Composite Technologies for 2020: Proceedings of the Fourth Asian-Australasian Conference on Composite Materials ACCM 4

"

\m Vf

p

with spherical reinforcements:

8-lOv, with nearly spherical shaped reinforcements:

A = KE-\ Verbeek model for tensile modulus (ref [18,19])

^ = Void content of composite Vp = Volume fraction of polymeric matrix (associated with zero void) X = Modified void content (void relative to polymer phase) MRF - Modulus reduction factor

(y-vPY$m A

vp{\-

,h-zfGp P

1

Vf

Em

fraction a = Reinforcement aspect ratio A = A constant which takes into account such factors as geometry of the reinforcing phase and Poisson's ratio of the matrix B = A constant which takes into account the relative modulus of the reinforcing and matrix phases Em = Tensile modulus of the reinforcement cp = A factor which depends on the maximum packing fraction 0m of the reinforcement m = Maximum packing fraction of reinforcement V! = Poisson's ratio of matrix

1-V,

GpVf

f

^

a

1

1

u

tanh(w)

u

<Jc=VpGp+KlzpMPF Nielsen model (ref [22]) Nicolais Narkis model (ref [16])

ac=ap(l-V/'3)K

Gp = Shear modulus of the polymer ac = Tensile strength of the composite TP - Shear strength of the polymer K3 — Correction factor MPF = Strength reduction factor

The values for all the constants and parameters used in these theoretical models are listed in Table III. TABLE III Value of parameters used in models Correction factor K3 Stress concentration factor K Einstein coefficient for MDPE matrix KE Poisson's ratio of matrix (MDPE) v, Maximum packing fraction of spherical glass beads (SGB) m

0.75 ref [191 1.0 ref [22] 2.25 ref [20] 0.4 ref [23] 0.63 ref [20]

158

Rotational Moulded Polyethylene Composites

Maximum packing fraction of irregular shaped reinforcements <j)m Tensile modulus of matrix (MDPE) Ep Tensile modulus of glass beads (SGB RGP) Em Tensile modulus of A12O3 Em Tensile modulus of SiC Em Tensile strength of the polymer aD Shear strength of the polymer rn

0.60 ref [24] 0.88GPa ref [121 64.4GPa ref [23] 54.7GPa ref [23] 58.2GPa ref [231 16.2MPa ref [12] 12MPa ref [18]

RESULTS AND DISCUSSION Tensile modulus of glass bead reinforced composites

In the case of spherical glass bead reinforced composites, Fig. 1 shows that the modulus values obtained from both the Halpin-Tsai-Nielsen and Guth models agree reasonably well with the experimental results. However, Guth model tends to overpredict the modulus when the volume fraction of reinforcement becomes higher than 10%. Despite the proven ability of the Verbeek model to predict the moduli of composites with some particulate reinforcements [18], it appears to be inadequate in modelling composites with spherical reinforcement as it constantly under-predicts the stiffness as shown in Fig. 1. With a close study of Verbeek model, it can be determined that the aspect ratio of the particle plays an important role in deciding the composite modulus. From Fig. 2, it is evident that the reinforcing effect of the added particles can only happen when their aspect ratio is larger than a critical value, which in this case is around 7. Due to the fact that all the particles used in this study have aspect ratios between 1.0 and 1.35, the Verbeek theory becomes unsuitable for modeling the composites properties. -Experiment results "Halpin-Tsai-Nielsen equation ~Guth equation -Verbeek equation

Volume fraction %

FIGURE 1. Comparison of the results between theoretical models and experiment showing the effects of different theoretical models on tensile modulus at various volume fractions of glass beads.

Rotational Moulded Polyethylene Composites =1

159

AR= 3 - - - -AR-6 — - -AR-9 — - -AR-12

1.5 "\

Increa sing Aspect Ratio

y

Matrix Polymer

y'

•

•

09 -

0.3

0.0 100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

Polymer Volume Fraction

FIGURE 2. The effect of changing aspect ratio on the predicted composite modulus at various polymer volume fractions according to Verbeek Model.

As demonstrated in Fig. 1, the Halpin-Tsai-Nielsen model appears to be the most accurate for predicting the tensile modulus of the particulate reinforced rotationally moulded products with a low volume fraction of reinforcement (<20%). This theoretical model will be adopted for modulus analyses in the later part of this study. Tensile strength of glass bead reinforced composites The comparison of tensile strengths obtained from different theoretical models and experimental results is shown in Fig. 3. Among the three models employed, Nicolais-Narkis model gives the best agreement with the experimental results, but the Verbeek's model again predicts less accurately than the other two models. As explained previously, the aspect ratios of the particles used in this study are too small to effectively use this the Verbeek theory for predicting the composite tensile

-Experimental results —Verbeek's mode -Nicolais-Narkis model "•Nielsen's model 10 Volume fraction %

FIGURE 3. Comparison of the results between theoretical models and experiment showing the effects of different theoretical models on tensile strength at various volume fractions of glass beads.

160

Rotational Moulded Polyethylene Composites

strengths. On the other hand, Nielsen's equation with stress concentration factor K (Table II) of 1.0 (i.e. no stress concentration) gives the results lying between those from Nicolais-Narkis and Verbeek models. A proper stress concentration factor can get the values of the composite tensile strength closer to the experimental results (in this case, K should be around 0.85). However, in order to determine a more accurate stress concentration factor to enable the effective application of Nielson model, it will need to systematically carry out more experiments. Therefore, the Nicolais-Narkis model is chosen for further analyses regarding the composite tensile strength. The effects of particle type on the tensile modulus and strength When different types of particles are used as reinforcements in rotomoulding composites, the tensile modulus get affected as shown in Fig. 4 with the volume fraction of up to 20%. It indicates that, when Halpin-Tsai-Nielsen model is used, the prediction of tensile modulus remains generally unaffected by the type of particle used in this study. The reasons may be attributed to the facts that the Poisson's ratio of the PE matrix is kept constant (0.4) resulting in the same value for the parameter A (Table II) irrespective of the type and shape of the reinforcement used, and secondly, the tensile moduli of the different particles do not vary much. In general, it can be seen from the experimental results that the moduli of the various particulate reinforced composite materials follow similar trends: that the reinforcing effect on the composite stiffness increases with the addition of particles up to 10 vol%; with further

10 Volume fraction %

15

FIGURE 4. The comparison of the results from Halpin-Tsai-Nielsen model (M) and experiments (E) showing the effects of particle types on tensile modulus at various volume fractions.

increase of particle content, the modulus either becomes stabilised or starts to decrease. This is different from what is predicted from the Halpin-Tsai-Nielsen model that shows a constantly increasing tendency. This discrepancy can be explained by the growing clustering of particles with the increasing particle volume fraction during the stress free rotational moulding that allows the particles to distribute naturally through a tumbling action. These particle clusters/chains can then cause stress concentrations due to the bridging between the boundaries of the particlepolyethylene system, which consequently affect the tensile modulus.

Rotational Moulded Polyethylene Composites

161

-•-Math model -*-RGP -#-AI2O3

-*-SCI

-•-SGB

-f-SGB +CA 10 Volume fraction °

FIGURE 5. The comparison of the results from Nicolais-Narkis model and experiments showing the effects of particle types on tensile strengths at various volume fractions.

When the Nicolais-Narkis equation is applied to evaluate the effects of different types of particulate reinforcement on the composite tensile strength, it produces a single set of predicted tensile strengths for the rotomoulded composites regardless of the different particles used, Fig. 5 because the theory solely depends on the matrix tensile modulus and the reinforcement volume fraction. Generally speaking, the tensile strengths calculated from this model agrees reasonably well with the experimental results when the volume fraction is less than 10%, but becomes overpredictive with a higher particle content. With the range of particles used in this study, both the experimental and theoretical results show a trend of decreasing strength with the volume fraction increasing. This could be due to the rising possibility of the formation of large particle clusters, resulting in a decrease of the load bearing capacity due to their inherent weak bonding. This undesirable effect warrants future study for finding a proper solution. Due to the lower aspect ratios of particles, it may be expected that the particulate systems could be more easily distributed in the rotational moulding process compared to the fibrous systems. Therefore, it is important to establish the validity of the theoretical predictions of final product properties. CONCLUSIONS From the research results described above, the following remarks may be made: > The theoretical models of Halpin-Tsai-Nielsen and Nicolais-Narkis can be used to predict the tensile modulus and the tensile strength respectively for the particulate reinforced composites produced by the rotational moulding process. > Different reinforcing particles, such as spherical shaped glass beads (90|am150um), irregular shaped glass beads (average 240|am), irregular shaped aluminium oxide (105|am -149um), irregular shaped silicon carbide (105(im 149um), do not make significant difference in the tensile moduli and tensile strengths of the final rotationally moulded products. > With the addition of small quantities of particulates (up to 10 %), the tensile modulus of the rotomoulded component increases, whereas the tensile strength always decreases with the addition of particulates in rotomoulding.

162

Rotational Moulded Polyethylene Composites

ACKNOWLEDGEMENTS The authors are thankful to the Foundation for Research Science & Technology New Zealand for providing the financial support for this research. Special thanks are also due to J. R. Courtenay (NZ) Ltd for supplying LMDPE material and allowing the free use of their industrial rotational moulding machine for producing the rotomoulded products. REFERENCE 1. Crawford, R.J., Rotational moulding of plastics (second edition). 1996: Research Studies Press LTD. 2. Crawford, R.J. and S. Gibson, Rotational moulding, the basics for designers. Rotation, 2000(July/August): p. 36. 3. Crawford, R.J. and P.J. Nugent, Impact strength of rotationally moulded polyethylene articles. Plastics, Rubber and Composites Processing and Applications, 1992.17(33-41). 4. Abdullah, M.Z., S. Bickerston, and D. Bhattacharyya. Enhanced Heat Transfer in Polymer Moulding Processes. Polymer Processing Society Asia/Australia Regional Meeting (PPS-2002), Taipei, Taiwan, November 4-8, 2002, G6. Thermoforming, Blow Molding and Rotational Molding, Paper No. 116. 5. Martin, D., et al., A summary of recent Australian R&D activities in rotational moulding. Rotation, 2001. January - February: p. 44-50. 6. Crawford, R.J. and A. Robert. Reinforcement of rotomoulded plastic parts - a challenge, in The 3rd Asian-Australasian Conference on Composite Materials. 2002. Auckland, New Zealand. 7. Harkin-Jones, E. and R.J. Crawford, Mechanical properties of rotationally molded Nyrim. Polymer Engineering and Science, 1996. 36(5): p. 615-625. 8. Harkin-Jones, E. and R.J. Crawford, Rotational molding of liquid Nyrim in biaxially rotating heated moulds. Plastics, Rubber and Composites Processing and Applications, 1995. 24(1): p. 1-7. 9. Blackburn, D.R. and O.K. Ademosu. An investigation of the production of rotationally moulded composites, in Fibre Reinforced Composites - International Comference - 9th. 2002. 10. Ward, J., Panigrahi, S., Tabil, L. G., Crerar, W. J. and Powell, T., Rotational Molding of Flax Fibre Reinforced Thermoplastics, Paper No: MBSK 02-209, An ASAE Meeting Presentation, 2002. 11. Yan, W., R. J. T. Lin, S. Bickerton, D. Bhattacharyya, Performance Evaluation of Moulded Polymeric Composites, Polymer Processing Society Asia/Australia Regional Meeting (PPS-2002), Taipei, Taiwan, November 4-8, 2002, G6. Thermoforming, Blow Molding and Rotational Molding, Paper No. 204. 12. Yan, W., R. J. T. Lin, S. Bickerton, D. Bhattacharyya, Rotational Moulding of Particulate Reinforced Polymeric Shell Structures, Materials Science Forum, Vol 437-438 (2003): p. 235-238. 13. Ahmed, S. and F.R. Jones, A review of particulate reinforcement theories for polymer composites. Journal of Materials Science, 1990. 25: p. 4933-4942. 14. Nielsen, L. E., Generalized equation for the elastic moduli of composite materials. Journal of applied physics, 1970. 41(11): p. 4626. 15. Gao, Z. and A. H. Tsou, Mechanical properties of polymers containing fillers. Journal of Polymer Science: Part B: Polymer Physics, 1999. 37: p. 155-172. 16. Nicolais, L. and M. Narkis, Stress-strain behavior of styrene-acrylonitrile/glass bead composites in the glassy region. Polymer Engineering and Science, 1971. 11(3): p. 194-199. 17. Guth, E., Theory of filler reinforcement. Journal of applied physics, 1945. 16(January): p. 20-25. 18. Verbeek, C.J.R., The influence of interfacial adhesion, particle size and size distribution on the predicted mechanical properties of particulate thermoplastic composites. Materials Letters, 2003. 57: p. 1919-1924. 19. Verbeek, C.J.R. and W.W. Focke, Modelling the Young's modulus of platelet reinforced thermoplastic sheet composites. Composites Part A: applied science and manufacturing, 2002. 33: p. 1697-1704. 20. Nielsen, L.E. and R.F. Landel, Mechanical properties of polymers and composites. 1994: Marcel Dekker, Inc. 21. Sahu, S. and L.J. Broutman, Mechanical properties of particulate composites. Polymer Engineering and Science, 1972. 12(2): p. 91-100. 22. Nielsen, L.E., Simple Theory of Stress-Strain Properties of Filled Polymers. Journal of Applied Polymer Science, 1966.10: p. 97-103. 23. Shackelford, J.F., W. Alexander, and J.S. Park, CRC Practical Handbook of Materials Selection. 1995: CRC Press, Inc. 24. Scott, G.D., Packing of spheres. Nature, 1960. 188: p. 908-909.

Morphology and Mechanical Properties of HDPE Reinforced with PET Microfibres R. Seltzer*, L. Fasce, P. Frontini INTEMA, Univ. Nac. Mar del Plata, Mar del Plata, Argentina V. J. Rodriguez Pita, E.B.A.V. Pacheco, M.L. Dias Instituto de Macromoleculas Professora Eloisa Mano, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil

ABSTRACT In this work compatibilized blends of PET and high density polyethylene (HDPE) with 1% and 7% ethylene/methacrylic acid copolymer (Nucrel®) have been prepared and their morphology and mechanical properties have been compared with those of the same uncompatiblized blends. Aiming to induce different morphologies the pellets of the blends were processed by three different procedures: compression molding, extrusion and extrusion followed by annealing. In every case, HDPE constituted the matrix and PET was the dispersed phase. PET adopted a nodular morphology in the compression molded samples, it took the form of microfibers (microfibrillar reinforced composites) in extruded samples, and it appeared flake like in the annealed extruded samples. According to tensile and fracture tests, extruded blends having 7% Nucrel appeared as the optimum combination of processing method and compatibilizer content.

INTRODUCTION Poly (ethylene terephtalate) (PET) and high density polyethylene) (HDPE) are extensively used in packaging of consumer and industrial products, being the most found in urban waste streams. One of the best way of reducing urban waste is by recycling. Then, it would be highly convenient, in economical terms, to blend both polymers. The obstacle is that these two polymers are incompatible, i.e. PET and HDPE are inmiscible in liquid state and there is lack of adhesion in solid state. The development of new multiphase blend materials is dependent primarily on two key requirements: control the interfacial chemistry and control of the microstructures [1]. Through this paper, the mechanical behavior of 50/50 PET/HDPE blends were assessed. Blends were prepared by reactive blending using an ethylene/methacrylic acid copolymer (Nucrel®) in different percentages as a compatibilizer agent. Guerrero et al. [2] reported a an increase in elongation at break and impact strength in the ternary blends due to compatibilization between PET and HDPE with similar agents. The blends were processed following three different procedures to promote de developing of different morphologies.

* Corresponding author, Universidad National de Mar del Plata, Argentina, fax:54-223-4810046, e-mail: [email protected]

164

HDPE Reinforced with PET Microfibres

MATERIALS AND PROCESSING The materials used were HDPE (Novatec JV060, Tm=133°C) provided by Poliaden and PET (Polyclear T86, Tm=260°C) provided by Hoechst. The compatibilizer was an ethylene/methacrilic acid copolymer (Nucrell202HC Tm=99°C) (Nu) provided by Du Pont. Before blending, the polymers were dried in an oven for 16 hours at 160°C (PET) and 60°C (acid copolymers and ionomers). PET/HDPE blends were prepared in 50/50 proportion, and the amount of compatibilizers varied from 0% to 7% weight. 50/50/xNu pellets were compounded in a Haake Rheocord 9000 extruder at 280°C and 60 rpm. Extruded ribbons of 1 mm thick were obtained from the same extruder by changing the die (50/50/xNu/E). In order to change ribbons structural properties [3], isotropization of the lower melting component (HDPE) with preservation of the oriented microfibriUar structure of the higher melting (PET) component was done (5O/5O/XNU/ET) by annealing them at 160 °C under a pressure of 10 Mpa for 15 minutes followed by cooling with running water. Compression molded plaques of 1 mm thick were processed by compression molding the pellets (50/50/xNu/C) at 270 °C and 75 MPa during 15 minutes followed by cooling with running water.

CHARACTERIZATION Morphology Blends morphology was examined by means of scanning electron microscopy, SEM (JEOL JMS-53OO), on samples broken in liquid nitrogen. Depending on the phase to be seen, these broken samples were etched dissolving selectively PET (trichlore benzene) or HDPE (xylene). Finally, they were gold coated.

FIGURE 1 SEM micrographs. Magnification xlOOO taken from the fracture surface of -a) 50/50/0Nu; b) 50/50/ONu/C after extraction of HDPE; c) 50/50/0Nu/C after extraction of HDPE; d) 50/50/lNu/C; e) 50/50/lNu/C after extraction of HDPE; f) 50/50/lNu/C after extraction of HDPE.

HDPE Reinforced with PET Microfibres

165

FIGURE 2 SEM micrographs. Magnification xlOOO taken from the fracture surface of -a) 50/50/ONu/E; b) 50/50/ONu/E after extraction of HDPE; c) 50/50/ONu/E after extraction of HDPE; d) 50/50/lNu/E; e) 50/50/lNu/E after extraction of HDPE; f) 50/50/lNu/E after extraction of HDPE; g) 50/50/7Nu/E; h) 50/50/7Nu /E after extraction of HDPE; i) 50/50/7Nu/E after extraction of HDPE

FIGURE 3 SEM micrographs. Magnification xlOOO taken from the fracture surface -a) 50/50/0Nu/ET; b) 50/50/ONU/ET after extraction of HDPE; c) 50/50/ONu/Er after extraction of HDPE; d) 50/50/lNu/Er; e) 50/50/lNu/Er after extraction of HDPE; f) 50/50/lNu/ET after extraction of HDPE; g) 50/50/7NU/ET; h) 50/50/7Nu/Br after extraction of HDPE; i) 50/50/7Nu/ET after extraction of HDPE

166

HDPE Reinforced with PET Microfibres

In the compression molded blends the dispersed PET domains are spherical in shape (Figure 1). In the binary blends (Figurelb) there is no evidence of adhesion between the two phases .The voids occurring where the particles were located show that they were attached only by weak mechanical adherence . Compatibilized blends (Figures le-f) show higher dispersion of the PET phase, i.e. more particles of smaller dimensions, though some inhomogenity is still displayed (Figure Id). The addition of the Nucrel to extruded blends (Figure 2) resulted in remarkable changes in the morphology. It can be seen that the dimension of the dispersed particles have decreased to a certain size so that the surface appearance is now quasihomogenous PET discontinuous phase is shaped into microfibers (Figure 2b). As compatibilizer content increases dissolution and extraction of HDPE from PET structure becomes less effective. This fact evidences compatibilization between both phases (Figure 2h, i). In annealed extruded blends (Figure 3) unfortunately the microfiber structure of the PET phase did not maintain although blends were reprocessed far below the melting temeprature of PET. As Nucrel content increases, higher deformation and coarsening of PET fibers is obtained upon annealing (Figures 3b, c, e, f, h, i) is detected. Thermal Properties Melting curves of two blends are shown in Figure 4. Each melting trace is characterized by two peaks: one peak around 130 °C corresponding to HDPE and the other at higher temperature, around 245 °C, corresponding to PET. It can be seen that compatibilized blends present displacements to the lower temperatures in PET and HDPE melting points. This behavior is indicative of compatibility between components [4]-

j

AH == 20.5 J/g peak = 253 °C

1—-—-__

O

Q Z LLI

;1

—-\

AH = 27 J/g peak = 248 °C

AH = 99 J/g AH = 74 J/g peak= 130 °C i peak=131°C

11

50

100

150

T°C FIGURE 4 DSC curves for blends.

200

250

50/50/0Nu;

300

50/50/lNu

Mechanical Properties Tensile properties were measured using an Instron machine mod. 4467, performing the tests on dumbell specimens cut from ribbons and plaques. The tensile properties, elastic modulus, E, tensile yield stress, ay, and elongation at break, £b, of all the investigated blends are reported in Table I. Compression molded and annealed extruded blends behave in a brittle manner and the elongation at break falls to very lows values. The latter arises from the photographs of the tested specimens (Figures 5-7), as well. Both extruded type blends display higher yield point than the compression

HDPE Reinforced with PET Microfibres

167

molded blends. The addition of 7% of Nucrel significantly improves elongation at break of the extruded blend promoting fibrillation during stretching (Figure 6). TABLE I Tensile properties Material 50/50 E (GPa) o v (Mpa) «*(%)

ONu/C

INu/C

ONu/E

INu/E

7Nu/E

ONu/Er

INU/ET

7NU/ET

1.7 12

1.9

1.1

1.6

1.9

1.7

33

35

1.5 29

2.0

22

28

29

33

1

1

4

60

>100

2

3

4

FIGURE 5 Fraelure pattern -n) 50/50/ONu/C; b) 50/50/lNu/C,

FIGURE 6 Fracture pattern of a) 50/50/ONu/E; b) 50/50/lNu/E; e)50/50/7Nu/E.

FIGURE 7 Fracture pnltorn ol -a) 50/50/0Nu/Br; b) 50/50/lNu/Er; o) 50/50/7Nu/Er.

Fracture tests were performed on an Instron machine mod. 4467 at Imm/min. DDENT cut from compression molded plaques, extruded ribbons and annealed extruded ribbons were used. Specimens nominal width, W, was 30 mm and a/W was 0.3, where a is the crack length. Blends were characterized by the stress intensity factor at maximum load, Kmax, K

=

1.122-0.564- - 0 . 2 0 5 ^ + 0 . 4 7 1 - + 0 . 1 9 ^ -

J where P is the maximum load in the load-displacement trace, B is the specimen thickness; and by the work of fracture , Wf, calculated as the total fracture energy divided by twice the ligament area. Kmax and Wf values displayed by each sample are presented in Table n. The highest values were found for the extruded blends while the lowest ones were obtained when compression molded samples were tested. Annealed samples showed intermediate behavior. Figures 8-10 show fracture patterns of the specimens. It is clearly observed that compression molded and annealed extruded blends behave in a brittle manner, while extruded blends do not present "in plane" crack propagation. Ligament stretches and fibrillates, instead. In uncompatibilized extruded and annealed extruded samples crack path deflects from mode I to mode II. This is due to lack of miscibility and adhesion between the uniaxially oriented phases. The energy required to separate the phases longitudinally is lower than the one involved in breaking the fibers transversally. The latter effect is not enhanced by the addition of Nucrel (Figures 9b, c; 10b, c). Material 50/50 K^MPa-m1") Sd K m a x wf(N/mm) Sd™,

ONu/C 0.90 0.03 3.1 0.2

TABLE II Fracture parameter values 7Nu/E ONu/E INu/E INu/C 1.47 0.85 1.56 1.44 0.12 0.08 0.05 0.08 40.3 1.3 39.5 30.2 2.6 0.1 1.0 5.1

0Nu/ET 1.11 0.14 6.8 0.6

INU/ET

1.29 0.07 4.2 0.5

7Nu/ET 1.39 0.30 8.4 1.2

168

HDPE Reinforced with PET Microfibres

-a FIGURE 8 Fracture pattern -a) 50/50/ONu/C; b) 50/50/lNu/C.

FIGURE 9 Fracture pattern of -a) 50/50/ONu/E; b) 50/50/lNu/E; c] 50/50/7Nu/E.

FIGURE 10 Fracture pattern of-a) 50/50/0Nu/ET; b) 50/50/lNu/Er; c) 50/50/7Nu/Er

CONCLUSIONS PET/HDPE blends are fragile materials with poor mechanical properties because of the incompatibility between the two phases. It emerges from the phase morphology generated that Nucrel can act as a compatibilizing agent when used as a third component. A significant improvement of the mechanical properties, in particular of the elongation at break and fracture toughness, can be achieved by inducing fibrillation of the PET phase in PE matrix by extruding the blends under adequate conditions. Processing techniques , like compression molding of extruded pellets, which are not capable of inducing fibrillation of the PET phase lead to blends having poor properties. Far from improving the mechanical properties, annealing of extruded blends disrupted PET microfiber structure which is responsible for high elongation and strength. The best overall properties were displayed by extruded blends compounded with 7% of Nucrel. ACKNOWLEDGEMENTS This work was supported by a SECyT-CAPES (BR/A00-EXII011) grant. REFERENCES 1.

2. 3. 4.

Davis BD, 2000. "Factors influencing the morphology of immiscible polymer blends in melt processing", in Polymer blends: performance. Paul DR, Bucknall CB, eds. New York: John Wiley & Sons; pp. 501-38. C. Guerrero, T. Lozano, V. Gonzalez, E. Arroyo, 2001,Vol 82 "Journal of Applied Polymer Science " 1382-1390. M. Evstatieva and N. Nicolova, S. Fakirovb, 1996, Polymer 37, 4455-4465 Utracki, L. A. Polymer Alloys and Blends; Hanser: Munich, 1989.

Mechanistic Evaluation of Environments on Degradation of E-Glass/Vinylester Composites Vistasp M. Karbhari, Wellington Chu and Lixin Wu Department of Structural Engineering, MC-0085 University of California San Diego. La Jolla, CA 92093-0085, USA

ABSTRACT E-Glass/Vinylester composite components, fabricated using processes that incorporate ambient and moderate-temperature cures, are increasingly being used in marine, offshore and civil infrastructure applications. This often results in the component being placed in use when cure progression has not reached one hundred percent result in competing mechanisms of deterioration associated with moisture and solvent sorption, and slow residual post-cure. This paper presents results of a detailed program aimed at the investigation of effects of water immersion on the durability and progressive degradation of this class of composites. Results are based on mechanical characterization, Dynamic Mechanical Thermal Analysis, and microscopy.

INTRODUCTION Due to their corrosion resistance, relatively high ultimate failure strains, and damage tolerance, E-glass/vinylester composites are increasingly being considered for use in cost-sensitive primary structural components in marine, offshore and civil infrastructure applications. Due to geometrical size requirements and those related to cost, nonautoclave processes such as wet layup, resin infusion, and pultrusion are the primary processes under consideration, with cure being achieved under ambient, or in the case of pultrusion, moderate temperature conditions with high throughput. Styrene in the monomeric form is used as a diluent in the resin in quantities between 20% and 60%. Although increases in styrene content can result in increases in hydrophobicity (and thus an effective decrease in the level of moisture absorption) it also results in an increase in shrinkage (resulting in the potential for significant microcracking in resin rich areas and high residual stresses in composites having high fiber volume fractions) as well as the possibility of incomplete polymerization. Incomplete polymerization not only leads to changes in properties with time due to slow changes in degree of cure, but also induces lower heat stability, lower resistance to hydrolysis and a greater degree of susceptibility of swelling in solvents [1,2]. In addition, the hydrolysis of ester groups can result in the formation of carboxyl groups, resulting in further decomposition due to autocatalysis [3]. In evaluating the applicability of composites for use in primary structural elements, for applications expected to show long service life, the assessment of effects of aqueous and hygrothermal exposure are critical. The diffusion and sorption of moisture in a polymer and the resulting composite is related to the availability of molecular sized * Corresponding author, Department of Structural Engineering; MC-0085; University of California San Diego; Building 409 University Center; La Jolla, CA 92093-0085, USA; Fax: (858) 534-6470; Email: [email protected]

170

Degradation of E-Glass/Vinylester Composites

holes, the affinity of the polymer for moisture, and the extent to which wicking can take place along the fiber-matrix interface. The overall kinetics, and the resulting materials level deterioration, thus depend on microstructure, morphology, cross-link density, molecular weight, fiber chemistry, and interfacial bonds. The results reported in this paper are part of an ongoing comprehensive investigation into the long-term durability of pultruded E-glass/vinylester composites. MATERIALS AND TEST DETAILS Unidirectional composites were pultruded in 1.6 mm thick strips using Hybon 2001 Eglass rovings of 23 m/kN (112 linear yards/lb) yield with a Dow Derakane 441-400 vinylester having a viscosity of 400 cps at 23°G and a styrene content of 33% by weight. Fiber loading, assessed through burn-off procedures, was determined to be approximately 62%. All specimens were preconditioned at 23°C and 46% relative humidity prior to initiation of the test program. In order to adequately assess changes in characteristics of the composite as well as mechanisms of degradation as a result of water sorption, the material was subjected to mechanical testing through tension (ASTM D3039) and short-beam-shear (ASTM D2344) modes. Dynamic mechanical thermal analysis (DMTA) was conducted at a frequency of 1 hz between 25°C and 200°C. Inductively coupled plasma (ICP) analysis was also conducted on solutions in which the material was immersed in order to assess leachate elements, and fourier transform infrared (FTIR) spectroscopy was used to assess changes in the polymer itself. Moisture uptake was assessed through gravimetric means and both optical and scanning electron microscopy (SEM) were used to study degradation. Composite and neat resin specimens, as appropriate, were immersed in deionized water at 23°, 40°, 60°, 80°C for periods of time up to 75 weeks, hi addition specimens were also stored at 23°C and 46% relative humidity RH, taken to be representative of ambient, "unexposed" conditions. In order to assess reversibility of moisture sorption effects, selected tests were also conducted on specimens that were reconditioned at 23°C and 46% RH for 28 days (equal to the original period of conditioning) after removal from the immersion environments. RESULTS AND DISCUSSION Mass uptake in the specimens immersed in deionized water showed Fickian response with rates of uptake and moisture content increasing with temperature of water. Overall uptake results in terms of maximum percentage weight gain over the period of time of investigation and diffusion coefficients are listed in Table I. TABLE I Characteristics of Moisture Kinetics Temperature Of Deionized Water (°C) 23 40 60 80

Neat Resin Maximum Coefficient of Moisture Uptake Diffusion (Wt. %) (xlO"7 mm2/s) 6.25 0.64 10.00 0.93 1.26 15.31 1.40 24.31

Composite Maximum Coefficient of Moisture Uptake Diffusion (Wt. %) (xl0"7mm2/s) 0.164 1.39 0.529 2.17 0.569 2.70 0.623 3.14

From theoretical considerations the maximum uptake can in the composite be determined to be 0.139%, 0.203%, 0.275% and 0.305%, at 23°C, 40°C, 60°C and 80°C, respectively. It is noted that at temperatures higher than 23°C the experimentally

Degradation of E-Glass/Vinylester Composites

171

determined values of maximum moisture uptake are higher than the theoretical ones. This is due to the activation of damage at the interface and bulk resin level resulting in additional uptake due to wicking along debonds and microcracks which results in additional flow and storage of water. Figure 1 shows paths at the interface due to debonding and initiation of fiber pitting and degradation through cracking can be seen in Figure 2 due to longer term immersion at the higher temperature levels.

FIGURE 1 Interface Debonding

FIGURE 2 Fiber Pitting and Cracking

A progression of change in tensile strength as a function of time and temperature of immersion is shown in Figure 3 from which it can clearly be seen that the level of degradation increases substantially with increase in temperature of the aqueous medium. At the end of 75 weeks, levels of retention are noted as 65.22%, 51.45%, 37.43% and 28.22% for the 23°C, 40°C, 60°C and 80°C cases, respectively. It is also noted that there is a relatively large loss in the first 5-10 weeks most of which is recovered on drying and is due to effects of matrix plasticization as a result of moisture uptake. Pitting seen on the fiber surface (Figure 2) is due to loss of K2O and Na2O from the fiber by dissolution and is corroborated by the ICP results. In a large number of applications, composites are unlikely to remain in a saturated condition due to loss of sorbed moisture with changes in the surrounding environment and it is thus not only of interest to compare changes in tensile strength prior to, and after reconditioning, but also to assess the level of regain due to "drying out" during reconditioning.

23 c

0

10

20

30

40

50

60

70

Time (Weeks)

FIGURE 3 Change in Tensile Strength

80

0

10

20

30 40 50 Time (Weeks)

60

70

FIGURE 4 Effect of Reconditioning

Figure 4 provides a comparison of level of percentage regain [4] due to reconditioning and it is seen that at almost all time periods percentage regain decreases with increase in the temperature of the deionized water emphasizing the increasing effect of temperature

Degradation of E-Glass/Vinylester Composites

172

(and by analogy of extended periods of exposure) on the level of irreversible change and damage. It can also be seen that percentage regain in each case reaches a minimum value and then increases again at the time corresponding to when degradation at the interface takes place resulting in additional wicking. Since the tests are conducted on unidirectional composites the effect of interfacial degradation is not as large as it would be in an off-axis case. Short-beam-shear (SBS) tests are often used to assess interlaminar shear strength and to compare the relative effects of environmental exposure As can be seen in Figure 5 there are significant losses in short-beam-shear strength as a function of time and temperature of immersion. While the reduction in SBS strength with time of immersion is almost linear at 23°C, it follows a stepped approach at 40°C, and the more commonly observed curve having a rapid initial decrease followed by a retardation is noted at 60°C and 80°C. The 23°C results are indicative of an almost pure interlaminar failure wherein changes in strength are dependent on interfacial mechanisms only [5] without substantial physical/mechanical degradation of the matrix. The step seen in the 40°C case is indicative of damage, primarily irreversible, occurring at the interfacial level in the form of fiber-matrix debonding, and osmotic cracking at the interface, resulting in enhanced moisture sorption due to wicking. This form of damage is irreversible, and this is clearly seen in comparing the results of SBS strength of samples tested after reconditioning (redryhig at 23°C and 46% RH for 28 days) wherein an identical stepped response is seen. Beyond this level changes to the material are not merely associated with plasticization and debonding, but also to resin hydrolysis and microcrack coalescence to form macro-transverse cracks. The latter also serve as a mechanism for enhanced wicking of moisture along the fiber. Fiber pitting and some longitudinal cracking is also seen as a result of the higher temperatures and longer periods of immersion, similar to the phenomena reported in [6-8].

-—I

-

23 C, after reconditioning

10

• - - - - 40 C

- - • - 80 C

40 C, after reconditioning

0

10

60 C

- * — 60 C, after reconditioning

20

30

40

"M— 8 0 C, after reconditioning

50

60

70

80

Time (W eeks)

FIGURE 5 Change in SBS Strength as a Function of Immersion Temperature and Time

Since the diffusion data for the 4 temperature levels provides a linear fit to the Arrhenius equation, in the form ,gri(D) = £n(DJ-Eil/(RT) it can reasonably be assumed, for purposes offirst-orderapproximation, that the material follows the same mechanisms of degradation thereby allowing for use of a time-temperature based acceleration procedure initially proposed in Litherland et al [9] and Proctor et al [10] wherein the results of plotting the logarithm of time to attain a set of levels of normalized performance versus 1000/T (where T is temperature in degrees Kelvin) can be used to predict service life at a given temperature (normally taken as the ambient, or serious

173

Degradation of E-Glass/Vinylester Composites

temperature) based on performance at higher temperatures. Using data from tests conducted on specimens immersed at 40°, 60° and 80°C predictions can be made for property retention as a function of time for the 23°C case for both tensile strength and short-beam-shear-strength and it is seen that the predictions compare well with experimental results till the 75 week level providing some level of assurance of accuracy. It can be noted that at the end of the 50 year prediction period the specimens immersed in water show 31.15% and 47.05% retention in tensile strength in the "wet" and "dry" cases, respectively, whereas the retention in. SBS strength is 62.42% and 74.37%, respectively. Water uptake by vinylesters and their composites is known to cause plasticization in the short-term and hydrolysis over the long-term through attack of the ester linkages. Both these phenomena induce higher levels of molecular mobility resulting in consequent decreases in the glass transition temperature, Tg, although the decrease can often be offset through residual cure of the vinylester itself in the aqueous solution. These competing phenomena result in fluctuations in the glass transition temperature as a function of period of exposure as shown in Figure 6. It is noted that the highest values of Tg, after initiation of immersion, are measured at the 10-15 week period, which coincides with the point at which the storage modulus shows a decrease after an initially significant increase. A significant increase in E is generally indicative of progression of cure with a decrease being representative of hydrolysis and plasticization dominating effects. The progression of hydrolysis was confirmed at a preliminary level through infrared spectroscopy wherein a decrease in the ester band intensity was noted with a change in peaks at about 1452 cm"1, which had been earlier noted by Ghorbel and Valentin [11] at 1450 cm"1 in their study on glass fiber reinforced vinylesters.

0

10

20

30

40

50

60

70

80

Time (weeks)

FIGURE 6 Effect on Glass Transition Temperature

0

10

20

30

40

50

60

70

80

Time (Weeks)

FIGURE 7 Effect on Crosslink Density

A study of Figure 6 shows further that the higher temperatures of immersion result in an overall lower level of decline in glass transition temperatures from the unexposed control (decreases of 8%, 8.3%, 4.9% and 5.7%, determined from values in °K are seen at the 75 week level at 23°C, 40°, 60°C and 80°C, respectively). This is due to increased leaching of hydrolyzed low molecular weight flexibilizing segments of the matrix at the higher temperatures which leads to network embrittlement, followed by further degradation through chain scission, while at lower temperatures this effect is not dominant. It is noted that the free hydroxyl groups are known to cause autocatalyzation of hydrolysis of ester groups in the bulk resin as well leading to a reduction in crosslink density which is also seen by a visible change in color of the composite specimens. As can be seen in Figure 7 the normalized average intercrosslink molecular weight shows a

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Degradation of E-Glass/Vinylester Composites

level of correlation to Tg in that it decreases with Tg. However, it is noted that the glass transition temperature is also affected by leaching and thus there is some variation at the higher temperatures of immersion over longer time periods. SUMMARY Although fiber reinforced polymer matrix composites show good durability as compared to conventional materials used in the marine, offshore and civil infrastructures areas, there is at present a lack of a comprehensive understanding of their response over long time periods. It is seen that due to specifics of the resin and fiber systems, as well as the progression of cure realized by the processes favored, deterioration mechanisms can be fairly different from those observed in prepreg based composites. The simultaneous sorption of moisture and slow progression of cure results in a competition between mechanisms that requires an indepth understanding of moisture kinetics and changes in the polymer system as a function of exposure type and time period. ACKNOWLEDGEMENTS The support of the California Department of Transportation is gratefully acknowledged. REFERENCES 1.

Apicella, A., C. Migliaresi, L. Nicolais, L. Iaccarino, and S. Roccotelli 1983. "The Water Aging of Unsaturated Polyester-Based Composites: Influence of Resin Composite Structure," Composites, 14 [4]:. 387-392. 2. Karbhari, V.M. and S. Zhang 2002. "E-Glass/Vinylester Composites in Aqueous Environments - I: Experimental Results," Applied Composite Materials, 34[1]: 19-48. 3. Apicella, A., C. Migliaesi, L. Nicodemo, L. Nicolais, L. Iaccarino, and S. Roccotelli 1982. "Water Sorption and Mechanical Properties of a Glass-Reinforced Polyester Resin," Composites, 13: 406-410. 4. Chu, W. and V.M. Karbhari 2003. "Effect of Water Sorption on Performance of Pultruded EGlass/Vinylester Composites," submitted to ASCE Journal of Materials in Civil Engineering. 5. Gautier, L., B. Mortaigne, and V. Bellenger. 1999. "Interface Damage Study of Hydrothermally Aged Glass-Fibre-Reinforced Polyester Composites," Composites Science and Technology, 59: 2329-2337. 6. Ishai, O. 1975. "Environmental Effects of Deformation, Strength and Degradation of Unidirectional Glass-Fiber Reinforced Plastics. I. Surveyr," Polymer Engineering and Science, 15 [7]: 486-499. 7. Ehrenstein, G.W. and R. Spaude 1984. "A Study of the Corrosive Resistance of Glass Fiber Resin Polymers," Composite Structures, 2: 191-200. 8. Karbhari, V.M. 2004. "E-Glass/Vinylester Composites in Aqueous Environments: Effects on SBS Strength," ASCE Journal ofComposites for Construction in press. 9. Litherland, K.L., D.R. Oakley, and B.A. Proctor 1981. "The Use of Accelerated Ageing Procedures to Predict the Long-Term Strength of GRC Composites," Cement and Concrete Research, 11: 455-466. 10. Proctor, B.A., D.R. Oakley, and K.L. Litherland 1982. "Developments in the Assessment and Performance of GRC Over 10 Years," Composites, 13 [2], pp. 73. 11. Ghorbel, I. and D. Valentin, D. 1993. "Hydrothermal Effects on the Physico-Chemical Properties of Pure and Glass-Fiber Reinforced Polyester and Vinylester Resins," Polymer Composites, 14 [4]: 324334.

High Value Composites from Recycled Polyolefins and Rubbers Alexander Fainleib*, Olga Grigoryeva, Alexander Tolstov, Olga Starostenko Institute of Macromolecular Chemistry of the National Academy of Sciences of Ukraine, Kharkivske shose 48, 02160 Kyiv, Ukraine

ABSTRACT The novel technology for producing high value thermoplastic dynamic vulcanizates (TDVs) from recycled polyolefins and ground tire rubber (GTR) has been developed. The producing high performance composites of tensile properties on the level of TDVs based on virgin components is assured by using ethylene-propylene-diene monomer rubber (EPDM) as a rubber compatibilizer, bitumen as a devulcanizing agent for GTR as well as plasticizing and compatibilizing agent for TDV components.

INTRODUCTION Polymer blends are an important class of engineering materials, as they exhibit synergetic effects due to their comprising useful properties. However most of them (for example - polyolefm/rubber) consist of incompatible components, i.e. they show a limited mutual solubility and often high interfacial tension [1]. As a result properties of such systems are poor [2-5]. Solving the problem of poor interfacial adhesion and use the post-consumer polyolefins and ground tire rubber (GTR) instead of virgin components could bring up such a material to a commercially leading position due to a favorable cost-performance [6-9]. In this study we have tried to solve the problem of poor properties of GTRcontaining TDVs. The only way to improve the properties is a development of a fine structure through increasing an interfacial adhesion between the TDV components. For this purpose we have sequentially applied a new technology of GTR surface activation by thermal-mechanical-chemical devulcanization and reactive compatibilization of the components through dynamic co-vulcanization of pre-devulcanized GTR with EPDM and unsaturated components of bitumen inside thermoplastic (polyolefin) matrix. EXPERIMENTAL Two methods of melt blending of recycled polyolefins HDPER, LDPER or PPR with EPDM as a fresh rubber and ground tyre rubber (GTR) were developed using Brabender plasticorder or extruder. First method includes blending of GTR with bitumen, mastication of GTR/bitumen blend with recycled thermoplastics (HDPER, LDPER or PPR) and EPDM in Brabender plasticorder and (optional) rolling of the * Correspondence Author, Institute of Macromolecular Chemistry of the National Academy of Sciences of Ukraine, Kharkivske shose 48, 02160 Kyiv, Ukraine, fax: (380)445524064, e-mail: fainleib(S>,i.kiev.ua

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High Value Composites from Recycled Polyolefins and Rubbers

blend after mastication. In all cases, polyolefin (HDPER, LDPER or PPR) was melted first for 2 min, then EPDM was added and melted for 2 min before the addition of the GTR/bitumen composition, and final mixing was continued for a further 10 min. Second method consists of blending of GTR with bitumen, extrusion of GTR/bitumen blend at 135/145/155 °C, mixing of extrudate with recycled thermoplastics (HDPER, LDPER or PPR) and EPDM in extruder at 155/165/175 °C, followed by granulation and second run in extruder. A GTR fraction with a particle size of 0.4 to 0.7 mm was kindly provided by Scanrub AS (Viborg, Danmark). The EPDM containing rubber (Buna® EP G 6470 of Bayer) with 71 wt.% ethylene and 4.5 wt.% ethylidene norbornen contents was used. The bitumen used was a BN-4 grade according to the State Standard SS 6617-76. The influence of heating and rolling GTR/bitumen blends on degree of GTR devulcanization have been studied by sol-gel analysis in o-xylene. For the rheological measurements disks of TDVs with diameter 32 mm and thickness 0.7 mm were pressed on a hydraulic press at temperature of 180°C. The shear viscosity of TDVs under study was measured with PIRS-03 rheometer with a cone-plane working unit. The shear rate (7) and shear stress (7) were calculated from the equations: y = 6.28 n /tan a , T = 3M l2nR\ where n is the cone rotation frequency, a is the cone angle, Mis the torque, R is the cone radius. The cone with R=0.02 m and a=0.035 radian was used. RESULTS AND DISCUSSION Sol-gel Analysis The gel-fraction content for different compositions is shown in Table I. Comparison of gel-fraction content for GTR and GTR/bitumen pre-heated and rolled blends shows that heating at 170°C for 4 hours leads to decreasing the gel-fraction content and the additional rolling pre-heated blends for 40 minutes increases the difference in the gel-fraction content between initial GTR and treated GTR or GTR/bitumen blends (AX=XGT«-Xlreated) providing the further devulcanization. It was concluded that the bitumen plays a role of softening and devulcanizing agent, which conduces a process of breaking sulphur bridges at high temperature, then extracts part of sulphur released and next is covulcanized (by extracted and own sulphur) with devulcanized GTR during reclaimed GTR revulcanization. Table I The gel-fraction content for TDV and components used Composition

Bitumen GTR GTR GTR/bitumen (1/1) GTR/bitumen (1/1)

Treatment conditions no no heating heating heating + rolling

Gel-fraction content (per GTR), X{%\

[%]

0 86.5 78.2 73.6 73.0

0 0 8.3 12.9 13.5

Thermal Stability Thermal stability of the TDV samples prepared in Brabender plasticorder was studied by TGA method. It is shown (see Figures 1-3) that the introduction of GTR to

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177

basic TDV decreases a thermal oxidative destruction in TDVs based on polyethylenes and completely suppresses it in TDV based on PP. Simultaneously the stages of intensive and high temperature decompositions shift to higher temperatures and a char residue increases. The best thermal stability is observed for TDVs containing GTR/bitumen component. The stage of thermal oxidative destruction at 150-250°C characterized for basic TDV is completely suppressed for all TDVs containing GTR/bitumen component independently of type of the recycled thermoplastics used. Am, %

Am x" , % min" o *

HDPE n EPDM HDPE :EPDM:GTR

0

HDPE < :EPDM:GTR/bitumen

-20 -

\

-40 -60 -80

-

l\

-

V

-100 1

i

,

i

I

400

.

