for any injury andor damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any method, products, instructions or ideas contained in the material herein.
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ZTUREK Research-Scientific Institute 00-950 Warsaw 1, P.O.Box 674 www.zturek.pl, e-mail [email protected]
V
Preface When organizing, for the first time, an international gathering of specialists in any given field a number of uncertainties present themselves e.g. is such a gathering necessary for the advancement of knowledge? will the chosen venue be appropriately attractive to overseas participants?, will sufficient authoddelegates attend? will the papers presented reflect state-ofthe-art advances in the field of research? will the gathering be a "one-off'' meeting making a valuable contribution to current knowledge and understanding or will it act as a catalyst for future developments in research and development leading to an ongoing dialog between specialists in the chosen area? will the resulting Proceedings Volume achieve international recognition as a valuable contribution to science? In essence, will the "Symposium" stand the test of time? Questions such as these must have invaded the mind of first undersigned editors in 1984 when he approached the Euromech Organization with a proposal to organize an International Symposium on Brittle Matrix Composites in the following year i.e. BMC 1 in November 1985. History has conclusively answered all of the aforementioned questions. The triennial BMC Symposia have gone on from strength to strength and are now firmly established both as a leading international gathering of specialist in brittle matrix composites and in the general field of composite materials. Few international conferences in any subject can plan for the future with the level of confidence enjoyed by BMC! Thus, the triennial International Symposia in Brittle Matrix Composites are now firmly established as a forum for diffusion of new solutions, ideas and methods related to brittle matrix composites. The BMC Symposia have provided for the past 18 years a convenient place for presentation of new research results and for discussion, among specialists, of recent developments in the field of brittle matrix composites. It is also the main conference in composites where researchers from Eastern and Western Europe, and many other countries outside of Europe, gather once every three years to update developments in composite research and development in their parts of the world. Innovative high performance materials are increasingly being used in diverse applications. Consequently, their properties, methods of composition and manufacturing, test methods, etc., are studied in many research centers in the world. Most often, however, they are presented separately, at specialized conferences dedicated to cement based materials, ceramics, and so forth. At BMC Symposia it is possible to compare solutions applied to similar problems in different domains. The present Symposium organised for October 13-15, 2003, maintains basically the same format as on previous occasions. It is focused on brittle matrix composites and covers a wide spectrum of topics with the following main groups of composites: - cement based composites, - ceramic composites, - brittle polymer matrix composites. In the papers various topics and issues related to brittle matrix composites are considered: - analytical and numerical studies, related to design of composites, - prediction of behaviour and verification of strength and stability, - testing methods and experimental test results, - manufacturing processes and repair of structures, - environmental effects and durability assessment, - specific applications in structures.
vi The papers have been selected on the basis of two-stage peer reviewing. The present volume proves that there are still many problems in the field of brittle matrix composites deserving theoretical and experimental investigations and that new solutions of these problems are needed for practical application in civil engineering, industrial structures, machinery and other domains. The relative brittleness of this class of materials is one of the problems that are considered as basic from both safety and durability viewpoints. In various structural and nonstructural elements the brittleness and cracking process must be controlled and maintained within acceptable limits. In the present volume new approaches are shown, e.g. artificial intelligence in prediction of composite properties, optimization as an integral part of material design, nondestructive testing and computer simulations, advanced test methods and stochastic analysis. Particular attention is paid to durability throughout all the life-cycle of the structures made of composite materials. This reflects a general trend in structural design: durability, sustainability and economical ’ calculations covering all stages of the life of a structure. The volume contains 55 papers prepared by 120 Authors from 22 countries from the entire world. Particular thanks are addressed to the Authors for their readiness to prepare and to present the results of their outstanding investigations in the form of original contributions and excellent reviews. There is no doubt that the papers contained herein address exciting new topics and advanced research methods. The cooperation of the Authors in accepting reviewers’ comments and suggestions and revising their manuscripts accordingly in order to obtain a consistently homogeneous book is greatly appreciated. Thanks are due to Members of the International Advisory Board for their significant help in reviewing the papers and in numerous other problems encountered during the organizational stages. Grateful thanks are extended to the Members of the local Organizing Committee for their efforts and creative attitude during preparation of the event. Without their dedicated work it would not have been possible to publish this volume before the Symposium date. The support from the Institute of Fundamental Technological Research of the Polish Academy of Sciences was essential for organization of this Symposium as well as in past years. Thanks are also due to the National Science Foundation (USA) for the financial support given to American scientists for their participation at BMC7. The Symposium has obtained the scientific sponsorship from RILEM, which is acknowledged with gratitude. We sincerely hope that this volume, along with the six previously published in this series, will contribute in development of science and technology in the field of composite materials.