I

,

I

600 o Temperature, C

200

200 400 600 o Temperature, C Temperature, C FIGURE 1. Thermograms of TDVs based on HDPER. 200

600

400

Am, %

Am x , % min LDPE :EPDM o

LDPE K :EPDM:GTR

»

LDPE R :EPDM:GTR/bitumen

if

0

w

-20 -40

1

-60 -80

-0,

^

-

u ll

-

ll

-100 200 400 600 o Temperature, C

-1,0

i

200

,

400

1

1

600

o Temperature, C

I

200

1

I

400

>

I

600

Temperature, C

FIGURE 2. Thermograms of TPVs based on LDPER.

200 400 600 o Temperature, C

200 400 600 o Temperature, C

FIGURE 3. Thermograms of TPVs based on PPR.

200 400 600 o Temperature, C

High Value Composites from Recycled Polyolefins and Rubbers

178

Rheological Properties Rheological characteristics, i.e. the logarithmic dependencies of shear stress (7) and the apparent viscosity (rj) on the shear rate (7), of the TDV samples prepared in Brabender Plasticorder are shown in Figure 4. As one can see from the Figure 4 (b), the considerable decrease of the apparent viscosity (17) of HDPER based TDVs with GTR/bitumen component in comparison with the basic TDVs takes place. An increase of rj with rise of temperature in the range of the low shear rate (7) (see Figure 4, b) for HDPER/EPDM based TDV may be connected with additional cross-link of samples at the temperature of the measurement. At increase of a shear rate the locations of flow curves change in such manner as if they rotate around a hinge "secured" in the region of log 7= 0.132 and log T = 7-104. The prominent decrease of "apparent viscosity" of TDVs in the range of the high shear rate (see Figure 4, f) probably is connected with a slip of samples relatively surface of a cone and plane. Note that the samples of LDPER/EPDM basic blend and all TDVs with GTR (without bitumen) were impossible to load into the working unit of a rheometer because of their very high viscosity (>105 Pa-s). The high viscosity of LDPE/EPDM basic blend is perhaps explained by partial crosslinking during TDV preparation. It should be concluded here that the TDVs containing GTR treated with bitumen could be easy reprocessed by injection molding, pressing and extrusion. HDPE -based TDVs :

a)

LDPE -based TDVs

c)

FIGURE 4. Rheological properties of TDVs: open symbols - recycled polyolefin/EPDM based TDVs; solid symbols - recycled polyolefiri/EPDM/(GTR/biturneri) based TDVs.

High Value Composites from Recycled Polyolefins and Rubbers

179

Tensile Properties and Chemical Resistance The tensile strength of different TDVs prepared are shown in Figure 5. One can see that introducing GTR into TDV decrease tensile properties drastically (especially for HDPER). However, using GTR modified with bitumen allows us to produce TDVs with tensile properties on the level of basic ones and even higher (for LDPER). From the analysis of data presented in Figures 5 one can conclude that such an improvement of tensile properties of GTR/bitumen-containing TDVs is a result of both the better compatibility of HDPER (LDPER) with EPDM rubber, as well as a significant effect of bitumen as a universal devulcanizing, plasticizing and compatibilizing agent. Some properties of few TDV samples obtained in extruder have been measured and are presented in Table 2. As can be clearly seen from the Table 2 the sample HDPER /EPDM/(GTR/bitumen)=40/35/25(l/l) is characterized by complex of properties required for TDVs.

• • TS, MPa EB,

15

900

r

600 CO LU CO 300

f

1

FIGURE 5. Tensile properties for TDVs studied, wt.%: LDPER/EPDM/(GTR/bitumen) = 40/60/(0/0) (1), 40/35/(25/0) (2), 40/35/(12,5/12,5) (3); HDPER/EPDM/(GTR/bitumen) = 40/60/(0/0) (4), 40/35/(25/0) (5) and 40/35/(12,5/12,5) (6).

Table II Characteristics for TDVs obtained by extrusion method HDPER/EPDM/ TS EB (GTR/bitumen) [MPa] [%]

50/25/25(1/1) 60/20/20(1/1) 40/35/25(1/1) 40/20/40(1/1) 40/0/60(1/1) b c

Hardness Frost[Shore A] resistance,

95 8.1 42 12.6 32 83 6.2 400 82 5.9 57 89 3.8 15 84 d- the temperature of destruction. Standard range of the values: 0-^45%. Standard range of the values: -30 - 20%.

Chemical resistance

Petrol", ;20% NaOH", 20% HC1C, Oil, id 1 Vl AV [ %] AM [ %] AM [ %] AM [ %] -39 -36 -41 -34 >0

63 42 115 48

22.5 13.7 37.8 20.2 0.6

-2.6 -2.7 -3.5 -3.1 -3.4

-3.3 -3.1 -3.5 -3.4 -3.4

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CONCLUSIONS The high value high performance composites from polyolefin and rubber waste have been developed. This is provided by using EPDM as a rubber compatibilizer, bitumen as a devulcanizing agent for GTR, as well as plasticizing and compatibilizing agent for TDV components and technology of dynamic vulcanization. ACKNOWLEDGEMENT The work was fulfilled under the financial support of EU (INCO-Copernicus contract No.: ICA2-CT-2001-10003 and STCU Agreement No.: 3009). REFERENCES 1. Karger-Kocsis, J. 1999. "Thermoplastic rubbers via dynamic vulcanization," in Polymer Blends and Alloys, G.O. Shonaike and G.P Simon, eds. New York: Marcel Dekker, pp. 125-153. 2. Y. Li, Y. Zhang and Y.X. Zhang. 2003. "Structure and Mechanical Properties of SRP/HDPE/POE (EPR or EPDM) composites," Polym. Test, 22:859-865. 3. Y. Li, Y. Zhang and Y.X. Hnsn%. 2003. "Morphology and Mechanical Properties of HDPE/SRP/elastomer composites: Effect of Elastomer Polarity," Polym. Test, 23:83-90. 4. Fainleib, O. Grigoryeva, O. Starostenko, I. Danilenko and L. Bardash. 2003. "Reactive Compatibilization of Recycled Low Density Polyethylene/Butadiene Rubber Blends During Dynamic Vulcanization," Macromol. Symp., 202:117-126. 5. O. Grigoryeva, A. Fainleib, O. Starostenko, A. Tolstov and W. Brostow. 2003. "Thermoplastic Elastomers from Rubber and Recycled Polyethylene. Structure and Property Enhancement through Chemical Reactions in Interphase," Polym. International, accepted for publication. 6. F. Cavalieri, F. Padella and F. Cataldo. 2003. "Mechanochemical Surface Activation of Ground Tire Rubber by Solid-State Devulcanization and Grafting," J. Appl. Polym. Sci., 90:1631-1638. 7. O. Grigoryeva, A. Fainleib, O. Starostenko, I. Danilenko, N. Kozak and G. Dudarenko. 2003. "Ground Tyre Rubber (GTR) Reclamation. Virgin Rubber / Reclaimed GTR (Re)vulcanizates," Rubber Chem. Tech., accepted for publication. 8. S. Rudheshkumar, I. Fuhrmann and J. Karger-Kocsis. 2002. "LDPE-Based Thermoplastic Elastomers Containing Ground Tire Rubber with and without Dynamic Curing;" Polym. Degr. Stab., 76:137-144. 9. O. Grigoryeva, A. Fainleib, O. Starostenko and A. Tolstov. 2003. "Structure-Property Relationships for Reactively Compatibilized Thermoplastic Elastomers from Recycled Polyolefins and Rubbers," Nonlinear Optics. Quantum Optics, accepted for publication.

Viscoelastic Behaviour, Thermal Properties and Morphology for New Composites from Recycled HDPE, EPDM, Ground Tyre Rubber (GTR) and Bitumen Olga Grigoryeva*, Alexander Tolstov, Olga Starostenko, Alexander Fainleib Institute of Macromolecular Chemistry of the National Academy of Sciences of Ukraine, Kharkivske shose 48, 02160 Kyiv, Ukraine Emilio Lievana, J. Karger-Kocsis Institut fur Verbundwerkstoffe GmbH (Institute for Composite Materials), University of Kaiserslautern, POBox 3049, D-67653 Kaiserslautern, Germany,

ABSTRACT Structure-property relationships for new composites prepared from recycled HDPE, EPDM, ground tyre rubber (GTR) and bitumen have been studied by a combination of DMTA, DSC and SEM techniques and tensile tests. The better mechanical performance determined for a composition containing a preheated and rolled mixture of GTR and bitumen have been explained by a better mixing of the components and formation of the essential interface layer due to the reclaiming (for GTR) and compatibilizing (for composite) role of the bitumen.

INTRODUCTION Thermoplastic elastomers (TPEs), especially blends of elastomer and thermoplastic obtained by dynamic vulcanization of rubber in thermoplastic and having characteristics of elastomers while maintaining the thermoplasticity [1] attract a great interest of scientists and producers. High value composites can be produced by a replacement of virgin components of TPEs (fully or partly) by recycled polymers. Obtaining materials of beneficial properties is not easy task due to very poor compatibility of the components. To be reactively compatibilized (it seems to be most effective method) the components (at least their surface) of high value composites including GTR should be activated by thermal, thermal-mechanical, thermal-chemical and other methods [2,3] and additional compatibilizers should be used [3-5]. In our previous works we have compared [6] behaviour of virgin and recycled polyethylenes (low and high density polyethylenes, LDPER and HDPER, respectively) in basic and compatibilized [7] composite formulations and combined [8-11] the methods of GTR devulcanization and the following reactive compatibilization of a reclaimed GTR with other components.

* Correspondence Author, Institute of Macromolecular Chemistry of the National Academy of Sciences of Ukraine, Kharkivske shose 48, 02160 Kyiv, Ukraine, fax:(380)445524064, e-mail: fainleib(a>.i.kiev.ua

182

New Composites from Recycled HDPE, EPDM, GTR and Bitumen

hi this study the reactively compatibilized high value composites based on recycled HDPE (HDPER), EPDM and partially devulcanized GTR were prepared. A new modifier, bitumen, contributing to GTR devulcanization and further compatibilization of all the composite components have been utilized. The structure-property relationships were investigated using DSC, DMTA and SEM techniques. EXPERIMENTAL Recycled high-density polyethylene (HDPER) from post-consumer bottle transportation crates collected in Kyiv (Ukraine) was used, the HDPER melt flow index (MF1) was: MFIm/2.i6 = 2.13 g/10 min. GTR fraction with a particle size of 0.4 to 0.7 mm was kindly provided by Scanrub AS (Viborg, Danmark). Ethylene/propylene/diene monomer (EPDM) containing rubber (Buna® EP G 6470 of Bayer) was used. The EPDM rubber with 71 wt % of ethylene and 4.5 wt % of ethylidene norbornen contents, respectively, had a Mooney viscosity, ML(l+4) 125°C, 59. Bitumen used was a BN-4 grade according to the State Standard SS 6617-76. HDPER and EPDM were used as received. GTR was used as received and in some TPE formulations it was mixed with bitumen (1/1 by weight) and the mixture was preheated at 170°C for 4 hours and further rolled for 40 min prior to introducing to TPE recipes. In all cases, the mastication of composition by Brabender Plasticorder was carried out at 160°C and 80 rpm for 15 min. The viscoelastic behaviour of the resulting TPEs was investigated using a DMTA device (Eplexor 150N of Gabo Qualimeter, Ahlden, Germany). Rectangular sheets having a dimension of 6x1x0.25 cnw were subjected to oscillating tensile loading. The testing temperature ranged from -105°C to 150°C selecting a heating rate of 3°C/min. Differential scanning calorimetric studies were carried out using a DuPont thermal analyzer model 910. The scans were taken in the temperature range from -100°C to 200°C with a programmed heating rate of 20°C/min. Melting temperature (7m) corresponding to the maximum in fusion endotherm, was noted. Tensile tests were performed on dumbbell specimens at ambient temperature at a crosshead speed of 100 mm/min using Instron-1122 type universal testing machine. The average data for 6-7 specimens were taken for consideration. The parameters such as tensile strength at break (75) and elongation at break (EB) were determined. The fracture surface of the specimens was inspected by using a scanning electron microscope JSM-5400 of Jeol (Tokyo, Japan). RESULTS AND DISCUSSION Dynamic Mechanical Thermal Analysis (DMTA) It was found that the damping behaviour (i.e., the character of E'=f(T) dependencies) of all of the blends studied is quite similar to HDPER and it is typical for thermoplastic compositions. We infer that in all the blends HDPER forms continuous thermoplastic phase (matrix) while crosslinked rubber components (EPDM, reclaimed GTR) form a dispersed phase. The Tg values of the TPEs and the individual components as well as the corresponding E" values at Tg are listed in Table I. HDPER/EPDM blend produced by the mastication in Brabender plasticorder exhibits the transition at -31°C (Tg2) as a result of overlapping Tg's of amorphous phases of EPDM (Tg2) and HDPER (Tg3), while a second transition at 68°C (7^) is characteristic for HDPER. Shifting the first

New Composites from Recycled HDPE, EPDM, GTR and Bitumen

183

lower Tg2 on 5°C towards higher temperature compared to (Tg2) of individual EPDM evidences of mixing amorphous phases of EPDM and HDPER. The damping behaviour of HDPER/EPDM/GTR TPE is characterized by appearance of new relaxation transition at -50°C (Tgi) characteristic for introduced GTR and by shifting other Tg's peaks towards lower temperatures. This, along with the lower values of storage moduli (E1) and higher values of E" at Tg evidences of significant growth of chain flexibility of the components, especially in rubber rich phases. It can be caused mainly by disordering the matrix due to dispersion of GTR crosslinked particles. The latter is confirmed by a significant growth of E" values (from ~ 20 up to 90 MPa) in the temperature region below Tgi. Table I DMTA data for individual components and TPEs Sample code

-

Composition [wt%]

Tg[°C] for Phases Rich in: GTR EPDM HDPEK Tg2

-

-

EPDM

-

-36

-

-

-

-31

-

68

-

134

-50

-42

54

160

150

Bl

HDPE /EPDM = 61.5/38.5*

B2

HDPE R /EPDM/GTR** = 4 0 / 2 5 / 3 5 R

Tg4

h, -

Tgi

HDPER

R

Tgi

E" Value at Tgl [MPal

4 5 6 0

h2

-

h3

ioo~

-

30

102

42 121 158 HDPE /EPDM/(GTR/bitumen)** = -49 -35 40/25/17.5/17.5 B4 HDPE R /EPDM/(GTR/bitumen)*** = -48 -33 53 63 110 40/25/17.5/17.5 * ratio of HDPER/ EPDM=61.5/38.5 wt % is equal to 40/25 wt % in the ternary blends; ** the TPE was obtained by mastication in Brabender Plasticorder; *** the TPE was obtained by preheating of GTR/bitumen blend followed by its rolling and then by mastication in Brabender Plasticorder. B3

h4

65

21 35

41

As for the damping behaviour of HDPER/EPDM/ (GTR/bitumen) TPEs one can see a shift of Tgi and 7b towards higher temperatures compared to the recipes without bitumen. This, along with decreasing E" values in the temperature region below TgJ} as well as increasing E' values in the region above Tgi transition, evidences of increasing crosslinking degree of the blends. It can be explained by the dynamic vulcanization of dispersed rubbers inside plastic HDPER matrix, confirming the role of bitumen as a curing agent for the rubbers. In addition, it was found that the B4 TPE is characterized by significant decrease of segmental motion onset (onset of Tgi) from -65°C to -75°C that means improving GTR chain flexibility, obviously due to bitumen induced degradation of GTR followed by (re)covulcanization of devulcanized GTR, EPDM and bitumen. Differential Scanning Calorimetry (DSC) DSC curves for individual polymers and TPEs produced are shown in Figure 1. First off all, both EPDM and FTDPER show a melting of their crystallites in the blends, i.e. have both amorphous and crystalline phases. Second, some depression of the melting temperature (7m) values for both EPDM and HDPER in the blends is observed in comparison to the individual polymers depending on the composition and processing conditions used (cf. Table II). The maximal reduction of Tm reaches ~5°C for EPDM and

184

New Composites from Recycled HDPE, EPDM, GTR and Bitumen

~6°C for HDPER for HDPER/EPDM/GTR/bitumen TPEs. It may be caused by formation of crystallites having a smaller size or by increasing unsoundness of crystallites formed. For HDPER matrix of the TPEs a significant shift of onset of melting temperature, Tmonset, towards higher temperature and narrowing a temperature interval of crystallites melting, ATm, is observed in comparison to individual HDPER. We suppose that the growth of Tmomet from 37°C (for individual HDPER) up to 70-75°C (for HDPER as a component in blend) observed can be caused by a disappearance of smaller less perfect crystallites involved into the amorphous phase. The narrowing the melting interval, ATm, for HDPER crystallites from 123°C (for individual polymer) up to 85°C (in HDPER/EPDM blends), and further to 71-76°C (for GTR-containing TPEs) testifies of decrease of dispersion of dimensions of HDPER crystallites in the blends. a)

EPDM

HDPE -100

-50

50

100

150

200

b) EM

B3

B2 B1

-100

-50

50 Temperature,

1 00

150

200

C

FIGURE 1. DSC traces for: (a) individual EPDM, HDPER and bitumen (indicated in the plot); (b) TPEs produced (the codes of the curves correspond to the compositions in the Table I).

New Composites from Recycled HDPE, EPDM, GTR and Bitumen

185

Table II DSC data and tensile properties of TPEs Sample code

Composition

7m

ATm = Tme:nd " Tmonset

[°iC]

[°C] EPDM HDPE K

EPDM HDPE K Bl B2 B3 B4

HDPEK EPDM HDPE R /EPDM HDPE R /EPDM/GTR HDPE R / EPDM / (GTR/bitumen) HDPE R / EPDM / (GTR/bitumen)

47 45 45 42 45

136 135 132 130 133

37 43 21 35 26

123 85 76 72 71

TS [MPa]

EB [%]

17.7 11.2

10 820 750 40 65 300

11.6 3.9 4.0 6.3

Scanning Electronic Microscopy (SEM) Figure 2 depicts SEM photomicrographs taken from the cut surface of the sheets of GTR-based TPEs listed in Tables I and H One can clearly see that GTR particles directly dispersed in HDPER/EPDM blend (sample B2) are very poorly bonded to the matrix and a lot of large and small strip breakages are observed. The GTR particles debond from the matrix indicating for lacking interaction between them and, as a result, the sample exhibits low tensile properties (cf. Table II).

FIGURE 2. SEM photomicrographs of surfaces for the TPE samples produced (the codes of the curves correspond to the compositions in the Tables I and II).

A better bonding between GTR particles and matrix is observed for the formulations produced by using bitumen (sample B3) and especially for TPE produced with GTR/bitumen preheating, rolling and further mastication by Brabender plasticorder (sample B4). It can be seen that surface of the last sample of TPE looks very homogeneous and there are no visible strip breakages that is a result of better bonding between GTR particles and thermoplastic matrix via formation of an improved interface layer. Understandably, the TPE sample (sample B4) exhibits high tensile properties (cf. Table II). CONCLUSIONS Thermoplastic elastomers containing recycled HDPER and GTR have been prepared by using technology of dynamic vulcanization and reactive compatibilization. Structureproperty relationships for TPEs produced have been investigated and the effectiveness of producing methods used has been compared. A significant improvement of both TS and EB values has been achieved for HDPER/EPDM/GTR/bitumen TPEs produced with preheating and rolling of GTR/bitumen before mastication of the formulation by

186

New Composites from Recycled HDPE, EPDM, GTR and Bitumen

Brabender plasticorder. The comparative analysis of DMTA, DSC and SEM experimental results has shown that significant improvement of tensile properties achieved in comparison to TPEs containing unmodified GTR is a result of the effect of bitumen as a suitable reclaiming agent for GTR, and further as a compatibilizer for GTR/bitumen containing TPEs. ACKNOWLEDGEMENT The work was fulfilled under the financial support of EU (INCO-Copernicus contract No.: ICA2-CT-2001-10003 and STCU Agreement No.: 3009). REFERENCES 1.

Karger-Kocsis, J. 1999. "Thermoplastic rubbers via dynamic vulcanization," in Polymer Blends and Alloys, G.O. Shonaike and G.P Simon, eds. New York: Marcel Dekker, pp. 125-153. 2. F. Cavalieri, F. Padella and F. Cataldo. 2003. "Mechanochemical Surface Activation of Ground Tire Rubber by Solid-State Devulcanization and Grafting," J. Appl. Polym. Sci., 90:1631-1638. 3. O. Grigoryeva, A. Fainleib, O. Starostenko, I. Danilenko, N. Kozak and G. Dudarenko. 2003. "Ground Tyre Rubber (GTR) Reclamation. Virgin Rubber / Reclaimed GTR (Re)vulcanizates," Rubber Chem. Tech., accepted for publication. 4. Y. Li, Y. Zhang and Y.X. Zhang. 2003. "Structure and Mechanical Properties of SRP/HDPE/POE (EPR or EPDM) composites," Polym. Test, 22:859-865. 5. Y. 'Li, Y. Zhang and Y.X. Zhang. 2003. "Morphology and Mechanical Properties of HDPE/SRP/elastomer composites: Effect of Elastomer Polarity," Polym. Test, 23:83-90. 6. O. Grigoryeva, A. Fainleib, O. Starostenko, A. Tolstov and W. Brostow. 2003. "Thermoplastic Elastomers from Rubber and Recycled Polyethylene. Structure and Property Enhancement through Chemical Reactions in Interphase," Polym. International, accepted for publication. 7. Fainleib, O. Grigoryeva, O. Starostenko, I. Danilenko and L. Bardash. 2003. "Reactive Compatibilization of Recycled Low Density Polyethylene/Butadiene Rubber Blends During Dynamic Vulcanization," Macromol. Symp., 202:117-126. 8. S. Rudheshkumar and J. Karger-Kocsis. 2002. "," Plastics, Rubber and Composites, 31:1-. 9. S. Rudheshkumar, I. Fuhrmann and J. Karger-Kocsis. 2002. "LDPE-Based Thermoplastic Elastomers Containing Ground Tire Rubber with and without Dynamic Curing;" Polym. Degr. Stab., 76:137-144. 10. O. Grigoryeva, A. Fainleib, O. Starostenko and A. Tolstov. 2003. "Structure-Property Relationships for Reactively Compatibilized Thermoplastic Elastomers from Recycled Polyolefins and Rubbers," Nonlinear Optics. Quantum Optics, accepted for publication. 11. A. Fainleib, O. Grigoryeva, A. Tolstov and O. Starostenko. 2003. "Reactively Compatibilized Recycled LDPE / Ground Tire Rubber Thermoplastic Elastomers," Macromol. Symp., submitted for publication.

Effect of Coupled Long-Term Seawater Exposure and BiAxial Creep Loading (2:1) on Durability of Fiber-Reinforced Polymer-Matrix Composites Xiaohong Chen, Emrah Gokdag and Su Su Wang* Composites Engineering & Applications Center (CEAC) and Department of Mechanical Engineering, University of Houston, Houston, TX 77204-0931, USA

ABSTRACT Lightweight, high-strength fiber-reinforced polymer-matrix composites have attracted increasingly interests in their use for offshore operations. It is well known that long-term environmental attack and mechanical loading may cause microstructural damage and property degradation. The composite property degradation during long-term multi-axial loading in seawater has been a major concern because offshore structural systems are designed on the basis of either their stiffness or strength. Advanced composite systems must be capable of withstanding severe environments and still maintain their structural integrity in the designed life, hi this paper, the effect of coupled long-term seawater exposure and bi-axial loading (2:1) on durability of advanced fiber composites is investigated. Accelerated bi-axial creep experiments have been conducted on carbon fiber/epoxy and glass fiber/epoxy composites in seawater. Critical material degradation and life prediction models are developed for the composite systems. With the aid of SEM observations, damage mechanisms and failure modes in the composites subject to combined long-term seawater exposure and bi-axial creep loading have also been identified. More general loading cases and their effects are reported elsewhere due to space limitation.

INTRODUCTION Lightweight, high-strength advanced fiber composites have attracted significant interests in their applications to offshore exploration and production (E & P) operations. Coupled long-term offshore environmental exposure and mechanical loading are expected to cause microstructural damage and composite property degradation. Understanding the effect of coupled long-term seawater exposure and bi-axial creep loading on durability of fiber-reinforced polymer-matrix composites is of vital importance for long-term safe and reliable applications of advanced fiber composites for offshore operations. A significant amount of research [1-6] has been reported on moisture, water or saltwater diffusion in neat epoxy resins and their fiber composites in a stress-free state. Since diffusion in a fiber composite depends on the fiber direction, the amount and properties of matrix resin, filler phase and the fiber/matrix interface, more complex behavior is expected than that in a monolith epoxy resin. It is also recognized that an * Corresponding author, CEAC, University of Houston, Houston, TX 77204-0931, USA, 1-713-743-5063, [email protected].

188

Durability of Fiber-Reinforced Polymer-Matrix Composites

external stress affects diffusivity in a neat resin [7, 8]. Nevertheless, little is known about the effect of a multi-axial stress state on diffusion in the composites. Severe degradation in mechanical properties, such as tensile strength, has been observed in epoxies and their composites when exposed to water [9, 10]. Matrixdominant properties such as transverse and shear strengths have been noted to degrade with moisture or water exposure, while fiber-dominated properties such as longitudinal strength is little affected except in glass/epoxy composite where fibers are known to degrade in water [11]. The fiber/matrix interface has been recognized to be a weak link and is a subject of many studies [12-15]. The bond strength is found to decrease with immersion time and its failure modes change with immersion time also. A wet environment significantly affects long-term composite creep behavior, especially for the transverse loading cases [16]. Creep rupture time is found to decrease with increasing temperature and moisture, hi fact, creep rupture occurs within a few hours in a glass/epoxy even at a low load when temperature and moisture content are high. Hale et al [17-19] have conducted three-point bending creep tests, and also uniaxial and bi-axial tensile tests, on E-glass fiber composite pipe with winding angles of + 55° after its elevated-temperature water exposure till saturation. The biaxial tensile failure envelopes have been given in terms of hoop and axial stresses, which are not in principal material directions. Hence, it is difficult to extend to other loading cases. Moreover, the coupled effects of combined water exposure and mechanical loading have not been investigated. hi this research, accelerated biaxial creep experiments are performed on filamentwound carbon fiber/epoxy and glass fiber/epoxy tubular specimens with winding angles of ±88.5° in seawater at an elevated temperature. The effect of coupled long-term seawater exposure and bi-axial creep loading on property degradation and failure life is assessed, hi conjunction with the experimental results, critical material degradation and life prediction models are then developed for the offshore composites. EXPERIMENTS The material systems used in the study are E-glass/epoxy (PPG1062/Epon862 with Epicure W agent) and carbon/epoxy (Grafil 34-700/Epon 862-Epicure W), typical for offshore applications. The vast amount of research conducted at the CEAC over the past years has provided a database for composite properties in the dry state [20]. Filamentwound tubular specimens with winding angles of ±88.5° with respect to the tube axis were used. The seawater was prepared by mixing tap water and Instant Ocean (2.3% NaCl by weight) [15]. Two sets of experimental facilities were used, depending on hoop-to-axial stress ratios. For instance, for the hoop-to-axial stress ratio ahlaa = 2, specially designed grip fixtures were used together with fluid pumps to add pressure on the tubular composite specimens soaked in a seawater tank at a prescribed temperature [Fig.l(a)]. Such an experimental set up with specially designed grip fixtures was relatively simple without resorting to a complex loading frame. However, it had a limitation on the range of applied ah/aa. Experimental facilities for achieving any combination of axial loading and internal pressure are shown in Fig.l(b). A creep test frame was used for applying axial loading, while a pressure intensifier with an aluminum mandrel for applying internal pressure. Specially designed grips were used to mount the aluminum mandrel and the specimen soaked in a seawater gasket on the test machine.

Durability of Fiber-Reinforced Polymer-Matrix Composites

(a)

189

(b)

FIGURE 1 Biaxial creep-diffusion experimental facilities.

THEORETICAL CONSIDERATIONS For a polymer composite under combined seawater exposure and mechanical loading, its leakage failure life, tf, may be considered as result of a rate process with the time required to cause polymer matrix fracture. Thus, the commonly used kinetic fracture model [21] for polymers is modified with inclusion of both stresses and seawater absorption, i.e.,

tf

[

RT

where t0 is a reference time; R, the gas constant; T, the absolute temperature; and AH, the activation energy, depending on stresses {cr,} and seawater absorptionM. Taking the first-order expansion of AH, one has AH(ai,M) = AH0- aiVi - AM + H.O.T.(CT,.,M)

(2)

where AH0 is the stress- and absorption-free activation energy; V,, activation volumes; and A, the seawater-polymer affinity. Expressing the first-stage seawater diffusion with the Fickian law, one may obtain the following creep stress-sorption-life equation for the composite in seawater at a constant temperature Tsubject to proportional pressure and axial loading: ^f- = Ao + 4 \og(tf ) + A2JlJ where tf=tf/t0; strength.

(3)

At = ,4/(f0,.Ar,7T); K = <Jh/cra], and X2 is the transverse tensile

Durability of Fiber-Reinforced Polymer-Matrix Composites

190

RESULTS AND DISCUSSION Owing to the space limit, selected results are presented here on long-term failure behavior of carbon fiber/epoxy and glass fiber/epoxy composites subject to combined seawater exposure and biaxial creep loading (K=2). More general loading cases and their effects are reported in [22]. Based on the aforementioned kinetic failure equation, the creep stress-sorption-life relationships have been established for carbon fiber/epoxy and glass fiber/epoxy composites in the following two forms: (a) transverse stress versus logarithmic failure time; and (b) transverse stress versus square root failure time. In Figs.2(a) and (b), composite creep failure lives clearly follow the creep stresssorption-life equation for both composite systems in seawater under 2:1 biaxial loading at 70°C. Solid lines are determined from a regression analysis of experimental data. When a high load and/or a short-time seawater exposure is applied, composite failure is governed by the stress level, as seawater diffusion takes time to reach a critical level. On the other hand, long-term failure of the composites in seawater under a low load is affected by the amount of seawater absorption and the stresses. The relationship is clearly shown in the a221X2~^t7T^ graph [Fig.2(b)]. It is also noted that the glass fiber/epoxy composite degrades more rapidly than the carbon fiber/epoxy composite with the same amount of seawater exposure time and biaxial creep loading.

K=2

Carbon/Epoxy

\ A

X. AA

Glass/Epoxy \ ,

0

(a)

1

2

(Vto)"2

3

(b)

FIGURE 2 Failure lives of carbon/epoxy and glass/epoxy composites in seawater at 70oC subject to proportional biaxial creep loading at K=2. (a) Logarithmic time scale, (b) Square root time scale.

Durability of Fiber-Reinforced Polymer-Matrix Composites

(a)

191

(b)

FIGURE 3 Fracture surfaces of fiber composites in seawater at 70oC subject to proportional biaxial creep loading (K=2) for 30 days, (a) Carbon/epoxy composite (320 psi), (b) Glass/epoxy composite (248 psi).

SEM observations have also been conducted on fracture surfaces of carbon/epoxy and glass/epoxy composites subject to combined seawater exposure and biaxial loading at K=2 [Figs.3(a) and(b)]. The composite failure modes are found to involve fiber-matrix interface degradation besides matrix cracking, fn comparison with that of the carbon/epoxy composite, severe interface degradation is observed in the glass/epoxy composite due to coupled seawater exposure and biaxial loading at 70°C for about 30 days. The degradation of advanced fiber composites is clearly governed by the time of seawater exposure, and the bi-axial stress state and magnitude. Based on the experimental data and the stress-sorption-life equation, one may construct failure envelops (or map) for fiber composites subject to long-term loading with any stress biaxial ratio. With such a failure map, it becomes possible to estimate the service lives of advanced fiber composites in a seawater environment in given loading conditions. REFERENCES 1.

2.

3.

4. 5.

6. 7. 8. 9.

Loos, A.C. and Springer, G.S. 1981. "Moisture Absorption of Graphite-Epoxy Composition Immersed in Liquids and in Humid Air," Environmental Effects on Composite Materials, Vol. 1., G.S. Springer, ed. Technomic Publishing Company, Inc., Westport, CT, pp.34-50. Woo, M. S. and Piggot, M.R. 1987. "Water Absorption of Resins and Composites: II Diffusion in Carbon and Glass Reinforced Epoxies," ASTM Journal of Composites Technology & Research, 9, 162-166. Chateauminois, A., Vincent, L., Chabert, B., Soulier, I P . 1994. "Study of the Interfacial Degradation of a Glass-Epoxy Composite During Hygrothermal Aging Using Water Diffusion Measurements and Dynamic Mechanical Thermal Analysis," Polymer, 35,4766-4774. Schutte, C.L. 1994. "Environmental Durability of Glass-Fiber Composites", Material Science and Engineering, R13, 265-322. Tsotsis, T.K. and Weitsman, Y. 1994. "A Simple Graphical Method for Determining Diffusion Parameters for Two-Stage Sorption in Composites," Journal of Materials Science Letters, 13, 16351636. Zhou, J. and Lucas, P. 1996. "Effects of Water on a Graphite/Epoxy Composite," Journal of Thermoplastic Composite Materials, 9,316-322. Fahmy, A. A. and Hurt, J.C. 1980. "Stress Dependence of Water Diffusion in Epoxy Resin," Polymer Composites, 1, 77-80. Neumann, S. and Marom, G. 1987. "Prediction of Moisture Diffusion Parameters in Composite Materials under Stress," Journal of Composite Materials, 21, 68-80. Browning, C.E., Husman, G.E. and Whitney, J.M. 1977. "Moisture Effects in Epoxy/Matrix Composites", ASTMSTP 617,481-496.

192

Durability of Fiber-Reinforced Polymer-Matrix Composites

10. Long, E.R. 1979. "Moisture Diffusion Parameter Characteristics for Epoxy Composites and Neat Resins," NASA TP-1474. 11. Hogg, P J. and Hull, D. 1983. "Corrosion and Environmental Deterioration of GRP", in Developments in GRP technology-I, B. Harris, ed. Applied Science Publishers, pp. 37-90. 12. Carlsson, L.A. 1993. "Influence of Seawater on Transverse Tensile Properties of PMC," NIST Special Publication 887,203-211. 13. Wagner, H.D., Lustiger, A. and Lin, S. 1993. "Assessing the Glass Epoxy Interface after Environmental Exposure", NIST Special publication 887, 213-225. 14. Bradley, W.L. and Grant, T. S. 1995. "The Effect of the Moisture Absorption on the Interfacial Strength of Polymeric Matrix Composites," Journal of Materials Science, 30, 5537-5542. 15. Wood, C. A. and Bradley, W. L. 1997. "Determination of the Effect of Seawater on the Interfacial Strength of an Interlayer E-Glass/Graphite/Epoxy Composite by In Situ Observation of Transverse Cracking in an Environmental SEM," Composites Science and Technology, 57, 1033-1043. 16. Scott, D.W., Lai, J.S. and Zureick, A.H. 1995. "Creep Behavior of Fiber-Reinforced Polymeric Composites: A Review of the Technical Literature," Journal of Reinforced Plastics and Composites, 14, 588-6.17. 17. Hale, J.M., Gibson, A.G. and Speake, S.D. 1998. "Tensile Strength Testing of GRP Pipes at Elevated Temperatures in Aggressive Offshore Environments," Journal of Composite Materials, 32 (10), 969987. 18. Hale, J.M., Gibson, A.G. and Speake, S.D. 2002. "Biaxial Failure Envelope and Creep Testing of Fibre Reinforced Plastic Pipes in High Temperature Aqueous Environments," Journal of Composite Materials, 36 (3), 257-270. 19. Hale, J.M., Shaw, B.A., Speake, S.D., Gibson, A.G. 2002. "High Temperature Failure Envelopes for Thermosetting Composite Pipes in Water," Plastics, Rubber, and Composites, 29 (10), 539-548. 20. Wang, S.S. and Srinivasan, S. 1996. "Long-Term Leakage Failure of Filament-Wound Fiberglass Composite Laminate Tubing under Combined Internal Pressure and Axial Loading," Technical Report CEAC-TR-96-0101, CEAC, University of Houston, Houston, TX, USA. 21. Hertzberg, R. W. 1989. Deformation and Fracture Mechanics of Engineering Materials, 3rd edition, John Wiley & Sons, Inc., New York. 22. Wang, S.S., Chen, X. H. andGogdak, E. 2003. "Coupled Long-Term Multi-Axial Creep and Diffusion in Advanced Fiber Composites in Saltwater Environment," Technical Report CEAC-TR-02-0102, CEAC, University of Houston, Houston, TX, USA.

Part III

Composite Structures

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Deformation Analysis of Kinematically Constrained Thermoplastic Composite Plates in Forming Temperature Hamid Reza Daghyani*, Mohammad Tahaye Abadi and Shahriar Fariborz Faculty of Mechanical Eng., Amirkabir University of Technology, Tehran, Iran

ABSTRACT A finite element (FE) formulation is developed to analyze the sheet forming process of multiply thermoplastic laminates reinforced with unidirectional continuous fibers. Each ply is analyzed using the plate theory considering the applied tractions over the ply surfaces as well as the kinematical constrains of matrix incompressibility and fiber inextensibility. The inter-ply shear deformation mechanism is modeled as a viscose film between plies that couples the deformation of plies. In order to avoid penetration of each ply into each other and into the tool surface, the Lagrange multipliers are defined in contact surfaces. The results of FE analysis are compared to the analytical and experimental outcomes.

INTRODUCTION Thermo forming is the most effective method in mass production of reinforced thermoplastic finished parts. High viscosity of thermoplastic materials in forming temperature and kinematical constrains of continuous fibers cause to consider some special requirements in order to produce defect free parts. Due to high expenses of the experimental investigations for production of high quality finished parts, a sheet forming model is needed to analyze the optimum conditions of geometry and loading parameters for production process. In previous research works two models were presented [1]: the kinematical model and the continuum mechanical model. In the kinematical model, the reinforced ply is mapped over the tool surface considering viscose matrix incompressibility, fiber inextensibility and fixed fiber distance constrains. The assumption of fixed fiber distance during forming process yields to incompatible results with experimental observations [2]. In the continuum mechanical models, the process is analyzed by defining a constitutive equation and solving equilibrium and continuity equations with respect to the kinematical constrains and boundary conditions. The later model gives stress states and deformation analysis of forming process during forming process while the first model gives kinematical results only in the fmial shape. Due to the difficulty of analytical solution in a continuum model, Bradaigh and Pipes [3] derived FE formulations and Bradaigh et al. [4, 5] solved them for plane stress and plane strain conditions without considering the ply interactions. Johnson and Pickett [6] derived shell formulations for deformation analysis of theroplastic plates ignoring out of plane stress and transverse shear strains. In our recent work [7], a FE formulation * Corresponding Author, Faculty of Mech. Eng., Amirkabir Uni. Of Tech. Tehran, 15914, Iran, Fax+98 21 6419736, e-mail: [email protected]

196

Kinematically Constrained Thermoplastic Composite Plates

was derived using the plate theory to analyze the deformation of a thermoplastic composite ply considering transverse intra-ply shear mechanism and applied surface tractions. In the present work, a FE formulation is developed to analyse the deformation and stress states during the sheet forming of multiply thermoplastic laminates reinforced with unidirectional continuous fibers. PLATE FORMULATION For the analysis of deformation state in composite laminates, it is most effective to describe the deformation of each thin ply in term of the deformation of its middle surface. The experimental observations show that the intra-ply shear strain causes the initial normal transverse plate to be rotated respect to the middle surface. Hence, The Kirchhoff hypothesis yields to the invalid results for sheet forming analysis of reinforced thermoplastic plies in forming temperature. Therefore, the velocity component y in each point (xux2,x3) of ply is stated by means of the ReissnerMindlin approximation [7] as:

^ , , V 3 ) = yvoUvX2)+x3wHxuXi)

+~xi2w1(v2)

(lc)

where v,. is the velocity component of middle plane, . is the rate of transverse plate rotation, w0 is the normal velocity component of middle plane, w, is the rate of thickness change and w2 is the rate of middle plane movement in thickness direction. The second order approximation of velocity in thickness direction is used for considering thickness variation and satisfying kinematical constrains. KINEMATICAL CONSTRAINS Three major assumptions are defined for kinematical constrains as: incompressibility of viscose matrix which is satisfied if the trace of strain rate tensor sets to zero, inextensibility of fibers which is satisfied if the projection of strain rate tensor along the fiber direction sets to zero and impenetrability to avoid the penetration of adjacent plies into each other or into the tool surface during numerical forming analysis where the kinematical constrains are applied to contact surfaces. Assuming an external normal pressure, the plies have similar normal velocities at contact surfaces. It can be stated as: Vjl) =K(1+I) i = 0,....n+\ (2) where n is the number of plies, F3(l)(z=l,....w) is the normal velocity of z'th ply, F3<0),F3("+1)are the normal velocities of lower and upper tool surfaces, respectively, (x1,x2,h/2)is a point on upper surface of zth ply and (x-l,x2,-h/2)is the corresponding point on lower surface of (/' +1) th ply.

Kinematically Constrained Thermoplastic Composite Plates

197

POTENTIAL FUNCTION The total potential function (PF) n is the sum of internal PF [/'„'', the external PFt/^J and the terms of kinematical constrains Uj£ considered with Lagrange multipliers for all layers [7]: ;=i

1=1

The internal PF can be calculated assuming the behavior of ply as an ideal fiber reinforced fluid (IFRF) [7].The external PF is given by: (0

„ (<)\

c+Wa

\

(4)

. (0 where W c is the contact work done by traction in lower and upper surfaces and °

(0

Wa is the work done by traction in the edge of i' ply. The contact work is due to the slip of adjacent plies relative each other or tool surface in resin rich film. If the resin rich layer in forming temperature behaves as Newtonian viscose fluid, the traction applied to the upper and lower surfaces can be stated as:

L

>~ V ( w»% w < V ' v> V l w,-*% w < ' V 0=1,2)

(5) where r\ is the resin shear viscosity and 8 is the resin rich layer thickness. Thus, the contact work can be written as:

(6) that Q(l) is the surface of ith ply. The work done in the edge of all plies can be given by:

-y2 (7) where tm,tnl and t are the normal, tangential and transverse tractions, respectively. The potential function due to previous defined constrains can be written as:

^ - t [ |»« Q

A

(8) where, T{>) ,p(i) and /l(Oare Lagrange multipliers, d^n is the component of strain rate tensor and a^is the component of unit vector in fiber direction of r'th layer. Integrating Eq. (8) over thickness yields: .n<"

(9)

198

Kinematically Constrained Thermoplastic Composite Plates

FINITE ELEMENT FORMULATION The FE formulations are derived by minimizing the potential function respect to the velocity functions defined in Eq. (1) and Lagrange multipliers. The velocity in each element of ith layer can be written in term of nodal values as: V(i)=Naf Using Eq. (1),N

(10)

anda(v()

can be stated in term of the velocity shape function Nv and '' as follows: the nodal values of velocity functions v .'\( a.. =

TV =

(11)

Nv

0

0

X}NV

0

Nv

0

0

0

0

Nu

0

0

0

( 12 )

0 0

Lagrange multipliers in each element of i' layer is stated in term of the nodal values as: T (0 = Nj.T(0 , P ( O s N p P ( O , A ' ^ N ^ 1 0 (13) Using shape function^, the terms in Eq. (13) can be defined as: 0

T<')lr •'l

Nr=N;>

J '

p(0 _ [p(

(14)

"I'll

_ IX o

~ [ o NL

Employing Eqs. (10) and (11), the PF in the whole plies can be written as follows: (15)

The matrices K ^ K ^ a n d K^were defined in our previous work [7] and for the sake of shortage, they are not brought here. The other matrices are defined as:

(16c)

-L

(16d)

where, G is defined as: 1 0 0" 0 1 0 0 0 0 The potential function must be minimized respect to the nodal values:

(17)

Kinematically Constrained Thermoplastic Composite Plates dU = 0. Sa!k> that yields to:

an Saf

C«)a«k) + 2C <

K ( T k) V v k) =0.

= 0.

k +1) ( k+ ) a v "

K« T a c v k ) =0.

an 3a

an

= 0.

199 (18)

= 0.

(k)

+ K =

«

•

(19) RESULTS AND DISSCUSSIONS During the sheet forming process of reinforced laminates, the fiber direction and thickness of each ply may be locally changed. Hence, a time dependent incremental analysis is processed to solve the equations. A software is developed to analyze the laminate deformed geometry, fiber directions, thickness, velocity, strain and stress in the whole elements. The meshes are generated using Q9/4/4/4 elements with nine points biquadratic shape functions for velocity and four Gaussian points bilinear shape functions for Lagrange multipliers. As an example, the pull out test used normally in experimental analysis to assess the shear properties of sheet forming process, is analyzed. As shown in Figure 1, a rigid plate that stacked in the middle of several plies is pulled out while compressed by two rigid plates. Hull et al. [8] proposed an analytical solution for such a problem by ignoring the normal pressure and Murtagh et al. [9] investigated it experimentally. This problem is analyzed using developed FE formulation for a Peek-Carbon fiber laminate with a longitudinal shear viscosity rjL = 6000Pa.s, transverse shear viscosity r/T = 4000Pa.s and the ratio of shear viscosity to thickness r//S = 2.2xlO7 Pa.s/m in resin-rich film. Because of symmetry only the upper plies are analyzed. Consider the normal velocity of upper and lower rigid plate is zero and the middle plate is pulled out with velocity of Vo .The velocity change in a two-ply laminate is calculated that is correlated well with the analytical solution as shown in Figure 2. Due to different fiber directions in

Fixed plate

FIGURE 1 Pull out test.

— •

Analytical results Finite element results

FIGURE 2 Analytical [8] and finite element results of pull out test.

200

Kinematically Constrained Thermoplastic Composite Plates

two plies and resin rich layer in their interfaces, the slips are observed, which are shown by horizontal jumps at the ply interfaces (Figure 2). The required pulling force for different pulling velocities in a constant normal pressure of 400 kPa is compare to the experimental results [9] shown in Figure 3. The experimental pulling force changes nonlinearly that is due to nonlinear behavior of resin-rich layer. Since in derivation of FE formulation, a Newtonian viscose fluid

- + - finite element results O Experimanlal analysis [91

o

| i I »

behavior is assumed for the resin rich film, some deviation from experimental results is observed in Figure 3.

y °

if

° ,f 0.15 0.2 0.25 0.3 shear velocity (mm/s)

FIGURE 3 Required shear stress for pulling out of the middle plate in different velocities.

CONCLUSIONS A FE is developed using Reissner-Mindlin approximation for sheet forming analysis of multiplies laminates reinforced with unidirectional fibers. The Kinematical constrains defined in each ply and in the interfaces of plies are well satisfied with this approximation. This formulation can be used for analysis of intra-ply shear and interply slip mechanisms in forming temperature while in-plane and out-of-plane tractions applied to the laminate surfaces. REFERENCES 1. 2. 3. 4.

5.

6. 7.

8.

9.

Lim, T.C., Ramakrishna, S., 2002, "Modeling of Composite Sheet Forming: A Review", Composites Part A, 33, pp. 515-537. Tucker, C.L., "Sheet Forming of Composite Materials", 1997, Advanced Composites Manufacturing, Editor: T.G. Gutowski, John Wiley, New York. CM. 6 Bradaigh and R.B. Pipes, 1991, "Finite Element Analysis of Composite Sheet-Forming Processes", Composites Manufacturing, Vol.2, Nos. 3 & 4, pp. 164-170. C. M. 6 Bradaigh, G.B. McGuinness and S.P. McEntee, 1997, "Implicit Finite Element Modeling of Composites Sheet Forming Processes", Composite Sheet Material, Composite Material Series, Vol.11, editor D.Bhattacharyya, Elsevier Pub.. S.P.McEntee and 6 Bradaigh, CM., 1998, "Large Deformation Finite Element Modeling of Single-Curvature Composite Sheet Forming With Tool Contact", Composites Manufacturing, 6, pp. 269-280. Johnson AF and Pickett AK, 1996, "Numerical simulation of the forming process in long fiber reinforced thermoplastic", CADCOMP '96, Udine, Italy. H. R. Daghyani, M. Tahaye Abadi and Sh. Fariborz, 2003, "Finite Element Analysis of Thermoplastic Composite Plates in Forming Temperature", submitted to Journal of Composite Materials. B.D.Hull, T.G.Rogers and AJ.M.Spencer, 1994, "Theoretical Analysis of Forming Flows of Continuous-fiber-Resin Systems", Flow and Rheology in Polymer Composite Manufacturing, Composite Materials Series, Vol. 10, editor S, G, Advani, Elsevier Pub. A.M. Murtagh and P.J. Mallon, 1997, "Characterizations of Shearing and Frictional Behavior during Sheet Forming", Composite Sheet Material, Composite Material Series, Vol.11, editor D.Bhattacharyya, Elsevier Pub.

Stability Analysis of Loaded Columns Made of Pultruded Composites Enayat Mahajerin* Saginaw Valley State University, U.S.A.

ABSTRACT In Pultrusion, a single reinforcement or a collection of reinforcements, saturated with a reactive resin, is pulled through a heated die that imparts a desired final geometry to the profile. Generally, the cross section of the profile is constant but it can be of arbitrary shape. These products have become very popular because they can be made to exhibit features found in components produced by other processes. In this paper, a method based on the combination of theoretical and numerical methods is developed to investigate effects of pertinent variables including geometric parameters, reinforcement types, and volume fractions of the constituents on the strength and stability of such composites. The energy method is used to establish the buckling criterion which leads to a two-dimensional, orthotropic partial differential equation (pde), for determination of the warping function. A numerical approach based on the Fundamental Collocation Method (FCM) is used for determination of the warping function. Consequently, the buckling criterion can be established, the eigenvalues of which are related to the critical buckling loads.

INTRODUCTION Recently, attention has been shifted, and toward manufacturing of pultruded composites because of their interesting characteristics including high strength-toweight ratios. Additionally, pultrusion can utilize a variety of fibers and produce complex thin or thick-walled shapes such as solid and hollow bars. The majority of pultruded components employ /^er-g/aM-reinforced polyester resins. Because of orthotropic physical and mechanical properties, and the arbitrary-shaped nature of the cross section, investigation of stability under applied loads requires a numerical method. Here, an approach based on the combination of the energy method and FCM is described.

FORMULATION We consider a general column made of a pultruded composite (Figure 1). The cross- section, R, lies in the x-y plane, and the normal, n, to the boundary, MR, makes an angle 0 (ccw) with the horizontal axis. The ends are at z=0 and z=L, and the column is subjected to an axial compression load P. Observations show that * Corresponding author, Professor of Mechanical Engineering, Saginaw Valley State University, University Center, MI 48710 USA. Phone:(989)964-4188, E-mail: mahaieri(a)/svsu.edu

202

Loaded Columns Made of Pultruded Composites

buckling of thin-walled columns often accompany twisting. A common theory that accounts for the combined effects of bending and twisting is to minimize the second variation of the strain energy, U, i.e., 8(82U )=0. Following the process for isotropic materials [1, 2], we extend the theory for orthotropic materials, and also integrate FCM in the formulation. Because 8 U is a second order, homogeneous quadratic function, it is written as (1) where q's are the amplitudes of displacements u, v, and w, in the x, y, and z directions, respectively. It can be shown that 8(82U)=0 leads to the following eigenvalue problem or the buckling criterion: an an au Det ai\ an an = 0

(2)

an O32 O33

in which 1

A T

-U1

flll = Ez

[lyy - (

I

e

—

(3)

an = Ez — - Le2 [Lx - (—^—

(4)

L

(5)

EzTI

(6)

= Ez

(7)

3 = a3i = Ez

(8)

= \\y dA

lyy =

\\X

dA

(9)

(10)

Loaded Columns Made of Pultruded Composites

203 (li)

(12)

dx

yf+Gzy{

+ xfdA

dy

l

dA

(14)

dA

(15)

= jjxw dA

(16)

where w(x,y) is the warping function of the Saint Venant torsion theory [3], s is the axial strain, and Le is the effective length of the column [4]. It can be shown that,

dx dn

=0,

dy

x,ysR

(17)

- xsm£>, x,yedR

(18)

Once (17) and (18) are solved for w(x,y), elements of the buckling criterion (2) can be determined from (3)-(8). The eigenvalues of (2) represent three principal strains, the smallest of which corresponds to the critical buckling load. For a special case in which Ixy=0, and the region R is symmetrical about the x- and y-axes, the buckling criterion becomes 011022033=0

(19)

This equation is satisfied if an=0, a22=0or a33=0, corresponding to: A

Flexural buckling in the x-direction: Flexural buckling in the y-direction:

.

JT Iyy

an = 0, i.e., £=—— t

a22 = v, i.e., e-

2

(20)

T

lxx

Ah a

Torsional buckling:

^ 3 = 0 , i.e., &r = — ( — S \ + — S i ) lp

Lz

(22)

Le

Using Hooke's law, s=a/E, (20) arid (21) lead to Euler's formulas for the flexural buckling, whereas (22) gives the critical strain causing torsional buckling.

204

Loaded Columns Made of Pultruded Composites

Infinite Plane

Q

W O

/

*

\

*

1

/

*

_/ o ft

R Xv^—_--~*"'""^ ^-^ •

o

FIGURE 1 Geometry

o

*

Field Points

•

Boundary Points

0

Source Points

FIGURE 2 Numerical Setup

NUMERICAL PROCEDURE Determination of the buckling criterion requires w(x,y) because parameters Si, S2, S3, and S4 are functions of w(x,y) and its derivatives. In the FCM process, the cross section, R, is imagined to be embedded inside an infinite plane of the same material where a series of point loads of initially unknown strengths, ck, is applied at source points (Xk,Yk), k=l,2,..,N. Normally, the sources are located outside the boundary, MR, at a finite distance, s, away (Figure 2). At any internal field point (x,y) we can write [5],

(23)

(24)

(25)

— = — cos 9 + — sin 6 dn dx dy

(26)

where ¥(x,y; Xk,Yk) denotes the influence function of (17), which is the solution at (x,y) due to a unit point load applied at the source point (Xk,Yk), and is given in [6],

Loaded Columns Made of Pultruded Composites

205

(27)

The weights, Ck, k=l,..,N, are the point load strengths, and can be adjusted via collocation so that the specified boundary conditions are satisfied at N boundary points, (Xj,yj), j=l,2,..,N. The procedure leads to a system of N simultaneous linear equations of the form

Kc=f

(28)

where K (kjj) is the NxN influence matrix, c is a column containing the unknown source strengths, and column f contains the prescribed boundary conditions. The system of equations (28) can be solved via Gaussian elimination for the weights, Ck, k=l,2,...,N. The computed weights can be inserted in (23)-(28) to find the warping function and its derivatives at any internal (field) point. Once w(x,y) and its derivatives are determined, the elements ay, i=l,..,N; j=l,...,N, of the buckling criterion (2), the eigenvalues, and consequently, the critical buckling loads can be determined.

EXAMPLES A series of pin-ended, axially loaded, "L-shaped" columns, 0.2- inch thick, made of composites with known properties (Table 1), with variable lengths and the "flange-to-web " aspect ratios, b/h, was analyzed. The critical buckling loads were computed using N=18 boundary points. Sources were distributed on a congruent boundary at a distance s (b<s
No.

Exx

GZy

Gzx

G2y

A

4166

2602

5105

1081

935

896

B

1991

1991

8105

810

810

711

C

3810

1564

5233

711

634

583

D

1462

611

2545

398

341

341

E

yy

CONCLUSIONS A suitable combination of the analytical and numerical methods for solving stability of pultruded composite columns has been presented. The method may be regarded as an efficient and straightforward tool for solving flexural-torsional buckling in any thin or thick composite column in which the cross section shape remains constant. Such characteristics are associated with bars made via pultrusion.

Loaded Columns Made of Pultruded Composites

206

I Oil

Hi)

14*

htt FIGURE 3 Critical load vs. L

Itt

02

«.3

0.4

(i.$

ft*

a?

OS

<

toft

FIGURE 4 Critical load vs. b/h

REFERENCES 1. Langhaar, H. L., Energy Methods in Applied Mechanics, J. Wiley, 1962. 2. Kappus, R. "Twisting Failure of Centrally Loaded Open-Section Columns in the Elastic Range," NACATM851, 1938. 3. Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, McGraw-Hill, 1970. 4. Gere, J. M. and Timoshenko, S. P., Mechanics of Materials, PWS, 1997. 5. Burgess, G. and Mahajerin, E., On the Numerical Solution of Laplace's Equation, International J. ofMech. Eng. Ed., vol. 13, no. 1, 45-54, 1985. 6. Kythe, P. K.. , "An Introduction to Boundary Element Method, "CRC, 1995. 7. Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, Mir Publishers, 1981.

Identification of Elastic Parameters for Cross-ply Laminated Plates and Shells Kenji Hosokawa* Faculty of Engineering, Chubu University, Japan Kin'ya Matsumoto Faculty of Education, Mie University, Japan

ABSTRACT An inverse analysis method has already been proposed by one of the authors to identify elastic parameters of laminated composite materials using the FEM eigenvalue analysis and the nonlinear optimization method. The purpose of this study is to apply the proposed method to a laminated square plate and a laminated shallow cylindrical shell made of the same composite material. The identified elastic parameters for the lamina of the plate were compared, and found to agree well, with that for the lamina of the shell.

INTRODUCTION Since composite materials such as fiber reinforced plastics (FRP) have high specific strength and high specific modulus, they have been used in many structural applications. It is therefore very important to make clear the dynamical properties of the laminated composites for the design and the structural analysis. Especially, elastic parameters are essential for the structural analysis. The elastic parameters of laminated composite materials, however, are difficult to determine by either theoretical or experimental approaches because of their anisotropy. On the other hand, one of the authors has already proposed an inverse analysis method to identify the elastic parameters for laminated composite materials using the FEM eigenvalue analysis and the sensitivity analysis [1], [2]. It is an advantage of this method that one can obtain nondestructively the elastic parameters of the products made of composite materials. Also, the authors applied the proposed inverse analysis method to a symmetrically and an antisymmetrically laminated square plate [3]. Furthermore, the inverse analysis method was applied to a laminated circular cylindrical shell [4]. From the comparison of these identified elastic parameters of the lamina and ones obtained by another experimental method, one can see the good agreements. However, in respect to the identification of elastic parameters, we can find few reports of the simultaneously identified elastic parameters for the laminated plates and shells made of the same composite material. For the above reason, in this paper, the proposed method is applied to a cross-ply laminated square plate and a cross-ply laminated shallow cylindrical shell. Naturally, the laminae of the plate and shell are made of the same prepreg sheets. The proposed method mainly consists of the FEM eigenvalue analysis and the nonlinear optimization method * Corresponding Author, Dept. of Mech. Eng., Chubu University, 1200 Matsumotocho, Kasugai, Aichi, 487-8501, Japan, fax:+81-568-51-1194, email:[email protected]

208

Elastic Parameters for Cross-ply Laminated Plates and Shells

considering the relation between elastic parameters and naturalfrequenciesas a nonlinear system. Firstly, by applying the experimental modal analysis technique to the cross-ply laminated square plate and shallow cylindrical shell, naturalfrequenciesand mode shapes are obtained. Secondly, from the obtained natural frequencies and mode shapes, the elastic parameters of the lamina are identified. Finally, in order to confirm the identified elastic parameters, it is shown that the estimated natural frequencies and mode shapes of the test pieces by using these identified elastic parameters. IDENTIFICATION METHOD The proposed identification method mainly consists of the FEM eigenvalue analysis and the nonlinear optimization method considering the relation between elastic parameters and naturalfrequenciesas a nonlinear system. Since the identification method was described in detail in Ref. [4], in the present paper, only an outline will be presented. Figure 1 shows the flow chart of the identification program. Firstly, the data about the geometrical configuration, initial material properties of the test piece, and natural frequencies measured by excitation test are given. Secondly, to calculate the natural frequencies and mode shapes, the eigenvalue analysis is carried out using the initial parameters. Next, the error function g(x) is estimated by the difference of the natural frequencies obtained by the eigenvalue analysis and the experiment, hi this phase, since the order of the natural modes may be replaced by the ratio of the elastic moduli of

START

)

Input of initial data Calculation of natural frequencies Calculation of error function Calculation of Jacobian matrix

g(x) J(x)

Improving the Hessian matrix H by SSR formulation or BFGS method Solving the equation Hd = —J (x)g(x) the Incomplete Cholesky method

by

Determination of step size by line searcher

Calculation of error function

g(x) No

FIGURE 1 Flow chart of identification

Elastic Parameters for Cross-ply Laminated Plates and Shells

209

anisotropic materials, the order of the natural modes is investigated by MAC (Modal Assurance Criterion). After that, elastic parameters are identified by the quasi-Newton method. Finally, if the calculated natural frequencies are converged into the experimental ones, the identification program is terminated. IDENTIFICATION OF ELASTIC PARAMETERS To identify the elastic parameters for the lamina of the laminated square plate and shallow cylindrical shell, experimental studies were carried out. As shown in Fig. 2, the configuration of the shallow cylindrical shell is a square planform (a=b=0.2[m\). The shell's thickness h is 1.60x10 [m]. The inside radius R of the shell is 0.4[m]. The density and the stacking sequence of the cross-ply laminated shallow cylindrical shell are 1557 [kg/m3] a n d [ 0 V 9 0 o 2 / 9 0 V 0 o 2 ] , respectively. The stacking sequence of the cross-ply laminated square plate is the same that of the laminated shallow cylindrical shell. The density of the laminated plate is 1549 [kg/m3]. The dimensions of the plate are of 0.2[m] long and 0.2[m] wide. The inside radius R of the plate is °°. The thickness of the laminated square plate is 1.59x10" [m]. Each layer material is graphite/epoxy. The laminae of these test pieces are made of the same prepreg sheets. Therefore, the elastic moduli for the laminae of the square plate and shallow cylindrical shell are due to have few differences. Natural Frequency and Mode Shape To satisfy the free boundary conditions, each test piece was hung from the ceiling by a

FIGURE 2 Laminated shallow cylindrical shell

Accelerometer Test piece impulse force hammer

FIGURE 3 Measurement of natural frequencies and mode shapes by experimental modal analysis technique

Elastic Parameters for Cross-ply Laminated Plates and Shells

210

fine string. The plate was divided into 7x7 points and 49 dividing points were used as reference points. Also, the shell was divided into 9x9points and 81 dividing points were used. To measure the transfer function (accelerance), an accelerometer was attached to one of the reference points and then all reference points were impacted by an impulse force hammer (See Fig. 3). The mass of the accelerometer is 0.48 [g]. From the obtained transfer function, the natural frequencies and mode shapes of the test pieces were estimated by applying the experimental modal analysis technique. Figure 4 shows the experimentally obtained natural frequencies and mode shapes of the each test piece. In this paper, for the mode shapes of the laminated shell, upper and lower edges are the curved edges. Identified Elastic Parameters From the experimental natural frequencies and mode shapes shown in Fig. 4, the elastic parameters for the lamina of the laminated square plate and shallow cylindrical shell were estimated by the proposed inverse analysis method. The computations were carried out using the FEM eigenvalue program with triangular shell elements. Each test piece is divided into 800 elements with 441 nodal points. In the numerical calculations, the mass of the accelerometer was not considered because the mass of the accelerometer is very small. The identified elastic parameters of the lamina are shown in Table 1. In Table 1, the elastic moduli EL, ET in the direction of the parallel and normal to the fiber and shear modus GLT are shown. Poisson's ratio vLT is assumed to be 0.32. From this table, one can find the good agreements between the identified elastic parameters for the lamina of the cross-ply laminated square plate and that of the cross-ply laminated shallow cylindrical shell. The difference between the identified elastic parameters of the plate and that of the shell is about 6.3% at the most. To confirm the identified elastic parameters, the FEM eigenvalue analysis was carried out by using the identified results. For the computation of natural frequencies and mode shapes, the mass of accelerometer was neglected because of it is very small compared to the test pieces' mass. Figure 5 shows the natural frequencies and mode shapes of these test pieces estimated by the eigenvalue analysis. From Figure 4 and Figure 5, one can see that the difference between the experimental natural frequencies and the numerically calculated ones is about 0.7% at the most and one can find the excellent agreements between these mode shapes of the test pieces. Test piece

Modal order

Cross-ply laminated plate

Mode shape Natural frequency [Hz]

Cross-ply laminated shell

1st

2nd

3rd

4th

5th

71.64

153.7

210.4

324.3

355.5

68.39

151.8

205.8

420.7

469.7

5

Mode shape Natural frequency [Hz]

FIGURE 4 Experimental natural frequencies and mode shapes of test pieces

Elastic Parameters for Cross-ply Laminated Plates and Shells

211

TABLE I Identified elastic parameters of lamina

Test piece Cross-ply laminated plate Cross-ply laminated shell Test piece

Modal order

Cross-ply laminated plate

Mode shape Natural frequency [Hz]

Cross-ply laminated shell

[GPa]

ET [GPa]

G LT [GPa]

119

8.19

4.36

122

8.51

4.10

1st

2nd

3rd

4th

5th

71.57

153.4

211.2

326.0

353.2

68.40

151.9

205.8

420.7

469.1

Mode shape Natural frequency [Hz]

FIGURE 5 Numerical natural frequencies and mode shapes of test pieces

CONCLUSIONS The inverse analysis method to identify elastic parameters of the laminated composite materials was applied to the cross-ply laminated square plate and the cross-ply laminated shallow cylindrical shell. One can find the good agreements between the identified elastic parameters for the lamina of the cross-ply laminated square plate and that of the cross-ply laminated shallow cylindrical shell. Also, to confirm the identified elastic parameters, the FEM eigenvalue analysis was carried out by using the above mentioned ones. From the results, one can see the good agreements with respect to the natural frequencies and mode shapes. Accordingly, it follows that one can accurately estimate elastic parameters for the lamina of the laminated composite materials by using the inverse analysis method proposed by the authors. REFERENCES 1.

2.

3.

4.

Matsumoto, K., M. Zako, and M. Furuno. 1996. "Identification of Anisotropic Parameters for Hybrid Laminated Composites Using FEM Eigenvalue Analysis," Transactions of the Japan Society of Mechanical Engineers (in Japanese), 62(596): 1341-1346. Matsumoto, K., M. Zako, M. Furuno, and T. Fujita. 1997. "Inverse Problem to Identify Equivalent Elastic Parameters of Honeycomb Sandwich Panels," Transactions of the Japan Society of Mechanical Engineers (in Japanese), 63(611):2256-2261. Hosokawa, K., K. Matsumoto, and M. Zako. 1998. "Identification of Elastic Parameters for Laminated Composites Using FEM Eigenvalue Analysis (Comparison of Numerical and Experimental Results)," Fatigue, Environmental Factors, and New Materials (Proceedings of PVP Conference), PVP-374:325-329. Hosokawa, K. and K. Matsumoto. 2002. "Identification of Elastic Parameters for Laminated Circular Cylindrical Shells (Comparison of Numerical and Experimental Results)," JSME International Journal, Series C,45(l):26-31.

Parametric Instability Analysis and Experiment of Laminated Composite Shell Meng-Kao Yeh and Hung-Chang Huang Department of Power Mechanical Engineering National Tsing Hua University Hsinchu 30013 Taiwan R.O.C.

ABSTRACT The parametric instability of graphite/epoxy laminated composite shell was investigated analytically and experimentally. The dynamic system of the laminated composite shell was derived based on the finite element modeling and the Lagrange's equation. The normalized modal expansions of the composite shells were then applied to obtain a dynamic equation of Mathieu's type, which contains parametric excitation terms. In experiment an electromagnetic device, acting like a spring with alternating stiffness, was used to excite the laminated shell parametrically in the transverse direction. The instability regions of the composite shell were identified by the transition curves, which were functions of the modal parameters of the composite shell and the position, the stiffness of the electromagnetic device attached on the composite shell. The experimental results were found to agree well with the analytical ones. INTRODUCTION Structural instability has been an important factor for the failure of structures, hi Bazant's review paper [1], several structural failure examples were pointed out due to their instability behavior, such as the failure of Quebec bridge at St. Lawrence in 1907, the collapse of Tacoma Narrows Bridge due to aerodynamic resonance in 1940, and the failure of Hartford Arena space frame in 1978. Dynamic instability is one of the significant issues in the structural instability. Bolotin [2] summarized the parametrically excited instability problems for various structural elements. Researchers also investigated the parametrically excited instability problem of the basic structural elements, such as beams, columns, plates and shells for different material properties, different boundary conditions, and different excitation forces analytically. Composite materials, with high specific strength, high specific stiffness and the ability of variable lamination to have required mechanical property, becomes an competitive substitute for use in various aerospace structures. Like the traditional metal structures, the composite structure may become unstable due to external dynamic disturbances resulted from external resonance or parametrically excited resonance, caused by periodic forces. Chen and Yeh [3] investigated the parametric instability of a beam under electromagnetic excitation. Yeh and Kuo [4] studied the dynamic instability of composite beams under parametric excitation analytically and experimentally. Yeh et al. [5] reported the measurement of dynamic regions for structures under parametric Professor, the corresponding author; Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu 30013 Taiwan, R.O.C, Fax: 886-3-5726414, E-mail: [email protected]

Parametric Instability Analysis of Laminated Composite Shells

213

excitation. Ng et al. [6] studied the dynamic stability of cylindrical panels with transverse shear effects; they found larger instability regions occurred for thicker panels. Lam and Ng [7] analyzed the dynamic stability of laminated composite cylindrical shells subjected to conservative periodic axial loads. Ganapathi et al. [8] studied the dynamic instability of laminated composite curved panels using finite element method. Argento [9] investigated the dynamic stability of a composite circular cylindrical shell subjected to combined axial and torsional loading. Bert and Birman [10] studied the parametric instability of thick orthotropic circular cylindrical shells; they found the compressive load reduced the vibration frequencies. From the above-mentioned literature, most researchers investigated the parametrically excited instability problem of structures analytically or numerically. The experimental work for parametrically excited composite shell is, to our knowledge, not reported yet. In this paper, the dynamic instability of graphite/epoxy laminated shells under parametric excitation was investigated analytically and experimentally. The electromagnetic device, acting as a spring of alternating stiffness, was used as a non-contacting transverse exciter in experiment, and the effects caused by the geometric imperfection, the eccentricity of the planar excitation forces could be avoided. INSTABILITY ANALYSIS OF COMPOSITE SHELL The dynamic instability equation of laminated shell is derived in this section and the instability regions of the laminated shell under parametric excitation were found. The laminated shell under electromagnetic excitation is idealized as shown in Figure 1. The electromagnetic device was modeled as a concentrated mass wo and a spring connected at point P(x0, yOi z0) on the mid-plane. The laminated shell, a part of a circular cylindrical shell, has length b=250 mm, radius of curvature R=100 mm, and arc span on the curved side 6 = ±35°, thickness h, and density p. The laminated shell, symmetric to the mid-plane, satisfies the Kirchhoff assumption and the Hooke's law. The gravitational effect was ignored FIGURE 1 Idealized model for laminated shell in analysis. under an electromagnetic excitation Finite Element Modal Analysis

Since one end of the laminated shell is clamped and the other three sides arefree,the exact solution for the vibration modes is not available. The finite element code ANSYS® [11] was used to obtain the natural frequencies and natural modes of the laminated shell. The three-dimensional Shell99 element was used in the analysis. Each element has 8 nodes and each node has 6 degrees of freedom. The attached electromagnetic device was modeled as a concentrated mass element, Mass21, located at the center of the device. After applying the boundary conditions, the natural frequencies and the corresponding modal vectors of the laminated shell can be obtained by using ANSYS code. Parametric excitation equation of composite shell The system dynamic equation can be derived from the Lagrange's equation {O}

(i)

214

Parametric Instability Analysis of Laminated Composite Shells

where [ M ] is the global mass matrix; [C] is the global damping matrix; [K\ is the global stiffness matrix; {Q} is the global nodal displacement vector, hi this study, the electromagnetic exciter is modeled as a spring of varying stiffness; therefore, the external force is zero. The nodal displacement vector {Q} can be assumed as

fe}= 1*^,(0

(2)

n=\

where <]>„ is the modal vector; Vn (t), function of time, is the modal displacement. Assuming the proportional damping, from the modal orthogonality relation and considering the effect of the electromagnetic spring, one obtain

n=l,2,...N (3) The above equation can be modified by the following dimensionless quantities: x = co/ ; 2c0j

C0j

2Mco,

the total mass of the composite shell. If the stiffness of spring is a constant, e(x) = 8. The natural frequencies of the transverse vibration of laminated shell shift from coM to Sw due to the spring effect. This was used to identify the spring stiffness s in experiment. If the spring has variable stiffness, say, s(x)= scos cox , then equation (3) becomes 'ra(x) = 0,n=l,2,...N

(4)

The above equation is a Mathieu equation, in which the excitation term contains the modal displacement Vn and the parametric excitation coefficient fnm, a function of the modes §n and the mass M of the composite shell. Criterion for Parametric Instability After obtaining the parametric excitation coefficient fnm, the instability bandwidth parameter Gnm can be calculated. The instability regions can be found from the instability bandwidth parameter Gnm, the amplitude of the spring, and the natural frequencies of the laminated shell <»„, coOT [3-5]. The transition curves separating the stable and unstable regions for simple resonance, combination resonance of sum type and difference type are co = 2coK + £G^< whenGnn > 0

_ _ _

V

co = con + com ± sG/2, when Gnm > 0

— —

(5) (6)

V

co = an - am ± sG/2, when Gnm > 0 (7) where Gnm is the instability bandwidth parameter as defined in reference [3-5]. The instability regions of the system, each separated by two transition curves, were found to be

Parametric Instability Analysis of Laminated Composite Shells

215

functions of the modal parameters of the laminated shell and the position and the excitation amplitude of the electromagnetic device on the laminated shells. PARAMETRIC INSTABILITY EXPERIMENT The instability experiment for graphite/epoxy composite shells using electromagnetic exciter was performed to verify the analytical solutions [3-5]. The laminated shell is made from the prepreg, which is assumed orthotropic with material principal axis on the mid-plane. The non-contacting electromagnetic exciter used is considered as a spring with alternating stiffness. The first part of the experiment was to identify the relation between the stiffness of the electromagnetic spring attached on the composite shell specimen and the DC coil current through the spring. The relationship between the fundamental frequency of the composite shell specimen and the DC coil current of the electromagnetic spring was obtained first. Giving different spring stiffness, the fundamental frequency of the shell-spring system was obtained from modal eigenvalue analysis. After comparing the experimental results with the analytical ones, the relations between the stiffness s and the DC coil current I of the electromagnetic spring were obtained for the specimen. The experiments were performed for each different specimen and repeated at each varied DC coil current. Figure 2 shows the experimental setup for measuring the parametric instability behavior of composite shells. The electromagnetic spring, powered with an AC source, was used to excite the shell specimen. The dynamic signal analyzer was used to analyze and to observe the dynamic signal from the accelerometer. During the experiment, the frequency was tuned step by step from a lower limit to a higher limit near twice the fundamental frequency. At each tuned frequency, the AC coil current of the electromagnetic spring was increased from zero to the maximum saturated current to observe the dynamic response of the composite shell. The instability of the composite shell was observed as rapidly increasing amplitude of transverse vibration occurred. Once the instability occurred, the AC current was cut off and the frequency and amplitude of the excitation current were recorded. Shell Specii

(a) Mode 1

(b) Mode 2 I

Signal Conditioner

Dynamic Signal Analyzer

FIGURE 2 Experimental setup for measuring the parametric instability of composite shells

(c)Mode 3 (d) Mode 4 FIGURE '3 Mode shapes of the composite shell ( J9O°]8 , R=100 mm, b=250 mm, 9 = +35° )

RESULTS AND DISCUSSION The laminated shell used has length b=250 mm, radius of curvature R=100 mm, and arc span on the curved side 9 = ±35°. The SHELL99 element was used in ANSYS analysis. To have efficient analytical results, the mesh density was studied. The first five natural frequencies of the composite shell become steady values for the model with

216

Parametric Instability Analysis of Laminated Composite Shells

element number higher than 100. Figure 3 shows the first four mode shapes of the composite shell with [90°]8. The first mode is a torsional one, the second a bending one and the rest are modes of coupling bending and torsion. The relations between the stiffness and the DC coil current of the electromagnetic spring were obtained for the specimen. The resonant frequencies and the corresponding modes were obtained by using ANSYS code. The relationship between the fundamental frequency of the composite shell specimen and the DC coil current through the electromagnetic spring was obtained from experiment. Giving different spring stiffness, the fundamental frequency of the shell-spring system was obtained from modal eigenvalue analysis. After comparing the experimental results with the analytical ones, the relations between the stiffness and the DC coil current of the electromagnetic spring were obtained for each specimen. For composite shell ([o°]4 , R=100 mm, b=250 mm, 9 = ±35°), a good linear relationship can be seen between the stiffness s and the DC coil current /of the electromagnetic spring was found. = 0.616/-0.002

(8)

00 0

1

2

3 4 5 Excitation Frequency ©

6

(a) 2co,, (b) to, + oo2, (c) 2co2, (d) 3 FIGURE 4 Dynamic instability regions of laminated shell ([o°\, R=100 mm, b=250 mm, 9 = ±35° ). analytical results; experimental results.

1.0

1.2

1.4

16 1.8 2.0 2.2 2,4 Excitation Frequency ta

2.6

28

3.0

FIGURE 5 Instability region at 2 co, for the laminated shell with [o°\ . results;

analytical

experimental results.

The instability regions of laminated shells were obtained from their modal parameters at the position of electromagnetic device,fromwhich the parametric excitation coefficient fnm, the instability bandwidth parameter Gnn and the transition curves separating the stable and unstable regions were found. In this study, the simple resonances, 2&\, 2co2,2co3, and the combination resonances up to ©2+CO5 are obtained. Figure 4 shows the dynamic instability regions at simple and combination resonant frequencies of the laminated shell with [0°]8, radius of curvature R=100 mm, length b=250 mm, and arc span 6 = ±35°. © is the ratio between the parametric excitation frequency and the fundamental natural frequency coj. co2 and ro3 denote the second and the third resonance frequencies after normalization by coj. The analytical results contain transition curves for the cases with damping coefficients ranging from 0 to 0.05. A maximum instability region occurs at twice the fundamental frequency 2c5j as shown in Figure 5. The reason is that the instability bandwidth parameter Gnm, related with the mass of the shell and the modal parameters at the position of the electromagnetic device, has higher value for the fundamental mode. The experimental results agree well with the analytical ones for the simple resonances at twice the fundamental frequency.

Parametric Instability Analysis of Laminated Composite Shells

217

CONCLUSIONS In this paper, the parametric instability of graphite/epoxy laminated shell was investigated analytically and experimentally. The system dynamic equation of the composite shell is derived to be an equation of Mathieu's type, in which the excitation term contains the modal displacement and the parametric excitation coefficient. The instability regions of the composite shell, each separated by two transition curves, were found to be functions of the modal parameters of the laminated shell and the position and the excitation amplitude of the electromagnetic device on it. The non-contacting electromagnetic device, attached on the laminated shell, excites the composite shell transversely. The effects caused by the geometric imperfection, the eccentricity of the in-plane excitation forces could be avoided effectively. The instability region agreed well with the analytical one for the simple resonance at twice the fundamental frequency. ACKNOWLEDGEMENTS The authors would like to thank the National Science Council, Taiwan, the Republic of China through grant NSC92-2212-E-007-061, for supporting this work.

REFERENCES 1. 2. 3.

Bazant, Z. P., 2000. "Structural Stability," International Journal of Solids and Structures, 37:55-67. Bolotin, V. V., 1965. The Dynamic Stability of Elastic Systems, New York, Holden-Day Inc. Chen, C. C. and M. K. Yeh. 2001. "Parametric Instability of a Beam under Electromagnetic Excitation," Journal of Sound and Vibration, 240:747-764. 4. Yeh, M. K., and Y. T. Kuo. 2002. "Dynamic Instability of Composite Beams Under Parametric Excitation," Proceedings of the 3rdAsian-Australasian Conference on Composite Materials, ACCM-3, July 15-17, Auckland, New Zealand, pp. 779-788. 5. Yeh, M. K., Y. T. Kuo, C. S. Liu and C. C. Chen. 2002. "Dynamic Instability Measurement of Structures Under Parametric Excitation," International Symposium on Experimental Mechanics, ISEM, December 28-30, Taipei, Taiwan, ROC, Paper No. A244. 6. Ng, T. Y., K. Y. Lam and J. N. Reddy. 1999. "Dynamic Stability of Cylindrical Panels with Transverse Shear Effects," International Journal of Solids and Structures, 36:3483-3496. 7. Lam, K. Y. and T. Y. Ng. 1998. "Dynamic Stability Analysis of Laminated Composite Cylindrical Shells Subjected to Conservative Periodic Axial Loads," Composites PartB, 29B:769-785. 8. Ganapathi, M., T. K. Varadan and V. Balamurugan. 1994. "Dynamic Instability of Laminated Composite Curved Panels Using Finite Element Method," Computer & Structures, 53:335-342. 9. Argento, A., 1993. "Dynamic Stability of a Composite Circular Cylindrical Shell Subjected to Combined Axial and Torsional Loading," Journal of Composite Materials, 27(18): 1722-1738. 10. Bert, C. W. and V. Birman. 1988. "Parametric Instability of Thick, Orthotropic, Circular Cylindrical Shells," Ada Mechanica, 71: 61-76. 11. ANSYS Theory Reference. 001369. Twelfth. SAS IP, Inc.

Bending Properties of Braided Composite Tubes Masanori Okano, Kenichi Sugimoto, Asami Nakai* and Hiroyuki Hamada Kyoto Institute of Technology, Japan

ABSTRACT In this paper, the effects of braiding angle on bending properties of braided composite tubes were investigated. The braided composite tubes with different braiding angle and number of layer were used and three-point bending tests were performed. Although the elastic modulus in longitudinal direction was high in the tube with small braiding angle, a large flat deformation was generated due to the low rigidity of circumferential direction compared to the tube with large braiding angle. Aimed at fabrication of the tube which has both high elastic modulus and low flatness ratio, the tube with hybrid laminate constitution was fabricated. In the tube that was combination of a large braiding angle in the inner part and a small braiding angle in the outer part, elastic modulus was as high as the tube with small braiding angle and the flatness ratio was the lowest.

INTRODUCTION Tubular structures are often used in the frame and a shaft part of structures. Hence in such tubular structure, not only tensile and compressive properties but also bending and torsional properties are important, and wide ranges of material design to satisfy various requirements are needed. In these circumstances, braiding technique can be adopted into tubular structure. As shown in Figure 1, braiding has a characteristic of yielding fibers that are oriented continuously in different directions. With braiding technique, the braiding angle can be changed easily and straight fibers can be inserted into braided fabric as middle-end fiber. The number and type of reinforcing fibers can be also selected. Consequently, the mechanical properties of pipe in longitudinal and circumferential direction can be controlled to meet requirements. It is expected that a wide range of material design can be carried out with braided fabrics. Concerning fabrication process of braided composites, it is possible to produce tubes with fiber bundle in three axes in one layer and a continuous fabrication process of braiding results in the reduction of manufacturing costs. Therefore, braided fabric is more suitable for reinforcements of pipe than not only unidirectional composite but also other textile fabrics. In the case of braided composite, the architecture of the braided fabric is complex and therefore, the parameters controlling its mechanical properties become numerous. In other words, the parameters such as braiding angle, the distance between braiding fiber bundles, the cross-sectional area, the geometry of cross section of the fiber bundles and fiber volume fraction within the fiber bundles exist. * Corresponding author, Gosyo-kaidoucyo, Matsugasaki, Sakyo-ku, Kyoto, 606-8585, JAPAN FAX: +81-75-724-7800 E-mail: [email protected]

Bending Properties of Braided Composite Tubes

219

These parameters are not independent each other and change with other parameters. Based on these parameters, crimp ratio of fiber bundle and fiber volume fraction of composite were decided. Therefore, it is difficult to evaluate only the braiding angle, and it is necessary to develop a design methodology for braided composites. In this study, bending properties of tubular braided composites have been studied with respect to braiding angle. Three types of the tube with different braiding angle were fabricated and three-point bending test were carried out. MATERIALS AND EXPERIMENTAL METHOD Glass fibers (ER1150 F-165N; Nippon Electric Glass Co. Ltd.) were used as reinforcement and vinylester (R-806B; SHOWA HIGHPOLYMER Co. Ltd.) was used as matrix resin. In order to clarify the effect of braiding angle on bending properties, three braiding angles 30°, 45° and 60° were chosen and six kinds of braided composite tubes with different braiding angle and number of layer were fabricated. The specification of each tube fabricated is shown in Table 1. A group " 1 " of the tube was a composite tube with small thickness and a group "2" of the tube was a composite tube with large thickness. The three-point bending test was performed by using special pulley unit. The pulley unit is capable of decreasing the stress concentration generated at the point of support and loading nose because of transference of load by contacting the tube at two points. A strain gage with three axes was stuck on the surface opposite to the loading point to measure the local strain of the tube and to calculate the principal strain. The bending test was performed by using an INSTRON testing machine at a constant cross-head speed of 5.0mm/min. The load-deflection curves and the load-principal strain curves are shown in Figure 2 and Figure 3. Here, the principal strain value is displayed from 0// e to 10000// e to explain the slope of the curves in the load-principal strain. Thus, the strain value does not correspond to the deflection value in the load-deflection curves. For example, the strain value 8000 ju e vs> corresponded to approximately 2mm in the deflection. Concerning the load-deflection curves, in the case of the group "1", the S30-1 tube showed the highest maximum load value of the three tubes. In the case of the group "2", the maximum load value of S30-2 tube displayed the highest of the three tubes. Thus, it may be inferred that tendencies of load-deflection curves depended on the thickness and laminate constitution. Concerning the load-principal strain curves, in the case of both the group " 1 " and the group "2", the slope of load-principal strain curve of S30 tube showed the largest of the three tubes. TABLE I Specification of the fabricated tube

Fiber bundle FIGURE

1 Schematic illustration of tubular braided fabric

Inside Outside The type of Number Braiding angle Thickness diameter diameter specimen of layer [degree] [mm] [mm] [mml 6 30 26.0 29.3 S30-1 1.65 26.0 5 45 29.3 1.67 S45-1 4 60 26.0 S60-1 30.1 2.03 S30-2 9 30 26.0 31.0 2.48 8 45 26.0 30.9 S45-2 2.47 6 60 26.0 32.0 2.98 S60-2

Bending Properties of Braided Composite Tubes

220

2

4 6 Deflection [mm]

2000 4000 6000 8000 Principal strain [ p. t ]

10000

FIGURE 2 Load-deflection curve of each tube

2000 4000 6000 8000 Principal strain [ y £ ]

10000

FIGURE 3 Load-principal strain curve of each tube

Then, the elastic modulus Ep.y calculated from the load-deflection curve, the elastic modulus Ep. c calculated from load-principal strain curve of all tubes and bending strength a/, are shown in Table 2 and Table 3. In the case of both the group " 1 " and the group "2", the bending strength of the S30 tube also showed highest value of the three tubes. The difference between maximum value and minimum value of the bending strength was approximately 50%. For the tube with braiding angle 60°, the difference of the bending strength between the S60-1 tube and the S60-2 tube was not seen. However, for the tubes with braiding angles 30° and 45°, when the thickness was large, the bending strength increased at approximately 15%. Surprisingly, the elastic modulus Ep.y and Ep. c evaluated from load-displacement curve and load-principal curve showed a different value. The differences between Ep.y and Ep. c were approximately 3.0 times in the case of the tube with braiding angle 30°, 2.5 times in the case of the tube with braiding angle 45° and 2.0 times in the case of the tube with braiding angle 60°. This difference which was not the error of the experiment should be noticed.

Bending Properties of Braided Composite Tubes

221

TABLE II Results of bending strength

TABLE III Results of bending modulus

Bending The type of strength specimen <7b[MPa] S30-1 168.8 S45-1 158.4 S60-1 114.4 S30-2 197.3 S45-2 189.7 S60-2 117.7

Bending Bending The type of modulus modulus specimen E^T[GPa] En.f [GPa] 13.8 45.6 S30-1 13.6 S45-1 30.5 9.7 20.4 S60-1 S30-2 16.4 45.8 34.1 S45-2 15.5 S60-2 10.5 22.0

FLAT DEFORMATION AND FLATNESS RATIO In this section, the actual flatness ratio was calculated for each tube. Here flatness ratio was defined as the ratio of actual deflection to theoretical deflection obtained by the strain. We can calculate the theoretical deflection of three-point bending performance of the tube, from the relationship between stress and strain. And we can also calculate the relationship between the experimental deflection yexp. and strain e as a slopes of load-strain and load-deflection were obtained from experiments. Consequently, as flatness ratio was defined as the ratio of actual deflection to theoretical deflection obtained by the strain, the flatness ratio is given by

(1)

The flatness ratio calculated from equation (1) is shown in Table 4. In the case of both the group " 1 " and the group "2", it was confirmed that the tube with braiding angle 30° was easily flattened by transverse load. On the contrary, in the tube with braiding angle 45° and 60°, those tubes were not easily flattened compared to the tube with braiding angle 30°.

TABLE IV Results of flatness ratio

The type of specimen yexp/ytheo. S30-1 S45-1 S60-1 S30-2 S45-2 S60-2

3.3 2.2 2.1 2.8 2.2 2.1

TABLE V Specification of the tube with hybrid laminate constitution Inside Outside Thickness The type of Number Laminate constitution diameter diameter [mm] specimen of layer H-1

5

H-2

5

In a30 o /3 + a60°/2 In a60°/2 + a3O°/3

rmmi 26.0

[mml 29.9

1.96

26.0

29.7

1.85

222

Bending Properties of Braided Composite Tubes

THE SUGGESTION OF HYBRID LAMINATE CONSTITUTION A hybrid laminate constitution which was a combination of braiding angle of 60° and braiding angle of 30° was suggested in order to obtain a tube with the high elastic modulus in longitudinal direction and the low flatness ratio. Table 5 shows the specification of the fabricated two tubes. The H-1 tube had hybrid laminate constitution which was a combination of braiding angle of 30° in inner part and braiding angle 60° in outer part. On the other hand, the H-2 tube had a hybrid laminate constitution which was a combination of braiding angle of 60° in inner part and braiding angle of 30° in outer part. And the same static bending test was carried out by using these tubes and the elastic modulus and the flatness ratio calculated from the equation (1) are shown in Table 6 and Table 7. With respect to the elastic modulus, the H-1 tube showed lower value than the S30 tube and S45 tube, however, showed higher than the S60 tube. On the other hand, the H-2 tube displayed higher value than the tubes of the group "1". Secondary, the flatness ratio of H-1 tube was 2.4. However the flatness ratio of H-2 tube was 1.8. The value showed the lowest of all fabricated tubes. That is to say, the tube in which elastic modulus in longitudinal axis is high and the flatness ratio is low could be fabricated by designing it to have high rigidity of circumferential direction in the inner part with low rigidity of circumferential direction in outer part. CONCLUSIONS In this study, the bending properties of braided composite tubes were investigated and static three-point bending testing was carried out. The effect of braiding angle on bending properties was clarified experimentally. It found that; 1. hi the tube with braiding angle 30°, the large flat deformation was generated because of the low rigidity of the circumferential direction and when the thickness of the tube was large, the flat deformation was improved. 2. The tube with braiding angle 60° was not easy to flatten because of the high rigidity of the circumferential direction and an increase in thickness of the tube was ineffective for improving the flat deformation. 3. The tube that consisted of a combination of braiding angle of 60° in the inner part and braiding angle 30° in the outer part, showed values that were comparable to the tube with braiding angle 30°, and it showed the lowest flatness ratio of all the tubes. TABLE VI Results of bending modulus of the all tubes

Name of specimen

H-1 H-2

Bending Bending modulus modulus Ep.y [GPa] Ep* [GPa] 11.9 28.8 14.4 25.6

TABLE VII Results of flatness ratio of the all tubes

Name of specimen

yexp/ytheo.

H-1 H-2

2.4 1.8

Analytical Stress Analysis of Rotating Composite Beams Due to Material Discontinuities M. Tahani1'*, A. Nosier2, J. Rezaeepazhand3, S. M. Zebarjad4 Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, P.O.Box 91775-1111, Mashhad, Iran 2 Department of Mechanical Engineering, Sharif University of Technology, P.O.Box 11365-9567, Azadi Ave., Tehran, Iran 4 Department of Materials Science and Metallurgy, Faculty of Engineering, Ferdowsi University of Mashhad, P.O.Box 91775-1111, Mashhad, Iran u

ABSTRACT Material discontinuity could cause in-plane stress gradients that it arises interlaminar stresses in regions of sudden transition of material properties. A layerwise laminated beam theory that is a modification of a layerwise laminated plate theory is developed and it is used to analyze analytically the interlaminar stresses at material discontinuities in rotating composite beams. Equations of motion are obtained by using Hamilton's principle. It is assumed that the beam is divided into two regions with different layups which are joined together. The predicted interlaminar stress distributions at the ply interfaces are shown to be in good agreement with comparative three-dimensional finite element analysis.