A.M. Brandt V.C. Li LH. Marshall Warsaw, Ann Arbor, Melbourne, July 2003
vii SYMPOSIUM CO-CHAIRMEN: Prof. A.M. Brandt, Warsaw - Poland Prof. V.C. Li, Ann Arbor - USA Prof. I.H. Marshall, Melbourne - Australia
INTERNATIONAL ADVISORY BOARD: Prof. B. Ban, Cardiff - UK Prof. A. Bentur, Haifa - Israel Prof. J.L. Chermant, Caen - France Prof. Zhao Guofan, Dalian - P.R. China Prof. J. Kasperkiewicz, Warsaw - Poland Prof. K. Kromp, Vienna - Austria Prof. S . Mindess, Vancouver - Canada Prof. Z . Mrbz, Warsaw - Poland Prof. Y. Ohama, Koriyama - Japan Prof. H.W. Reinhardt, Stuttgart - Germany Prof. S.P. Shah, Evanston -USA Prof. H. Stang, Lyngby - Denmark Prof. P. Stroeven, Delft - The Netherlands Prof. R.N. Swamy, Sheffield - UK Prof. A. Vautrin, St. Etienne - France ORGANIZING COMMITTEE: Prof. J. Kasperkiewicz Prof. M.A. Glinicki Mrs. A. Gutweter Dr. M. Marks Mr. M. Sobczak Mrs. J. Tymkiewicz
ix
Table of Contents
Preface ......................................................................................................
v
PLENARY INVITED PAPER (1)
On a very high rate sensitivity of concrete failure at high loading rates and impact Janusz R. KLEPACZKO, France ..................................................................................
1
CONTRIBUTIONS Design of Engineered Cementitious Composites (ECC) for processing and workability requirements Gregor FISCHER, Shuxin WANG i d Victor C. LI, USA .........................................
29
Drying shrinkage and crack width of an Engineered Cementitious Composites (ECC) Martin B. WEIMANN and Victor C. LI, USA .............................................................
37
Time-dependent response of highly ductile fiber-reinforced cement-based composites Sarah L. BILLINGTON and J. Matt ROUSE, USA .....................................................
47
Preliminary findings on size effect in ECC structural members in flexure Michael LEPECH and Victor C. LI, USA ....................................................................
57
Static and dynamic properties of dry and wet cement mortar A. M. BRAGOV, L. KRUSZKA and A. K. LOMUNOV, Poland and Russia ........67 Investigation of static and dynamic loading of dioxide-zirconium ceramics and zirconium alumina concrete F. AKOPOV, A. M. BRAGOV, L. KRUSZKA, A. K. LOMUNOV, V. MINEEV, and I. V. SERGEICHEV Poland and Russia ........................................
75
Thermal shock crack propagation in functionally graded strip T. SADOWSKI and A. NEUBRAND, Poland and Germuny. ....................................
81
Experimental testing of concretes subjected to impact and explosive loads M. BRAGOV, P. DEMENKO, L. KRUSZKA, A. K. LOMUNOV and R. REKUCKI, Poland and Russia .......................................................................
91
Application of UV image analysis for evaluation of thermal cracking in concrete Michal A. GLINICKI and Agnieszka LITOROWICZ, Poland ................................
101
X
Assessing damage localization in concrete cylinders tested in compression Sunil PURI and W. Jason WEISS, USA ...................................................................
111
Quantitative damage analysis of concrete Piet STROEVEN, The Netherlands ............................................................................
121
Implications of the law of aggregation of matter in concrete technology Piet STROEVEN. The Netherlands ...........................................................................
129
The influence of particle size distribution on the microstructure of model cement Jing HU and Piet STROEVEN, The Netherlands ......................................................
143
Assessment of deteriorated concrete cover F. BUYLE-BODIN, B. PIWAKOWSKI, A. FNINE, M. GOUEYGOU and S . OULD-NAFFA. France ........................................................................................
153
Measurement of the durability of glass fibre reinforced concrete and influence of matrix alkalinity H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M. RAUPACH, Belgium and Germany.............................................................................
163
Bridge reconstruction with one layer concrete overlay Jure GALIC, I. BANJAD-PECUR, N. STIRMER and V. UKRAINCZYK, Croatia.................................................................................................
173
Cement-based thin bonded overlays: numerical study of the influence of bonds defect and fibre reinforcement Vincent SABATHIER, Jean-Louis GRANJU, Benoit BISSONNETI'E, Anaclet TURATSINZE, and Basile TAMTSIA, France and Canada ......................
181
Debonding of FRC composite bridge deck overlay Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jflrgen GIMSING, Denmark ......................................................................
191
PLENARY INVITED PAPERS (2 and 3) Multi-exponential models as descriptive tools for plain concrete and FRC Ming Kien LEE and B. BARR, UK ...........................................................................
201
Design equations to predict the ultimate punching shear strength of slab-column connections D. THEDOROKOPOULOS and R.N. SWAMY, Greece and UK ...........................
21 1
xi CONTRIBUTIONS Mechanical properties of concrete reinforced with AR-Glass fibers Tejal DESAI, Rimpal SHAH, Alva PELED and Barzin MOBASHER, USA and Israel ........................................................................................
223
Behaviour of glass-filament-yarns in concrete as a function of time and environmental conditions Jeanette ORLOWSKY, U. ANTONS and Michael RAUPACH, Germany .............. 233 Design of hybrid-fiber reinforcement for shrinkage cracking by crack width prediction Michele F. CYR, Chengsheng OUYANG and Surendra P. SHAH, USA .................243 The cracking behaviour of SFRC beams containing longitudinal reinforcement David DUPONT and Lucie VANDEWALLE, Belgium ...........................................
253
Tensile behavior of a recycled concrete Hiroshi AKITA, Hideo KOIDE and Mitsuo OJIMA, Japan .....................................
263
Toughening mecha9isms in concrete: influence of aggregate type Vlastimil BILEK, Zbyngk KERSNER and Pave1 SCHMID, Czech Republic ..........269 Failure of normal and high strength concrete under monotonic and cyclic tensile loading Christoph KESSLER-KRAMER, Viktor MECHTCHERINE and Harald S . MULLER, Germany ............................................................ 277 The use of viscosity enhancing admixtures to improve the homogeneity of fibre distribution in steel fibre reinforced concretes Liberato FERRARA, Italy .........................................................................................
287
Optimisation of the rheological and fracture mechanical properties of lightweight aggregate concrete Victor MECHTECHERINE, Michael HAIST, Lothar STAERK and Harald S.MULLER, Germany ...................................................................................
301
Design and testing of self-compacting SIFCON produced with low strength slurry Lucie SVERMOVA, Mohammed SONEBI and Peter J.M. BARTOS, Czech Republic and U K ...........................................................................
31 1
The influence of select composition factors on rheological properties of fibre reinforced fresh mortar Tomasz PONIKIEWSKI and Janusz SZWABOWSKI, Poland ................................