INTRODUCTION The problem of interlaminar stress analysis at the free edges and bonded joints of composite structures have been under investigation continuously ever since the original paper of Pipes and Pagano [1], Numerous papers have been published on the subject over three decades (see, for example, [1-7]). In these studies, interlaminar stresses appear at the free edges of finite composite laminates under different loading conditions have been considered. It is well known that interlaminar stresses arise in order to satisfy equilibrium at locations with in-plane stress gradients. Material discontinuity (i.e., a sudden change of material properties) is another source of arising in-plane stress gradients and, therefore, interlaminar stresses appear near the material discontinuities. Bhat and Lagace [6] evaluated interlaminar stresses at material discontinuities using the principle of minimum complementary energy. They analyzed laminates with different layups which had been joined together. They mentioned such cases occurred at regions of implants within adaptive structures. The advent of adaptive structures has resulted in sensors made of various materials being implanted within laminated composites by cutting some plies of the laminate and placing the sensor in that location. Also a damaged region such as that caused by impact is another example of material Corresponding author. Tel: +98-511-8615100; fax: +98-511-8629541, E-mail address: [email protected] (M. Tahani)

224

Analytical Stress Analysis of Rotating Composite Beams

discontinuity. They showed interlaminar stresses are produced in the vicinity of these material discontinuities. Investigations of interlaminar stresses in rotating composite beams have been rare. Rotating beams are often used as the simple model for propellers, turbine blades, and satellite booms. Hence, in this paper, analysis of interlaminar stresses in composite beams especially due to material discontinuities are interested. A layerwise laminated plate theory is used to develop a layerwise laminated beam theory. The results obtained from this theory are compared with those obtained by using a finite element method. The correlation among the results indicates the theoretical approach is feasible as a conceptual design tool. THEORETICAL FORMULATION It is intended here to determine interlaminar stresses in a rotating composite beam with uniform cross-section. Displacements of the beam are defined in a rotating rectangular Cartesian coordinate system, rigidly tied to the beam (see Figure 1). The beam is assumed to has the length 2L and thickness h. It is noted that only one symmetric half of the beam is shown in Figure 1. Here a layerwise laminated plate theory is developed and then it is simplified for analysis of beam structures. It is considered that the beam rotates with a constant angular velocity O.. Therefore, the displacement field is assumed to be independent of time.

Region B

Region A O'Ply 90" Ply 90" Ply O'Ply a

O'Ply O"Ply O'Ply O'Ply L

FIGURE 1 The geometry of problem with a [0° / 90° ] s laminated beam in transition to a [0° ] 4 laminated beam.

Plate Equations In this study, a layerwise laminated plate theory is used in deriving the laminated beam theory. Therefore, the following displacement field is considered:

u2(x,y,z) = Vk(x,y)<&k(z), u3(x,y,z) = Wk(x,y)®k(z)

(1)

where the displacement components, the global interpolation function, and N have been defined in [7]. It is to be noted that a repeated index indicates summation over all values of that index. Upon substitution of Eqs. (1) into the linear strain-displacement relations of elasticity, the following results will be obtained:

Analytical Stress Analysis of Rotating Composite Beams

225

Yy.=vk<&k+wkjbk, r»=u,P'k+wkjbk,

(2)

rxy = {uk,y+vktI)ok

where a prime indicating an ordinary derivative with respect to the independent variable z and a comma followed by a variable indicates differentiation respect to that variable. Using the Hamilton principle, 3(N+1) equations of motion corresponding to unknowns Uh Vk, and Wk can be shown to be: 5Uk: Mkxx +

Mkxyy-Qk=-Ikn2x-IkJUp2

5 Vk : MkViX + Mky - Qk = -IkQ2y - f'Vp2

(3)

where the generalized stress resultants have been defined in [7] and the mass terms are defined as follows: (/*,IkJ)= [h'2 p(O,,O, O.)dz J-A/2

*

*

(4)

;

V

'

It is noted that the underlined terms in Eqs. (3) may be neglected in contrast to IkCl2x and IkQ2y. The boundary conditions for a laminated plate with a rectangular platform in the layerwise theory at an edge parallel to y axis involves the specification of Uk or Mk, Vk or Mky and Wk or Rk. Similarly, at an edge parallel to x axis, the required boundary conditions can be specified. It is assumed that the laminate is laminated of orthotropic laminae, with respect to the x-axis. The constitutive relations for the Mi orthotropic lamina with respect to the laminate coordinate axes are {af =[C]m {sf' where [C] w are the transformed stiffness matrix of the Mi layer. Using Eqs. (2) and the constitutive relations the generalized stress resultants are obtained which can be represented as follows:

y

j

k

hy

(5)

k

{Q x,R x) = (A*B%)Uj + (A%,BlWj + (B£M)WLx + (B*,Di)Why where therigidityterms are given in [7]. Beam Equations It is assumed that the stress resultants are functions of x only. Hence, Eqs. (3) yields to: K.*-Q*=-Ik&x,

M^-g;=0,

RXiX-Nk=O

(6)

Also it is supposed that the strains are functions of x and z only. Therefore, Eqs. (2) are simplified as follows: ex=Uk'
sy=0,

ez=WkO't,

ry,=Vk^'k,

rxz=Uk
Yxy=Vk'Q>t

(7)

226

Analytical Stress Analysis of Rotating Composite Beams

According to the Eqs. (7), it is more reasonable for a beam to let M* be equal to zero. Substitution of this condition into the stress resultants in Eqs. (5) results in:

y

j

(8)

where the coefficients are defined in Appendix. Upon substitution of Eqs. (8) into Eqs. (6) the following governing equations of motion are obtained:

j

^

!

j (Bki - B*) w; = 0

(9)

k

(B&-B*)Uj' +{B i -B*)Vj' +D*sWj' -A^Wj = 0

ANALYTICAL SOLUTIONS In this study the local linear Lagrangian interpolation functions (j>'k through the thickness are used (see [7]). It is to be noted that there exist repeated zero roots (or eigenvalues) in the characteristic equation of the set of equations in (9). The procedure used here for solving Eqs. (9) are similar to the one suggested by Tahani and Nosier [7] and for brevity are not taken up here. RESULTS AND DISCUSSION In what follows a numerical example is presented for a rotating composite beam that composed of two different layups which are joined together (see Figure 1). The regions A and B are made up of [0°/90"]J and [0°]4beam, respectively, as shown in Figure 1. Also it is assumed that the beam has the length 2L, thickness h, with L=5h and a=U2, and is rotating with a constant angular velocity. In this particular problem, it is assumed that Q = 1000rad/sec and h = 0.0lm . To analyze this problem, two coupled differential equations for regions A and B have to be solved. The boundary conditions for this problem are:

where the superscripts (A) and (B) show regions A and B, respectively. Also the following continuity conditions at x=a must be satisfied:

= u(kB),

v{kA) = vtB), R^=R^->

(11)

This particular problem is chosen because interlaminar stresses arise only near the material discontinuities. Due to identical ply orientations in region B no free-edge effects exist at x=L. Also because the beam has length 2L and it has symmetric boundary conditions at x=0 no interlaminar stresses arise at this point.

Analytical Stress Analysis of Rotating Composite Beams

227

The material properties of the layers are taken to be those of a T300/5208 lamina [8]: £,=132 GPa, £ 2 =£ 3 =10.8 GPa , Gl2 = G13 = 5.65 GPa, G23= 3.38 GPa vl2 = v13 = 0.24 , v23=0.59, p = 1540kg/m3 (12) where the subscripts 1,2, and 3 indicate the on-axis (i.e., principal) material coordinates, hi what follows, the interlaminar stresses are determined by using Hooke's law with six numerical layers in each physical lamina (see [7]). The in-plane stress ax at z=h/4 in 0° plies in regions A and B is shown in Figure 2a. Also the in-plane stress <JX at z=h/4 in 90° ply in region A and 0° ply in region B is presented in Figure 2b. It is seen that stress distributions are discontinues near x=a. It is seen that there are close agreements between the present solutions and those obtained by the finite element method using ANSYS software [9].

4 3.5 3

5

2

D

"1.5

1.5

05

1 0.5

1 0.5 0

0.2

0.4

0.6

0

0.8

0.2

0.4

0.6

x/L

x/L

(a)

(b)

0.8

FIGURE 2 Distributions of in-plane normal stress ax at z=h/4 (a) in 0° plies in regions A and B and (b) in 90° ply in region A and 0° ply in region B.

0.1 0.05 0 2-0.05

s X-o.

[ :

/

~ ~ — ^

-0.1 O-

Present FEM

i

-0.15

s B

-0.2 -

-0.2 -0.25

i

0-

0.2

< • < < • • •

0.4

0.6

0.8

-0.3,

x/L

(a) FIGURE 3 Distributions of interlaminar stresses (a) az at the middle plane and (b) aa at z=h/4 along the 0790° interface in region A and along the 070° interface in region B.

228

Analytical Stress Analysis of Rotating Composite Beams

Distribution of interlaminar normal stress <JZ at the middle plane is shown in Figure 3a. The results show that there are sharp interlaminar stress gradients near the material discontinuity and decays away from the region of discontinuity as expected. The current solutions are seen to match the finite element solutions reasonably well except in the region close to the material discontinuity where the stresses have a steep gradient. Also Figure 3b illustrates the distribution of interlaminar shear stress <JXZ at z=h/4 along the 0°/90° interface in region A and along the 0°/0° interface in region B. It is noted that <JXZ at the free edge (x=L) meet the stress free boundary condition with a good approximation, even though this condition has not been enforced a priori. CONCLUSIONS A layerwise laminated beam theory are developed by using a layerwise laminated plate theory and it is used to predict interlaminar stresses in the vicinity of material discontinuities in rotating composite beams with general laminations. Governing equations of motion are obtained by using Hamilton's principle. The results obtained from this theory are compared with those obtained by a finite element method. The results indicate that there are severe interlaminar stresses in regions near the sudden transition of material properties (material discontinuities). These stresses may initiate heterogeneous damage in the forms of delamination and transverse cracking and may cause the damage to propagate to a substantial region of the beam, resulting in a significant loss of strength and stiffness. To this end, these stresses must be considered in design of such structures. APPENDIX The coefficients appearing in Eqs. (8) are defined as: [Aii] = [An]-[B23]T[D22T'[B2i],

[Bn] = [Bti]-[Dl2][D22T'[B2i]

[B,6 ] = [5 36 ] - [D26 ] [D22 r ' [5 23 ] , [ A , ] = [ A , ] - [Dl2 ] [D22 ]"' [Dl2 ] [A.] = [Di6l-[Dl2][D22r[D26],

[D66] = [D66]-[D26][D22y[D26]

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Pipes, R. B. and N. J. Pagano. 1970. "Interlamiiiar Stresses in Composite Laminates under Uniform Axial Extension," J. Compos. Mater., 4: 538-548. Hsu, P. W. and C. T. Herakovich. 1977. "Edge Effects in Angle-Ply Composite Laminates," J. Compos. Mater., 11: 422-428. Wang, A. S. D. and F. W. Crossman. 1977. "Some New Results on Edge Effect in Symmetric Composite Laminates," J. Compos. Mater., 11: 92-106. Pagano, N. J. 1978. "Free Edge Stress Fields in Composite Laminates," Int. J. Solids Structures, 14: 401-406. Wang, S. S. and I. Choi. 1982. "Boundary-Layer Effects in Composite Laminates: Part 2- Free-Edge Stress Solutions and Basic Characteristics," J. Appl. Meek, 49: 549-560. Bhat, N. V. and P. A. Lagace. 1994. "An Analytical Method for the Evaluation of Interlaminar Stresses Due to Material Discontinuities," J. Compos. Mater., 28(3): 190-210. Tahani, M. and A. Nosier. 2003. "Three-Dimensional Interlaminar Stress Analysis at Free Edges of General Cross-Ply Composite Laminates," Materials & Design, 24(2): 121-130. Herakovich, C. T. 1998. Mechanics of Fibrous Composites, John Wiley, New York. ANSYS, Release 5.4 UP19970828, SAS IP, Inc., 1997.

Thin-Plate Splines for Thick Composite Plate Analysis Antonio J. M. Ferreira* Departamento de Engenharia Mecanica e Gestao Industrial, Faculdade de Engenharia da Universidade do Porto, Portugal

ABSTRACT Composite laminated plates are a typical and relevant application of composite materials in various industries. Such structures are heterogeneous in the thickness direction and orthotropic in each lamina plane. Most of the methods for plate analysis are based on the finite element method. In this paper it is proposed to interpolate the system of partial differential equations by radial basis functions, in particular by thin-plate splines. The thin-plate splines (TPS) method represents an alternative to multiquadrics (MQ) radial basis functions. The TPS method does not rely on a shape-parameter like the MQ method, being this a more stable approach. Composite structures can be analysed by various sets of shear deformation theories: the classical Love-Kirchhoff plate theory, the first-order shear-deformation theory, the third-order shear deformation theory and layerwise theories. In this paper we apply the TPS method together with the third-order shear deformation theory for the analysis of moderately thick laminated plates. The methodology proves to be stable and accurate. INTRODUCTION Collocation with radial basis functions is a recent meshfree collocation method with global basis functions. The multiquadric method for the solution of partial differential equations (PDEs) was first introduced by Kansa in the early 1990s and showed exponential convergence for interpolation problems. In this paper we formulate and discuss the use of thin-plate splines radial basis functions in the solution of moderately thick laminated composite plates using a third-order shear deformation theory. Composite materials are a very important class of engineering materials with great properties and applications in a variety of complex structures, such as those typically found in space, automobile and civil applications. The correct design of such structures requires adequate stress analysis and in particular numerical tools. The proper modeling of composite laminates remains an open field of discussion and developments as a consequence of their complex behavior. It is very important to accurately determine the transverse shear stresses since they are the reason why delamination mechanisms are active. A proper laminate theory that accounts for shear deformation and an adequate numerical tool are needed in order to capture all such effects. Several laminate theories have been proposed in the literature. The simplest one is the classical laminate theory (CLT) [1] which is based on the Kirchhoff-Love theory of plates. The CLT neglects shear deformations and can lead to inaccurate results for moderately thick composite laminated or sandwich plates. The first-order shear deformation theory (FSDT) for laminated composite plates was developed as an * Corresponding Author, Departamento de Engenharia Mecanica e Gestao Industrial, FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal, Fax +351 22 9537352, email: [email protected]

Thin-plate Splines for Thick Composite Plate Analysis

230

extension of the theory of Mindlin [2] for isotropic plates which considers shear deformations and gives satisfactory results for a wide range of structures, in particular for moderately thick laminates [3-5]. The FSDT efficiency is dependent on a good choice of shear correction factors. This is not trivial and is dependent on the lamination scheme and on the deformation. Whitney [4] and Ferreira [5,6] have developed procedures for such calculation, based on cylindrical bending. The higherorder shear deformation theories (HSDT) have been developed to obviate the limitations of FSDT [7]. Following the research by the author with FSDT and MQ in the analysis of laminated composite plates [8], this paper addresses the application of thin-plate radial basis functions and HSDT to the analysis of moderately thick composite laminated plates. THIRD-ORDER THEORY OF PLATES The third-order theory of Reddy [7] is based on the same assumptions than the classical and first-order plate theories, except that the assumption of straightness and normality of a transverse normal after deformation is relaxed by expanding the displacements (u,v,w) as cubic functions of the thickness coordinate. The displacement field is then obtained as dw u(x,y,z)=u\x,y)+z(j)x '—f (1) ~dx dw (2) ' V" ) ^ 1" ) • V~ >J I ' " Yy 11,2 ~dy~ w(x,y,z)=w°(x,y) (3) where u and v are the inplane displacements at any point (x,y,z), u° and v° denote the inplane displacement of the point (x,y,0) on the midplane, w is the deflection, (j>x and <j)y are the rotations of the normals to the midplane about the y and x axes, respectively. The strain-displacement relationships are given as: ^xx

e

yy

y(0) /xy

city tiyy

'xy

du0 dx dv^ dy dun _ dvn

t XZ

fy?

(0) / xz

eO)

yy y(3) 1 xy

+ z2

/yz

ri 2)

y(l) /xy

dx dx

dx Cyy

~?>y

dx

dy

dy

dx

y(2) 1 xz

(4)

y(2) 1 yz

dx

-+ •

dy

+ z3

+ Z

%

(5)

dy

/xy

dy

dx

dw0 x

dx dwn

i

(6)

dy + dy = 3c,. Neglecting az for each orthotropic material layer, the stresswhere c, = strain relations in the fiber local coordinate system can be expressed as

Thin-plate Splines for Thick Composite Plate Analysis Qn

2,2

0

0

Qn

222

0

0

0

0

233

0

0

0

0

244

0

0

0

0

231

(7) Qs.

Here subscripts 1 and 2 are, respectively, the fiber and the normal to fiber inplane directions, 3 is the direction normal to the plate, and the reduced stiffness components, Qy are given by ii

=

~

ten

-

>

1 — 1/1/

I — V

V

=G 23 ;g 55 =G 3I ;v 21 = v ] 2 - ^

Qn =

(8)

in with £ , , £ 2 ) v12, G12, G23 and G31 are materials properties of the lamina. By performing a coordinate transformation, the stress-strain relations in the global x-y-z coordinate system can be obtained as X

Gy

Txy Tyz

Tzx

Qn

2,2

2,6

0

0 0

By

0

Yxy

245 255

Yyz

Qn

222

226

0

= 2,6

226

266

0

0

0

0

0

0

0

244

£

x

(9)

Yzx

The third-order theory of Reddy [7] satisfies zero transverse shear stresses on the bounding planes. The equations of equilibrium of the third-order theory are derived from the principle of virtual displacements as: dx dx

dy

3h2 { 8x2

^-2>o;'

\., d • + •

dx

(10)

dy2

dxdy dy

•-O

=0

(11)

with (12) In previous equations Q^R^M^^y, are the shear forces and bending moments, respectively. The Euler-Lagrange equations can be written in terms of the displacements by substituting strains and stress resultants into this equation. For example, equation (10) is given as

232

3h2

Thin-plate Splines for Thick Composite Plate Analysis

n

[dxdy2

dx2dy J

9h4

i

\dy2dx

' dx2dy ' "dy2dx2

hi this equation, stiffness components are obtained as A

a = tMl'J

= 4 ' 5 ;^ = T £ ^ W + . -zt3J,7 = 1,2,3,4,5 L ~z5JJ = 1.2.3JH, = ^£ei;W + 1 -^>-J = 1,2,3

(15)

hi (14) and (15), zk and zt+l are the lower and upper z coordinates of the A:'* layer. RADIAL BASIS FUNCTIONS The radial basis function method relies on the Euclidian distance between nodes and in some cases on a shape parameter, user-defined and object of various discussions. The influence of such parameters not only defines the RBF but also may provide illconditioned problems with inadequate solutions. To obviate the use of such parameter it is proposed in this paper the use of thin-plate splines. An RBF depends only on the distance to a center point x ; and is of the form g (Ik - x;. |h. Consider a set of nodes xux2,...,xN

EQCJ!",

The radial basis functions centered at xy. are defined as R\j=l,...,N

(16)

where x - x ; is the Euclidian norm. The thin-plate splines RBFs are given as = ||x - x.|2m logfx - Xjf ;m = 1,2,... (17) An important feature of the RBF method is that is does not require a grid. The only geometric properties needed in an RBF approximation are the pairwise distances between points. Working with higher dimensional problems is not difficult as distances are easy to compute in any number of space dimensions, hi this paper it is proposed to use Kama's unsymmetric collocation method [11]. Consider a boundary-valued problem with a domain Q c R" and a linear elliptic partial differential equation of the form Lu(x)=s(x)cR";Bu(x)]BQ =f(x)eR" (18) where dQ represents the boundary of the problem. We use points along the boundary (Xj,j = l,...,NB) and in the interior (xy., j = NB +1,...,N). Let the RBF interpolant to the solution w(x) be gj(x)

Thin-plate Splines for Thick Composite Plate Analysis

233

Collocation with the boundary data at the boundary points and with PDE at the interior points leads to equations

sB(x,c) =

(20)

= O(xi),i=NB

X -X;

(21)

where -^(x,), (x;) are the prescribed values at the boundary nodes and the function values at the interior nodes, respectively. This corresponds to a system of equations with an unsymmetric coefficient matrix, structured in matrix form as

(22)

NUMERICAL EXAMPLE A square laminate of side a and thickness h is composed of four equally thick layers oriented at (0°/90°/90°/0°). It is simply supported on all edges and subjected to a sinusoidal vertical pressure of the form:

. (nx\ . (ny\ pz =Psm — sin —

V a ) \ a ) being the origin of the coordinate system located at the lower left corner of the middle plane. The material properties are given as Ei = 25.0£2;G12 = Gn = 0.5E2;G23 = 0.2E2;v12 = 0.25 The numerical results are presented in table I, in a normalized form, as _ \02w(a/2,a/2,0)h3E2_ axx{al2,al2,hl2)h2 _ _ ayy(a/2,a/2,h/4)h2 ~<Jxx

=•

Pa' Pa2 Pa2 Tzx{0,a 12,first _ layer)h _ Txy(a,a,h/2)h Pa '* Pa2 In this table a laminated composite plate is analyzed with N = 11x11,15x15 and 21 x21 points. It can be seen that the present methodology is very accurate for the analysis of composite laminates. Both the transverse displacement, normal and transverse stresses are accurately predicted. Transverse shear stresses are calculated by the equilibrium equations. CONCLUSIONS In this paper the thin-plate splines radial basis function method and a third-order shear deformation theory were applied to the structural analysis of isotropic and symmetric laminated composite thick beams and plates. Results were compared with existing solutions showing excellent performance. Results obtained using an unsymmetric collocation strategy give very good agreement with available theories or previous results. This method, based on radial basis functions has very large potential for the

234

Thin-plate Splines for Thick Composite Plate Analysis

solution of structural problems, as a real meshless method, insensible to spatial dimension. TABLE I Composite plate a/h 100

20

10

4

N

w

11 15 21 Exact [12] 11 15 21 Exact [12] 11 15 21 Exact [12] 11 15 21 Exact [12]

0.5250 0.4575 0.4409 0.4347 0.5116 0.5029 0.5084 0.517 0.7050 0.7115 0.7133 0.743 1.8288 1.8509 1.8686 1.954

°* 0.6421 0.5650 0.5463 0.539 0.5465 0.5364 0.5423 0.543 0.5376 0.5452 0.5433 0.559 0.6289 0.6601 0.6614 0.720

a

y

0.3684 0.3434 0.3373 0.271 0.3663 0.3623 0.3657 0.309 0.4333 0.4368 0.4374 0.403 0.6175 0.6212 0.6261 0.666

0.4701 0.4295 0.4011 0.339 0.2149 0.2056 0.5906 0.328 0.1341 0.3553 0.3551 0.301 0.4422 0.1796 0.2208 0.270

0.0304 0.0238 0.0219 0.0214 0.0207 0.0221 0.0214 0.0230 0.0218 0.0238 0.5252 0.0276 0.0225 0.0315 0.0372 0.0467

REFERENCES I.

Reissner, E. and Stavsky, Y., 1961, "Bending and stretching of certain types of heterogeneous aelotropic elastic plates", J. Appl. Mech., 28 :402-412. 2 . Mindlin, R. D., 1951, "Influence of rotary inertia and shear in flexural motions of isotropic elastic plates", J. Appl. Mech., 18: 31-38. 3 . Yang, P. C. and Norris, C. H. and Stavsky, Y., 1966, "Elastic wave propagation in heterogeneous plates", Int. J. Solids and Structures, 2:665-684. 4 . Whitney, J. M., 1973, "Shear correction factors for orthotropic laminates under static load", J. Appl. Mech., 40:302-304. 5 . Ferreira, A. J. M. and Barbosa, J. T., 2000, "Buckling behaviour of composite shells", Composite Structures, 50:93-98. 6 . Ferreira, A. J. M. and Camanho, P. P. and Marques, A. T. and Fernandes, A. A., 2001, "Modelling of concrete beams reinforced with FRP re-bars", Composite Structures, 53:107-116. 7. Reddy, J. N., 1984, "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51:745-752. 8 . Ferreira, A. J. M., 2003, "A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates", Composite Structures, 59(3):385-392. 9 . Reddy, J. N., 1997, Mechanics of laminated composite plates, CRC Press, New York 10 . Hardy, R. L., 1971, "Multiquadric equations of topography and other irregular surfaces", Geophys. Res., 176:1905-1915. II. Kansa, E. J., 1990, "Multiquadrics- A scattered data approximation scheme with applications to computational fluid dynamics. I: Surface approximations and partial derivative estimates", Comput. Math. Appl., 19(8/9): 127-145. 12 . Pagano, N. J., 1970, "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Comp. Mater, 4, 20-34.

Part IV

Delamination

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Evaluation of Fatigue Delamination Behavior in Hybrid Composite Material Using the Delamination Shape Parameters Sam-Hong Song Department of Mechanical Engineering, Korea University 1, 5ga, Anam-dong, Sungbuk-gu, Seoul 136-701, Korea Cheol-Woong Kim Mechanical System, fnduk Institute of Technology San 76, Wolgye-dong, Nowon-gu, Seoul 139-749, Korea Dong-Joon Oh Department of Mechanical Education, Andong National University 388, Songchun-dong, Andong, Kyoungbuk 769-749, Korea

ABSTRACT The applicability of the hybrid composite materials such as Al/GFRP laminates is restricted due to the frequent delamination of different materials at interlaminar. The previous researches showed that the major parameter to control the delamination of Al/GFRP laminates was a crack (a). On the other hand, it was also shown that a delamination width (b) could strongly effect on the delamination behavior. Therefore, the aim of this research is to define the delamination behavior using the above correlation. We obtained result as follow. The delamination aspect ratio (b/a) that was suggested from the increasing a-b relationship was decreased with increasing of a/W. The suggested the delamination area rate ((^DVAXDW) which represented the growth rate of delamination area (Ap), was going higher while a/Wv/as increasing.

INTRODUCTION Hybrid composite materials such as Al/GFRP laminates show a superior fatigue behavior to general metallic materials [1-4]. In spite of it, the reason why the applicable fields were restricted is the delamination caused between the Al layer and fiber/epoxy one. This delamination greatly decreases the fiber bridging effect. Therefore, the fatigue behavior of Al/GFRP laminates based on the delamination had been evaluated. The delamination was not determined just by the crack even though the first parameter to control the delamination was the crack. The second parameter to control the delamination was delamination width (b). However, it is difficult to fine the quantitative study of delamination using the a-b relationship. Therefore, the aim of this study is to evaluate the delamination behavior by a-b relationship. The details are as follows. 1) Analysis of crack (a) - delamination width (b) relationship. 2) Estimation of delamination aspect ratio (b/a) * Correspondence Author, Address : San76, Wolgye-dong, Nowon-gu, Seoul 139-749, Korea Fax : +82-2-921-8532, E-mail: woong25(a!korea.ac.kr

238

Evaluation of Fatigue Delamination Behavior 4-O10.5

2.1 Cross-section of A-A1 Drilled holes ••s

!

80 150

(a) Geometries of AI/GFRP laminates specimen

Bending f I J Moment! E 3

f

Saw-Cut

i_^..0^^=^-——J E B ^ S ^ ^ p l

Q Attending H Moment

Aluminum alloy UD Glass/epoxy: [0]2 (b) Cross-section of AI/GFRP laminates specimen

F I G U R E 1 Geometries and cross-section o f AI/GFRP laminates (unit: mm)

delamination area rate {(AD)N/(AD)Aii) relationship. 3) The effect of the b/a on the delamination shape factor (fs) and delamination growth rate (dAr/da). Through the above facts, the new parameters required for the delamination evaluation of the AI/GFRP laminate was proposed and the applied results were discussed. FABRICATION OF SPECIMEN AND EXPERIMENTAL METHOD Fabrication of AI/GFRP Laminates Specimen AI/GFRP laminates were manufactured as the 2/1 type that the unidirectional glass fiber/epoxy was inserted between two A15052 alloy sheets. During the curing, the postheating procedure was used to reflect the Differential Scanning Calorimeter (DSC) results of GFRP prepreg and it made the specimens more stable chemically. The geometries of AI/GFRP laminates were shown in Figure 1. Pre-crack was made at the low edge of the specimens by a wheel cutter and four holes were drilled at the fixing area of specimens. Fatigue Test Method The fatigue tests were performed by the bending & torsion fatigue testing machine (TB-10B, Shimadzu Co.) whose maximum moment was 98 N-m. The cyclic bending moment of 3.92 N-m was applied and the fatigue cracks were measured at 100 magnifications by the traveling microscope. C-scan (Mi-SCOPE exla, Hitachi Co.) was used to obtain the delamination images between the Al alloys sheet and glass-fiber/epoxy one and those of corresponding cyclic delamination were recorded. RESULTS AND DISCUSSION Relationship Between Crack Length (a) and Delamination Width (b) Unlike the monolithic Al alloy, AI/GFRP laminates did not show the sudden change of the crack growth with increasing of cycles [3]. During the second half of loading, this crack growth was the same as that of the first half of loading even though increasing of the crack length caused decreasing of ligament. Consequently, linear a-N relationship was obtained as Figure 2 (i). This phenomenon resulted from the stress bridging effect of fiber laminates. However, if the crack propagated the delamination field between the Al alloy layer and the glass-fiber/epoxy one was initiated and grown. When the major axes of delamination expansion direction were determined as x- andy- direction, it was know that the delamination length of x-axis direction was equal to the crack length. In the meantime, the delamination width (b) corresponding to ^-direction was broadened normal to the crack growth direction. From these facts, a lot of information about delamination behavior could be obtained using the a-b relationship. The triangle model (c=l) was selected for this study. If the triangle model was applied, the contour (c) and delamination area (AD) could be obtained easily by the a-b. The calculation of the b was carried out by the C-scan

Evaluation of Fatigue Delamination Behavior

239

c = 1, Triangle*

Bendin<| Momer t = 3.9N Stress Ratio (R) = -1

40

c = 2, Ellipse-I* B

I 30

c = 3, Ellipse-M* Delamination zone

Crack Length, a

CO D) 2 0
10

o

r 0

\DelE

Bending Fiber moment | Orientaion

Vidth. b

u y

1x10 5

2x10 5

3x10 5

4x10 5

L.

5x10 ;

*: Delamination contour type

Number of cycles, N (No.) (i) Crack length (a) - delamination width (b) relationship

(ii) Configuration of delamination zone

FIGURE 2 The relationship between the crack length (a) and the delamination width (b)

images of Figure 3. They were used to measure the basic elements of delammation such as width (b), contour length (2c) and area (AD). The a-b relationship in Figure 2 and Figure 3 was investigated. It was as follows. While the crack growth showed linearity from the beginning to the end of cyclic loading, the increase rate of b became lower along a quadric curve. Examining the increase of a and b, a seemed to be equal to bfromthe beginning to N = 1.5 x 105 cycles but a was greater than b after N~ 1.5 x 105 cycles. After b became about 18 mm, the growth rate of b was slow. This phenomenon could be observed by the delamination images in Figure 3. The above regions (a) ~ (e) of Figure 3 showed a = b and the middle ones (f) ~ (k) of Figure 3 mean a > b. The bottom ones (1) ~ (o) of Figure 3 were the independent area where only the delamination grow after Al alloy sheet was fully fractured. Relationship Between the Delamination Aspect Ratio (b/a) and the Delamination Area Rate ((AD)N/(AD)AU)

It was known that the growth rate of crack was constant but that of b was decreased with increasing of Nor a/Wby the examination of the a-b relationship. Using a-b relationship,

(a) 3.0x10" cycle

(b) 6.0 x 10" cycle

(c) 9.0 x 10" cycle

(d) 1.2 x 10 5 cycle

(e) 1.5 x 10 5 cycle

(f) 1.8 x 1 0 5 cycle

(g) 2.1 x 10= cycle

(h) 2.4 x 10 5 cycle

(i) 2.7 x 10 5 cycle

(j) 3.0 x 10 5 cycle

(k) 3.3 x 1 0 5 cycle

(I) 4.2 x 10 5 cycle

(m) 4.5 x 10 5 cycle

(n) 4.9 x 10 5 cycle

(o) 5.1 x 10 5 cycle

FIGURE 3 Ultrasonic C-scan images of the delamination shape parameters (a, b, c) in Al/GFRP laminates

240

Evaluation of Fatigue Delamination Behavior

a new parameter such as the delamination aspect ratio (b/a) was suggested to obtain the delamination growth characteristic of the longitudinal direction (x-direction) and the longitudinal transverse direction (y-direction). A new parameter such as the delamination area rate ((AD)NI(AD)AU) was also proposed to calculate the growth rate of AD using an area rate (the total area ((AD)AH) to be observed for the delamination over the delamination area ((AD)N) at the specific cycle), b/a - a/W relationship as well as (AD)NI(AD)AU - a/W was shown in Figure 4. b/a was steadily decreased as a/W was increased. The reason was while the growth rate of crack was constant with increasing of a/W. The growth rate of b was gradually decreased. On the other hand, the growth rate of (AD)NI(AD)AII was slowly increased as a/W was increased. While a/W was increased, the growth rate of b was decreased but that of a was constant. It resulted in the gradual increase of (AD)N/(AD)AH- If the growth rate of b was arithmetic, which of AD could be geometric. It was possible to observe the sudden increase of the delamination after a/W= 0.8. At first, it was guessed that the growth rate of crack would be faster due to the expansion of the damaged region if (AD)NI(AD)AU became increased. Consequently, the crack growth characteristic was linear tendency as shown in Figure 2 (i). In other words, it was clear that the magnitude of AD did not affect the crack growth characteristics. The Effect of Delamination Aspect Ratio (b/a) on the Delamination Shape Factor (fs) and on the Delamination Area Rate ((AD)NI(AD)AU) It was shown that b/a was decreased as a/W was increased. It was believed that the change of b/a could affect a major parameter to determine the delamination shape factor (fs) and the delamination growth rate (dAo/da). Considering b/a as well z&fs and dAo/da proposed by previous research [5], it was discussed at this section whether any change could be made. It was confirmed that the delamination growth depended on the crack length (a) rather than on the number of cycle (N) from the previous researches. The equation to relate the expansion ratio of AD to the increase of crack length was called the delamination growth rate (dAo/da) and was written as Equation (1). Where, fs was called the delamination shape factor. fs would be changed by the delamination type of the triangle (c=l), the ellipse-I (c=2) or the ellipse-I (c=3) like c suggested in Figure 2 (ii). Considering b/a,fs could be written as Equation (2). Where, s and D were the saw-cut length and the sum of the saw-cut and the crack lengths, respectively. Number of Cycles, N 1x105

2x105

3x105

4x105

1.4

5

1.2

1.2

b/a

1.0 DC •3

0.8

2

0.8 S TO

0.6 0.4

0.4

0.2

O oo0

0.0 -0.2 0.0

0.0 JS 0.2

0.4

0.6

0.8

1.0

Normalized Crack Size, a/W

FIGURE 4 Delamination aspect ratio (b/a) - normalized crack size (a/W) relationship and delamination area rate ((AD)i/(AD)Aii) - normalized crack size (a/W) relationship in Al/GFRP laminates

Evaluation of Fatigue Delamination Behavior

241

They were clearly demonstrated in Figure 2 (ii). c = 1,2 and 3 represent the delamination of triangle, ellipse-I and ellipse-II, respectively. (1)

= 1. / , = i l 4 ,

C = 2, / , = * ! - -M

-C = 3, / , = & , ! - ^

(2)

Figure 5 (i) showed the changing appearance of/j (fsi,fs2,fs3) obtained from the above equations as a/W was increased. The fs of ellipse-II (fsi) was greater than that of ellipse-I (fsi) and that of triangle (fsi) was the smallest in Figure 5 (i). While fS3 was three times bigger than/j; at the beginning, the difference between^ andfsi was slowly decreased as a/W was increased. Especially, the change offsi,fs2 and/j? was not observed from a/W= 0.8 and their differences were also very small. Consequently, it was known that the effect of delamination shape on the delamination behavior was strong at the beginning but it was diminished as the crack grew. The effect of three delamination shape factors (fsnfs2 and fsi) on the behavior of dAr/da was considered in Figure 5 (ii). Figure 5 (ii) showed the behavior of dAr/da according to the increase of JV. There were two cases that three/? (fsi, fs2,fsi) were considered for dAr/da and were neglected. In general, dAr/da of the former was lower than that of the latter. Particularly, dAr/da offsi became lower than those of/b and fss. hi other words, it was known that dAr/da of the triangle was distributed at lower part than those of the ellipses. For ellipses, it was clear that dAr/da oifs2 was also lower than that of/sj. The average offsi,fs2 and/jj obtained from Figure 5 (i) were fsi = 0.57, fS2 = 0.70, fs3 = 0.87. Comparing them with Figure 5 (ii), they were as follows. When dAr/da to consider/s compared with dAr/da to neglect fs, the latter was regarded as 100%. It was shown that dAr/da to consider fsi,fs2 and/s, were decreased about 43 %, 30 % and 13 %, respectively. Therefore, among three dAr/da to consider fs, dAr/da of the ellipse-II (fsi) was the greatest but dAr/da of the triangle was the smallest. It was reported by Roebroeks [6] that the fiber bridging effect of the triangular delamination was superior to that of the ellipse ones. For this reason, it was believed that the superiority of thefiberbridging effect

2.0

10J

- Delamination Contour Factor C = 1 : Triangle, fs1 = (b/a) (1 - (s/D)) C = 2 : Ellipse-I, f = (b/a) (1 - (s/D))"2 C = 3 : Ellipse-II, fs3 = (b/a) (1 - (s/D)2)"

T3 CD

102

• o A V

dAD/da c = 1, dAD/da = fs,(dAD/da) c = 2, dAD/da = y d A D / d a ) c = 3, dAD/da = fS3(dAD/da)

e CD

E c = 2,fS2 = (b/a) ( 1 - (s/D))"

ID Q

0.2

0.4

0.6

0.8

1.0

Normalized Crack Size, a/W (i) fs — a/W relationship

S2

10'

c = 3, f

S3

= (b/a) (1 - (s/D) 2 ) 1 ' 2

JX!

10°

10b

Number of Cycles, N (ii) dAc/da - N relationship

FIGURE S The effect of delaminaion shape factors (fsi,fs2 and_/jj) on the delamination growth rate {dAjJdd) in Al/GFRP laminates

242

Evaluation of Fatigue Delamination Behavior

made dAr/da lower. It implied that dAz/da of the triangular delamination became lower than that of the elliptical ones. This result agreed well with the conventional ones. CONCLUSIONS Using the crack (a) - delamination width (b) relationship, the delamination behavior of Al/GFRP laminates was evaluated and the next conclusions were obtained. (1) While the crack growth of Al/GFRP laminates showed linearity from the beginning to the end of cyclic loading, the growth of delamination width (b) was lowered along the quadric curve as the number of cycles (N) was increased. Therefore, it was known that the a-b relationship reminded a = b at the beginning of cyclic loading but a was greater than b after the middle of cycling. (2) It was shown that the delamination aspect ratio (b/a) was slowly decreased and the delamination area rate ((AD)N/(AQ)AH) was increased as the normalized crack size (a/W) was increased. However, the crack growth was nearly constant from the beginning to the end of loading even though (AD)V'(AD)'AH was increased. Consequently, it was believed that the magnitude of delamination area was not the parameter to control the crack growth characteristic. (3) The delamination shape factor (fs) was changed by the delamination shape such as the triangle or ellipse./? of the ellipse-H (fsi) was greater than that of the ellipse-I (fsi) but that of the triangle (fsi) was less than that of the ellipse-I (fsi)- While the differences among fsi,fs2 sn&fs3 seemed greater at the beginning of loading, these differences were decreased and became constant as the crack grew. Namely, the effect of the delamination shape on the delamination behavior was strong at the beginning of the cyclic loading but it was gradually diminished according to the increase of a/W. (4) Considering the effect of the delamination shape factors {fsi,fs2 and/b) on dAp/da, it was clear that dAr/da of the triangle was lower than that of the ellipse. This result was well coincident with the previous work that the fiber bridging effect of the delamination triangular shape was superior to that of the elliptical ones. ACKNOWLEDGEMENT This work supported by grant No. R01-2003-000-10567-0 from the Korea Science & Engineering Foundation.

REFERENCES 1.

Marissen, R. 1988. "Fatigue Crack Growth in ARALL ; A Hybrid Aluminum-Aramid Composite Material : Crack Growth Mechanism and Quantitative Prediction of the Crack Growth Rates," Ph. D. Thesis, Delft Univ. of Tech., Netherlands. 2. Guo, Y. J. and Wu, X. R. 1999. "Bridging Stress Distribution in Center-Cracked Fiber Reinforced Metal Laminates: Modeling and Experiment," Engineering Fracture Mechanics, Vol. 63, pp. 147-163. 3. Takamatsu, T., Matsumura, T., Ogura, N., Shimokawa, T. andKakuta, Y. 1999. "Fatigue Crack Growth Properties of a GLARE3-5/4 Fiber/Metal Laminates," Engineering Fracture Mechanics, Vol. 63, pp. 253-272. 4. Jin, Z. H. and Mai, Y. W. 1997. "Residual Strength of an ARALL Laminate Containing a Crack," Journal of Composite Materials, Vol. 31, No. 8, pp. 746-761. 5. Song, S. H. and Kim, C. W. 2003, "The Analysis of Fatigue Behavior Using the Delamination Growth Rate and Fiber Bridging Effect Factor in Al/GFRP Laminates," Transactions of the KSME, A, Vol. 27, No. 2, pp. 317-326. 6. Roebroeks, G. H. J. J. 1987. "Constant Amplitude Fatigue of ARALL-2 Laminates," Report LR-539, Dept. of Aerospace Engineering, Delft Univ. of Tech., Netherlands.

The Effect of Stitch Distribution and Stitch Pattern on Mode I Delamination Toughness of Stitched Laminated Composites Michael D. K. Wooda, Xiannian Suna, Liyong Tonga*, Anthony Katzos and Adrian Rispler a School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney University, New South Wales 2006, Australia b

Boeing subsidiary, Hawker de Havilland, Australia

This research is part of the ARC SPIRT program in collaboration with Boeing subsidiary, Hawker de Havilland and Boeing Phantom Works, Seattle, USA

ABSTRACT In this paper, a modified double cantilever beam (MDCB) test is performed on Vectran® stitched laminated composites with varying stitch distributions and stitching patterns. The woven carbon fibre plies were laid-up in a symmetrical manner [0,±45,90]2 then stitched in a dry preform state followed by a resin film infusion (RFI) stage. To prevent the stitched specimens from failing in flexure, a known failure mode for such samples, thick aluminium Al-1050 reinforcing tabs were adhesively bonded to either side of the composite specimen along with loading blocks. An INSTRON5567 screw-driven testing machine was used to test the specimens at a crosshead velocity of 0.5mm/min with crack lengths, crack opening displacements (COD) and peak load data being recorded after the crack front had propagated several millimetres. A variation of the compliance method was used to post process the test data revealing differences in strain energy release rates (SERR), G/r, for both plain stitched and zigzag stitched specimens, with varying stitch distributions and with stitch densities of approximately 0.033 stitches/mm2. Keywords: Modified Double Cantilever Beam, Stitching, Stitching Distribution, Stitching Pattern, Strain Energy Release Rate

INTRODUCTION Laminated carbon composites are well known to possess excellent specific strength in weight critical applications but poor interlaminar strength especially in relation to damage tolerance. It is this specific strength that has ensured composites their outstanding suitability for the aircraft industry [1]; however the second factor reduces the materials resistance to damage, in particular low velocity impact.

* Correspondence Author. Email: rtong(a),aeromech.usyd.edu.au Fax:+61-2-93514841 Phone:+61-293516949

244

Effect of S titch Distribution and S titch Pattern

To retard progressive delamination and subsequent catastrophic failure, laminated composites can be reinforced in the through-the-thickness (TTT) direction by means of stitching [2] or z-pin reinforcement [3]. Z-pinning, as it has come to be known, involves the mechanical insertion of solid or fibrous independent pins aligned in the TTT direction of the laminate. Stitching of laminated composites is similar to its textile counterpart, differing only in stitch type, where a modified lock stitch is used. Stitching can be interconnected or independent with the latter requiring an extra machining process to shear off the surface loop of the continuous stitch. Presently there is significant empirical [4] and analytical [2] data available supporting the positive contribution of TTT reinforcement in bridging delamination cracks, with many researchers reporting the importance of stitch fibre diameter, stitching density and interfacial shear stress. Recent finite element analysis (FEA) conducted by Sun et al [5] has shown that stitch distribution is an influential parameter when predicting the improvement in mode I delamination toughness. The research showed that for identical stitch densities with varying stitch distributions, the resulting R-curve behaviour can be highly dissimilar. Furthermore, Lui et al [6] concluded through compression after impact (CAI) experiments that stitch pattern can change the shape of the impending delamination but not the affected area. hi this paper, Mode I delamination toughness experiments are conducted on stitched laminated woven carbon fibre modified double cantilever beam (MDCB) specimens. Both plain (straight interconnected) and zigzag (interconnected) stitching are used. The results bore behavioural resemblance to those found in [5] with patterns of identical stitch densities but varying stitch distributions producing different results. DCB SPECIMENS AND TESTING PROCEDURE Ideal for quantifying the mode I delamination toughness of a laminated composite is the mode I interlaminar fracture toughness test for fibre-reinforced polymer matrix composites [7]. The test specifies specimen (Figure 1) dimensions of at least 125.0mm (5.0 in.) long and nominally 20.0 to 25.0mm (0.8 to 1.0 in.) wide, however, specimen width is not a critical parameter. The laminate thickness should be between 3.0 and 5.0mm (0.12 and 0.2 in.) with a variation over the length of the specimen of no more than 0.1mm. A release film insert 15/an in thickness was placed in between the centre plies of the laminate lay-up to facilitate crack initiation. To avoid premature failure, in the specimen substrate arms, in flexure; thick aluminium tabs were bonded to either side of the test specimen. Loading blocks were subsequently adhesively bonded to the 1050 Aluminium tabs to enable loading. In order to assist in crack initiation and avoid any instability due to bonding through the release film insert, the pre-crack can be wedged open with a razor blade. The specimen is then mounted on an INSTRON 5567 testing machine equipped with a 10£N load cell. The specimen is then pin-loaded using displacement control where the cross-head rate is preset at 0.5mm/min in order to enable slow crack propagation. Once the crack has progressed several millimetres the specimen is unloaded at the same rate and the crack tip marked; this cycle of loading and unloading takes place 15-20 times for every specimen or until failure occurs. A digital data logger was used to continuously record the load verses cross-head displacement over time.

Effect of Stitch Distribution and Stitch Pattern

245

FIGURE 1 Specimen geometry concealing the lower tab-loading block assembly

STITCHING Four specimen groups were manufactured in this program using an industrial sewing machine adjusted to produce a modified lock stitch (MLS). A control batch with no TTT reinforcement, two sets of plain stitched specimens and one set of zigzag specimens. It should be noted that the zigzag stitch is incapable of incorporating a MLS. Over all the stitched specimens the stitch density was maintained constant at approximately 0.033stmm"2. Shown below are schematics of the stitched specimens.

.Stitching

4.06

i

W

W

!_)

-•

•

o

-•

•

o

»

•

o

*-•

•

o

5.0 ' 5.0' 25.0

1

5.0'

25.0

5.0'

*—:—•

(a)

(b)

(c)

FIGURE 2 (a) Plain short pitch (PSP) (b) Plain long pitch (PLP) and (c) Zigzag stitched

INTERLAMINAR FRACTURE TOUGHNESS CALCULATION The direct method [8], like all compliance methods, depends on the Irwin-Kies equation relating strain energy release rate (SERR) Gic to the compliance, C, which is the ratio of deflection over load. The method allows for mode I SERR values to be calculated as long as the crack propagation is stable. The mode I interlaminar fracture toughness may be written as follows

.EL w

El

5Guhcw

(1)

Effect of Stitch Distribution and Stitch Pattern

246

Where P is the peak load, w and h the specimen width and thickness respectively, El, the flexural rigidity takes into account the thick aluminium tabs as well as the carbon composite, x is t n e correction factor which takes into account the additional deflection due to rotation of the beams, Gn is the interlaminar shear modulus and a is the crack length, hi this paper, the critical strain energy release rate is taken to be the peak value prior to the first stitch breaking. RESULTS AND DISCUSSION Shown in Figure 3 are the results of the MDCB test for the unstitched specimens. Figure 3a depicts the load versus crack opening displacement (COD) curve for the first specimen only. The peak load for this specimen type occurs, on average for unstitched specimens, at approximately 1050N. The composite toughness follows an almost linear path until it reaches an asymptotic or steady state value. The length of this linear path is due to the increased length of the process zone present in MDCB tests. This SERR value is referred to as the critical SERR Gic and occurs at a crack length of roughly 60.0mm for the unstitched specimens. At this stage if the SERR value continued to increase it was noted in the experimental log that some form of fibre bridging across the crack wake was present. The average critical SERR for the unstitched specimens was 0.78KJ/m2. The G/c value, presented in this paper, is taken to be the point at which the first stitch has failed.

1.4 . UnstitchecM 1.2

600

400

I III!/, 1

1

x

»

x

x Unstit ched4 ••

x Unstit ched 5

•

x

1 0.8 *

*

*

' A

S 0.6 0.4 I

0.2 0

2

ched2 . Unstitched3

3 COD (mm)

4

: • "

60 a (mm)

100

120

FIGURE 3 a) Load verses COD for unstitched specimen 1, b) GIr - Aa curve for all unstitched specimens

In comparison to the unstitched specimens; the zigzag stitched specimens with a stitching density of 0.0336stmm"2, shown in Figure 4a and 4b, performed considerably better with an average peak load of 2500N, roughly 2.5 times greater than that of the unstitched specimens. As the crack front reached the first row of stitches, the R-curve slope raises rapidly with an increase in the number of bridging entities until the crack wake is saturated. The critical average SERR, G/c, is achieved in the region of 53.0mm at a value of 3.47KJ/m2. The scatter of data points after 53.0mm can be attributed to the fracture behaviour of the stitch fibres. Since the zigzag stitch cannot produce an ideally modified lock stitch [9], due to the necessity for even tension on both the needle and bobbin threads respectively, the lock location cannot be controlled effectively. This reason alone contributed to the variability in asymptotic GIr values

Effect of Stitch Distribution and Stitch Pattern

247

for zigzag stitches with close to 50% of all stitches failing and pulling out to either side of the MDCB specimen.

5

At

x Stitch .ocatior

4.5

• Zigzag 1

4

• Zigzag 2

1000

• . . .

x Zigzag 4 « Zigzag 5

£ 3

\

A

-

• Zigzag 3

3.5

•

*

* * x

§2.5

1

S 2

J

*

1.5

1

X—X—X-) —X—X—X-

1 0.5 ***** 0 COD (mm)

20

40

60 a (mm)

80

100

120

FIGURE 4 a) Load verses COD for zigzag stitched specimen 1, b) Glr - Aa curve for all zigzag stitched specimens

For both PLP and PSP stitched specimens shown in Figure 5a, 5b, with stitching densities of 0.0372stmm"2 and 0.0348stmm"2 respectively, the results show clear differences in Gjc values and R-curve behaviour. With a critical Gjc of 2.82KJ/m2 achieved at a crack length of 55.0mm, the PSP specimens obtained an average peak load of 2275N. The PLP stitched specimens attained a critical GIc equal to 4.47KJ/m2 at roughly 55.0mm, 58% and 29% higher than for PSP and zigzag stitched specimens respectively. The PLP distributed stitch pattern reached the highest peak load of 2780N, 22% and 11.2% larger than for PSP and zigzag specimens respectively. The main reason for this increased load capacity of the PLP stitch distribution could be put down to a larger number of bridging fibres being utilised in the first row of the PLP specimens. As the crack front propagates, the induced moment at the first stitch row increases with increasing crack growth making the distribution of the stitches in the crack wake significant. The increased potential for stitching fibre abrasion sustained during the PLP sewing process as well as increased stress concentrations at the stitch lock due to the small stitch pitch distances involved in this stitch pattern may have also reduced the peak load and critical G/c values. This is reflected in the failure data where 88% of all PLP stitches failed at the surface loop and pulled out to the needle thread side where as 96% of all PSP stitches failed at the surface loop. However, the results show that stitch density alone, as a defining parameter, is not sufficient in predicting the potential resistance to crack propagation. Stitch distribution defined by stitch pitch distance and stitch line spacing must be thoroughly considered when tailoring material properties.

248

Effect of Stitch Distribution and Stitch Pattern 4.5 x Stitch Location

x Stitch Location -

• PLP 1

4

• PLP 2

3.5

. PSP 1 .PSP2 •

• PSP 3

• PLP 3 • PLP 5 • •

A

x

«PSP4

4

xPLP4

I"2

a

xPSP5

\

1

. *

* x

x

*

-

i

1.5

i

•

—X—X—X-

1 a

p

** * 0.5

; * *

60 a (mm)

40

60 a (mm)

FIGURE 5 a) Glr - ha curve for all plain long pitch stitched specimens, b) G/r — ha curve for all plain short pitch stitched specimens

CONCLUSION The results suggest that for identical stitching densities, the R-curve behaviour, peak loading and asymptotic strain energy release rates can be highly dissimilar. When tailoring stitched CFRP properties, stitch distribution should be thoroughly considered. REFERENCES [1]

[2] [3]

[4]

[5]

[6] [7] [8]

[9]

A. P. Mouritz, M. K. Bannister, P. J. Falzon, and K. H. Leong, "Review of applications for advanced three-dimensional fibre textile composites," Composites Part A, vol. 30, pp. 14451461, 1999. K. A. Dransfield, L. Jain, and Y.-W. Mai, "On the Effects of Stitching in CFRPs-I. Mode I Delamination Toughness," Composites Science and Technology, vol. 58, pp. 815-827, 1998. G. Freitas, C. Magee, P. Dardzinski, and T. Fusco, "Fiber Insertion Process for Improved Damage Tolerance in Aircraft Laminates," Journal of Advanced Materials, vol. 25, pp. 36-43, 1994. A. P. Mouritz and L. K. Jain, "Further Validation of the Jain and Mai models for Interlaminar Fracture Toughness of Stitched Composites," Composites Science and Technology, vol. 59, pp. 1653-1662, 1999. X. Sun, L. Tong, M. D. K. Wood, and Y.-W. Mai, "Effect of stitch distribution on mode I delamination toughness of laminated DCB specimens," Composites Science and Technology, Accepted, 2004. D. Liu, "Delamination Resistance in Stitched and Unstitched Composite Plates Subjected to Impact Loading," Journal of Reinforced Plastics and Composites, vol. 9, pp. 59-69, 1990. ASTM D5528-01, "Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites," 2001. L. K. Jain, K. A. Dransfield, and Y.-W. Mai, "Effect of Reinforcing Tabs on the Mode I Delamination Toughness of Stitched CFRPs," Journal of Composite Materials, vol. 32, pp. 2016-2026, 1998. K. Dransfield, C. Baillie, and Y.-W. Mai, "Improving The Delamination Resistance of CFRP by Stitching - A Review," Composites Science and Technology, vol. 50, pp. 305-317, 1994.

Dynamic Analysis for Delaminated Composites with Arbitrary Shaped Multiple Delaminations Based on Higher-Order Zig-Zag Theory Maenghyo Cho , Jinho Oh School of Mechanical and Aerospace Engineering, Seoul National University San 56-1, Shillim-Dong, Kwanak-Ku, Seoul 151-744, Korea Jun-Sik Kim Department of Aerospace Engineering, The Pennsylvania State University, University Park, U.S.A. Gun-In Kim Department of Weapon Engineering, Korea Military Academy, P. O. Box 77, Gongnung, Nowon, Seoul, Korea

ABSTRACT A finite element based on the efficient higher order zig-zag theory with multiple delaminations is developed to refine the predictions of frequency and mode shapes. Displacement fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Through the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

INTRODUCTION Recently, development of advanced composite materials is paid special attentions to their potential applications of aircraft, marine, and automobiles owing to their high specific strength and stiffness. In particular, analysis of dynamic characteristics is quite important to understand the stability and strength of structures. Especially for structural design in the critical environments, highly accurate dynamic analysis is required. For the enhanced analysis of laminated composite plates, so-called "zig-zag" theories have been paid a lot of attentions because of their accuracy and efficiency in the ply-level analysis. Correspondence Author : Maenghyo Cho, Fax : +82-2-886-1693, E-mail address: [email protected]

250

Dynamic Analysis for Delaminated Composites

Most of the theories assume that interfaces are perfectly bonded. However, in many applications, this assumption is not adequate for the prediction of the behaviors of composite laminates. Low-speed impacts by foreign objects or imperfections in the manufacturing process may generate multiple delaminations in composite laminates. Strength and stiffness of composite structures with delaminations decrease significantly compared to the undelaminated composite plates. For the analysis of laminated plates with arbitrary shaped multiple delaminations, finite element method is a suitable choice to treat the general loading, boundary conditions, layups, and geometry. Even though finite element based on layerwise plate theory [ 1 ] can provide an adequate framework for the delamination analysis, this theory is not computationally efficient since the number of degrees-of-freedom of this theory depends upon the number of layers. Thus to reduce the active degrees-of-freedom of the problem, a global-local approach has been proposed in the refs [2-4]. In the present study, we focus on the dynamic version of composite laminated plates with multiple delaminations. The model is based on the efficient higher order zig-zag plate theory with minimal degrees of freedom. The violation of unilateral contact conditions in the delaminated region is prohibited by imposing contact constraints through the Lagrange multipliers. Eigenvalue problems and time responses are analyzed. The present results of natural frequencies and time responses are compared to those of the previously reported results. The numerical verification for the developed finite element is made on laminated composites with circular, elliptic, and rectangular shaped delaminations, respectively. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations. Displacement Model Displacement field of composite plates with multiple delaminations is considered. The deformation behavior is assumed within the range of linear elasticity. The configuration of composite plate with multiple delaminations is shown in Fig. 1. Higher-order zig-zag in-plane displacement field with delaminations is obtained by superimposing zig-zag linear field and piecewise constant delamination field to the globally cubic varying field. The starting displacement field can be written as follows,

f

tfCz-z,)

i Delaminations

FIGURE 1 Configuration of laminated composite plate with multiple delaminations

(2)

Dynamic Analysis for Delaminated Composites

251

where u°a, w denote the displacement of a point O J on the reference plane. y/a are the rotations of the normal to the reference plane about xa axis. N is the number of total layers. D is the number of the delamination interfaces. H(z - zk) is the Heaviside unit step function. The terms u^,wd represent possible jumps in the slipping and opening displacements, which permit incorporation of delamination for laminated composites. The deformed schematic configuration and the kinematic variables are shown in Fig. 2. By applying top and bottom surface transverse shear stress free conditions and interface transverse shear stress continuity conditions, the following displacement field is obtained. (3) (4) 3A ,

in which,

(5)

The displacement field is the same as that proposed by Cho and Parmerter [5,6]. Finite Element Formulation To assess the validity of the dynamic version of EHOPTWD (Efficient Higher Order Plate Theory With Delamination) [7], a finite element is developed for two-dimensional problems. The present laminated plate theory which have been developed has second derivative of w(transverse deflection at the reference plane). Thus C1 continuous (slope-continuous) functions are required. However, it is well known in plate theory that it is difficult to impose normal slope continuity conditions at the interfaces between elements in arbitrarily oriented quadrilateral and triangular elements. The DKQ element developed by Batoz and Tahar [8] is the simplest elements which pass the patch test and satisfy Kirchhoff constraints. In the present study, we adopted the concept of DKQ element to overcome the continuity problem of deflection w and delamination deflection wd. For the four-noded quadrilateral element, nodal displacement vector is given by {a}e = [u°a, w ,

a, u * , w'', w* f

(6)

Natural coordinates £ and 77 are used in the shape functions and coordinate transformation functions. The primary displacement unknowns are expressed in terms of nodal variables and shape functions as

FIGURE 2 Deformed configuration of laminates with multiple delaminations

252

Dynamic Analysis for Delaminated Composites u°=YN,u°., ud = u

I cct '

^^j

(7)

j

ex

(8)

K = 2] w.,

(9)

where Nt are the conventional bilinear shape functions, and Nai, Pai, and Haj are shape functions of the DKQ element. However, the DKQ element cannot define the transverse deflection inside an element. It only specifies along the edge of the element. When a mass matrix is required, the transverse deflection needs to be described within an element. Therefore to compute element mass matrix, a refined nonconforming quadrilateral element proposed by Cheung Y. K. [9] is adopted. NUMERIC EXAMPLES Eigenvalue Problems For the numerical evaluation of the performance of the proposed model, cantilever composite plate with center delamination is considered. The stacking sequence of the delaminated composite is [(0/90)2]s and the thickness of plate is 1.016mm. The plate has length a=127mm, and width b=12.7mm. The density is 1477kg/m2. The material properties employed in the present numerical examples are given in the ref. [10]. As shown in the Table. 1. First, second, and third bending natural frequency are predicted very accurately compared to the results of ref. [10]. First bending natural frequency is higher than those of the experiment results [10]. As the size of delaminated zone increases, natural frequency decreases. TABLE I (a) First bending frequency HOT 1 0

Present

81.75(Hz)

82.1

81.7(Hz)

78.16(Hz)

80.429(Hz)

80.8

80.2(Hz)

Delamination

Experi-ment

Nastran 10

length

10

3D (element)

0(mm)

79.83(Hz)

25.4(mm)

Theory

50.8(mm)

75.37(Hz)

75.136(Hz)

77.7

76.1 (Hz)

76.2(mm)

66.95(Hz)

66.531(Hz)

68.3

67.2(Hz)

101.6(mm)

57.54(Hz)

55.809(Hz)

59.8

56.1(Hz)

(b) Second bending frequency

Delamination

Nastran 10

length

3D (element)

0(mm) 25.4(mm)

HOT"'

Present

510.7(Hz)

513.4(Hz)

510.1(Hz)

504.1 (Hz)

499.6(Hz)

509.2(Hz)

Theory

50.8(mm)

478.6(Hz)

515.7(Hz)

488.1 (Hz)

76.2(mm)

399.3(Hz)

420.8(Hz)

385.7(Hz)

101.6(mm)

305.7(Hz)

346.7(Hz)

325.4(Hz)

Dynamic Analysis for Delaminated Composites

253

Dynamic Responses Deflection of intact zone and delaminated zone are obtained by using time integration considering Lagrange multiplier for penetration violation. fn the delaminated zone, when the relative displacement is positive, contact spring force is set to zero. On the contrary, if the relative displacement is negative, contact spring force is imposed. Dynamic response considering unilateral contact constraint is simulated in the Fig. 3. Dynamic response with rectangular and circular delamination is shown in Fig. 3. The rectangular and circular delamination size is 40% of whole structure. Thus, in the dynamic analysis, we can obtain the result that unilateral contact spring constraint can prevent penetration violation.

FIGURE 3(a) Dynamic response with one rectangular delamintion

0.010 •

— • — upper 1 IBVBT

— — uPpar2layer 0.005-

\ /

'

1

N "°°

0.00

0.01

0.02

0.03

0.04

0.05

0.06

FIGURE 3(b) Dynamic response with two rectangular delamintions Circular shape delamination

FIGURE 3(c) Dynamic response with one circular delamintion

254

Dynamic Analysis for Delaminated Composites

CONCLUSIONS In the present study, a finite element based on higher order zig-zag theory with multiple delaminations has been developed in order to analyze the dynamic behavior of composite plates with multiple and arbitrary shape delaminations. By imposing transverse shear stress free condition of top and bottom surfaces and stress interface continuity conditions between layers with delaminations, layer-dependent displacement variables were eliminated. Final displacement fields of undelaminated zone have only reference primary variables. In the delaminated zone, the minimal number of degrees-of-freedom is still retained. Thus this theory can be applied to the problems with many thick layers and multiple delaminations. Also, this theory can analyze composite structure with arbitrary shape delamination since the present non-conforming element can pass the bending patch test in arbitrary shaped quadrilateral mesh. Through the analysis of eigenvalue problem of composite plate with multiple delaminations, it is observed that the natural frequencies predicted by the present EHOPTWD are in good agreement with experiment data, HOT, and Nastran-3D solutions. The present finite element based on the zig-zag higher order theory demonstrated accurate predictions of natural frequencies and mode shapes for various types of delaminations in the thick plate range. REFERENCES 1.

Lee, J., Gurdal, Z., and Griffin, O. H. 1993. "Layer-Wise Approach for the Bifurcation Problem in Laminated Composites With Delaminations," AIAA J, Vol.31, pp. 331-338 2. Cho, M., and Kim, J. S. 1997. "Bifurcation Buckling Analysis of Delaminated Composites Using Global-Local Approach," AIAA J, Vol.35, pp. 1673-7676. 3. Cho, M., and Lee, S. G. 1998. "Global/Local Analysis of Laminated Composites With Multiple Delaminations of Various Shapes," Proceedings of the AIAA/ASME/ASCE/AHS/ASC 39th Structures, Structural Dynamics and Materials Conference, Long Beach, CA, AIAA, Reston, VA, pp. 76-86. 4. Kim, J. S., and Cho, M. 1999. "Postbuckling of Delaminated Composites Under Compressive Loads Using Global-Local Approach," AIAA J, Vol.37, pp. 774-777. 5. Cho, M , and Parmerter, R. R. 1992. "An Efficient Higher-order Plate Theory for Laminated Composites," Composite Struc, Vol.20, pp.113-123. 6. Cho, M., and Parmerter, R. R. 1993. "Efficient Higher Order Composite Plate Theory for General Lamination Configurations," AIAA J., Vol.31, No.7, pp.1299-1306. 7. Kim, J. S., and Cho, M., 2002. "Buckling Analysis for Delaminated Composites Using Plate Bending Elements Based on Higher-Order Zig-Zag Theory," Int. J. for Num. Meth. in Eng., Vol.55, No. 11, pp.1323-1343. 8. Batoz, J. L., Tahar, M. B. 1982. "Evaluation of a New Quadrilateral Thin Plate Bending Element," Int. J. for Num. Meth. in Eng., Vol.18, pp. 1655-1677. 9. Cheung, Y. K., Zhang, Y. X., and Wanji, C. 2000. "The Application of a Refined Non-Conforming Quadrilateral Plate Bending Element in Thin Plate Vibration and Stability Analysis," Finite Element in Anal, and Design, Vol.34, pp. 175-191. 10. Chattopadhyay, A., Radu, A. G., and Dragomir-Daescu, D. 2000. "A Higher Order Plate Theory for Dynamic Stability Analysis of Delaminated Composite Plates," Computational Mechanics, Vol.26, pp. 302-308.

PartV

Design and Optimisation

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Application of Stochastic Optimization to Reconstruction of Random Microstructures Ryszard Pyrz Aalborg University, Denmark Bogdan Bochenek Cracow University of Technology, Poland

ABSTRACT In the present paper the simulated annealing procedure is used to reconstruct plane and spatial dispersions of inclusions as observed on reference images of respective microstructures. The dispersion of centres of particles serve as reference distributions for reconstruction. The integral correlation function is used to define an objective function, which is identified as a sum of squared differences of nodal points of the integral correlation function for a reference and reconstructed dispersions. The reconstruction process is subject to various types of constraints. The geometrical constraint of topological entropy introduces a measure of arbitrariness of the polygonal or polyhedral tessellation associated with the point pattern of inclusion centers. The second geometrical constraint can be taken either as a pre-selected difference between a mean and standard deviation of distances of neighbouring inclusions or as a fulfilment of statistical t-tests and F-test for mean and standard deviation of distances, respectively. An attempt to implementation of constraints related to maximal stresses calculated at the inclusion interfaces has been also made and for plane dispersions effective results have been obtained. The results show, that reconstructed families of dispersions resemble the reference patterns with respect to selected criteria and, therefore, can be used for a further analysis to predict overall properties of underlying materials.

INTRODUCTION Mesoscopic modelling of microstructures can be performed for different systems. We may draw a major difference between those systems for which a volume averaging of selected representative volume element is sufficient, and those for which one has to construct many realizations of the microstructure. Volume averaging is often done by an effective medium approach, and is suitable for predicting properties such as stiffness or conductivity. Combination of ensemble-volume averaging has been used in [1-3] for determination of effective moduli of elastic particulate composites at not dilute concentrations and effective elastoplastic behaviour. However, fracture or electrical breakdown will depend on specific details in the microstructure and usually volume averaging is not acceptable. A short range * Corresponding Author, Institute of Mechanical Engineering, Aalborg University, Pontoppidanstraede 101, 9220 Aalborg East, Denmark, fax: (+45) 9815 9305, e-mail: [email protected]

258

Application of Stochastic Optimization

interactions between microstructural entities which are sensitive to their exact positions and sizes play a dominant role in non-homogeneous local variations of field quantities. For not dilute concentrations where the interaction effects between neighbouring inclusions are highly influential on the overall behaviour of the material, one must check the specific observable property for many realizations of the micro structure. Furthermore, only a tiny fraction of the original material specimen can actually be analyzed. Modern experimental techniques such as X-ray microtomography provide tools for visualization and non-destructive microstructural measurements on material samples [4-8]. In order to assess all details of the microstructure the sampling volume must necessarily be on a scale of a few hundred microns. Then an appropriate sampling procedure has to be applied to macrospecimen to guarantee that measured volume is statistically representative for a bulk material [9]. A destructive sampling procedure and the cost and labour associated with experiments might be not acceptable for many practical applications aiming to model material behaviour. It is mandatory to reconstruct the microstructure that would have similar geometrical characteristics as the microstructure acquired from the limited experimental observations. From this limited view we have tried to understand how the properties of the material relate to microstructure. The approach must necessarily be statistical in particular with respect to the measurements of the microstructure. A virtual experiment that allows to reconstruct the microstructure and subsequently to find an ensemble average of a given property provides means for this statistical assessment. The principle of this experiment is that we want to produce a statistical sample of the microstructure. The reference microstructure is characterized by a set of geometrical parameters and functions, which assign the microstructure to a certain family. Rather than simply generating and sampling the microstructure we pose an inverse problem of reconstructing the reference microstructure based upon the limited information contained in the descriptors. The solution is not unique as we are not in a position to know all necessary information for the reference microstructure. Nevertheless, this procedure may result in generation of realizations, which at least match the reference microstructure to the degree embraced by the selected geometrical descriptors [10,11]. In the present paper the methodology is presented for reconstruction of two- and three-dimensional microstructures of unidirectional fiber reinforced composites and particulate composites, respectively. The reference images are acquired with X-ray microtomography. The pair correlation function or its counterpart, integral correlation function serves as an objective function in the optimization procedure. Topological entropy and the stress interaction parameter are used as constraints for reconstructions of two-dimensional microstructures. The stress interaction parameter is expressed in geometrical terms but is correlated with stresses occurring at the fiber-matrix interphase. Thus not only the microstructure geometry but also field quantities are indirectly included in the reconstruction procedure. The three-dimensional reconstruction is formulated slightly differently. The calculation of stresses at an arbitrary point within a representative volume element with several hundreds of inclusions presents still computational problems [12,13]. Using the same objective functions as for the two-dimensional case and a first constraint on the topological entropy the second constraint is imposed either as a pre-selected difference between a mean and standard deviation of distances between neighbouring inclusions or as a fulfillment of statistical t-test and F-test for mean and standard deviation of distances, respectively.

Application of Stochastic Optimization

259

RECONSTRUCTION OF PLANAR DISPERSIONS The problem of reconstruction of dispersion pattern can be formulated as an optimization task. A sum of squared differences of nodal points of integral correlation function X(r) for a reference and optimized pattern is then the objective function and coordinates of inclusions center points are treated as the design variables for that problem. The objective function is minimized subject to two constraints. First constraint is imposed on values of topological entropy S, which represents first order correlation of the pattern [14]. A physical interaction between embedded inclusions is controlled by a second constraint imposed on stress interaction parameter C, which represents maximal radial stresses at inclusions interfaces [15]. A regular pattern with constraints, which correspond to the values of C and S selected for the reference dispersion is chosen as the starting configuration. Subsequent new configurations are generated by randomly disturbing coordinate of inclusion position. The Simulated Annealing global method has been chosen to solve the optimization problem [16]. The major advantage of Simulated Annealing over other methods is the ability to avoid becoming trapped at local minima. The reference image has been taken from X-ray microtomographic image of unidirectional glass-epoxy composite material, as illustrated in Fig.l. After several morphological image transformations, the centre points of fibres are recovered, which constitutes reference dispersion of points.

V-::-:::-.>"ri:-.':^/; ••.•;.•••::•. .'••'••.••'.•••• *'• ' , * * ' . ' • ' . ' .

(b)

(c)

FIGURE 1 Original reference image and three reconstructed patterns (a,b,c)

As can be seen from Fig.2, the optimization procedure leaves integral correlation functions of the reference and reconstructed pattern very close to each other. The constraints for reference pattern were found to be S=1.37 and C=13.6. The same parameters for reconstructed patterns a, b and c are respectively 1.31, 1.38 and 1.32 for the topological entropy S and 12.2, 13.0 and 12.4 for the stress interaction parameter. Lower values of C for reconstructed patterns indicate that we may expect slightly higher maximal radial interfacial stresses present in the reconstructed dispersion as compared with reference dispersion. This conclusion is supported in Fig.3, which shows longer tail values of the distribution functions for reconstructed patterns than for the reference pattern.

260

Application of Stochastic Optimization REFERENCE L JSTRUCTED

REFERENCE

L

02

0.25

\

\

\

-'

T 01

0.05

mum 0.2

, • 1'" 01b

- • i l l

025

0.05

0.1

distance r

0.15

(b)

distance r I

REFERENCE L JSTRUCTED

\ —

,

0.05

0.1

. , T-_• • « • _ • _ 0.15 02

0.25

(c)

distance r

FIGURE 2 Comparison of X(r) functions for reference and reconstructed patterns

1.2

1.4

1.6

1.8

2.0

1.2

Maximal radial stress [MPa]

A

I 3

1.4

1.6

1.8

2.0

2.2

Maximal radial stress [MPa]

reference — - reconstructed (c)

82 1.0

12

1.4

1.6

1.8

2.0

2.2

2.4

Maximal radial stress [MPa]

FIGURE 3 Stress density distributions for reconstructed patterns

If generated patterns are subject to the only constraint of non-overlapping, the corresponding density functions for the maximal radial stresses at fibre interfaces are shown in Fig.4 for three simulated patterns. There is a significant difference between stress density functions for this case and corresponding functions for reconstructed patterns. Tails of simulated dispersions are wider as compared with the reference pattern. It means that there are more fibres in the simulated dispersions than in the reference pattern, which are subject to interfacial stresses having values from the tails of the density distribution. Further discrepancies between reconstructed and simulated dispersions can be observed on the diagrams representing nearest neighbour distance distribution, Fig.5. While reconstructed dispersions provide reasonable distribution of

Application of Stochastic Optimization

261

nearest neighbour distances, the simulated patterns yield far too short nearest neighbour distances. The consequence of this fact is that corresponding stress density distribution exhibits longer and higher tails for larger stress ranges as observed in Fig.4.

— •°

reference simulated (a)

" • " reference — simulated (b)

3

I

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

1.0

Maximal radial stress [MPa]

k 1.5

2.0

2.5

3.0

3.5

Maximal radial stress [MPa]

reference simulated jc)

4

Der sity fu iction

u 0.85 1.10

Jl v^ 1.35

1.60

1.85 2.10 2.35 2-60

2.85

Maximal radial stress [MPa]

FIGURE 4 Stress density distributions for simulated patterns

0.10 0.08

A //X\\

. , ,-' ' *

I feference| I — simulated |

c g

? 0.06 t 004

1 1

; )L

-. \ V *•

0) Q

0.02-

20

Nearest neighbour distance [urn]

30

Nearest neighbour distance [u.m]

FIGURE 5 Nearest neighbour distance distribution for reconstructed and simulated patterns

RECONSTRUCTION OF SPATIAL DISPERSIONS The procedure for the reconstruction of spatial dispersions is slightly different as compared with similar procedure for planar dispersions. An efficient method to predict local stresses in representative volume element containing several hundreds of inclusions is non-existent [13] and, therefore the physical constraint related to the local stress distribution at interphases is not taken into account. Instead, the procedure of reconstruction of spatial reference pattern is performed with integral correlation function taken as the objective function and for the two cases of constraints set. The constraint imposed on values of topological entropy S is common for both cases but

262

Application of Stochastic Optimization

the second constraint is taken either as a pre-selected difference between a mean and standard deviation of distances of neighbouring inclusions (A) or as a fulfillment of statistical t-test and F-test for mean and standard deviation of distances (B). The t-test is performed to check if mean values for the analyzed distributions are equal (or not) at some confidence level. The result of F-test indicates whether variances (standard deviations) for these two distributions are (or are not) significantly different. The suitable significance level values are calculated for both tests in order to determine if these values fall within the zone of acceptance. This allows treat the distributions as consistent. Otherwise they have to be treated as different.

FIGURE 6 Reference dispersion (a) and its reconstructed counterpart (b) with Gauss radii distribution

- REFERENCE . RECONSTRUCTED

REFERENCE RECONSTRUCTED

— — »

-A \ "" 0.1

—

n.

- 1

0.15

distance r

Reference pattern

Reference pattern

Reconstructed pattern

Reconstructed pattern

IV

)5

Density line of distances to the neighbours

0.030

0.055

OQBO

0105

0.130

0.155

0.1E

Density line of distances to the neighbours

FIGURE 7 Integral correlation function and density of distances to the near neighbours for reference and reconstructed patterns with constraints A (left) and B (right)

Figure 6 shows reference and reconstructed patters for spatial dispersion with Gauss radii distribution. The comparison of results is shown in Fig. 7 where integral correlation functions and density of distances to the near neighbours are plotted for

Application of Stochastic Optimization

263

reconstructed patterns obtained when first (A) or second (B) constraints set has been applied. Values of topological entropy, mean neighbour distance and its standard deviation for the reference pattern differ from corresponding values of the reconstructed pattern by 2.8%, 9.9% and 6.2%, respectively. For constraints imposed on entropy and significance level values from t-test (for means) and F-test (for variances) values of topological entropy, mean neighbour distance and its standard deviation for the reference pattern differ from corresponding values of the reconstructed pattern by 1.7%, 2.6% and 2.7%, respectively. It is worth noting that a good agreement of results obtained for various formulations of optimization tasks is observed. CONCLUSIONS We have analysed reconstruction algorithm for spatial dispersions of inclusions. It can be used both as a method of data analysis or as a structural modelling tool to make predictions about the system, which are based on ensemble averaging methodology. The obtained solutions are not unique and a true test of their usefulness has to be performed on locally dependent physical phenomena such as nucleation and evolution of damages and initiation of failure. The reconstruction algorithm can be further extended to take into account other lower or higher order statistical descriptors that characterize the microstructure. Identification and reconstruction of micro structures with several descriptors would determine the extent to which a variety of statistical descriptors can reproduce the reference microstructure, thus shedding light on the nature of information contained in the descriptors. Furthermore, one can construct microstructures that correspond to a given set of descriptors and employ them to investigate and simulate physical phenomena where spatial patterns are of primary importance. REFERENCES 1. 2. 3. 4.

J.W. Ju and T.M. Chen, Ada Meek, 103, (1994), 103. J.W. Ju and T.M. Chen, Ada Meek, 103, (1994), 123. J.W. Ju and H. Tseng, Int. J. Solids Structures, 33, (1996), 4267. Kinney,J.H., Haupt, D.L., Nicols, M.C., Breunig, T.M., Marshall, G.W & Marshall, S.J. Nucl. Inst. andMeth. in Phys. Res. A., 347; (1994) 480. 5. Erre, D., Thomas, X., Mouze, D., Patat, J.N., Trebbia, P. & Cazaux, J. Surf. Interface Anal, 19, (1992), 89. 6. Pyrz., R. in Proc. World Aviation Conf. San Francisco, CA, paper no. 1999-01-5614,(1999). 7. Pyrz, R., in Porous, Cellular and Microcellular Materials, V. Kumar (ed), ASME MD-Vol.91, New York, 2000, p. 63. 8. Pyrz, R. & Nygaard, J., in Proc. Int. Conf. Composites in Construction - CCC2003, D. Bruno et al (eds.), Editoriale Bios, Cosenza 2003, p. 189. 9. E.R. Weibel, Stereological Methods, Academic Press, London, 1980, vol. 1 and vol. 2. 10.C.L. Yeong and S. Torquato, Phys. Rev. B, 57, (1998), 495. 11 .C.L. Yeong and S. Torquato, Phys. Rev. B, 58, (1998), 224 12.SchJ0dt-Thomsen, J. and R. Pyrz, in Proc. Int. Conf. Mesomechanics 2002, R. Pyrz et al. (eds.), Aalborg University, 2002, p. 75. 13,SchJ0dt-Thomsen, J. and R. Pyrz, in Proc. 14th Int. Conf Comp. Mat., H.T. Hahn and M. Martin (eds.), July 2003, San Diego, CD-ROM edition, ISBN 0-87263-685-2, paper no. 999. 14.Pyrz R., in Comprehensive Composite Materials, Vol.1 Fibre Reinforcement and General Theory of Composites, ed. T W Chou, Elsevier, 2000, London, 465. 15.Pyrz, R. and B. Bochenek, Int. J. Solids Structures, 35, (1998), 2413. 16.S. Kirkpatrick, C D . Gelatt Jr. and M.P. Vecchi, Science, 220, (1983), 671.

Optimal Design of Filament Wound Structures Based on the Semi-geodesic Path Algorithm Cheol-Ung Kim, Dong-Hoon Kang, Chang-Sun Hong and Chun-Gon Kim Division of Aerospace Engineering, KAIST, Korea

ABSTRACT This research aims to establish an optimal design method of filament wound structures. Filament winding is one of the most reliable and affordable production techniques for high performance composite structures such as pressure tanks, pipes and motor cases of rockets which are widely used in the aerospace application. However, the problem with filament winding is that the trajectory of the fiber path and the corresponding fiber angles cannot be chosen freely because of the stability requirement of fiber path. Most design and manufacturing of filament wound structures are based on manufacturing experiences, and there is no established design rule. In this research, possible winding patterns considering the windability and the slippage between fiber and mandrel surface were calculated using the semi-geodesic path algorithm. In addition, finite element analyses using commercial code, ABAQUS, were performed to predict the behavior of filament wound structures. On the basis of the semi-geodesic path algorithm and the verified finite element analysis method, an optimal design algorithm for filament wound structures was suggested using the genetic algorithm.

INTRODUCTION Finite element analyses, which can predict the deformation of filament wound structures, have been performed by many researchers. However, the results have been utilized only to understand structural characteristics of filament wound structures because some limited path equations were applied to the analyses. Even though such finite element analyses are helpful to design filament wound structures, most design and manufacturing of filament wound structures have been based on manufacturing experience and experiment. Thus, most designs are not optimized to account for filament wound structures. Previous research about filament wound structures are categorized into fiber path predictions, structural analyses and designs. However, there is no established design method for general filament wound structures under internal pressure satisfying given design requirements. In this study, an optimal design method of filament wound structures under internal pressure was established. Possible winding patterns considering the windability and the slippage between fiber and mandrel surface were calculated using the semi-geodesic path algorithm. In addition, finite element analyses using commercial code, ABAQUS, were performed to predict the behavior of filament wound structures. On the basis of the Correspondence Author : Division of Aerospace Engineering, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, Republic of Korea. Tel: (82-42) 869-3719, Fax: (82-42) 869-3710, Email: [email protected]

Optimal Design of Filament Wound Structures

265

semi-geodesic path algorithm and the finite element analysis method, an optimal design algorithm was suggested using the genetic algorithm and applied to a symmetric composite pressure vessel. SEMI-GEODESIC PATH ALGORITHM The design of a filament wound structure consists of the design of the mandrel shape and the calculation of the fiber path. In general, the mandrel shape can be determined by imposed design requirements such as internal pressure, volume and manufacturing convenience. When the liner or mandrel surface is given without considering winding patterns, various slip conditions must be taken into account. In this study, the semi-geodesic path equation was utilized in order to describe the realistic winding pattern on general filament wound structures [1]. da dx

1(A2 sin2 a-rr" cos2 a)~r'A2 sin a rA1 cos a

(1)

Equation (1) is defined on an arbitrary surface where a, x, 0, r, X are the winding angle, the axial coordinate parameter, the circumferential coordinate parameter, the radial coordinate parameter and the slippage tendency between the fiber and the mandrel. And more detailed derivation is shown in Reference [1]. By integrating Equation (1) with a known value, the winding angle can be calculated for the entire mandrel surface. There are two assumptions in the calculation of the thickness: the fiber volume fraction is maintained consistently and the number of fibers in a cross section is always constant. With these assumptions, the thickness along the longitudinal direction can be derived as follows:

Im, cos a, w 27ircosa

t =

r, cos a r cos a

(2)

where rc, ac, tc, np , w are radius, winding angle, thickness, number of fiber bands in a layer, and band width, respectively.

input

calculate B of • whole structure '

r(x), A,W.

calculate a range ! i

find possible a 1 i n S

^

1

^''

calci Iculate possible! wiiinding patterns |

FIGURE 1 Semi-geodesic path algorithm

266

Optimal Design of Filament Wound Structures

Windability is very important because some of the patterns calculated by Equation (1) maybe useless for the manufacture of filament wound structures unless uniform coverage is considered. The concept of windability was presented concurrently by Lossie [2] and Lowery [3]. Though notations used in the two studies are different, fundamental concepts are identical. The semi-geodesic path algorithm suggested in this study considers the fiber slippage and the windability. Figure 1 is the flow chart of the semi-geodesic path algorithm. In this research, a GUI (graphic user interface) based program was developed using Microsoft Visual C++ to perform the semi-geodesic path algorithm. PROGRESSIVE FAILURE ANALYSIS In this research, the 3-D layered solid element was utilized for finite element modeling. Progressive failure analysis was performed for the forward part of the ASTEB by the commercial code, ABAQUS. The finite element model are shown in Figure 2. In the modeling, C3D20 type elements with 20 nodes per element were used. The model has 100 elements and 1113 nodes. The modeling was performed for a 1.5 ° strip of a full tank using a cyclic symmetry boundary condition. The element size is larger at the center of the dome than that near the interface of the dome/cylinder and dome/polar opening. In the cylindrical part, 20 elements to the x-axial direction were enough to gain a converged result, but 60 elements to the meridian direction were used in the dome area. The winding path was calculated using the established semi-geodesic path algorithm. And, a preprocessor PREAFT which imposes the calculated path information on each element was developed and used. The inner pressure is 13.79 MPa (2000psi).

layered solid element 100elem. 1113nodes

cyclic symmetric

/•G plane symmetric -

x 5 scale

FIGURE 2 Finite element model and deformed shape

Optimal Design of Filament Wound Structures

267

In order to perform the progressive failure analysis, the modified Hashin's failure criterion, which is commonly used in recent studies and has many failure modes, was selected and applied to the analysis and optimal design in this research. For the purpose of failure analysis, a subroutine, USDFLD of ABAQUS ver 6.3 was coded to define the change of mechanical properties due to failure. An element failure is first identified and later the failed element is replaced with a degraded element. The degradation method should be carefully chosen because the results of progressive failure analyses often depend on the mesh size, degree of reduction, the increment size, etc. The equivalent properties of the damaged element might exist between zero values and solid ones. In this study, the stiffness reduction coefficient(SRC) varies from 0.1 to 0.9 by using Reddy's method [4]. When SRC is 0.1, the failed elements almost lose their load-carrying capacity. SRC of 0.9 means that the mechanical properties of the failed element do not decrease much compared to those of unfailed ones. The case of SRC<0.1 was excluded because the analysis becomes a conservative one. The deformation of each case is magnified 5 times in Figure 2. Figure 3 shows the comparison of results between the finite element analysis using the modified Hashin's failure criterion and the water-pressurizing test of our previous research [5]. It shows good agreement between them both in trend and quantity. Therefore, this analysis method is suitable for applying to the optimal design.

0.011 0.010

-FEM Experiment

0.009 0.008

°C

c

0.007

2

0.006

a

0.005

LL

0.004 0.003 0.002

0.001 0.000 -100

-80

-60

-40

-20

0

20

40

60

80

100

x (mm) FIGURE 3 Comparison of fiber strains between analysis and experiment

OPTIMAL DESIGN USING GENETIC ALGORITHM Design algorithm hi this study, the optimal design algorithm was established, which includes the semi-geodesic path algorithm, progressive failure analysis and genetic algorithms [6]. Figure 4 shows the flow chart of the suggested optimal design algorithm. The genetic algorithm controls the overall procedure. The windows based program for this algorithm was developed using C++ language, and it was named TDOTCOMFW.

Optimal Design of Filament Wound Structures

268 SL.11

y | Confirm design requirements Set winding angle

Calculate the range of winding angle

3: Find possible winding angles

Calculate the circumferential angfe of the whole structure

Calculate possible winding patterns

Generate initial population

Make input for FEA w

—i

save to winding f angle database V

Finite element analysis using ABAQUS -M

Change winding angle

Read output of FEA I I Genetic algorithm I I MSG path algorithm r^pa FEA

Calculate fitness

FIGURE 4 Optimal design procedure for axisymmetric filament wound structures

Application and verification The established optimal design algorithm was applied to a symmetric pressure tank of type 3 with a load sharing metallic liner for verification. The half shape of the tank is the same as the forward part of the ASTEB. The material of the composites is T800/Epoxy, and the liner is aluminum alloy 7075-T6. Basic design requirements are as follows: 1. Maximum operating inner pressure is 13.79 MPa(2000 psi). 2. The yield of the liner is not permitted. 3. The safety factor of the composite is 3.0. 4. The weight reduction is the most important goal of this design. The objective function is defined as follows J

>^Iiner

w r

yield ®yield ^^fiber

~

^f,design

>

^f,design

fiber

_ >°'liner ^ °'yield J

&

°fiber

fiber

>°'liner > °'yield

where Wmm , W, af4esign, aflber, ayidi, aliner are the possible maximum weight, the weight of the design point, the fiber directional strength considering the safety factor, the maximum fiber directional stress of the design point, the yield strength of the liner, and the maximum von Mises stress of the liner of the design point, respectively. Four design variables(the number of helical layers, the number of hoop layers, the winding angle of the cylinder part and the thickness of the liner) were set up and used in this optimal design because the goal of this application is the verification of the suggested algorithm and program. Each of them was separated to discrete values as many as 2 bits, 4

Optimal Design of Filament Wound Structures

269

bits, 5 bits and 4 bits in order to be applied to the genetic algorithm. From our previous researches, we determined the required parameters for genetic algorithm as follows; the population size was set as 100, the maximum number of generations as 100, the probability of crossover as 0.7, the probability of mutation as 0.1 and the tournament size for the genetic algorithm as 10. The initial seed value was generated randomly, and a total often optimal designs were performed. Table 1 shows the design results. Results of seven kinds were drawn. Among them, the best case, which satisfies the given design requirements, is a tank with a weight of 4.44 kg. TABLE I Design results Cases

Helical layer

Hoop layer

Winding angle

Liner

Weight

1

2

9

33.5°

1.9 mm

4.44 kg

2

3

10

34.5°

1.7 mm

4.47 kg

3

2

9

31.5°

1.9 mm

4.45 kg

4

3

10

28.0°

1.7 mm

4.50 kg

5

2

10

33.0°

1.9 mm

4.51kg

6

2

9

33.5°

1.9 mm

4.44 kg

7

2

9

33.5°

1.9 mm

4.44 kg

8

3

10

33.0°

1.7 mm

4.48 kg

9

3

9

34.0°

1.8 mm

4.58 kg

10

2

9

31.5°

1.9 mm

4.45 kg

CONCLUSION In this research, possible winding patterns considering windability and slippage were calculated using the semi-geodesic path algorithm. In addition, progressive failure analyses were performed to predict the behavior of filament wound structures. In particular, suitable element types and failure criteria for filament wound structures were studied, hi addition, on the basis of the semi-geodesic path algorithm and the finite element analysis method, an optimal design algorithm was suggested using the genetic algorithm. Finally, the developed design code was applied to a symmetric composite pressure vessel for verification. REFERENCES 1. 2. 3. 4. 5.

6.

J. Scholliers. 1992. "Robotic Filament Winding of Asymmetric Composite Parts," Ph. D Thesis (K.U.Leuven) M. Lossie. 1990, "Production Oriented Design of Filament Wound Composites," Ph. D Thesis (K.U.Leuven) P. A. Lowery. 1990. "Continued Fractions and the Derivation of Uniform-Coverage Filament Winding Patterns," SAMPE Journal, 26:57-64. Y. S. N. Reddy, C. M. Dakshina Moorthy, J. N. Reddy. 1995. "Non-linear Progressive Failure Analysis of Laminated Composite Plates," Int. J. Non-Linear Mechanics, 30(5):629-649. J. S. Park, C. S. Hong, C. G. Kim, C. U. Kim. 2002. "Analysis of Filament Wound Composite Structures Considering the Change of Winding Angles through the Thickness Direction," Composite Structures, 55:33-71. D. E. Goldberg. 1989. Genetic Algorithm in Search, Optimization, and Machine Learning, Addison-Wesley Publishing Company

Development of a Material Mixing Method for Topology Optimization of Multiple Material Structures Seog Young Han*, Soo Kyoung Lee, Jae Yong Park School of Mechanical Engineering, Hanyang University, 17 Haendang-dong, Sungdong-Gu, Seoul, 133-791, Korea

ABSTRACT This paper suggests a material mixing method to mix several materials in a structure. This method is based on ESO(Evolutionary Structural Optimization), which has been used to optimize topology of only one material structure. In this study, two criterions for material transformation and element removal are implemented for mixing several materials in a structure. Optimal topology for a multiple material structure can be obtained through repetitive application of the two criterions at each iteration. Two practical design examples of a short cantilever are presented to illustrate validity of the suggested material mixing method. It is found that the suggested method works very well and a multiple material structure has more stiffness than one material structure has under the same mass.