321
Mix design of the self-compacting concrete Maria KASZYNSKA, Poland ...................................................................................
331
xii
Influence of cement and superplasticizeron rheological properties of mortars Jacek GOLASZEWSKI and Janusz SZWABOWSKI, Poland ..................................
339
Analysis of concrete property fields and search for the best compositions using Monte Carlo method T. LYASHENKO, V. VOZNESENSKY, S. BOIKO, D. SHTAKELBERG, Ukraine and Israel .............................................................................
351
Cement-based materials incorporating rubber aggregates: shrinkage length changes Anaclet TURATSINZE, Sandra BONNET and Jean-Louis GRANJU, France........ 359 Advanced construction materials from fly ash Hwai-Chung WU and Peijiang SUN, USA ..............................................................
369
Implications of maturity and ultrasonic wave speed measurements in QC/QA for concrete Cole GRAVEEN, W. Jason WEISS, Jan OLEK and Tommy NANTUNG, USA ....379
PLENARY INVITED PAPERS (4 and 5)
On the determination of elastic constants with brittle matrix composites Dieter LOIDL, Stephan PUCHEGGER, Herwig PETERLIK and Karl KROMP, Austria .................................................................................................
389
A mechanial study of reinforced-concrete beams repaired with composite sheets Stkphane AVRIL, Alain VAUTRIN, Patrice HAMELIN, and Yves SURREL, France .......................................................................................
401
CONTRIBUTIONS Progress in ultrasonic testing of concrete Sandor POPOVICS, USA ........................................................................................ 421 Internal structure of concrete with artificial aggregate Elsadeg A. ABDALLA and Wojciech RADOMSKI, Libya and Poland ..................431 Influence of gas inflow surface on measured permeability of concrete Jacek SLIWINSKI, Tomasz TRACZ and Aleksander KOZAK, Poland
..................443
Influence of coarse aggregate size and cement matrix strength on stress-crack width Relationship of concrete Jun ZHANG, Qian LIU and Lin WANG, P.R.China .................................................
449
...
XI11
Prediction of non-uniform multiple cracking in polymer composites using an energy-based probabilistic model K. P. HERRMANN and Junqian ZHANG, Germany and P.R.China.........................
459
Fracture mechanics and plasticity modelling of the split cylinder test John Forbes OLESEN, Lennart 0STERGAARD and Henrik STANG, Denmark ................................................................................................. 467 Fatigue sensitivity analysis for the curved layered composite beam Lukasz FIGIEL and Marcin. KAMINSKI, Germany and Poland ............................
477
Durability of new polymer mortar using waste expanded polystyrene solution N. CHOI and Y. OHAMA, Korea and Japan...............................................
485
Application of experimental - statistical modeling to evaluate influence of amount and grading of sand and regime of burning upon compressive strength and water absorbability of building ceramics Beata BACKIEL-BRZOZOWSKA, Poland ..............................................................
495
The pultrusion technology for the production of fabric-cement composites Alva PELED and Barzin MOBASHER, Israel and USA ...........................................
505
Method of determination of creep and shrinkage of SFRC DuSan SPORA, Jan VODICKA, Jifi KRATKY, and Marian ABRAMOWICZ, Czech Republic and Poland .......................................
515
Lime mortars with natural fkbres MiloS F.DRDACKY and Dagmar MICHOINOVA, Czech Republic .......................
523
Effects of accelerated curing conditions on strength properties of epoxy-modified mortars without hardener Y. OHAMA and S . TAKAHASHI, Japan ..................................................
533
FRP debonding from a concrete substrate: conventional belief and new findings
Christopher K.Y. LEUNG, Hong-Kong .....................................................................
543
Performance characteristics of basalt rebar reinforced concrete beams V. RAMAKRISHNAN a d Ramesh K. PANCHALAN, USA ..................................
553
INDEX OF CONTRIBUTORS .......................................................................................
563
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