INTRODUCTION Topology optimization is very useful in making a conceptional design when considering weight and cost in the early design stage. An important development in topology optimization was made by Bendsoe and Kikuchi[l] who proposed the homogenization method, in which a material with an infinite number of microscale voids is introduced and the optimization problem is defined by seeking the optimal porosity of a porous medium using an optimality criterion. Mlejnek et al.[2] has accomplished shape and topology optimization using a simple energy method and a special type of function, that is, Kreisselmeier-Steinhauser function[3] for calculating effective properties. Recently, a simple method for shape and topology optimization, called Evolutionary Structural Optimization(ESO), has been proposed by Xie and Steven [4] and Chu[5], which is based on the concept of gradually removing redundant elements of the low stressed part of the material from a structure to achieve an optimal design. hi the area of MEMS, topology optimization techniques have also been actively applied. Especially, one of the thermal actuators, microgripper, has been designed by a bimorph structure[6] consisted of two materials with the different thermal strains, so that the improvement of its performance has been achieved by controlling the direction and magnitude of overall displacement effectively. hi this study, a material mixing method was suggested in order to obtain an optimal topology of a multiple material structure with the maximum stiffness under a static load based on ESO.

Correponding Author, School of Mechanical Engineering, Hanyang University, 17 Haendang-dong, Sungdong-Gu, Seoul, 133-791, Korea, FAX : 082-02-2298-46341, Email: [email protected]

Material Mixing Method for Topology Optimization

271

MATERIAL MIXING METHOD The explanation of the material mixing method for a bimaterial structure is given here in brief. Let the larger and the smaller stiffness and density of the two materials set material 1 and material 2, respectively. First of all, consider a design region made of material 1. Apply both the transformation and the removal lines for material transformation and element removal, respectively. As the first step, the elements having lower level of strain energy than the transformation line are transformed into material 2. As the second step, the elements having lower level of strain energy than the removal line which is established as the lower level of strain energy than the transformation line, are removed. An optimal topology can be obtained by iteration of this procedure at each iteration. Transformation and Removal Line TRANSFORMATION LINE The transformation line defined as eq. (1) is obtained from a journal paper [7] in this study. And the efficiency factor, a of strain energy in each element after stress analysis is defined as eq. (2). If a of a certain element is smaller than the transformation line, that is, eq. (3) is satisfied, the element is transformed from material 1 to material 2. TL = amm+Aax(

vol

5=1)"

(1)

V l

° ini,ial

« e = J ^r

(2)

a"
(3)

where, t] is the penalty factor and the threshold ratio Aa can be selected as very small value depending on the problem since it controls the range of the elements to be transformed. The elements on the area of diagonal lines under the transformation line as shown in Fig. 1 are to be transformed. This concept is similarly applied to the removal line. Penalty factor is induced to obtain an optimal topology effectively by controlling the range of the transformed elements, that is, gradually reducing the range as the number of iteration increases. It can be seen in Fig. 2 that the number of the transformed elements is reducing as iteration goes on. REMOVAL LINE The removal line was defined as eq. (4) in this study. If a of a certain element is smaller than the removal line, that is, eq. (5) is satisfied, the element is removed from the structure. The threshold ratio and the penalty factor were similarly applied for determination of the removal line. The removal line under the transformation line was obtained by controlling the sizes of the threshold ratio and the penalty factor. Procedure of Topology Optimization Optimal topology based on ESO has been obtained through stress analysis by the finite element method, material transformation by the transformation line and element

272

Material Mixing Method for Topology Optimization

removal by the removal line. Theflowchartof topology optimization process is shown in Fig. 3. This procedure is iterated until satisfying the prescribed mass or deflection constraint. = amiR+Aax(

vol

presen

'y

(4)

V0l

ini,ial

ae
(5)

EXAMPLES A Short Cantilever Beam Subject to a Concentrated Force at the Center of Free End When a short cantilever shown in Fig. 4 was subjected to a concentrated force of 300 kN at the center of free end, optimal topologies of single and two-multiple material structures were obtained using the suggested material mixing method. The quadilateral element was used and the beam was divided into the grid of 32 x 20. The used elastic modulii are listed in Table I . It was assumed that the elastic modulus of material 2 is 40% of material 1.

Element Number

FIGURE 1 Transformation and removal line

10

20

30

40

50

60

Iteration number

FIGURE 2 Reduction of the number of transformed elements

Material Mixing Method for Topology Optimization

273

FEA nf a stn inti im

Calculation of transformation & removal lines

Transformation of low strain energy efficiency elements

Removal of low strain energy efficiency elements

No

Yes

Yes

Output of topology optimization

FIGURE 3 Flowchart of the optimization process

TABLE I Material property

Material 1 Material 2

Young's Modulus 207 GPa 82.8 GPa

Density 7280 kg/mJ 3128kg/mJ

Poison's Ratio 0.3 0.3

Lx= 0.16 m

t = 0.001 m

L y = 0.10 m p ,

r

FIGURE 4 Conditions of a short cantilever

In order to investigate the topology optimization process as the materials are mixing, topology optimizations were performed for the following four cases. Those are, (1) a single material structure of material 1 with 50% mass constraint of initial mass of material 1 (2) two-multiple material structure with 40% mass constraint (3) two-multiple material

Material Mixing Method for Topology Optimization

274

structure with 30% mass constraint and (4) a single material structure of material 2 with 20% mass constraint. The obtained optimal topology of each case is shown in Fig. 5. The optimal topologies of the cases (1) and (4) are shown in Fig. 5(a) and 5(d). The results are the same as those obtained using ESO[8]. Figure 5(b) and 5(c) indicate the material mixing process of two materials properly as the mass of a structure decreases. And the deflections tend to increase as the mass of a structure decreases. Therefore, it can be verified that topology optimization was properly performed.

safes

,,K (c)

(a)

(b)

Material 2

" Material 1

FIGURE 5 Optimized topology obtained for;

(a) case(l), (b) case(2), (c) case(3), (d) case(4)

TABLE II Material property

Material 1 Material 2 Material 3

Young' s Modulus 207 GPa 144.9 GPa 82.8 GPa

Material 1

Density 7280kg/mJ 5474 kg/mJ 3128kg/mJ

(b) Material 2

Poison's Ratio 0.3 0.3 0.3

Material 3

FIGURE 6 Optimized topology obtained for a structure consisted of (a) one material (b) two materials (c) three materials

Material Mixing Method for Topology Optimization

275

TABLE IH Final masses of optimal topologies

Constitution Mass

1 Material 0.0500 kg

2 Materials 0.0475 kg

3 Materials 0.0449 kg

A Short Cantilever Beam Subject to a Concentrated Force at the Right End of Free End When a short cantilever beam is subjected to a concentrated force of 300 kN, and the maximum deflection is limited to 0.8 mm at the right end of free end instead of the center of free end in Fig. 4, optimal topologies of single, two and three multiple structures were obtained using the suggested material mixing method. The elastic modulii used in this example are listed in Table II. Since this example dealt with a three multiple material structure, two transformation and one removal line were implied. The obtained three optimal topologies are shown in Fig. 6, and the final masses were obtained under the maximum deflection constraint as shown in Table IH. Since the optimal topology of a three-multiple material structure has the smallest mass, it is known that a three-multiple material structure has the largest stiffness comparing with the other optimal structures under the same mass constraint. CONCLUSIONS hi this study, a material mixing method has been developed based on ESO in order to obtain an optimal topology of a multiple material structure. From the results of the presented examples, the following conclusions are obtained: (1) Introducing the concepts of the transformation and removal lines, optimal topologies have been obtained by iterating material transformation and removal. (2) Inducing the threshold ratio and penalty factor to establish the transformation and removal lines, the removal ratio was varied from 20% at the beginning to 1% at the last iteration. Therefore, it is known that the convergence rate in this study is much faster than the ordinary ESO, of which removal ratio is usually chosen as 1 or 2% in static problems. (3) It was found that the optimal topology of multiple materials has larger stiffness than that of single material under the same mass. REFERENCES 1. 2. 3. 4. 5. 6.

7. 8.

Bends0e M. P. and Kikuchi N., 1988, "Generating Optimal Topologeis in Structural Design Using a Homogenization Method," Comp. Meth. Appl. Meek Engng., Vol. 71, pp. 197-224. Mlejnek H. P. and Schumacher R., 1993, "An Engineer's Approach to Optimal Material Distribution & Shape Finding," Comp. Meth.. Appl. Mech. Engng., Vol. 106, pp. 1-26. Kreisselmeier G. and Steinhauser R., 1979, "Systematic Control Design by Optimizing a Vector Performance Index," IFAC Symp. Computer Aided Design of Control Systems, Zurich, Switzerland. Xie Y. M. and Steven G. P., 1993, "A Simple Evolutionary Procedure for Structural Optimization," Comput. Struc. Vol. 49, pp. 885-896. Chu D. N., Xie Y. M., Hira A. and Steven G. P., 1996, "Evolutionary structural optimization for problems with stiffness constraints," Finite Elements in Analysis and Design, No. 21, pp. 239-251. Luzhong Yin, G. K. Ananthasuresh, 2002, "A novel topology design scheme for the multi-physics problems of electro-thermally actuated compliant micromechanisrns," Sensors and Actuators A: Physical, Vol. 97-98, pp. 599-609. Qing Li, Steven G.P., Querin, O.M., Xie Y.M., 2000, "Structural Topology Design with Multiple Thermal Criteria," Engineering Computations Vol. 17, pp. 715-734. Han S. Y., 2000, "An Improved Element Removal Method for Evolutionary Structural Optimization," KSME International Journal, Vol. 14, No. 9, pp. 913-919.

Structural Design of a 750kW Composite Wind Turbine Blade C. K. Jung, S. H. Park and K. S. Han* Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, KOREA

ABSTRACT A GFRP based composite blade was developed for a 750kW wind energy conversion system of type class I. The blade sectional geometry was designed to have a general shell-spar structure. The load cases specified in the IEC61400-1 international specification were considered. For withstanding all relevant extreme loads and fatigue loads, the structural analysis for the complete blade was performed using a commercial FEM code. The static load carrying capacity, buckling stability, blade tip deflection, natural frequencies at various rotational speeds and fatigue strength were evaluated to satisfy the strength requirements in accordance with the D3C61400-1 and GL Regulations. The fatigue life more than 20 years was calculated on the basis of the Miner's rule and the Goodman diagram. For designing a lightweight blade, the thickness and the lay-up pattern of the skin-foam sandwich structures were optimized iteratively using the DOT program. T-bolts were used for joining the blade root and the hub, which were modeled using a 3D FE volume model. In order to confirm the safety of the root connection, the static stresses of the thick root laminate and the steel bolts were predicted by taking account of the bolt pretension and the root bending moments. The calculated stresses were compared with the material strengths.

INTRODUCTION As the wind turbine size grows to MW class, the wind turbine blade also becomes bigger. Therefore the material of the blade has been changed from metals and woods to composites to achieve high structural performance. Nowadays most wind turbine blades are made of GFRP to reduce the weight though CFRP is also used for limited case because of high price. The wind turbine blade should have an operation life more than 20 years. During operation, continuous loads such as drag, lift and gyroscopic force, exist. Also the wind fluctuation and yawing of thee turbine cause the blade to vibrate. Accordingly, a wind turbine blade should be designed in consideration of these static, vibration and fatigue problem to obtain the structural stability. And the blade-hub connection should sustain all the loads from blade in lifetime, hi the connection, the laminate and bolts are deformed unevenly because of their differing forms and stiffnesses, so the detail analysis of this part should be considered [1]. hi this paper, the structural design and analysis for a 750kW wind turbine blade are presented. The stress analysis for extreme loads, natural frequency extraction, buckling * Corresponding Author, Department of Mechanical Engineering, Pohang University of Science and Technology, San31 Hyoja-dong, Nam-gu, Pohang, 790-784, KOREA, fax: +82-54-279-2845, [email protected]

277

Structural Design of a 750kW Composite Wind Turbine Blade

stability analysis, fatigue life estimation and T-bolt connection analysis are performed. For light blade design, the thickness and lay-up pattern of laminate are optimized by iterative calculations. STRUCTURAL DESIGN Structure and Materials The blade is designed for type class I system according to the IEC61400-1 [2]. The total length of the blade is 24.3m. A typical structure of wind turbine blade is Fig. 1. It consists of an upper and a lower shell with spar consisting of UD(uni-directional) spar caps and one multi-axial sandwich spar web each as supporting structure. The spar caps are designed in UD glass/epoxy prepreg, the shells and the spar webs in biaxial glass/epoxy prepreg and the blade root reinforcement in a mixture of UD and biaxial glass/epoxy prepreg. Where the UD spar caps do not support the shell, it is built as sandwich structure with glass reinforced PUR(polyurethane) foam. Material properties are listed in Table I. The ultimate strength and strain are the characteristic value [3]. FINITE ELEMENT ANALYSIS Model The finite element program is ABAQUS. The element is 4-node S4 shell element [4] and the total number of element is 5600. 33 element groups along the span direction are used to model the thickness distribution of each material. Along the chord direction, the skin is separated into three parts that have different material thickness. Basically the thickness is maximum value at the blade root and becomes thin along the span direction. Total mass of the model is 1900kg.

Trailing Edge

FIGURE 1 Typical configuration of wind turbine blade

TABLE I Material properties

Ei(MPa) E 2 (MPa) V

G 12 (MPa) p(kg/m3) SL(MPa) eL(%)

U D prepreg 41600 7300 0.3 4000 1768 959 2.15

Biaxial prepreg 22000 22000 0.3 5500 1518 401 2.12

PUR foam 70 70 0.2 19 119 -

Structural Design of a 750kW Composite Wind Turbine Blade

278

TABLE II Flapwise deflection and maximum stress/strain Wind Speed [m/s]

Deflection|m]

Max. Stress[Mpa]

Max. Strainfus]

10 25 70

1.45 1.30 2.14

41.6/-33.8 38.3A32.6 82.1/-79.7

1547/-1334 1416/-1191 3184/-3190

Static Analysis Three load cases are considered for stress/strain analysis. First two are lOm/s and 25m/s wind condition during normal operation. The last is 50-year extreme wind speed case. The load safety factor is 1.35 and the material safety factor is 2.70. The flapwise tip deflection, maximum stress and strain for each load case are listed in Table H Comparing with the ultimate strength, the maximum stress of 70m/s wind case results in the minimum reserve factor of 1.81. The stain is also small and the reserve factor is 6.7. Fig.2 and Fig.3 are the stress contours of the skin and the web for 70m/s wind condition. The maximum stress occurs in the middle of blade where the thickness changes steeply from thick root area to thin profile area. The allowable stress in the skin is 148Mpa and the results show the stress is low to have sufficient static safety.

FIGURE 2 Stress contour for 70m/s wind (skin)

FIGURE 3 Stress contour for 70m/s wind (web)

Structural Design of a 750kW Composite Wind Turbine Blade

15

20 25 rpm

30

35

279

40

FIGURE 4 Campbell diagram

The stress in the web is low but the stress concentration occurs at the joint between the webs and the spar caps. Like the stress distribution of the skin, the upper side is under compression and the lower side is under the tension. Natural Frequency Analysis The blade should be designed to avoid resonance during operation. The 1st flapwise and edgewise natural frequencies are calculated as 2.4 and 3.9, respectively. Fig. 4 is the Campbell diagram which shows the natural frequencies vs. various rotational speed of the blade. Fl and LI mean the 1st flapwise and 1st lead-lag(edgewise) frequency, respectively. To avoid resonance, the 1st flapwise natural frequency should have ±10% difference from the excitation frequencies at the nominal rotational speed of 25rpm. For three-bladed wind turbine, 3P is most important excitation frequency. The Campbell diagram shows that the resonance will not occur in the operation range of 9-27 rpm. Buckling Analysis The buckling modes and corresponding eigenvalues are analyzed for the load case of 70m/s wind condition. First three eigenvalues(or load factors) are 1.479,1.481 and 1.499. The buckling load factor of 1.479 means the 1st mode buckling occurs at the base load times the load factor. The buckled positions are R=19m, R=7m and R=l 3m at middle skin area where the maximum compressive stresses occur. It can be concluded that the buckling stability is fairly obtained, because the base condition of the buckling analysis is 70m/s wind condition. Fatigue Analysis 14 load cases are simulated numerically as 10-minites time series for fatigue. To estimate the load series during 20-year operation, Rayleigh distribution is assumed for one-year wind distribution. This load-time series are converted into strain-time series using unit load and unit strain concept. Then the random strain-time series are transformed via a rainflow cycle counting method into a sequence of bins of constant strain mean and amplitude, which generate the From-To-matrix(Markov matrix) that contains the number of cycles counted at an combination of mean and range. The allowable cycles for each

280

Structural Design of a 750kW Composite Wind Turbine Blade

Laminate Extension bolt \

Pitch bearing \

\ Transverse bolt FIGURE 5 Composition of T-bolt connection

combination of mean and range can be calculated with S-N curve and strain based Goodman diagram for the composite laminate. Finally, the total fatigue damage is estimated using Eq.(l). The damage cannot exceed 1 for 20-year fatigue life [5,6]. The reserve factor of element 3464(R=llm, lower middle skin) and element 4145(R=8.8m, lower middle skin) shows the minimum value of 1.2. This area is the weakest point against fatigue.

where D is the fatigue damage, ns is the counted cycle, N{ is the allowable cycle at a certain mean and amplitude combination, R is the reserve factor and k is the reciprocal gradient for S-N curve [3]. T-bolt Connection Analysis The blade connection to the' pitch bearing is established with so called T-bolt-connection consisting of an extension bolt and a cylindrical cross bolt. Fig. 5 is a typical view of the T-bolt connection [7]. The cross bolt transmits the loadsfromthe blade root to the extension bolt and the loads passed through the extension bolt reach the pitch bearing. The laminate thickness of the root is 75mm. The diameters of the extension bolt and the cross bolt are 27mm and 54mm, respectively. The total number of T-bolt is 40. The stress is calculated for the maximum root bending moment. The result is listed in Table III. Comparing with the ultimate strength of the bolt, the static safety factor comes to be 1.3. It can be concluded the connection is safe for all load cases. TABLE III Maximum stress and strength of T-bolt connection

Root Laminate Bolts

Max. Stress[Mpa] 44/-230 809/-376

Strength[Mpa] 690/-900 1040

S.F. 65~ 1.3

Structural Design of a 750kW Composite Wind Turbine Blade

281

CONCLUSIONS A structural design procedure for IEC type class I composite wind turbine blade using finite element analysis is presented. Our conclusions are as follows 1. The blade structure is analyzed by means of static stress/strain, natural frequencies, buckling and fatigue analysis according to IEC standard. 2. The material thickness is optimized by iterative calculations of stress, natural frequencies, buckling stability and fatigue life to minimize the weight of the blade. 3. The T-bolt connection is designed with 3D volume FE model and the safety is calculated.

ACKNOWLEDGMENTS This work was supported by Korea Energy Management Corporation and UNISON.

REFERENCES 1.

2. 3. 4. 5.

6. 7.

Ladean R. McKittric, Douglas S. Cairns, P.I. John Mandell, David C. Combs, Donald A. Rabern and R. Daniel VanLuchene. 2001. "Analysis of a Composite Blade Design for the AOC 15/50 Wind Turbine Using Finite Element Model", SAND2001-1441 IEC. 1999. IEC Standard 61400-1 Part I : Safety Requirements Germanischer Lloyd. 1999. Regulations for the Certification of Wind Energy Conversion Systems HKS Inc. 2002. ABAQUS6.3 User's Manual T.P. Philippidis, A.P. Vassilopoulos, K.G. Katopis and S.G. Voutsinas. 1996. "THIN/PROBLEM : A Software for Fatigue Design and Analysis of Composite Rotor Blades", Wind Engineering, 20(5):349-362 Marshall, L. Buhl. 2002. GPP Version 6 User's Guide, NWTC, pp. 28-29. R. Osthorst, R.Fuhrhoff and R.Kortemkamp. 2002. "Measurements and Calculations with the Aim of Optimizing the T-bolt Blade-Connection Joint", Technical Report, Aerodyn

Axiomatic Design of Composite Track Pin Dong Chang Park, Seong Su Kim, Seung Min Lee, Dai Gil Lee Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Korea

ABSTRACT Track links for high mobility tracked vehicles usually consist of track shoe bodies, track pins, rubber pads, end-connectors, and rubber bushings. Since the track pin is subjected to large transverse track tension from the track link, conventional track pins for high mobility vehicles are usually made of high strength steel, such as forged chrome-molybdenum steel, which increases the weight of tracked vehicles due to the high density of steel. Weight reduction has been the principal goal of many of the experimental track programs since World War II. However, great weight reduction in the track pin has not been achieved for several decades except a few experimental works. Therefore, in this paper, the axiomatic design approach was employed to design a lower weight track pin with composite materials. From the design of composite track pin, the weight reduction of 50% as well as better endurance life was achieved.

INTRODUCTION In these days, the weight reduction of track links for military vehicles has been great concern to improve the mobility and operational cost of tracked vehicles. The operational cost is mainly due to high fuel consumption and short life of the track components of military tracked vehicles. Therefore, the weight reduction of track links with the required durability is indispensable. Track links for high mobility tracked vehicles usually consist of track shoe bodies, track pins, rubber pads, end-connectors, and rubber bushings. In general, the conventional track link occupies about 10% of the gross vehicle weight (GVW), and the track pin's weight is about 25% of the track link weight. For example, the weight of the track pin comes up to 1500 kg for the GVW of 60 tons. Therefore, the weight reduction of track pin is necessary to develop the light weight track. The track link transfers the driving torque from the engine to the vehicle by the friction force between the ground and the track rubber pad. In addition to torque transmission, the track link absorbs impact load from the ground. The required strength of the track link is order of 105N in the longitudinal direction, in addition to various smaller loads from the ground and roadwheels. Since the track pin is subjected to large transverse track tension from the track link, conventional track pins for high mobility vehicles are usually made of high strength steel, such as forged chrome-molybdenum steel rods, which increases the weight of tracked vehicles due to the high density of steel. The increase of track weight also increases the rolling resistance of tracked vehicles, which decreases the fuel efficiency and mobility of the tracked vehicle. Therefore, the weight reduction of track * Corresponding Author, Department of Mechanical Engineering, KAIST, 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea, Phone: +82-42-869-3261,5202, Fax: +82-42-869-5221, e-mail: [email protected]

Axiomatic Design of Composite Track Pin

283

pins is an important design factor for tracked vehicles. Another design requirement for the track pin is high flexural rigidity to distribute track tension load uniformly on the rubber bushing. Pins with low flexible rigidity cause uneven load distribution and excessive bushing wear at the ends of pin due to the pin bending [1], which results in the decrease of bushing life. Another important requirement for the new track pin is easy maintenance requirements that the new track pins should be fully replaceable and interchangeable with the conventional ones. These three requirements of "to transmit the required track tension load", "to make the endurance life of the rubber bushing longer than the required life"," and "to provide an easy maintenance", under the constraints such as cost and weight reduction target, are not easy to satisfy simultaneously with conventional metal, but can be satisfied by fiber reinforced composite materials. Carbon fiber reinforced composite materials might be employed to solve the problem of cylindrical pins owing to its high specific stiffness and high strength [2]. However, there have been few attempts on the composite track pins, and the relation between the rubber bushing life and the composite track pin stiffness was little investigated. Therefore, in this paper, several composite materials were employed for the track pin design to reduce the weight of track pin as well as to enhance the fatigue life of rubber bushings. Especially the effects of shear stiffness of the composites on the life of rubber bushing were investigated. CONCEPT OF AXIOMATIC DESIGN The basic postulate of the axiomatic approach to design is that there are fundamental axioms that govern the design process [3]. Two axioms were identified by examining the common elements that are always present in good design. They were also identified by examining actions taken during the design stage that resulted in dramatic improvements. The first axiom is called the 'Independence Axiom'. It states that the independence of functional requirements (FRs) must always be maintained, where FRs are defined as the minimum set of independent requirements that characterizes the design goals. The second axiom is called the 'Information Axiom', and it states that among those designs that satisfy the Independence Axiom, the design that has the smallest information contents is the best design. When the information content is greater than zero, information must be supplied to satisfy the FRs at all times. Because the information content is defined in terms of probability, the second axiom also states that the design that has the highest probability of success is the best design. DESIGN OF COMPOSITE TRACK PIN hi the double pin type track link as shown in Figure 1, the shoe bodies are connected with each other by the track pin and the end-connectors. When the track tension force, F, is applied on the track link, the concentration of shear forces occurs at both ends of the track pin near the end-connectors. Also the shear force in the rubber bushing is produced as the rubber bushing is pressed on the pin. The calculated maximum stress for the current steel pin was 1080 MPa, due to the track tension based on the simply supported beam under a central concentrated load. The high strength steel pin of 1200 MPa has been used for the track pin. During the operation of tracked vehicles, relative rotation between the adjacent track shoe body and the pin was ±8 degrees. Figure 2 shows the free body diagram of the track pin during rotation.

284

Axiomatic Design of Composite Track Pin

rubber bush

shoe body

TRACK PIN

T/L

FIGURE 2 Torque on the track pin and rubber bushings

FIGURE 1 Schematic diagram of a track assembly

The functional requirements of the track pin are FRi = Transmit the required track tension (100,000 N). FR2 = Make the rubber bushing life longer than the required life. FR3 = Provide an easy maintenance. Three DPs for satisfying these FRs are stated as DPi = Strength of pin material DP2 = Stiffness of pin material DP3 = Pin end shape To be competitive with the conventional steel track pin, the cost of the composite track pin with maintenance cost should be lower than the conventional high strength steel track pin. Also, the weight reduction of the new track pin should be larger than at least 50% compared with the conventional track pin to earn the budget to develop the new track pin. Therefore, the constraints for the new track pin design may be dictated as follows. Ci = Weight of the track pin (smaller than 50% of the conventional track pin weight). C2 = Minimize the total life cost of the track pin. The design equation for the track pin may be written as FR X FR [- 0 FR X

0 X 0

0 \DPA 0 X

W k

(1)

Since the configuration of a track pin is limited by the dimension of the track shoe body, there is littlefreedomto change the shape of track pin to reduce the pin weight and to meet the bushing life requirement. The only way to fulfill the FRi and through DPi is to use fiber reinforced composite materials without violating the constraint Ct because metal materials such as steel or aluminum have low specific strength. Therefore, unidirectional glass fiber/epoxy composites (UGN 150, SK Industries) and carbon fiber/epoxy composites (USN 150, SK Industries) were chosen as substitutes for the present high

Axiomatic Design of Composite Track Pin

285

in

Track Tension

Rubber bushing FIGURE 3 Finite element model of the bushing and pin

strength steel, because the tensile strengths of the glass and carbon fiber/epoxy composites are 1000 MPa and 2300 MPa, respectively. Decomposition of FR 2 and DP 2 Branch The endurance life of the rubber bushing is affected by its compressive and shear strains because the rubber bushing is deformed in shear and compressive modes as shown in Figure 3. Therefore decompositions of FR2 and DP 2 branch were performed considering both shear and compressive strains. The decompositions of FR 2 and DPs for satisfying the decomposed FRs are stated as FR2i = Reduce the compressive strain of the rubber bushings FR22 = Reduce the shear strain of the rubber bushings DP12 = Flexural stiffness of pin material DP 22 = Shear stiffness of pin material The design equation for the impact beam may be written as

FR.

X

0

DR

FR12

0

X

DP,

(2)

Since the design matrices are half triangular and diagonal, respectively, the new track pin with composite materials can be realized. EFFECTS OF PIN STIFFNESS ON THE RUBBER BUSHING LIFE hi order to investigate the relation between the rubber bushing strains and the pin stiffness, the stresses and strains of the rubber bushing under torque were calculated using finite element analysis using ABAQUS 6.3 (Hibbitt, Karlsson & Sorensen, Inc., USA) - a commercial software. Besides the finite element analysis, the closed form solution for the shear strain distribution of single lap joint was adopted [4]. The track pin and shoe body were considered as the inner and outer adherends, respectively. The rubber bushing was considered as an adhesive with linear elastic material properties. Even though the strain of the bushing could be calculated easily using the closed form solution, the strains from the linear analytic model were found to be much smaller than those of the finite element analysis results because the linear joint model could not depict well the nonlinear elastic behavior of the rubber bushing when the shear strain was above 50%. Therefore, the finite element analysis was employed to calculate the strain of the bushing with the nonlinear elastic rubber properties.

Axiomatic Design of Composite Track Pin

286 - Track Pin -Rubber Bushing

(a) - Track Pin -Rubber Bushing

1

z

— Center Line

z = 280

(b) FIGURE 4 Finite element model of the bushing and pin, (a) solid pin, (b) hollow pin

Figure 4 shows the finite element mesh for the rubber bushing and the track pin in which quadratic quadrilateral axisymmetric elements with torsion (CGAX8R) were used for the track pin and the rubber bushing. Figure 4(a) shows the finite element model of the solid pin. Figure 4(b) shows the finite element model of hollow type track pin in which the total numbers of nodes and elements were 800 and 2641, respectively. The size of the elements was decreased towards both ends of rubber bushing range for the accurate calculation of the shear strain. All the nodes on the outer surface of the rubber bushing were fixed because there is no sliding between the bushing and the shoe body. The Mooney Rivlin model with constants Cio = 0.25 MPa and Coi= 0.18 MPa were used to model the hyper-elastic properties of the rubber bushing as follows:

+ x3 -:

(3)

where, W'x& strain energy function, Xis extension ratio. ANALYSIS AND EXPERIMENTAL RESULTS In order to investigate the effect of torsional rigidity of the pin on the strain of the rubber bushing, four kinds of material were employed for the track pin such as steel, unidirectional glass fiber/epoxy composites, hybrid composites composed of glass and carbon fiber/epoxy, and carbon fiber/epoxy laminates. The cross sections of the three pins were same. The shear moduli of the materials were 80 GPa, 4.4 GPa, 11 GPa, and 24 GPa, respectively. The rubber bushing has the maximum shear strain at the both ends (z=0, z=280 mm), and the minimum strain at the center of the track pin (z=140 mm) as shown in Figure 5(a). The shear strains of the rubber bushing on the four kinds of pins were compared as shown in Figure 5(b), where shear strain ratio value is 1.0 for the maximum strain of the bushing on the solid steel pin. The shear strain of the rubber bushing decreased as the shear modulus of the pin material decreased. The strains of the steel solid pin and hollow pin were almost same with each other. The shear strain of the rubber bushing on the glassfiber/epoxycomposite pin was 31% ~ 60% less than that on the steel pin, which was caused by the low torsional rigidity of the composite pin (5.5% of the steel pin). The low shear strain of the bushing might increase the endurance life of the bushing, because the fatigue life of rubber part, Nf, is given by Nf = oW*3 (a and j3: material constants, and W: strain density) [5]. Flexural tests were performed for the conventional steel track pin and the newly developed composite track pin, and the deformations of the pins were measured as shown in Figure 6. The maximum compressive strain of the rubber bushing could be obtained from the above pin deformation. The composite pins satisfied

Axiomatic Design of Composite Track Pin

287

the FR], and the compressive strain of the rubber bushing on the composite pin is bigger than that on the steel pin by 13%. But, rubber bushing is more vulnerable to fail under high shear strain than under high compressive strain. Therefore, the life of rubber bushing on the composite track pins will be longer than that on the steel pin. Figure 7 shows the newly developed composite track pin whose weight is only 50 % compared with the conventional steel pin. Pin end was designed to have grooves at both ends to satisfy FR3 through DP3.

Solid Steel Hollow Steel UGN150 Hybrid USNLam. ...

% 0.6

120

150 180 210 240

-+~ Max Strain • • • M i n . Strain

270

10 20 30 40 50 60 70 SO Shear Modulus of Track Pin (GPa)

Z (mm)

(a) (b) FIGURE 5 Rubber bushing strain w.r.t the composite track pin stiffness, (a) rubber bushing strain variation in longitudinal axis, (b) effects of pin shear modulus on the bushing shear strain

Steel Cap

1.5

2.0

2.5

3.0

3.5

Displacement (mm) Composite Tube 2"

FIGURE 6 Deformation of the bushing

Composite Tube 1

FIGURE 7 Configuration of the composite track pin

DISCUSSIONS hi this research, composite track pins for high mobility tracked vehicles were designed using the axiomatic design approach. The weight reduction for the composite pin was 50% compared to the conventional steel pin while the composite track pin satisfied all the functional requirements or the track pin. It is expected that the endurance life of the rubber bushing will be increased because the shear strain of the rubber bushing on the composite pin is 31% less than that of the conventional steel pin. REFERENCES 1. 2. 3. 4. 5.

U.S. Army Material Command. 1967 AMCP 706-356, Automotive Series Automotive Suspensions, Engineering Design Handbook. Wiesner et al. 1988. "Arrangement for the connection of the track links of endless crawler track vehicles", U.S patent no. 4735465. Lee, D.G., and Suh, N.P. 2004(will be published). Axiomatic Design and Fabrication of Composite Structures, Oxford University Press Adams and Peppiatt. 1977. "Stress analysis of adhesive bonded tubular lap joints," Journal of Adhesion, Vol. 9, pp. 1-18. Mars and Fatemi. 2002. "A literature survey on fatigue analysis approaches for rubber," International Journal of Fatigue, Vol. 24, pp. 949-961.

Characterization and Design Optimization of FRP Composite Modular System for Slab-on-Girder Bridges Lijuan Cheng and Vistasp M. Karbhari Department of Structural Engineering, MC-0085 University of California, San Diego, La Jolla, CA 92093-0085, USA

ABSTRACT This paper presents the analytical and experimental characterization results of a modular slab-on-girder bridge system consisting of a steel-free concrete slab reinforced by fiber reinforced polymer (FRP) composite deck panels and composite rectangular girders. The analytical predictions using finite element method compared well with the full-scale experimental results of the components and system tests.

INTRODUCTION Concrete slab-on-girder bridges have conventionally been the most common and basic solutions for short and medium span bridges. However, many existing reinforced concrete bridges have been found to be structurally deficient due to steel corrosion and subsequent concrete degradation [1]. Fiber Reinforced Polymer (FRP) composite materials have been found to have potential as replacements for the steel reinforcement in concrete slabs in the form of tendons, 2D/3D continuous grids and gratings [2] and flat panels [3]. Research work on bridge girders made of composite materials has also been performed [4,5]. Recent investigations on bridge systems have been focused on configurations consisting of all-FRP decks supported by steel/concrete or FRP beams [3,6]. However, research work on hybrid FRP/concrete modular bridge systems via both component/system level investigation and field demonstrating project has been limited. This paper presents results of an ongoing study on a new steel-free FRP/concrete slab-on-girder bridge system recently developed at UCSD. The system uses rectangular box girders made of hybrid E-glass-carbon fiber reinforced composites and a steel-free concrete slab cast on carbon fiber reinforced composite deck panels that are snap-locked to the girder top as shown in Figure 1. Prefabricated carbon fiber reinforced composite snap-in stirrups are provided for the horizontal shear transfer between the slab and girders. The objective of this study is to fully characterize structural response at both component and system levels through full-scale experiments and numerical analysis.

'Correspondence Author. Department of Structural Engineering, University of California, San Diego, 9500 Gilman Dr., Mail Code 0085, La Jolla, CA 92093-0085, Fax: (858) 534-6373, Email: [email protected]

FRP Composite Modular System for Slab-on-Girder Bridges

© Shsar Stirrup

289

(Unit: mm)

© Fiber Reinforced Concrete Deck

FIGURE 1 Steel-free FRP/concrete modular slab-on-girder bridge system

STEEL-FREE FRP/CONCRETE DECK The deck panel, serving as both flexural reinforcement and permanent formwork for concrete slab, includes a bottom plate with end hooks and rectangular stiffeners as well as surface shear ribs. Figure 2 shows good correlation between Finite Element Analysis (FEA) based simulations [7] and test results from full-scale flexural test of two simply supported 610-mm wide slabs with an AASHTO wheel load applied at mid-span. Diagonal cracks initiated at the shear ribs were observed due to combined flexural compression and tension shear. In the FEA model, 4-node linear-elastic shell elements were used for the FRP composites and 8-node brick elements with nonlinear response were used for concrete. Perfect bond was assumed for the slab-deck interface. 0.2

5

Mdspan Displacement (in) 04 <X6_

10 15 tvfidspan Displacement (mm)

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0 1500 3000 Mdspan Strain (le-6)

4500

6000

FIGURE 2 Flexural test of steel-free FRP/concrete deck

FRP COMPOSITE RECTANGULAR GIRDER The rectangular composite girders are formed of E-glass/vinylester with an additional layer of unidirectional carbon fiber within the girder bottom flange. A "dovetail" shape is designed for the girder cap to provide an anchorage zone for the panels and the shear stirrups and the cavities are filled with polymer concrete to stabilize the composite walls. Shear ribs are included along the central strip of the cap for shear interlock. Figure 3 shows good correlation between a FEA model and test

FRP Composite Modular System for Slab-on-Girder Bridges

290

results from a 8.534-m long wet lay-up composite girder tested under four-point bending with simple supports at the ends. The encountered failure mode seen after large displacement was initiated by debonding of the short lap splice length in the glass fabric at girder bottom flange at mid-span and followed by debonding and rupture of the unidirectional carbon fiber layers. ~—Test * Beam

Midspan displacement (in) . __ _4 6 8_...

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FIGURE 3 Four-point bending test of composite rectangular girder

A refined numerical analysis of the laminated composite girder was performed using CLT and the Tsai-Wu failure criterion. First-Ply-Failure (FPF) Criterion was implemented and the results compared well with test data as seen in Figure 3. 2500( 2000

Midspan displacement (m) 4 6 8

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FIGURE 4 Girder load-displacement response using ply failure criteria TABLE I Failure progression history Failure sequence 1 2 3 4 5 6 7 8 9 10 11 12 13

Location

Ply #

GBOT' GBOT GBOT GBOT GBOT GBOT GWEB" GWEB GWEB GWEB GWEB GWEB GBOT

1 4 24 36 43 46 1 4 33 30 23 11 48

When Scathon reaches the design ultimate

Failure load kN[kip] 1592 [358] 1600 [359.5] 1642 [369] 1641 [368.8] 1642 [369] 1646 [370] 1736 [390] 1738 [390.5] 1562(3511 1584 [356] 1602 [360] 1651 [371] 2059[463]

Displacement at failure mm [in] 197 [7.756] 198 [7.795] 200 [7.884] 204 [8.039] 205 [8.069] 206 [8.128] 219 [8.629] 220 [8.655] 198 [7.8141 203 [7.981] 206 [8.124] 214 [8.4171 268 [10.54]

Failure mode TRT'" TRT TRT TRT TRT TRT TRT TRT TRT TRT TRT TRT TRT

Strain in carbon (mm/mm) 0.008471 0.008554 0.008720 0.008763 0.008814 0.008882 0.009419 0.009467 0.009014 0.009197 0.009359 0.009699 0.012160

220 [8.673]

--

0.010000

1694 [381]

GBOT - girder bottom flange; GWEB - girder web;

100

Dead load i

TRT - transverse resin tension failure

FRP Composite Modular System for Slab-on-Girder Bridges

291

In addition, a simple beam theory model was used based on the criteria that the carbon fiber in the bottom flange reaches strain design limit of 0.01. Figure 4 shows the girder mid-span displacement response using Ply-by-Ply-Failure (PPF) Criterion and the sequence of ply failures is shown in Table 1. A parametric study was conducted to assess the effect of girder overall depth, carbon fiber amount and girder span length (Figure 5). The FPF load was found to increase with carbon fiber amount and this increase was more substantial for deeper girders at shorter spans than for shallower girders with longer spans. Total Thickness of Carbon Fiber Layer (in)

¥ 6000

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FIGURE 5 Parametric study of rectangular girder

SLAB-ON-GIRDER SYSTEM ASSEMBLY The entire bridge can be assembled from the modular components by first placing the deck panels on the top of the girders, then installing the shear stirrups by snapping them through the girder top groves, and finally casting the polypropylene fiber reinforced concrete slab mixed with fibers on top of the panels. A full-scale twogirder system assembly was experimentally tested with pins at one end and rollers at the other. No visible damage was observed under flexural loading under simulated wheel loads equivalent to 2 times the factored axial load applied on the center of the slab (Figure 6). Midspan Displacement (in) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 150

2 x Factored wheel load 600

400

Factored wheel load

j

200

5

10 15 Midspan Displacement (mm)

20

FIGURE 6 Load-displacement response of slab flexural test of system assembly

292

FRP Composite Modular System for Slab-on-Girder Bridges

Application of wheel loads on the slab directly above the girders (instead of slab center) to simulate global flexural behavior showed linear elastic response (Figure 7). Slippage at the girder-deck interface was observed at the shear span regions with the maximum value of 1 mm in the middle of the shear span but not in the middle pure bending region. Midspan Displacement (in) 0.8 1.2 1.6

0.4

400

3.5 x Factored shear demand /•* [Factored F

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flexural demand

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FIGURE 7 Global flexural test results of system assembly

At final failure, the load-displacement response of the system displayed essentially bi-linear response with a "softening point" (Figure 8), beyond which both cracking in the slab and slippage at deck-girder interface began to develop substantially. A quarter-span finite element model with idealized rigid connections for the deck-slab and deck-girder interfaces was used and results were seen to correlate closely to the test results (Figures 6, 7, and 8). c

1

Midspan DispU cement (in) 2 3 4

>t: Phase5 4000 _—•—Te • -Tc t: Ptase3 * FCA (Strain Criteria)

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Quarter span finite element model of two-girder system: Number of elements Number of nodes Number of D.O.F.'s

: 18363 :24023 : 90078

FIGURE 8 Final failure of system global flexural and finite element model

SUMMARY The characterization results for the structural behavior of the steel-free FRP/concrete modular slab-on-girder bridge system are presented in this paper. Good performance was obtained at both the full-scale component and system levels. Finite element analysis method and moment-curvature analysis method were found to be capable of predicting the structural response of the bridge components and the assembled system.

FRP Composite Modular System for Slab-on-Girder Bridges

293

ACKNOWLEDGMENTS The research presented in this paper was supported by the Federal Highway Administrations, State of California Governor's Office, and the California Department of Transportation, support of which is gratefully acknowledged.

REFERENCES 1. 2. 3.

4.

5. 6. 7.

Dunker K.R. and Rabbat, B.G. 1995. "Assessing infrastructure deficiencies: the case of highway bridges," Journal of Infrastructure Systems, 1(2): 100-119. Yost, J.R. and Schmeckpeper, E.R. 2001. "Strength and serviceability of FRP grid reinforced bridge deck," Journal of Bridge Engineering, 6(6):605-612. Reising, R.M.W., Shahrooz, B.M., Hunt, V.J., Lenett, M.S., Christopher S., Neumann, A.R., Helmicki, A.J., Miller, R.A., Kondury, S., and Morton, S. 2001. "Performance of five-span steel bridge with fiber-reinforced polymer composite deck panels," Transportation Research Record 1770, Paper No. 01-0337, pp.113-123. Salim, H.A., Davalos J.F., Qiao, and Barbero, E.J. ,1995. "Experimental and analytical evaluation of laminated composite box beams," 4tfh International SAMPE Symposium, May 8-11, pp.532539. Deskovic, N., Triantafillou, T.C., and Meier, U. 1995. "Innovative design of FRP combined with concrete: short-term behavior," Journal of Structural Engineering, 121(7): 1069-1078. Salim H.A. and Davalos J.F. 1999. "FRP composite short-span bridges: analysis, design and testing," Journal of Advanced Materials, 31(l):18-26. ABAQUS/Standard User's Manual, Version 5.8, 1998, Version 6.3, 2002.

Design of Composite-Antenna-Structures with High Electrical and Mechanical Performances Chi-Sang You and Woonbong Hwang Department of Mechanical Engineering, Pohang University of Science and Technology, Korea

ABSTRACT hi this paper we developed load-bearing outer surface that provides antenna performances, and it is termed Composite-Antenna-Structures(CAS). CAS is composite sandwich structure in which antenna part is inserted between honeycomb core and lower facesheet. Design procedure is presented including structure design, material selection and design of antenna elements in order to obtain high electrical and mechanical performances. Optimized honeycomb thickness is selected, in which maximum gain is obtained by resonance condition. Measured electrical performances show that CAS has wide bandwidth over 10% and higher gain by 3.5 dBi than initially designed antenna, and no doubt it has excellent mechanical performances by composite laminates and honeycomb cores. The CAS concept can be extended to give a useful guide for manufacturers of structural body panels as well as antenna designers, promising innovative future communication technology.

INTRODUCTION "Structural surface becomes an antenna." Structures, materials and antenna designers have recently joined forces to develop a new high payoff technology called smart skin or CLAS, for "conformal load-bearing antenna structure" [1-4]. The embedding of radio frequency (RP) antennas in load-bearing skin is a new approach to the integration of antennas into structural body panels. It emerged from the need to improve structural efficiency and antenna performances. It demands integrated product development from disparate technologies including structures, electronics, materials and manufacturing in order to generate a realistic design. The classic of division between structures and antennas is bridged in CLAS and the technical challenge is to satisfy structural and electrical requirements that often conflict. The present study aims to design electrically and structurally effective antenna structures for the next generation of structural surface technology [5,6]. This is termed Composite-Antenna-Structures (CAS). Design procedure is focused on high gain and wide bandwidth in the electrical part, and high strength, stiffness and environmental resistance in the mechanical part. Direct-feeding stacked patch antenna is used for the antenna performances and composite sandwich structure for structural performances. Measured electrical performances are presented.

Corresponding author, Department of Mechanical Engineering, Pohang University of Science and Technology, San 31, Pohang, Kyungbuk, 790-784, Republic of Korea, Tel: +82-54-279-2174, Fax: +82-54-279-5899, E-mail: [email protected]

Composite-Antenna-Structures

295

STRUCTURE AND MATERIALS The fundamental design concept for the CAS panel is an organic composite multi-layer sandwich panel in which microstrip antenna elements are inserted. As shown in Fig. 1 direct-feeding stacked patch antenna elements are used for the antenna performances. The basic panel layers are: two facesheets, two honeycomb cores and antenna elements with dielectrics. The facesheets carry a significant portion of the in-plane loads, contribute to overall panel buckling resistance, and provide low velocity impact and environmental resistance, however outer facesheet that is placed above upper patch provides signal loss by its high electrical loss (tan8). For the facesheet Glass/Epoxy[0/90]2s (UGN200, SK chemicals) of 1 mm is used. The honeycomb cores transmit shear load between layers induced from bending loads in the panel, support the outer facesheet against compression wrinkling, provide impact resistance and increase the overall panel buckling resistance. The thickness of honeycomb core contributes to the overall rigidity that they should be selected between panel thickness requirement and structural rigidity. Between outer facesheet and upper patch Nomex honeycomb core is inserted for mechanically high flexural strength. The thickness of this honeycomb core (h) will be selected for the most efficient antenna performances. For wideband performance, two radiating patches are used. Upper patch is placed on the Duroid 5880 (Rogers corp.) of 0.254 mm, and lower patch and feedline on the Duroid 5880 of 0.762 mm with ground plane on the other face. Upper patch and lower patch are separated by air gap that is provided by Nomex honeycomb of 2.54 mm. Though Duroid 5880 has good electrical properties of low dielectric constant and electrical loss, it doesn't contribute to structural performances. Consequently, CAS is composite sandwich structure in which antenna part is inserted between honeycomb core and lower facesheet. In order not to lower antenna efficiency by outer facesheet that is structural material with high electrical loss, the thickness of honeycomb core must be adjusted in the design procedure.

Glass/Epoxy[0/90]2s (1 mm) o= 4, tanS=0.03

Honeycomb (h mm) er=1.1

Upper Patch

Duroid 5880 (0.254 mm) er= 2.2, tanb=0.0009

Honeycomb (2.54 mm) zr=1.1

Lower Patch Feedline

Duroid 5880 (0.762 mm) er= 2.2, tan&=0.0009

Ground Glass/Epoxy[0/90]2s (1 mm) er= 4, fan8=0.03

FIGURE 1 Configuration of Composite-Antenna-Structures

Composite-Antenna-Structures

296 DESIGN PROCEDURE

In our design procedure, antenna performances are aimed for Ku-band satellite communication, frequency range between 11.7 and 12.75 GHz. At first, antenna elements are designed. The sizes of rectangular patches are 7.6 and 8 mm for upper and lower patches respectively. And then facesheets and honeycomb core are added. Fig. 2 and 3 show reflection coefficient and radiation pattern variations respectively for honeycomb thickness h by computer simulation and the performances of initially designed antenna are also presented by h = infinite. Gain in the broadside direction reaches maximum at h = 10 mm, at which it is approximately half a wavelength between lower patch and outer facesheet at central frequency 12.2 GHz, and reflection coefficient is also satisfied in the desired frequency range with bandwidth of 1.5 GHz.

1

CO

Nci

-10<4—

0

o O

-20-

\ \

8 mm —•—10 mm —<^14mm

\

—A—

.g -30"o

«etle

—o— infinite —•— 4 mm

—T—18 mm

v x ? ^A^ \|»3 0 /\^x

A " \ / W X

-4D-

11

12

14

13

Frequency (GHz)

FIGURE 2 Reflection coefficients for the thickness of honeycomb core (h)

12-,

8-

4-

m

o-

"c" -40

-8-12-16 -90

-60

-30

0

30

60

90

Degrees

FIGURE 3 Radiation patterns for the thickness of honeycomb core (h) at 12.2 GHz (H-plane)

Composite-Antenna-Structures

297

ELECTRICAL MEASUREMENTS In the design procedure, optimized honeycomb thickness h of 10 mm is selected, in which maximum gain is obtained by resonance condition [7], half a wavelength distance between lower patch and outer facesheet at central frequency 12.2 GHz. Measured electrical performances of initially designed antenna and CAS with honeycomb thickness of 10 mm are shown in Fig. 4 and 5. Reflection coefficient variation of CAS is almost same as that of antenna, which means that outer facesheet above antenna elements doesn't affect impedance characteristic of antenna for the designed CAS. Radiation patterns are measured at 12.2 GHz in the compact range. The pattern is narrower and gain is higher by 3.5 dBi for the CAS, compared with radiation characteristics of initially designed antenna. It is considered that structural resonance condition by outer facesheet make beam more concentrated to the broadside direction.

QQ

11

12

13

Frequency (GHz)

FIGURE 4 Reflection coefficients of CAS and antenna

20-i

15-

CAS(/?=10mm) --Q-- Antenna

10CO

2, c "co CD

50-5-10-15 -90

-60

-30

0

30

60

Degrees

FIGURE 5 Radiation patterns of CAS and antenna

90

298

Composite-Antenna-Structures

CONCLUSIONS Composite-Antenna-Structures having both high electrical and mechanical performances is designed. CAS is composite sandwich structure in which microstrip antenna is placed between honeycomb core and lower facesheet. For the wide bandwidth, two radiating patches of different sizes are used. Honeycomb thickness between outer facesheet and upper radiating patch is selected for structural resonance condition, at which the maximum gain is obtained. The outer facesheet rearranges the radiation field distribution. It can be considered as a structure invoking multiple reflections used to concentrate the radiated power in broadside direction. Measured electrical performances show that CAS has wide bandwidth over 10% and higher gain by 3.5 dBi than initially designed antenna, and no doubt it has excellent mechanical performances by composite laminates and honeycomb cores. The CAS concept can be extended to give a useful guide for manufacturers of structural body panels as well as antenna designers, promising innovative future communication technology. REFERENCES 1. 2.

3.

4. 5.

6.

7.

A. J. Lockyer, et al. 1994. "A Qualitative Assessment of Smart Skins and Avoinics/Structures Integration," SPIE Smart Structures and Materials: Smart Materials, 2189: 172-183 A. J. Lockyer, et al. 1999. "Design and Development of a Conformal Load-Bearing Smart-Skin Antenna: Overview of the AFRL Smart Skin Structures Technology Demonstration (S3TD)," SPIE Smart Structures and Materials: Industrial and Commercial Application of Smart Structures Technologies, 3674: 410-424 A. J. Lockyer, et al. 1997. "Conformal Load-Bearing Antenna Structure (CLAS): Initiative for Multiple Military and Commercial Applications," SPIE Smart Structures and Materials: Smart Electronics and MEMS, 2189: 182-196 A. J. Lockyer, et al. 1996. "Conformal Loadbearing Antenna Structure," presented at 37th AIAA SDM Conference, Salt Lake City, UT, April 1996 C. S. You , R. M. Lee, W. Hwang, H. C. Park and W. S. Park. 2003. "Microstrip Antenna for SAR Application with Composite Sandwich Construction: Surface Antenna Structure Demonstration," Journal of Composite Materials, 37(4): 351-364 J. H. Jeon, C.S. You, C. K. Kim, W. Hwang, H. C. Park and W. S. Park. 2002. "Design of Microstrip Antennas with Composite Laminates Considering their Structural Rigidity," Mechanics of Composite Materials, 38(5): 447-460 X. H. Shen, P. Delmotte and G. A. E. Vandenbosch. 2001. "Effect of Superstrate on Radiated Field of Probe Fed Microstrip Patch Antenna." IEE Proc.-Microw. Antennas Propag., 148(3): 141-146

Filament Wound Spherical Composite Pressure Vessel Design by an Energy Method 1

Byung-Sun Kim , Chee-Ryong Joe Composite Materials Lab, Korea Institute of Machinery & Materials(KIMM) 66 Sangnam-dong, Changwon, Kyungnam, 641-010, Korea 2

Department of Mechanical Design and Manufacturing Engineering, Changwon National University 9 Sarim-dong, Changwon, Kyungnam, 641-773, Korea

ABSTRACT A design method for filament wound spherical composite pressure vessels is suggested. This method utilizes an energy method to yield a simple equation, which can easily be applied to design spherical pressure vessels by on-site engineers. Generally, the design of a filament wound pressure vessel involves repeated and complicated structural analysis to find an optimal fiber orientation. But the orientation of fibers to form a spherical vessel cannot be decided just by the aspect of structural effectiveness. The way of winding a spherical vessel may vary due to the manufacturing hardware conditions as well as the software. The out look appearance of the surface of the vessel is also an important aspect. Thus, it takes prolonged time to design a filament wound pressure vessel using a general structural analysis. In this study, a simple design equation for filament wound spherical composite pressure vessels is suggested. This equation can be applied to design any spherical composite pressure vessel as long as the end-boss diameter of the vessel is relatively small, and the total thickness of the filament composite layers over the inner liner is equal, no matter what the winding sequence is. This equation can easily be used by on-site engineers to design spherical composite pressure vessels.

DESIGN OF COMPOSITE LAYERS Selection of Design Method The Composite Group of KIMM has developed two computer programs suitable for Composite Pressure Vessel Design, which are called 'KJMMPV and 'DOME' [1, 2]. 'DOME' decides the profiles of the dome area for cylinder type vessel by the tensile stress only without any bending stress. Under the assumption that Helical winding is applied on entire vessel and Hoop winding is for the cylinder part only, 'KHVIMPV' decides the number of Helical and Hoop layers, respectively, under the constant winding tension. 'KIMMPV' design concentrates more on the cylinder than dome area. Near spherical vessel in present study, does not require design in the cylinder area. The design in this case may be carried out by Laminated Plate Theory [4]. The theory may be applied appropriately when the vessel is composed of uniform ply angles or finite number of uniform plies. * Corresponding author, KIMM, 66SangnamDong, Changwon, Korea, 641-010, Fax : 82-55-280-3883, [email protected]

300

Filament Wound Spherical Composite Pressure Vessel

For the case of near spherical vessel, the finite number of various angle plies may be wound since the optimized design could be achieved when the symmetric winding shape is maintained with respect to the center of the sphere. Thus, instead of following up with Classical Plate Theory, it is more appropriate to design with Virtual Energy Method by introducing Virtual Displacement concept for the reinforcing fibers that provides endless variation of stacking angles. Virtual Energy Method

FIGURE 1. Spherical vessel with thickness much smaller than its radius

When internal pressure, P, is applies to a vessel in Fig. 1, the stress on the vessel when rearranged from P • n r1 = a • t • 2nr is Pr

m (1)

When the same situation is applied with Virtual Energy Method, under the assumption that the vessel contains non-compressible liquid and a small amount of same liquid is added by A V and the diameter, r, is increased to a • r. Then, the surface area and the volume of the vessel becomes Surface Area: 4 n r1 -» 4 n {a • r ) 2

(2)

4 4 Volume: — n r 3 -» — n (a • r ) 3 3 3 Here, the work for the pressure applied to the volume, A V, is £1=P-AF = ^-JP{(ar)3-r3}

(3)

The energy stored by elastic energy due to the increase in the surface area, AS, is E2 = a • t • AS = a • t • 4 n {{arf

- r2 }

(4)

(here, a is the tensile stress on the vessel) Since the work and the stored energy are equal, E{ = E2 Substituting equations (3) and (4) into equation (5),

(5)

Filament Wound Spherical Composite Pressure Vessel Pr(a3

301

-1)

3 t ( a 2 - 1) Since the radius increase is extremely small and limiting above equation, ,. P-r(a3 - 1 ) P-r .. ( a 3 - 1 ) hm a = lim —^ = hm - — «-*' "^ 3t(a2 - 1 ) 3; «-i(a2-l) According to the Lopital's Theorem,

(7)

,. ( a 3 - l ) ,. 3 a 2 3 hm -— = hm =«-' ( a 2 -1) «-i 2a 2

(8)

Thus, from equations (7) and (8), Pr a - -

(9,

Equation (9) is exactly same as equation (1), proving that Virtual Energy Method can also be applied accurately for the stress analysis of the composite pressure vessel.

Stress Analysis of Filament Wound Spherical Pressure Vessel by Virtual Energy Method A spherical composite pressure vessel with radius, r, and composite thickness, t, much smaller than radius is completely filled with incompressible fluid that provides pressure, P. To the vessel, a small amount of same liquid is add by AV and the diameter, r, is increased to a • r. Then, the volume of the vessel becomes 4 4 Volume: - n r3 -+-n{arf

(10)

Here, the work by adding AV to pressure, P, is same as equation (3). When the radius is increased to a • r, the total length of composite robin wrapped on the vessel is also increases b y a . Total Length of Composite Robin: /—>«;/ All reinforcing fibers should withstand uniform tension. If the tension on one reinforcing fiber robin is assumed to be F under the pressure, the energy stored for the elastic extension A/ by AV is E3 =F -Al = Fl(a - 1 )

(11)

When the manufactured vessel is pressurized, the elastic deformation will also occur in the matrix and some energy will be stored in the matrix. However, since the presence of

302

Filament Wound Spherical Composite Pressure Vessel

the micro cracks in the matrix during the internal pressure test was reported [2], it is not safe to rely on the strength of the matrix. In the present study, the reinforcing fibers' strengths were only considered in the stress analysis for safer design. Since the work and the stored energy are same = E3

(12)

Substituting equations (3) and (11) into (12) and rearranging for F F-

03,

(2-1

Applying lim on equation (13)

lim F =

-\

3/

a

APnP 3/

J

-

-I

3/

«->' >'

1

—

Arranging equation (14) for/,

Since F is the tension on a single fiber, F = as-

df-tf

(16)

<JS : Fiber Tensile Strength df : Fiber Robin Width tf : Fiber Robin Thickness

Combining equations (16) and (15), the total length,/, of reinforcing fiber robin is An r • P as

• df

• tf

Thus, the total volume, Vr, becomes Vr=l-df-tf=

4 n r3 • P

(18)

If the Fiber Volume Fraction of Filament Wound Pressure Vessel is vf, the total volume of the composite part is

Filament Wound Spherical Composite Pressure Vessel 4 ri p Vc=L-= « -

303

(19)

For composite thickness, t, and radius, r, the volume of the composite is Vc = An r2 • t

(20)

Equating equations (19) and (20), and arranging for t t

P-r =

—

(21)

This equation can easily be used by on-site engineers to figure out the thickness of the composite layer in near spherical composite pressure vessels. Even if it is not used as the final design value, it can be at least a good estimation to start with.

DESIGN EXAMPLE hi equation (21), substituting as = 4902 (MPa ), Vf = 0.5 P = 62 (MPa ) 0.5, r = Ro = 495 .7 (mm )

The composite thickness, t, becomes 62x495.7 t =

= 12.6 (mm) 4902x0.5

Since the outer radius of PE Liner is 497.5 mm and the composite thickness is 12.6 mm, the outer diameter of the final vessel becomes 1016.6mm which exceeds the required max, diameter of 994.2mm. Therefore, the vessel needs to have small portion of cylinder shape in the middle part of the vessel maintaining near spherical shape. Now, when the outer diameter of the vessel is 994.2mm and the Skirt's thickness is 5.4mm, the outer diameter of the cylinder is 983.4mm. Since the diameter of the vessel is reduced, the thickness of the composite could become thinner slightly. However, adopting the thickness of 12.6mm to this, the vessel design would be safer on the sidewall. The thickness of the PE liner is 6.7mm, and the inner diameter of the PE in the cylinder area is 944.8mm. If the length of the cylinder is L, the vessel's internal volume is

K, =„ ( »*£>.. I + ± , <»£«,.

(22)

However, the required final total volume is v, = 0.4883 x 109 mm 3 and the volume will be reduced by the insertion of the Metal End Boss at each ends of the vessel. Equating v, = 0.4883 x 109 • ' to equation (22)

304

Filament Wound Spherical Composite Pressure Vessel

0.4882 x 10' =

(23)

L+-.

Rearranging, 0.4883 x 109 - - K (472.4)3 L =

= 67 (mm)

n (472.4)'

Finally, Inner diameter of the liner on the cylinder = 944.8 mm Length of the liner on the cylinder = 67 mm Radius of the liner in Dome area = 472.4 mm Total thickness of the composites = 12.6 mm And the Schematic drawing of the composite pressure vessel is shown in figure 2.

FIGURE 2. Schematic Diagram of the Pressure Vessel

REFERENCES 1. 2. 3.

KIMM Report, 'Development of FRP Pressure Vessel©', MOST, BSM 160-1244.C, 1989 KIMM Report, 'Development of FRP Pressure Vessel(II)', MOST, BSM 203-1426«C, 1990 E. J. Jun, W.I. Lee, K. J. Yoon and T. W. Kim, 'Latest Composites', Kyohaksa Pub. Co., ISBN 89-09-01638-8 93580, 1995

Part VI

Failure Analysis

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Numerical Study on Buckling of Z-pinned Composite Laminates Wenyi Yan* Computational Engineering Research Centre, Faculty of Engineering and Surveying, the University of Southern Queensland, Toowoomba, QLD 4350, Australia Hong-Yuan Liu and Yiu-Wing Mai Centre for Advanced Materials Technology, School of Aerospace, Mechanical and Mechatronic Engineering, the University of Sydney, Sydney, NSW 2006, Australia

ABSTRACT Z-pinning is a newly developed technique to enhance the strength of composite laminates in the thickness direction. Recent experimental and theoretical researches manifest that z-pins can significantly improve mode I fracture toughness in doublecantilever-beam tests and mode II fracture toughness in end-notched-flexure beam tests. From a practical point of view, buckling accompanying delamination is a typical failure mode in laminated composite structures. For the purpose of a complete understanding on the z-pinning technique towards an improvement of the mechanical behaviour of laminated composites, in the present study, a numerical approach is applied to investigate the buckling of z-pinned composite laminates with initial delaminations under compression. The numerical results indicate that z-pinning can effectively increase the compressive strength of composite laminates provided that the initial imperfection is within a certain range. The magnitude of the improvement is consistent with available experimental data.

INTRODUCTION While recognizing the superiorities of composite laminates with high strength/ weight ratio and designable in-plane strength, the weak point of composite laminates with low delamination toughness has never been neglected. Over the last decade, many techniques have been developed to enhance the strength of composite laminates in the thickness direction, that is, z-direction. Among them, a novel approach, so-called zpinning has been developed by Foster-Miller hie in the USA [1]. In this technique, short stiff fibres initially contained in foam are inserted into the uncured composite in the zdirection through a combination of heat and pressure compacting the foam. After curing, a simple 3D structured laminated composite is created. Well designed z-pinning process can minimize the amount of in-plane fiber damage. Compared to other techniques of through-thickness reinforcement, such as stitching and weaving, z-pinning is reckoned as a convenient and cost-effective approach. The size of pin diameter is normally from 0.15 mm to 1 mm. The pin can be made of composite, such as carbon fibre/BMI or metallic materials from titanium to stainless steel [2]. * Corresponding author, Faculty of Engineering and Surveying, the University of Southern Queensland, Toowoomba, QLD 4350, Australia, Fax: ++61 7 4631 2526 Email: [email protected]

308

Buckling of Z-pinned Composite Laminates

Recent experimental and theoretical researches confirm that z-pins can significantly improve mode I fracture toughness in double-cantilever-beam (DCB) and mode II fracture toughness in end-notched-flexure (ENF) tests [3-6]. Depending on pin density, experimental data shows that the mode I fracture toughness of pinned laminates can be improved by about 20 times and mode II fracture toughness can be improved by about 9 times [3]. Theoretical and numerical investigations reveal that a large amount of energy absorption is caused by the pull-out process of the z-pins, which results in a much higher fracture energy release rate during delamination growth in the z-pinned laminates [4-6]. In practice, buckling accompanying delamination under compression is a typical failure mode in laminated composite. Compression after impact becomes a routine test either to evaluate the impact damage or to investigate the influence of delamination on buckling strength, or damage tolerance. Generally, two kinds of buckling modes have been observed in practice: local buckling and global buckling, which are illustrated in Fig. 1 for z-pinned laminates. Z-pins IP

a. Local buckling mode

Z-pins IP

-*—

4d

IP

b. Global buckling mode

FIGURE 1. Global and local buckling modes in z-pinned composite laminate under compression.

Figure 1 (a) shows a case of local buckling. Under edge compression the composite laminates might separate along the initial delamination (damage) plane, or one of the initial delamination planes in the case of multiple delaminated plies due to impact. After that, the separated sub-laminates collapse simultaneously. Due to the relatively low interlaminar fracture toughness, local buckling can normally trigger an unstable delamination growth. On the contrary, the initial delamination surfaces will not separate in a global buckling and the sub-laminates collapse in the same direction, as shown in Fig. l(b). Clearly, initial delamination has minor influence on global buckling. For the purpose of examining damage tolerance, or the reduction of compression strength resulted from the delamination, boundary conditions are normally set properly to avoid global buckling in experiments so that only local buckling is allowed to take place [7, 8]. In a z-pinned laminated composite, due to opening of the delamination under the bending moment in local buckling, the pins will be forced to pull out, which is shown in Fig. l(a). Certainly, the reaction of the pulling force on the pins will try to bridge the sub-laminates together, i.e., resist the buckling deformation. Furthermore, similarly to the case of fracture in a double-cantilever-beam, the pins will provide bridging forces to hinder delamination from growing. Hence, it is expected that z-pins will enhance the local buckling strength

Buckling of Z-pinned Composite Laminates

309

of a composite laminate under edgewise compression, fn 1993, Shu and Mai presented their original studies on delamination buckling with stitching [9, 10]. It was found that through-thickness stitching delayed both buckling and delamination extension. The present study is aimed to numerically quantify the influence of z-pinning on the local buckling strength. It is obvious that z-pinning should only have a minor effect on global buckling because the pins will not be pulled out in this case. Some experimental studies on compression after impact tests on z-pinned laminates were conducted at Cranfield University [11-13]. In these tests, the initial delamination damage in the pinned laminates was induced by low velocity impact. After that, in-plane compression experiments were carried out to measure the compression strength/buckling strength, which is generally called compression after impact (CAT) test. The first stage of the test to initiate delamination by impact also served to evaluate the influence of zpinning on impact damage, which was quantified by the projected delamination area. Zhang et al. [13] reported that z-pinning reduced impact damage area by 19% to 63% in their tests and the mechanism is that z-pins can effectively improve the mode II fracture toughness against shear-induced delamination under impact loading. In their CAI tests, an averaged 45% increase of compression strength was measured in z-pinned laminates. To obtain a complete understanding of z-pinning technique towards improvement of the mechanical behaviour of composite laminates, in the present study, a numerical approach is applied to investigate the buckling of a z-pinned composite laminate with initial delaminations under edge compression. The influence of z-pins is demonstrated by comparing with the results derived from unpinned samples. NUMERICAL ANALYSIS Description of buckling model To analyze the effect of z-pinning on the buckling strength of composite laminates, only the local buckling failure mode with z-pins pulling out during the buckling process will be considered. Generally, the damage due to impact is quite complicated, which includes multi-layer delaminations, fibre breaking and matrix cracking. For simplicity, a symmetrical structure with three initial interlaminar delaminations is considered in our study. The major longer initial delamination is assumed to locate in the middle plane of the laminate and two minor shorter initial delaminations are in the middle of the sublaminates. Due to symmetry, only a quarter of the whole problem is simulated in our finite element model, which is illustrated in Figure 2.

U(P)

] /

•

(m hr> pp pp pp (m qp o"o pp pp go op 1 1 1 1 1 1 1 1 1 1 1 1 1 111 1 1 1 11 I I I I I I I 1 1 1 1 1

da

FIGURE 2. Numerical model for local buckling analysis.

Here, we consider a plane strain problem with the y-axis in the direction with zero normal strain. The symmetrical planes, one horizontal and one vertical, are replaced by simply supported boundary conditions in the FE model. L in Figure 2 represents the half

310

Buckling of Z-pinned Composite Laminates

length of the laminate and h is the half-thickness. The compressive displacement, U, corresponding to the compressive force per unit width, P, for half of the laminate is applied at the right end of the model. The initial damage of the major delamination is represented by two parameters, da and du da is the half-size of the delamination area and di is the initial displacement from the separated surfaces of the major delamination to the middle plane at the centre of the initial delamination zone, which represents the out-ofplane damage and is called an imperfection here. This initial displacement is assumed to disappear linearly towards the border of the delamination zone, which is the crack-tip in terms of fracture mechanics. The thickness of the minor delamination with a length of dm is treated as zero. This simplified damage description can be viewed as a proper approximation of a typical practical case. The distance between adjacent pins is represented by dc. The values of all the parameters are summarized in Table I, which are consistent with similar experimental tests [13]. TABLE I. Values of parameters to describe FE model and z-pinning. h (mm) 2

L (mm) 75

da (mm) 20

4(mm)

rf, (mm) 0.01-0.3

15

dc(mm) 1.75

Sa (mm) 0.1

2

The composite laminate is simplified as transversely isotropic elastic with the x-y plane, i.e., 1-2 plane, as the plane of isotropy. According to the elasticity of anisotropic materials, 5 independent material constants are required to determine the elastic behavior and which are chosen based on [12] and listed in Table II. TABLE II. The material constants of the composite laminate. E, (GPa) 67.8

E2 (GPa) 11

Vl2

Vl3

M-12 ( G P a )

0.34

0.3

15

Z-pin pullout simulation During the buckling process, the z-pins in the delamination zone will be pulled out. General discussion and experimental work on the z-pin pullout can be found in [14, 15]. In this paper, a simple bi-linear bridging model is adopted, which was proven to be very effective to capture the z-pinning bridging effect in previous studies [5, 6]. This model is represented by the function between the bridging force, P, and the pullout displacement, S, which is: P=

\ \PB-Pa(S-Se)Hh-Sa),

0<5<8a 8<5
(1)

where Pa is peak bridging force and its corresponding pullout displacement is 8a. The ultimate pull-out displacement, h, is equal to half-thickness of the laminate. The bridging force is zero when the pin is completely pulled out from the composite, that is, when 5 = h. The values of P a and 8a are listed in Table I. The deterioration of the impact on the z-pin bridging behavior is reflected by choosing a lower value of Pa than that in our previous study. A set of non-linear springs are used in the finite element model to simulate the pullout process of the individual pins [5].

Buckling of Z-pinned Composite Laminates

311

RESULTS AND DISCUSSION The buckling problem without delamination growth is studied in this paper, which corresponds to the composite laminates with high fracture toughness. Figure 3 shows the variation of the compressive force per unit width, IP, with the applied compressive displacement, U, for a given imperfection 4=0.08 mm. Both unpinned sample and zpinned specimen are analyzed. As shown in Fig. 3, the compressive force increases linearly with the displacement at the initial stage. The unpinned sample bifurcates first and no more compressive force can be applied, which leads to buckling of the structure. In contrast, the z-pinned specimen can continuously support an increasing force linearly over the bifurcation point of the unpinned sample until the force reaches a higher value. After that, it collapses quickly with a sudden force reduction and reaches the postbuckling state. Here, Riks method is applied to capture the post-buckling state of the zpinned laminate [16]. To obtain the compressive critical force, 2Pcr, simple static analysis can give exactly the same result. Figure 3 clearly manifests that the compressive strength has been increased from 0.84 to 1.28 kN/mm caused by z-pinning. This increase is in good agreement with available experimental results of Zhang et al. [13].

Unpinned sample Z-pinned specimen with Riks method

Compressive displacement, U, (mm)

FIGURE 3. The compressive force versus compressive displacement for unpinned sample and z-pinned specimen with 4=0.08 mm.

Our analysis indicates that the predicted compressive strength, oc=Pc/h, depends on the imperfection, dt. Figure 4 shows a c as a function of dt. To demonstrate the effect of zpinning on the compressive strength, the results from the unpinned samples are also shown by the solid curve in Figure 4, which indicates that the compressive strength is slightly reduced with increasing imperfection size. However, the compressive strength of z-pinned specimens is reduced more sharply with increasing size of the imperfection. Eventually, the two curves merge together when d, reaches 0.3 mm, which means the influence of z-pinning can be neglected if dt is over 0.3 mm. Larger di means higher initial bending moment applied on the sub-laminates under a given compressive force, which in turn creates a higher bending deflection. Thus, the pins can be forced out more easily due to the higher deflection. No experimental evidence, however, is yet available to verify this prediction. SUMMARY A finite element model is developed to evaluate the influence of z-pinning on the buckling behavior of composite laminates with initial interlaminar delaminations. The bridging effect of z-pins during local buckling is simulated by a set of non-linear springs.

312

Buckling of Z-pinned Composite Laminates

Our results indicate that z-pinning can effectively increase the compressive strength of composite laminates due to the failure of local buckling provided that the initial size of the imperfection is no larger than a certain value. Further parametric study is under way to examine this problem in detail, especially buckling-induced delamination growth.

- Unpinned sample • Z-pinned specimen

Imperfection, d}, (mm)

FIGURE 4. Predicted compressive strength as a function of imperfection size, dj.

ACKNOWLEDGEMENT The authors would like to thank the Australian Research Council for the support of this project on the effect of z-pinning on composite laminates. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14.

15. 16.

Freitas, G., C. Magee, P. Dardzinski and T. Fusco. 1994. "Fiber insertion process for improved damage tolerance in aircraft laminates," J. Adv. Mater., 25(4):36-43. http://www.aztex-z-fiber.com/ Cartie, D. D. R., I. K. Partridge. 1999. "Delamination Behaviour of Z-pinned Laminates," in Proceedings of the 12'h international conference on composite materials, ICCM12, Paris 5th-9th July. Liu, H.-Y., Y.-W. Mai, 2001. "Effects of z-pin reinforcement on interlaminar mode I delamination," in Proceedings of the 13th International Conference on Composite Materials, ICCM13, Beijing. Yan, W., H.-Y. Liu, Y.-W. Mai. 2003. "Numerical study on the mode I delamination toughness of Zpinned laminates'" Comp. Sci. Tech., 63:1481-1493. Yan, W., H.-Y. Liu, Y.-W. Mai. "Mode II delamination toughness of Z-Pinned Laminates," to appear in Comp. Sci. Tech. Pavier, M. J. and M. P. Clarke, 1995. "Experimental techniques for the investigation of the effects of impact damage on carbon fibre composites," Comp. Sci. Tech., 55:157-169. Short, G. J., F. J. Guild and M. J. Pavier, 2001. "The effect of delamination geometry on the compressive failure of composite laminates," Comp. Sci. Tech., 61:2075-2086. Shu, D. and Y.-W. Mai, 1993. " Delamination Buckling with Bridging", Comp. Sci. Tech., 47:25-33. Shu, D. and Y.-W. Mai, 1993. "Effect of Stitching on Interlaminar Delamination Extension in Composite Laminates," Comp. Sci. Tech., 49:165-171. Cartie, D. D. R. 2000. "Effect of z-fibres on the delamination behaviour of carbon fibre/epoxy laminates," PhD thesis, Cranfield University, U. K. Negre, P. 2000. "Compression-after-impact performance of z-pinned carbon fibre/epoxy laminates," Master thesis, Cranfield University, U. K. Zhang, X., L. Hounslow and M. Grassi, 2003. "Improvement of low-velocity impact and compressionafter-impact performance by z-fibre pinning," in Proceedings of the 14th international conference on composite materials, ICCM14, San Diego, California. Liu, H.-Y., W. Yan and Y.-W. Mai, "Z-pin bridging force in composite delamination," Fracture of Polymers, Composites and Adhesives II", ESIS Publication 32, Editors: B. R. K. Blackman, A. Pavan and J. G. Williams, 491-502. Dai, S.-C, W. Yan, H.-Y. Liu and Y.-W. Mai. "Experimental study on z-pin bridging law by pullout test," submitted to Comp. Sci. Tech. ABAQUS 2002 Version 6.3. Providence, RI: HKS Inc.

A Three Dimensional Approach of Fatigue Crack Propagation for Aluminum Panels Repaired with Single-Sided Composite Laminates H. Hosseini-Toudeshky*, G. Sadeghi Aerospace Engineering Dept. - Amirkabir University of Technology, Tehran, Iran H. R. Daghyani Mechanical Engineering Dept. - Amirkabir University of Technology, Tehran, Iran

ABSTRACT hi this paper fatigue crack growth of centrally cracked aluminum plates repaired with single-sided composite patches are studied. Three dimensional finite elements analysis of the repaired aluminum panels were performed to obtain the crack-front shape and fatigue crack growth life of them. The crack front shape was obtained using the variation of stress intensity factors along the crack-tip during the propagation, hi this procedure crack-tip fracture parameters of J and Ki were calculated using Equivalent Domain Integral (EDI) method. Fatigue crack growth lives for a certain crack growth length calculated from this procedure are also compared with those obtained assuming that the crack front is perpendicular to the plate surfaces.

INTRODUCTION Adhesively bonded composite patches or reinforcements are structurally efficient and much less damaging to the structure than traditional repairs based on mechanically fasteners metallic patches. Baker and Jones [1] studied the repair technique using adhesively bonded Boron/Epoxy composite patches which is widely considered as a cost effective and reliable method. One of the most challenging aspects of bonded composite repair technology has been the stress analysis of repaired panels and the subsequent fracture parameters calculations. The difficulty arises from the fact that a metallic panel under in-plane loading would develop highly complicated three dimensional stresses, if composite patches are bonded to its surface un-symmetrical (single-sided repair). In many studies, the variation of stresses over the thickness of the cracked plate has not been considered in the fracture analyses or crack propagation procedure [1-4]. In many studies the stresses and strains fields of the mid-plane have been used to calculate the fracture parameters, however, the maximum stresses and strains occur on the un-patched surface of the cracked plate [5]. In this paper, three dimensional finite elements analysis of the repaired aluminum panels with single-sided composite patches were performed to obtain the crack front shape during the propagation and fatigue crack growth life of them. The crack front shape was calculated using the obtained stress intensity factors along the crack-tip. * Corresponding author, E-mail: [email protected]

314

A Three Dimensional Approach of Fatigue Crack Propagation

Crack-tip fracture parameters of J and Ki were calculated using Equivalent Domain Integral (EDI) method. Fatigue crack growth life of the panels obtained from this procedure are also compared with those obtained assuming that the crack front remains perpendicular to the plate surfaces during the crack propagation. EDI TECHNIQUE AND 3D CRACK GROWTH In general, 3-D crack problems can be analyzed using finite elements method. Arbitrary crack configurations can be modeled using different methods such as Crack Opening Displacement (COD) and Virtual Crack Closure Technique (VCCT) to evaluate strain energy release rate and stress intensity factor, but they can be used for linear elastic problems only. EDI can be used for elastic-plastic fracture analysis of the components. This method is based on three dimensional calculation of J-integral parameter, taking into account the non-elastic strains. It is a path independent integration and could be used for arbitrary crack front shapes. It can be used to calculate the variations of fracture parameters along the crack front of the single sided repaired panels during the crack propagation. The J-integral definition considers a balance of mechanical energy for a translation in front of the crack. Using the divergence theorem, in linear elastic condition and in the absence of surface loads the following representation of J for 3-D problems [6] is obtained: J f = -[

\W

dxt

IJ

8xk8xj

where W is strain-energy density; tj is traction component; u,- are displacements components, the value of S at crack-tip is zero and varies through the crack-tip elements in radial direction, and f is the width of crack-tip element. Having the Jintegral value from the above equation the stress intensity factors are obtained using K, = TJE'JJ [6]. Where E* is equal to E in plane stress and E* = £7(1-o 2 ) in plane strain conditions. Having the variations of stress intensity factors and material properties along the crack-front one may use Paris law to calculate the crack propagation life for a certain crack growth length. In the current study variation of crack growth length are calculated along the crack-front for a certain number of loading cycles in each step. FINITE ELEMENTS MODELING Several aluminum panels repaired with single sided adhesively bonded composite laminates were analyzed using finite elements method. Typical geometry and loading of aluminum panels, adhesive layer and composite patch are shown in figure 1. The panels were assumed to be made of 2024-T3 aluminum alloy. Material properties and dimensions of panels, adhesive layer and composite patches are listed in Tables 1 and 2. The Paris Law constants are c = 2.44E-8 and m = 2.601 for the aluminum alloy [5]. hi these three dimensional modeling a 20-node singular solid elements was used to model the crack front. This element gives enough strains to calculate equation (1) numerically at 8 gauss points for in each element. An isotropic 8-node-solid element was used to model the aluminum panels and adhesive. Furthermore, a layered 8-nodesolid element was used to model the laminated composite patch. 10 and 2 elements

A Three Dimensional Approach of Fatigue Crack Propagation

315

t t t t t t t t t t

,rTTTTTTT7V |^

2W (Plate)

^J

FIGURE 1 Typical geometry and loading of single-sided repaired panels TABLE I Material properties

E (MPa) V

Al. panel 71.3E+3 0.33

adhesive 1.89E+3 0.33

patch Ex = 208E+3, Ey = 25.4E+3 v

xr -vxz

=

0.1677 ,vm

=0.035

TABLE II Dimensions of the models

L (mm) W(mm) t (mm)

Aluminum panel 75 50 2.29,3.50

Adhesive 30 20 0.1016

patch 30 20 0.127 per layer

were used in the thickness of plate and adhesive respectively and a very fine mesh was generated for the area near the crack-tip. The patches material was Boron/Epoxy composite and unidirectional lay-ups were used for the patches in all models. The stress and strain fields of the repaired panels were obtained using ANSYS finite elements program. A macro program was also developed to handle the crack growth modeling procedure and to find the crack front shape during the crack propagation. In this analysis we assumed that there is no debonding between the cracked plate and patch. A dynamic mesh generation using automesh capability of the code was also used to generate the mesh of the repaired panels at each crack growth step. The Jintegral and Ki values were computed for the crack-front in each step. Then the crack growth increment was calculated and the geometry was updated for "the new crack shape. The above procedure was repeated for several steps to find the crack-front shape along the crack propagation. RESULTS AND DISCUSSIONS Figures 2(a) and 2(b) show the variations of normalized stress intensity factor versus normalized thickness of the panel and patch respectively for initial crack condition. Stress intensity factor (SIF) is normalized using the following expression: - * * - \ln*m

"

(2)

In this equation a = 5 mm is half of the initial crack length and a^ is remotely applied unit tensile stress. Panels are bonded with 2, 6, 12 and 18 layers Boron/Epoxy

316

A Three Dimensional Approach of Fatigue Crack Propagation

composite patches. For panels without repair SIF is uniformly distributed along the crack-tip except at edges. When the composite laminates are bonded, SIF has a nonuniform distribution along the thickness. The SIF value at the un-patched surface of the repaired panels is larger than those obtained for the mid-plane and patched surface of the panel. The un-patched SIF are increased for small patch thicknesses with respect to the un-repaired panels SIF. But, by more increasing the number of patch layers the SIF at un-patched surface is reduced. This is due to the effect of composite laminates to stop the opening of the crack faces and decreasing the displacements against the induced extra bending. Therefore by increasing the number of patch layers the un-patched surface SIF is reduced. Mid-plane SIF is significantly decreased by increasing the number of patch layers. 1.4 1.2-

o 0. 0.204

0.6

Normalized thickness.

(a)

0.5

1

1.5

2

Patch thickness (mm)

(b)

FIGURE 2 (a)Normalized SIF along the thickness at crack-tip for various patches (b) Normalized SIF versus patch thickness at un-patched surface and mid-plane Panel thickness t = 2.29 mm

Figure 3 shows the crack front curve during the propagation for various numbers of load cycles and for a typical repaired panel with panel thickness of 2.29mm and 18 layers patch. This figure shows that the crack is quickly started to grow from unpatched surface side of the initial crack-tip to generate the new crack-front shape. Then it will grow along the panel thickness in an almost uniform manner after a few steps. The crack growth rate on the free surface is bigger than the mid-plane and patched surface of the cracked panel. Figure 4 shows the variation of normalized crack growth life versus patch thickness of the repaired panels for two typical panels. These lives were estimated for a certain crack growth from a=5mrn to a=8rnm and were normalized with respect to the un-repaired panel life. This curves show that the fatigue crack growth life of the repaired panels are increased significantly using small patch thicknesses, but there is a small and almost steady changes in the crack growth life for the patch thicknesses of bigger than 0.3mm (2 layers). Crack growth life extension of the repaired panels using various number of layers are listed in table 3. These lives were obtained for a certain crack growth from a=5.0mm to 3=8.0"™ at un-patched surface of the panel. The remotely applied stresses were the same for all repaired panels. These tables show that the patches are more efficient in life extension for thin plates. The life extension rate of the panels resulted from the panels with thin patches are much bigger than those obtained from the thick patches.

A Three Dimensional Approach of Fatigue Crack Propagation nitial crack

= ^

317

•— 465000 <~ 909000 »~1176500 — 1382400 »—1568700

056000 2S3500 4 78200 807500

I ! 5

1i 6

7

Crack front shape after 1807500 cycles

8

Crack-tip position along the thickness of cracked plate (m

FIGURE 3 Crack-front configurations for several loading cycles

0

0.5

1

1.5

2

Patch thickness (mm) FIGURE 4 Normalized crack growth life versus patch thickness for various panels Table III Life extension of composite laminates for different repaired panels a- Panel thickness t = 3.50 mm Number of Layers 0 2 6 12 18

Cycles (10*6) 0.798 1.112 1.179 1.230 1.276

Life extension (%) 0 39.42 47.76 54.21 60.02

b- Panel thickness t = 2.29 mm Number of Layers 0 2 6 12 18

Cycles (10*6) 0.775 1.213 1.446 1.586 1.664

Life extension (%) 0 56.60 86.68 104.74 114.89

Fatigue crack growths of the repaired panels were also studied based on the assumption that the crack front remains perpendicular to the panel surfaces during the propagation using three dimensional finite elements analysis. Figures 5(a) and 5(b) show the normalized fatigue life versus patch thickness of the repaired panels with 2.29 mm thickness based on the new assumption and real crack-front shape. The performed results in figures 5 (a) and 5(b) were obtained for a certain crack growth from a=5.0mm to a=8.0mm at mid-plane and un-patched surface of the panels respectively. As figure 5 (a) shows, the estimated lives based on the mid-plane crack growth length and fracture parameters considering the real crack-front shape are smaller than those obtained using the assumption of crack-front perpendicular to the

A Three Dimensional Approach of Fatigue Crack Propagation

318

panel surfaces, but they have similar general behaviors. Therefore the estimated life extension based on this assumption may lead to the non-conservative results. Figure 5(b) shows that the estimated lives based on the un-patched surface crack growth length and fracture parameters considering the real crack-front shape are bigger than those obtained using the assumption of crack-front perpendicular to the panel surfaces. The calculated lives based on the new assumption leads to the un-valid results especially for the repaired panels with small patch thickness.

1

1.5

Patch thickness (mm)

(a)

0.5

1

1.5

Patch thickness (mm)

(b)

FIGURE 5 Normalized life versus patch thickness of repaired panels (panel thickness = 2.29 mm) (a) using mid-plane parameters, (b) using un-patched surface

CONCLUSION Fatigue crack growth was studied for centrally cracked aluminum plates repaired with single-sided composite patches. The crack front shape during the crack propagation and fatigue crack growth life of the repaired panels were obtained using three dimensional finite elements analysis. The un-patched SIF are increased for small patch thicknesses with respect to the un-repaired panels SIF. But, by more increasing the number of patch layers the SIF at un-patched surface is reduced. Mid-plane SIF is also significantly decreased by increasing the number of patch layers. The estimated lives based on the mid-plane crack growth length considering the real crack-front shape are smaller than those obtained using the assumption of crack-front perpendicular to the panel surfaces, but they have similar general behaviors. Therefore the estimated life extension based on this assumption may lead to the nonconservative results. The calculated lives based on the new assumption using unpatched surface parameters leads to the un-valid results. REFERENCES 1. Baker, A. A. and Jones, R.," Bonded repair of aircraft structures", Martinus Nijhoff Publisher, Dordrecht, Netherlands, 1988, 2. Ratwani, M. M., "Analysis of Cracked Adhesively Bonded Laminated Structures", AIAA J., Vol.17, No. 4, 1979, PP. 988-994 3. Rose, L. R. F., "A Cracked Plate Repaired by Bonded Reinforcements", Int. J. Fract, Vol. 18, No. 2, 1982, PP: 135-144. 4. Hosseini-Toudeshky H., Shahverdi H., and Daghyani H. R., "Fatigue life assessment of repaired panels with adhesively bounded composite plates" (Second Asian Australian Conference on Composite Materials, ACCM- 2000, Kyonju, Korea, 18-20 August, 2000) 5. Hosseini-Toudeshky, H., Mohammadi, B., and Daghyani, H. R., "Effects of patch lay-up configuration on fracture parameters and fatigue life of single-sided repaired panels in mixedmode conditions", 4th Iranian Aerospace Society Conference, 23-27 Jan. 2003, Tehran 6. G. P. Nikishkov, S. N. Atluri 1987. "Calculation of Fracture Mechanics Parameters for an Arbitrary Three Dimensional Crack, by the 'Equivalent Domain Integral' Method" Int. J. for Numerical Methods in Eng., 24:1801-1821.

Time-temperature-water Absorption Superposition Principle for Flexural Fatigue Strength of Unidirectional CFRP Laminates Jun Ichimura* and Naoyuki Sekine Graduate School, Kanazawa Institute of Technology, Japan Masayuki Nakada and Yasushi Miyano Materials System Research Laboratory, Kanazawa Institute of Technology, Japan

ABSTRACT This paper is concerned with the influence of water absorption on the time-temperature dependent flexural fatigue strength of unidirectional CFRP laminates, which consist of carbon fiber and epoxy resin. The CFRP laminates were prepared under three conditions of Dry, Wet (percentage of water content: 1.0% and 2.0%) and Wet+Dry. Three-point bending constant strength rate (CSR) and fatigue tests for these three kinds of CFRP laminates were carried out under various loading rates and temperatures. It is cleared that the flexural CSR and fatigue strengths of CFRP laminates strongly depend on the water absorption as well as time and temperature, and the time-temperature-water absorption superposition principle holds for there flexural CSR and fatigue strengths.

INTRODUCTION Recently carbon fiber reinforced plastics (CFRP) has been used for the primary structures of airplanes, ship, spacecraft and others, in which the high reliability should be kept during the long operating period. Therefore, it is strongly expected that the accelerated testing methodology is established for the long-term life prediction of composite structures exposed under the actual environment of temperatures, water and others. The mechanical behavior of polymer resins exhibits time and temperature dependence, which is called viscoelastic behavior, not only above the glass transition temperature Tg but also below Tg. [1-8] Furthermore, the viscoelastic behavior of polymer resins also depends on water absorption.[9-12] Thus, it can be presumed that the mechanical behavior of polymer composites significantly depends on water absorption as well as time and temperature. This paper is concerned with the influence of water absorption on the time-temperature dependent flexural strength of unidirectional CFRP laminates. The CFRP laminates which consist of PAN-based carbon fiber and epoxy resin were treated under three conditions of Dry, Wet and Wet + Dry after molding. Three-point bending constant strength rate (CSR) and fatigue tests for these three kinds of CFRP laminates were carried out under various loading rates and temperatures. The influence of water absorption on time-temperature dependent flexural CSR and fatigue strengths is * Corresponding author, 3-1 Yatsukaho, Matto, Ishikawa 924-0838, Japan, Fax:+81-76-274-9251,

Time-Temperature-Water Absorption Superposition Principle

320

evaluated, and the applicability of time-temperatures-water absorption superposition principle is discussed for the flexural fatigue strength as well as the flexural CSR strength for this CFRP laminates.

EXPERIMENTAL PROCEDURE The CFRP pre-preg sheets are made of unidirectional carbon fiber (Fortafil 510, Fortafil) and epoxy resin (Cape 2002, Cape). The CFRP laminates were formed by hot pressing these 15 pre-preg sheets at 130°C for lhour. The fiber volume fraction of the laminates was approximately 53%. The thickness of CFRP laminates was 3mm. These laminates were cut to the transverse direction of fibers, and the length and width were 80mm and 10mm, respectively. The test specimens were treated under three conditions of Dry, Wet and Wet + Dry. Details of treated conditions are shown in Table 1. The Dry specimens were obtained by holding the cured specimen in the oven at 150°C for 2 hours. The Wet specimens were obtained by soaking the Dry specimens in hot water at various temperatures and times. The Wet + Dry specimens were obtained by dehydrating the Wet specimens in the oven at 150°C for 2 hours. TABLE I

Treated conditions for Dry, Wet and Wet + Dry

Water content Dry

0%

Wetl.O-a Wetl.O-b Wet2.0 Wetl.O+Dry Wet2.0+Dry

1.0% 1.0% 2.0% 0% 0%

hi oven 150°Cx2h 150°Cx2h 150°Cx2h 150°Cx2h 150°Cx2h 150°Cx2h

f

hi water

f (-

80°C x 144h 95°Cx24h

f +f

95°Cx48h 80°C x 144h 95°C x 48h

H^

In oven

HH HH

150°Cx2h 150°Cx2h

RESULTS AND DISCUSSION Flexural CSR Strength The left side of Fig. 1 (a)-(f) shows the flexural CSR strengthCTSversus time to failure ts at various temperatures T for Dry, Wetl.O and Wet2.0 and Wetl.O + Dry and Wet2.0+Dry specimens, where ts is the time period from initial loading to maximum load during testing. The master curves of a s versus the reduced time to failure ts' were constructed by shifting a s at various constant temperatures along the log scale of ts. Since the smooth master curve of a s for each specimen can be obtained as shown in the right side of each graph, the time-temperature superposition principle is applicable for each as. From Fig.l (b) and (d), it was cleared that c s decreases with water absorption. The chain line in Fig.l(c) show the master curve of a s for Wetl.O-a. Since the master curve of o"s for Wetl.O-a and Wetl.O-b agree well with each other, the master curve of as for wet specimens depend on the amount of water absorption regardless of soaking time and temperature. The 0S for Wetl .0+Dry specimen return perfectly to that of Dry specimen by drying after water absorption, however o s for Wet2.0+Dry specimen did not return to that of Dry specimen by drying after water absorption as shown in Fig.l (e) and (f).

Time-Temperature-Water Absorption Superposition Principle Reduced temperature T' f ] 25 50 70 80 90100 120 1 1 i I 1 1

321

Reduced temperature T' [°C] 25 50 70 B0 90 Dry

V1mln

5

20

""

Q,

-

A*

A X

25°C 50DC

-

o 70t O 80°C

O 100°C n 120°c 1 i rO i i i 0 2 •2 0 2 4 - 2 log t, [mini

i 4

1 1 1 6 8 10 12 14 16 18 log V [min]

log ts [min]

log V [mini

(b)Wetl.O-a

(a) Dry Reduced temperature T' pc] 25 50 70 80 90

Reduced temperature T [°C] 25 50 70 80 90

(c)Wetl.O-b

(d) Wet 2.0

Reduced temperature T [°C] 25 50 80 100 120

Reduced temperature T' [°C] 25 50 80 100 120

•51100

1

I

P

Dry 80

±JL ml

W= 0% (Wet2.0+Dry) T0=25"C_ ^Imin

A

\

\\ Vo

I

4

6 8 10 12 14 16 18 log ts' [min]

-

25"C 50"C o 70°C O 80-C 90°C o 100"C D 120°C A X

^4-2 0 2 4 - 2 log t« [min]

0

Jo

40 > t3

20 i 2

i 4

i i 6 8 10 12 14 16 1 log y [min]

0

(e)Wetl.0+Dry (f) Wet2.0+Dry FIGURE 1 Master curves of flexural CSR strength

25 I

f. -2

I

~J -4

I I I

f

I

5

Temperature T [°C] 50 SO 100 120 1 I ' I 1 T 0 =25°C W 0 =0%

"12 -16 -18

O Dry AWeH.O - AWet2.0 DWet1.0+Dry l I l 34 32 30

1 28

1 26

24

FIGURE 2 Time-temperature shift factors of flexural CSR strength

The time-temperature shift factors aTo(T) of crs for all specimens are shown in Fig.2. These aTo(T) are in good agreement with two Arrhenius' equations with different activation energy AH. The knee point temperature of aTo(T) decreases with water absorption and returns to that for Dry specimen by drying after water absorption. Figure 3 shows the SEM photographs of fracture surface for Dry, Wet and Wet + Dry specimens after flexural CSR test at temperature T=25°C. The Dry, Wetl.O-b and Wetl.O+Dry specimens were failed mainly by cohesive fracture of matrix resin.

Time-Temperature-Water Absorption Superposition Principle

322

The Wet 2.0 and Wet2.0 + Dryspecimens were failed mainly by interfacial fracture of carbon fiber between matrix resin. It can be considered that this change of fracture mode is caused by water absorption, and the imperfect recovery by dehydratiy of the CTS for Wet2.0+Dry specimen is caused by this change offracturemode.

(a)Dry

(b)Wetl.O-b

(c)Wetl.0+Dry

(d)Wet2.0 FIGURE 3 SEM photographs of flexural CSR strength

(e)Wet2.0+Dry

The left side of Fig.4 shows the master curves of crs for Dry, Wetl.O and Wet2.0 specimens. A smooth gland- master curve of crs was obtained by shifting the master curves of as for Wet 1.0 and Wet2.0 specimens along the log scale of reduced time to failure t s ' until they overlapped each other. There fore, the timetemperature-water absorption superposition principle (TTWSP) holds for CTS. The time-temperature-water absorption shift factor a-ro,wo(T,W) obtained experimentally from Fig.4 were plotted in Fig.5. 1Q0 -4

-2

0

Reduced time to failure log t,' [min] 2 4 ' 6 8 10 12 14

16

16

TD=25°C

25 \

Temperature T [°C] 50 80 100 120 Do of Wetl.O

T0=25°C Wo=0%

Dry Wetl.O ' Weti.O+Dry

-

T0=25t W0=0%

-

Dfy • WeH.O Wet1.0+Dry

I

°-4

-2

I

34

32

30

28

26

[

0 2 4 6 8 10 12 14 Reduced-reduced time to failure log t,," [mln]

16

18

FIGURE 4 Grand-master curve of flexural CSR strength

FIGURE 5 TTWSP shift factor of flexural CSR strength

24

323

Time-Temperature-Water Absorption Superposition Principle Fatigue Strength

The flexural fatigue strength Cf versus number of cycles to failure Nf for the Dry and Wet 1.0 specimens at frequency f=2Hz and stress ratio (minimum stress/ maximum stress)R=0.05 are shown in Fig.6. The upper portion of Fig.7 shows a f versus the reduced time to failure tf' obtained from the S-N curves at various temperatures shown in Fig.6 based on the time-temperature superposition principle for CSR strength. Each point on these curves of constant reduced frequency represents the number of cycles to failure. Connecting the points of the same Nf with these curves, the master curves of c?f for constant Nf are constructed as shown in the lower side of Fig.7. The left side of Fig.8 shows the master curves of af for Dry and Wet 1.0 specimens obtained in Fig.7. These fatigue master curves can be superimposed by shifting there curves along the log scale of reduced time to failure tf' using the time-temperature-water absorption shift factor aTO,wo(T,W) for CSR strength as. Therefore, the TTWSP for a s also holds for af.

Wet1.0(Tv,=80'C) f=2Hz R=0.05

0

1

2 3 4 5 Number of cycles to failure log N,

0

1

2 3 4 Number of cycles to failure log N,

(a) Dry (b) Wet 1.0 FIGURE 6 Flexural fatigue strength versus number of cycles to failure at frequency 2Hz

25

Reducedtemperaturer f C] 50 80 1QQ

2 4 6 8 10 12 14 Reduced time to failure log tf' [min]

25

16

18

-2

0

Reduced temperature V p 50

2 4 6 8 10 12 14 Reduced time to failure log tf' [min]

(a) Dry (b)Wetl.O FIGURE 7 Master curves of flexural fatigue strength

16

18

Time-Temperature-Water Absorption Superposition Principle

324

£ 100 t? 80

f.

60

o

40

I E

T0=25°C Dry Wet 1.0

-

T0=25*C W0=0%

- . ~^.

N-1/2

^ Q \

N,=10=

-

\ 20 I

1

I

I 4

I

!

V •^1

6 8 10 log V [min]

i

i. ^n—~i

12

14

16

-4

-2

Dry WeH.O i i 0

2

I 4

I

I

I

6 8 10 log t," [min] •

I ""^T^Trx). 12

14

16

18

FIGURE 8 Grand-master curve of flexural fatigue strength

CONCLUSION The influence of water absorption on the time-temperature dependent flexural fatigue strength of unidirectional CFRP laminates, which consist of carbon fiber and epoxy resin were discussed. The CFRP laminates were prepared under three conditions of Dry, Wet and Wet+Dry. Three-point bending CSR and fatigue tests for these three kinds of CFRP laminates were carried out under various loading rates and temperatures. It is cleared that the flexural CSR and fatigue strengths of CFRP laminates strongly depend on the water absorption as well as time and temperature and the time-temperature-water absorption superposition principle holds for these flexural CSR and fatigue strengths. ACKNOWLEDGEMENTS This work was supported by the National Science Foundation (No. CMS-9812758), and the Asian Office of Aerospace R&D (No.AOARD-03-4062). REFERENCES 1. 2. 3. 4.. 5.

Aboudi, J. and Cederbaum, G, Composite Structures, 12: 243-256 (1989). Sullivan, J. L., Composite Science and Technology, 39:207-232 (1990). Gates, T., Experimental Mechanics, 68-73 (1992). Miyano, Y, Kanemitsu, M., Kunio, T. and Kuhn, H., J. Composite Materials, 20: 520-538 (1986). Miyano, Y, McMurray, M. K., Enyama, I , and Nakada, M., J. Composite Materials, 28: 1250-1260 (1994). 6. Miyano, Y, K. McMurray, M., Kitade, N., Nakada, M. and Mohri, M., Advanced Composite Materials, 4: 87-99 (1994). 7. Miyano, Y, Nakada, M., and McMurray, M. K., J. Composite Materials, 29:1808-1822 (1995). 8. Miyano, Y, Nakada, M., McMurray, M. K. and Muki, R., J. Composite Materials, 31:619-638 (1997). 9. Shen, C. H and Springer, G S., J. Composite Materials, 10: 2-20 (1976). 10. Kibler, K. G, AGRD Conference Proceedings, 8-1, (1980). 11. Neumann, S. and Marom, G, Polymer Composites, 6: 9-12 (1985). 12. Selzer, R., and Friedrich, K., Composites Part A, 28A: 595-604 (1997).Aboudi, J. and Cederbaum, G, Composite Structures, 12: 243-256 (1989).

Buckling of Composite Plates with Cutouts Jalil Rezaeepazhand* and Ali Moein Darbari Department of Mechanical Engineering, Ferdowsi University of Mashhad P.O. Box: 91775-1111, Mashhad, Iran

ABSTRACT Thin-walled shells and panels of various constructions find wide use as primary structural elements in simple and complex configuration. In aerospace structures, panels with variously shaped cutout are often used. The understanding of the effects of cutout on the buckling behavior of such plates has grown in importance with the increasing need for lightweight structures. The excellent mechanical properties of advanced composite materials make them prime candidates for a wide variety of application in aerospace, mechanical, civil and other branches of engineering. A finite element analysis, using commercial finite element software, is used to study the buckling behavior of laminated composite plates with different central cutout. Particular emphasis is placed on fiat square plates subjected to a uni-axial compression load. The main objective of this study is to demonstrate the buckling behavior of composite plates with central cutout. The effect of cutout geometry (circular, square, or special cutout), fiber angle, stacking sequences, and cutout size are discussed.

INTRODUCTION Use of reinforced composites in light-weight aerospace structures has increased steadily over the years. The outstanding mechanical properties of advanced composites provide the engineer with potential to optimize properties specific to application. The increasing use of laminated composite components for a wide variety of applications in aerospace, mechanical and other branches of engineering requires extensive experimental evaluation of any new design. The enormous design flexibility of advanced composites is obtained because of the large number of design parameters. The correct and effective use of advanced composite materials requires complex analyses in order to achieve good understanding of the system response characteristics to external causes. Different cutout shapes in structural elements are needed to provide access to other parts of the structure and to reduced the weight of the system. With a view to better understanding of buckling behavior of composite plates with central cutout, a numerical investigation was undertaken. This type of investigation can save considerable expense and time, and provide the necessary information on behavior of systems. Particular emphasis is placed on the case of simply supported square laminated composite plates with a central cutout. In the

"Corresponding Author, Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-111, Mashhad, Iran, [email protected].

326

Buckling of Composite Plates with Cutouts

present studies, the material behavior is assumed to be linearly elastic. Furthermore, it is assumed that the plate is without any imperfections. LITERATURE REVIEW Studies on the buckling behaviors of isotropic and composites plates with and without cutout are reported extensively. Nemathfl] presented an interesting review on earlier works on buckling behavior of composite plates with centrally located cutouts. The effect of cutout size and shape on the buckling and postbuckling response of quasi-isotropic plates subjected to uniaxial compression is presented by Bailey and Wood[2]. They investigated stability of perfect and imperfect square plates with circular and square cutouts. Both finite element and experimental results are presented. Ko[3] investigated the effect of plates aspect ratio, hole sizes, and boundary conditions on buckling of MMC composite plates with central square cutouts. Waas et al.[4] conducted a series of experiments to determine the failure mechanisms in compressively loaded laminated composite plates with a circular cutout. Hilburger et al.[5] presented a numerical and experimental study on the buckling behavior of quasi-isotropic curve panels with a centrally located cutout. Due to complexity involved in analysis of perforated plates, the closed form buckling solution are practically unobtainable. Numerical analysis using commercial finite element software is an attractive option for study the buckling behavior of perforated plates. This study investigates the problem of elastic buckling of simply supported laminated composite square plates with central cutout subjected to uniaxial compression load. Numerical studies using commercial finite element code, Ansys, were conducted to investigate the effects of variation in cutout geometries and shapes, laminate stacking sequences and fiber orientation on linear buckling responses of laminated composite plates with centrally located cutout. MATERIALS AND METHODS A square plate of dimensions 1000xl000x5mm is considered in this study. A circular cutout of diameter D is located at center of plate. The cutout ratio(DAV) is defined as the ratio of the cutout diameter to width(W) of the plate. Similar models were considered for rectangular, triangular and rhombic shape cutouts. Figure 1 shows these types of cutouts.

circular

square

triangular

rhombic

FIGURE 1: Different cutout shapes

Two types of compression loads, uniform displacing (displacement-loading) and uniform stressing (stress-loading) can be modeled [1]. Different types of loading, boundary conditions and plates aspect ratios have been investigated[6]. hi this paper, only results of displacement-loading are presented. A uniform inplane compression

Buckling of Composite Plates with Cutouts

327

load which applied in the edges perpendicular to longitudinal axis presents this type of loading. Both, simply supports and clamped supports are considered. The material properties of each ply are boron/epoxy with material properties given in Table 1. TABLE I : Material properties Al2024-T6 E = 70.02 GPa v = 0.32

Boron/Epoxy E, = 208 GPa E2 = E3 = 25.4 GPa G12 = 7.2. GPa v !2 = 0.1677

FINITE ELEMENT MODELS A finite element model is created for each case. The shell91 layered element is used to model the composite plates. This element has 8 nodes with 6 DOF at each node[7]. For each case, mesh sensitivity is performed in order to achieve an acceptable mesh density. Validation study for finite element modeling is carried out by comparing the analytical buckling loads of perfect aluminum and boron/epoxy square plates with those results from Ansys software. Good agreement is achieved[6]. RESULTS AND DISCUSSION Various cutout shapes and laminate parameters such as fiber angles, and stacking sequences are considered in this study. Effect of Boundary Conditions Figure 2 presents critical loads of especially orthotropic plates with a central circular cutout as a function of cutout ratios for simply(S-S) or clamped (C-S) supported boundary conditions. It is clear that, for S-S plates, increases in cutout diameter, increases the load carrying capacity(critical load) of the perforated plates. However, for C-S plates, introducing a small size cutout reduces the critical load. But large size cutouts increase the load caring capacity of plates. Effect of Cutout Shapes In order to study the effect of cutout shapes on buckling response of composite plates, three different central cutouts, rectangular, triangular and rhombic shape cutouts are compared with circular cutouts. Figure 3 compares change in critical loads of plates with rectangular and circular cutouts for different cutout dimensions. For identical cutout area, circular cutout has higher critical loads than rectangular cutouts. Similar results are shown in figure 4 for triangular and rhombic cutouts. Based on

Buckling of Composite Plates with Cutouts

328

0.2

D/w

0.6

0.4

CUTOUT AREA(m2)

FIGURE 2 Buckling loads of simply and clamped supported orthotropic plates with circular cutouts.

0.1

0.2

0.3

FIGURE 3 Buckling loads of S-S plates with circular and rectangular cutouts.

0.1

CUTOUT AREA (m )

FIGURE 4 Buckling loads for S-S orthotropic plates with triangular and rhombic cutouts.

0.2

0.3

0.4

0.5

0.6

0.7

D/W

2

FIGURE 5 Buckling loads of orthotropic and cross-ply plates with circular cutouts.

presented results, triangular cutouts yield higher critical loads than rhombic and rectangular shape. Effect of Stacking Sequences and Fiber Orientations To demonstrate the effect of fiber orientation and stacking sequence in critical load of perforated plates, different lay ups with equal number of plies are considered in this section. It is assumed that, all plates have a central circular cutout and S-S boundary conditions. Figure 5 compares the critical buckling loads of 20 layers especially orthotropic plates( 0 = 0 or 90) with a symmetric cross ply (0/90)5S plate with the same number of plies. It is clear that, cutout dimensions have similar effect

Buckling of Composite Plates with Cutouts

329

on these laminate configurations. However, when all fibers are located in load direction (9 = 0), increase in critical loads is higher than two other configurations. The effect of fiber orientation on buckling response of symmetric angle ply laminates (±9)5S is presented in figure 6. Three different cutout ratios(D/W=0.1,0.3, and 0.5) are considered. It is shown that, fiber angle has considerable influence on critical loads of perforated plates. For small cutout ratios, a maximum critical load can be achieved when 6 = 30. Figure 7 presents variations of critical loads as a function of cutout ratio for isotropic, quasi-isotropic and orthotropic materials. It is clear that, as cutout ratio increases orthotropic plates achieved higher critical load than quasi-isotropic and isotropic ones.

0

15

30

45

60

75

90

Angle FIGURE 6 Effect of fiber orientation on buckling loads of (±8)5s perforated plates.

FIGURE 7 Buckling loads for isotropic, quasiisotropic and orthotropic perforated plates.

CONCLUSIONS AND RECOMMENDATIONS This study investigates problems associated with laminated composite plates with centrally located cutouts. Such study is important since it provides the necessary design information for buckling behavior of perforated composite plates. Linear elastic buckling responses of laminated composite plates with various cutout shapes and sizes, stacking sequences and fiber orientation have been studied. The results presented indicated that, buckling response of laminated composite plates is significantly changed by cutout size and shape, fiber orientation, stacking sequences, and boundary conditions of perforated plates. The results presented herein indicate that, for a perforated composite plate a set of cutout shape and size can be found which increase the load carrying capacity of the perforated plates. Some recommendations for future research include a) study the effect of initial geometric imperfection, b) study of the effect of other boundary and load conditions, and c) initiation of an experimental program for validation.

330

Buckling of Composite Plates with Cutouts

REFERENCES 1. Nemeth, M. P., 1996. "Buckling and Post buckling behavior of laminated composite plates with a cutout" , NASA technical paper 3587. 2. Bailey, R and Wood, J. 1996. "Stability characteristics of composite panels with various cutout geometries", Composite Structures 35 , pp 21-31 3. Ko, W. L, 1998. "Anomalous buckling characteristics of laminated MMC plates with central square holes", NASA/TP-1998-206559. 4. Waas, A.M., Babcock, C. D. Jr. and Knauss, W.G., 1998 "An experimental study of compressive failure of fibrous laminated composites in the presence of stress gradients", International Journal of Solids and Structures, Vol. 26, No. 9/10, pp. 1071-1098. 5. Hilburger, M. W. et al., 1999. "Buckling behavior of compression-loaded quasi-isotropic curved panels with a circular cutout", Proceeding of 40' AIAA/ASME/ASCE/AHS/ASC, SDM conference, April 12-15, St. Louis, Missuri, AIAA paper 99-1279. 6. Moein Darbari, A. 2003, Buckling analysis of plates with central cutouts, MS. Thesis, Ferdowsi University of Mashhad, Iran.(in Persian). 7. ANSYS User's Manuals.

Fatigue Crack Propagation in Graded Composites Matthew Tilbrook*, Lyndal Rutgers, Robert Moon and Mark Hoffman School of Materials Science & Engineering, University of New South Wales, Australia

ABSTRACT Material structures exhibiting- a tailored variation in properties are collectively termed functionally graded materials (FGMs). Despite the considerable advances in understanding of FGMs over the past decade, several key areas require further work, including the fatigue behaviour of, and crack propagation paths in, FGMs. Graded alumina-epoxy composite samples, exhibiting an approximately continuous spatial variation in composition and properties, have been produced via an infiltration process. Fatigue cracks have been initiated and propagated under cyclic four-point bend loading. Crack deflection has been observed, along with subsequent deviation and curvature as the crack moves through the graded region. A variation in fatigue crack growth resistance was observed as the crack moved through regions of varying composition. A finite element model, which employs automatic crack extension and remeshing, has been developed to simulate the propagation process. Particular attention was paid to the criteria used for crack propagation and deflection, and to the effects of bridging on crack path. Experimental results and modeling predictions are presented and compared.

INTRODUCTION Functionally graded materials (FGMs) represent a solution to problems that can arise at interfaces between different materials, due to elastic property mismatch and poor adhesion. FGMs, which are usually composite materials, have been a key focus in composites [1] and fracture [2] research over the past decade. In spite of this and the fact that high performance materials often fail due to damage sustained under cyclic loading [3], research on fatigue crack propagation in graded materials has been limited [4-6]. This paper details an investigation, through experiment and simulation, of crack propagation in functionally graded material specimens. Graded alumina/epoxy composite samples have been produced via an infiltration process, and fatigue cracks have been initiated and propagated within them under cyclic four-point bend loading. To enable simulation of crack propagation, effective composite properties were quantified and a finite element model, which employs automatic crack extension and remeshing, was developed. Experimental results and modeling predictions are presented and compared in Section 4, demonstrating good agreement. EXPERIMENTAL PROCEDURE Graded alumina-epoxy composite specimens, exhibiting an interpenetrating network structure, were produced by a multi-step infiltration process, as in [6] and [7]. * Correspondence Author, School of Materials Science & Engineering, University of New South Wales, Sydney NSW 2052 Australia. Email: [email protected] Fax: (02) 9385 5956.

332

Fatigue Crack Propagation in Graded Composites -40 mm

Length -130 mm

95%A"-iv..

Notch-12 ran/

o

V .::>••:.

ABCDE

FIGURE 1 Schematic of graded composite four-point bend specimen. Approximate compositions for the gradient steps: A: 30% alumina/70% epoxy, B: 45/55, C: 55/45, D: 70/30, E: 85/15.

The processing steps were as follows: (1) Open-celled polyurethane (PU) foam (Bulpren S-31048, Eurofoam, Troisdorf, Germany, 90 pores/inch) was used as an preform for the interpenetrating network structure. Foam pieces were compressed from an initial density of 2.5% to obtain the required volume fractions of foam and air. (2) These were positioned in a stepped configuration and infiltrated with a suspension of alumina particles (99.99% AI2O3, Taimicron TM-DAR, Taimei Chemicals Co Ltd, Japan) under cycled pressure conditions then allowed to dry. (3) The foam was then pyrolysed at 800°C, leaving a ceramic green-body (approximate dimensions: 60 x 35 x 9mm3) with a network of interconnecting pores, and a graded pore distribution. The ceramic was sintered at 1500°C for one hour leading to ~ 10% shrinkage in each dimension. (4) Ceramic pieces machined to remove excess material with rotary grinding wheel. (5) Ceramic pieces were positioned in silicone moulds and epoxy resin (Epofix, Struers, Germany) was infiltrated into the ceramic under varying pressure then cured at room temperature. (6) Specimens were then ground to size (approximate dimensions: 130 x 30 x 6 mm3) with a 600 grit diamond grinding wheel, and polished with an automatic polisher and diamond paste down to a diamond particle size of 1 micron in the final step. The final dimensions of a typical graded specimen are shown in Figure 1. A variety of gradient specimens were produced and tested, enabling examination of the effects of variation in gradient and notch parameters on crack propagation. Microstructural characterisation of the graded composite samples was conducted via optical microscopy. Optical micrographs are shown in Figure 2, in which phase continuity at step-interfaces may be clearly observed. Phase volume fractions were determined from relative areafractionsof each phase in the micrographs. Crack propagation in graded samples under cyclic four-point bend loading was conducted using an hydraulic MTS in load control. Crack initiation occurred from a notch sawn into the graded region. The notches were sharpened using a razor blade and diamond paste to obtain a notch root radius around 10-20 microns. Crack extension was observed with a microscope (Olympus ) and digital camera (Optronics ) which enabled fatigue crack growth rates to be measured. COMPOSITE PROPERTY DISTRIBUTION Accurate prediction of crack propagation in graded specimens requires detailed knowledge of the spatial distribution of effective composite properties within the graded region. Elastic properties of homogeneous alumina-epoxy composites have previously been quantified, from which the distributions of properties within the graded samples were estimated. Non-graded specimens, with compositions ranging from 95% alumina to 50% alumina, were produced in a manner similar to that in Figure 1, and characterised via microanalysis and impulse excitation measurements, with results published in full elsewhere [9].

Fatigue Crack Propagation in Graded Composites

333

Fatigue testing was also conducted on notched homogeneous composite beams under cyclic four-point bend loading. They generally exhibited Paris-law behaviour, as illustrated in Figure 3(a), with large values (-24) for the exponent, m, as expected for brittle materials. An increase in crack-growth resistance with crack extension was observed, and attributed to crack-wake effects. This is demonstrated in Figure 3(b), which shows that, while the applied SIF for crack propagation tended to increase with crack extension, the resultant crack propagation rate tended to decrease. In general, composite specimens with increased epoxy volume fractions exhibited significantly decreased stiffness and intrinsic toughness, as illustrated in Figure 4 which shows the compositional and corresponding property distributions across one of the graded specimens.

i ii •

Ml!

5% epoxy

45° o epoxy

epoxy

FIGURE 2 Optical micrographs of graded composite specimens showing interfaces between steps. Approximate compositions of steps are given and positions of the interfaces are indicated.

; 30% Epoxy

;;

45% Epoxy/ m = 25 o ,'

• •'a 1

P o,1 ° a

en: °:

* it • » > \\ 11 x \ s e % Epoxj • 4 ^ m = 27

D

9.' i'o

(a) 10"'

; :

11% Epoxy * ^ ' | m = 24 ;;»

10 10 Applied Stress Intensity Factor Range, AK [MPa m 1 / 2

0.5

1

1.5

Crack Extension, Aa [mm]

FIGURE 3 Results of fatigue tests on homogeneous composite samples, (a) Fatigue crack growth rates for several different compositions, showing Paris law behaviour, (b) Systematic decrease in crack growth rate with crack extension, with increased applied SIF range, indicative of crack-extension toughening effects.

Fatigue Crack Propagation in Graded Composites

334 1

— ID

- Volume fraction (epoxy) - Relative E - Relative Kc

S o-s •9* O 0.6 CO

jjO.4

-

0 >

1

— 02 CD

U

a: i

n

I

5

i

1

10

- 1

15

20

Position across gradient, x [mm]

FIGURE 4 Material Gradient: Measured compositional distribution for a graded composite sample, along with stiffness and toughness distributions calculated from experiments on homogeneous specimens.

FINITE ELEMENT SIMULATION A finite element model has been developed to simulate the process of fatigue crack propagation in graded specimens. The commercial FEA software package ANSYS (Version 6.1, ANSYS Inc, Canonsburg, Pennsylvania) was utilised, with a number of modifications specific to graded materials. Full details of this model, and various aspects of its validation, are given by Tilbrook et al. [10] however several key aspects warrant mention here: 1) The spatial distributions of effective properties, in particular stiffness and fatigue resistance, were calculated from the compositional distribution and the experimental results for homogeneous composites described above. 2) Application of material stiffness gradient. As ANSYS does not allow graded elements, this was achieved by defining temperature-dependent properties, and assigning nodal temperatures individually, leading to a spatial temperature and property gradient. 3) Calculation of fracture parameters. Mode I and II stress intensity factors were determined from crack-opening and crack-sliding displacement values respectively for nodes near the crack-tip. Crack propagation was assumed to occur for: where Kc(x, Aa) was estimated to include crack-extension toughening effects. 4) Determination of crack propagation direction. The local symmetry criterion (Kn = 0) was used. A test kink was extended from the crack-tip and its angle varied to minimise Kii. The size of the test kink was 50 microns, which corresponded to <0.5% of the original crack length. 5) Crack propagation was simulated automatically with a routine to delete the mesh and areas around the crack, extend the crack, and then redefine the geometry and mesh. The crack was extended in increments of 0.5 mm, <5% of original crack length. This model has been used previously [10] to investigate the influence of various gradient parameters on crack-tip stresses and crack paths. In the current work, the model was used firstly to predict crack paths for comparison with experiments, and secondly to analyse the experimental fatigue data, as expressions relating applied load to crack-tip stress intensity factor are not known for graded materials, particularly for curved cracks.

Fatigue Crack Propagation in Graded Composites

335

RESULTS & DISCUSSION Initial deflection of cracks toward the more compliant epoxy section was observed as expected [12], followed by further deviation as the crack progressed through the graded region, as shown in Figure 5. Some key results of fatigue experiments on FGMs and corresponding FE simulations are presented and compared in Figures 6 and 7. Figure 6 shows crack paths in FGM specimens with similar gradient profiles but differing gradient widths. The effect of gradient steepness on deflection is clearly observed as cracks in the narrower, steeper, gradients deflected more (-50°) than those in wider gradients (-25°). This comparison is illustrated in Figure 5(b) and (c). The effects of varying initial notch position and length do not appear significant over the ranges investigated, which is concordant with previous conclusions from FE simulations [10]. In Figure 7, the variation in applied cyclic loading with crack length is shown for an FGM specimen. These loads are close to those required for fracture, because the range of cyclically applied loads over which crack propagation occurs is very small for brittle materials (Figure 3(a)). The experimental load variation is compared with FE predictions, and demonstrates far better agreement with predictions for which R-curve behaviour was taken into consideration, than with those for which it was neglected. This indicates that R-curve behaviour can influence failure strength significantly, although it does not appear to affect crack propagation path significantly.

(b)

(a)

(O

FIGURE 5 Images of cracks in graded specimens, (a) initial deflection from notch-tip and further propagation across specimens with (b) wide and (c) narrow gradient.

:

(a)

16 -

E

14 -

y

*= 12

10 -

6

8

10 •

12

14

16

18

20

Displacment from ceramic-gradient interface, x [mm]

0

2

4

6

8

10

12

Displacement from ceramic-gradient interface, x [mm]

FIGURE 6 Crack propagation paths in graded samples under four-point bending - experimental results and modeling predictions for cracks in gradients of (a) 20mm and (b) 10 mm approximate width.

336

Fatigue Crack Propagation in Graded Composites

Experiment - FEM - with R-curve • FEM - without R-curve

Crack Extension, Aa [mm]

FIGURE 7 Applied loading profile for crack propagation in a graded sample under four-point bending.

CONCLUSIONS Graded alumina-epoxy samples have been produced via infiltration for investigating the effect of material property gradient on crack propagation, in conjunction with homogeneous composite characterisation and finite element modelling. Crack deflection was observed, with close agreement between measured and predicted deflection angles. Higher deflection was observed for steeper gradients and for cracks initially situated within the epoxy-rich region of the gradient. Crack-wake effects were observed for both homogeneous and graded composites. Whilst these effects have a notable influence on crack propagation resistance, they do not appear to influence the crack path significantly.

REFERENCES 1.

Neubrand A., J. Rodel, 1997. "Gradient Materials: An Overview of a Novel Concept," Zeit. f. Met. 88:358-71. 2. Paulino G.C. (ed), 2002. "Fracture of Functionally Graded Materials," Eng. Fract. Mech. 69:1667-78. 3. Ritchie R.O., 1999. "Mechanisms of fatigue crack propagation in ductile and brittle solids," Int. J. Fract. 100:55-83. 4. Tilbrook, M.T., RJ. Moon, and M. Hoffman, 2003. Crack Propagation in Graded Composites, Comp. Set. Technol. (accepted). 5. Forth S.C., L.H. Favrow, W.D. Keat, J.A. Newman, 2003. "Three-dimensional mixed-mode fatigue crack growth in a functionally graded titanium alloy", Engng. Fract. Mech. 70:2175-2185. 6. Xu F.M., S.J. Zhu, J. Zhao, M. Qi, F.G. Wang, S.X. Li, Z.G. Wang, 2003. "Fatigue crack growth in SiC particulates reinforced Al matrix graded composite," Mat. Sci. Engng. A 1-6. 7. Cichocki F.R., K.P. Trumble, and J. Rodel. 1998. "Tailored Porosity Gradients via Colloidal Infiltration of Compression Molded Sponges," J. Am. Ceram. Soc, 81(6): 1661-1664. 8. Neubrand, A., T.-J. Chung, J. Rodel, E.D. Steffler and T. Fett, 2002. "Residual stresses in functionally graded plates,"./. Mater. Res., 17 (11): 2912-2920. 9. Tilbrook M.T., R J. Moon and M. Hoffman, 2003. "On the Mechanical Properties of Alumina-Epoxy Composites with an Interpenetrating Network Structure," Mat. Sci. Engng. A (submitted). 10. Tilbrook M.T., RJ. Moon and M. Hoffman, 2003. "Finite Element Analysis of Crack-Tip Stresses and Crack Propagation in Functionally Graded Materials," Engng. Fract. Mech. (submitted). 11. Bittencourt T.N., P.A. Wawrzynek, A.R. Ingraffea and J.L.A. Sousa, 1996. "Quasi-automatic simulation of crack propagation for 2D LEFM problems," Engng. Fract. Mech. 55:321-324. 12. Gu P. and Asaro R.J., 1997. "Crack Deflection in Functionally Graded Materials," Int. J. Sol Struct. 34(24):3085-98.

Dynamic Response Behavior of Stiffened Delaminated Plates Considering Failure Ruixiang Bai, Haoran Chen* State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P.R.China Man Wang. Dalian Institute of Light Industry 116034, P.R.China

ABSTRACT The paper is to study on dynamic response behavior of the stiffened delaminated composite plates considering failure process. A formula of element stiffness and mass matrices for the composite laminated plate and beam are deduced by using the first-order shear deformation theory. A damping model is constituted on the basis of Raleigh damping model in conjunction with Adams' strain energy method (MSE). A delaminated constrained model and a virtual interface element are also developed for avoiding the overlap and penetration phenomenon between the upper and lower sub-laminates at the delamination region. The failure analysis method is established by Tsai's failure criterion and corresponding reduced stiffness role. Some numerical examples show that the effects of frequency of dynamic load, delamination location, and reduction of structure stiffness during the failure process dynamic behavior of the delaminated composite laminates are significant.

INTRODUCTION The initial-delamination caused by the external low velocity impact by foreign objects during the manufacturing process and/or in the service life and the progressive failure under dynamic load for the stiffened composite plates can significantly alter the dynamic properties and response of composite structures, hence a clear understanding of their dynamics behaviors is of extremely importance in designing and maintaining the laminated composite structures. The investigation and analysis of dynamic response for stiffened delaminated plates are of great interest to engineers and mechanics scientists and so far many valuable papers have been published [1-6], however they haven't considered the progressive failure. Therefore, the investigation in this paper is a significant engineering subject need to be solved. The paper is to deal with dynamic response behavior of the stiffened delaminated plates, especially, considering progressive failure process. The methodology, model and corresponding analysis method method established and conclusions given by some typical examples would be useful for composite structures designers.

* Corresponding Author, Email: [email protected].

338

Dynamic Response Behavior of Stiffened Delaminated Plates

ANALYSIS THEORY For the sake of simplicity, consider a stiffened laminated plate with an arbitrarily located through-width delamination, which can be divided into three spans wise regions, namely one delamination and two perfect regions, as shown in Fig.l.

X

—\ y \

\

\ \

\

\

\ \ /^—— \ "l '^

\ Upper sublami.

FIGURE 1 Delamination model of stiffened composite laminated plate

Based on first-order shear deformation theory and Hamilton's principle, The formulae of element stifmess and mass matrices for the plate have been deduced by authors in Refs. [2,4,7], as

K=L BTDBdQ M = \a NTRNdQ

(1)

Where D and R denote the generalized stiffness and mass density matrix, and B and N are the geometry and shape function matrix, respectively. Assuming the damping behavior of the laminates to be slight weakness, an approximate energy method proposed by Adams can be employed in the dynamic analysis of the structures [8]. According to the measured specimen's loss factor matrix 77, the specific damping capacity y/j corresponding toj-th mode can be determined by the following formulation:

y/ . =

AU

i

'- = -^—'

(2)

Here {$•} is the j-th modal shape of the structures, [K"] and [^5] denote the structural stiffhess and the damped structural stiffhess matrix, respectively. If § i s defined as the modal damping ratio for the y'-th mode, thus y/j=AnZj

(3)

Furthermore, the damping matrix [C] can be given by Raleigh damping model. Employing Hamilton's principle, the motion equation can be given as

Dynamic Response Behavior of Stiffened Delaminated Plates Mu + Cu+Ku=P(t)

339 (4)

where M> C and K are the total mass matrix, stiffness and the damping matrix, while u and P(t) are the total displacement and the force vector of the structure. To ensure integral stability in time domain, the Eq. (4) is transformed into the following precise time-integration iteration formulation [9]: v = Hv + r

(5)

Where

H = \°

7

\B G\ B = -M'K

0

l v = R r-M-'P(t) \U\

G=

-MC

hence, PD-S(Sinusoidal) formulation as[10]: v

(^i+i) = ^(T)[v(.h ) ~

a

sin(o^) - b cos(ft)^)] + a sin(e#k+1 ) + b cos(atk+l)

(6)

Here

b = (a I + H 2 / a}' (-r, - Hr2 / w)\

MEDELING AND FAILURE CRITERION In accordance with the requirement of displacement continuity at the nodes along the delaminated front between perfect and delamination regions, the following additional continuity conditions must be imposed as [7]: M

u2

v

v2 =vs+0x3(H-hu)/2 w2= w3

i =u,+0y,(H-h,)/2

i =v3-6x3(H-h,)/2 w, =w3

=u3-0yi(H-hu)/2 (8)

H, hu and hi are the thickness of the base, upper and lower sub-laminates respectively. Next, the virtual interface piecewise linear spring elements are inserted along the delamination interface surfaces for preventing penetration of the upper and lower sub-laminates during dynamic analysis process [5,7], The stiffness matrix of element as "" 1 - 1 " (9)

['•M-.

Here k is a specified stiffened factor, which is defined to be zero in the separated state or a linear function of the transverse relative displacement between the upper and lower sub-laminates in contact. In addition, Tsai-Hill failure criteria is employed for

340

Dynamic Response Behavior of Stiffened Delaminated Plates

predicting the local damage failure occurrence and the following stiffness degradation rules are applied to determine the reduced material properties during the dynamic analysis process [11]: E2 =0.56E2 =

(10)

G,*2=0.44G12

jul

NUMERICAL EXAMPLE AND DISCUSSION Dynamic Response and Failure of Perfect Bare and Stiffened Laminated Plates Excited by Sinusoidal Uniform Distributed Load Consider a [0/90/90/0]4S perfect bare and stiffened laminated square plates with simply support along the four edges. The length and thickness are 400mm and 10mm for both plates; and the width and distance between the [0]64 stiffeners are 10mm and 200mm; respectively. The mechanical properties and strength parameters for both plates are£,=135.0Gpa, £2=8.80Gpa, v12=0.33, Gn = G23 = G13 =4.47Gpa, p= 1380Kg / m \ yl =0.43%, y/2 = 3.86%, tf/4 =i//5 =y/6 = 5.72% and Xt =Xc = 1447Mpa, Yt = 52Mpa, Yc = 206Mpa, S = 93Mpa, respectively. The exciting sinusoidal uniform distributed load q = 530 sin (a aot) kpa, here, a>0 denotes the natural frequency in the first mode for the laminates and a is a specified constant. Fig.2 plots the normalized dynamic midpoint deflections (w/H) versus the normalized time t / T within the first period for a = 0.691 case. The curves marked land 1 denote the midpoint deflections for the bare laminates ignoring and considering failure, while the curves marked 2 and 2 represent the midpoint deflections of stiffened laminates for ignoring and considering failure effect, respectively. It is clear that the dynamic deflections for stiffened plate are obviously lower than that for bare plate; and the normalized dynamic midpoint deflections of the both laminates for considering failure effect case are significantly larger than that for ignoring failure effect case. Hence the stiffeners can improve the dynamic stiffness of the laminates considerably and the effect of stiffness degradation caused by progressive failure upon the dynamic stiffness cannot be ignored for both laminates.

0.20

0.40

0.60

0.80

1.00

FIGURE 2 Dynamic deflections at middle point with and without considering failure for perfect bare and stiffened laminated plates in CC=0.691case

1.00 0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

FIGURE 3 Variation of magnification parameters with a for perfect stiffened laminated plate

Dynamic Response Behavior of Stiffened Delaminated Plates

341

Fig.3 illustrates the variation of magnification parameters with a for the stiffened laminated plate, in which the curves marked 1 and 2 represent the results for ignoring and considering failure effect cases, respectively. Compared curve 1 and 2 shows that the values of X in the first three resonant peak points for ignoring failure effect are less than that for considering failure effect, and the variation rate of X with the exciting load frequencies approaching to the resonance stage for former is not steeper than the latter. The reason is the plate near the resonance stage appears in grave failure. Thus the stiffness degradation and exciting load frequency are two significant aspects affecting the dynamic deflection of stiffened laminated plate. Dynamic Response and Failure of Stiffened Delaminated Laminates Excited by Sinusoidal Uniform Distributed Load Consider a [O2 /904]s stiffened delaminated plate with boundary conditions as simply supports along the x directional edges and free along the y directional edges, which is excited by a sinusoidal uniform line distributed load q =1000sin (200 ^t) kPa in the middle span, The length, width and thickness the base-plate are 600mm, 200mm and 15mm; the thickness and distance between [0]e4 stiffeners are 10mm and 100mm respectively. A through width delamination with length 120mm is located at middle span of the plate. The material properties of the plate are the same as foregoing example. The Fig.4 (a) and (b) depict the curves of (w/H) - (t / T) for the plates with different delaminaton locations along the thickness direction for ignoring or considering failure effect respectively: where the cures from the bottom to the up denote that for hi/ h=l/6, 1/4, 1/2, 3/4 and 5/6; respectively.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

( a ) Ignoring failure

-0.50 L 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

( b ) Considering failure

FIGURE 4 D dynamic deflection at middle point for upper sub-laminates with deferent delamination locations

It can be also indicated that the effect of delamination and progressive failure decrease the dynamic stiffness of the stiffened plates, significantly, which depend on the frequency of dynamic load, delamination location and shapes. ACKNOWLEDGEMENTS The authors are grateful to the support of National Natural Science Foundation in China, Grant No. 10272025

342

Dynamic Response Behavior of Stiffened Delaminated Plates

REFERENCES 1.

Saravanos D A and Hopkins D A. 1996. "Effects of Delaminations on the Damped Dynamic Characteristics of Composite Laminates: Analysis and Experiments," Sound Vibration, 195(5): 977-993. 2. Hong M and Chen H R. 1999. "Vibration frequency, mode and damping behavior of laminated composite plates with delamination," J. Ship Mechanics, 3(6):28-38. 3. Luo H and Hanagud S. 2000. "Dynamics of delaminated beams," / Solids and Struct., 37:1501-1519. 4. Hong M and Chen H R. 2000. "Dynamic behavior of laminated composite plates with delamination," J of Shipbuilding Structural Mechanics, 4(6): 28-38. 5. Wang J, Tong L. 2002. "A study of the vibration of delaminated beams using a nonlinear anti-interpenetration constrained model," Compos Struc, 57:483-488. 6. Kim H Y, Hwang W B. 2002. "Effect of debonding on natural frequencies and frequency response functions of honeycomb sandwich beams," Compos Struct., 55:51-62. 7. Chen H R and Bai R X. 2003. "Study on failure process of delaminated stiffened composite plates under compression," Ada Mechanica SINICA, 19(4):289-299. 8. Adams R D and Bacon D G C. 1973. "Effect fiber-orientation and laminate geometry on properties of CFRP. J. Comp Mater., 7:402-428. 9. Zhong W X. 1994. "On precise time-integration method for structural dynamics," J. Dalian University of Technology, 34(2):131-136.(in Chinese) 10. Lin J H. 1995. "On precise time-integration method for structures under random exciting dynamic load," J. Dalian University of Technology, 35(5):600-606.(in Chinese) 11. Tsi S W. 1986. "Composites Design," United State Air Force Materials Laboratory Press.

Tensile Behaviour of Polymer Coated Optical Fibres Susan Law Australian Photonics/Optical Fibre Technology Centre, The University of Sydney, NSW 2006, Australia Cheng Yan and Lin Ye Centre for Advanced Materials Technology, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia

ABSTRACT It is still arguable if the standard testing method for fibre using a mandrel can be used to investigate the tensile behavior of a coated optical fibre. In this work, the failure mode of an optical fibre with polymer coating was examined using different gripping methods. The results indicated that the tensile behavior of the fibre was closely associated with the gripping methods. If the fibre was only gripped on the coating, the failure was dominated by delamination between the fibre core and the coating due to high shear stress. The maximum failure load was observed in the sample when the gripping point (epoxy drop) was over the fibre core and the end of the coating. The implications of these results on the design of photonic packaging were also discussed.

INTRODUCTION Fibre termination assemblies pervade photonics in all its forms from connectors in networks to hermetic feedthrough terminations in components to sensor tips in photonic thermometers. Wherever optical fibre is used, there is a requirement at some point for it to be engineered into a structure for connection to some other device. The recognition that failure of these terminations was a major cause of failure in photonic devices has led to work such as Suhir's studies of the structural mechanics of polymer-coated silica fibre [1] and Matthewson's work on the reliability of silica fibre [2]. Despite this, the intrinsic brittle nature of glass means much more work needs to be done [3], especially on the failure mechanisms of fibres and coating under mechanical and thermal loading. Traditionally "pigtailing fibre", the fibre used to provide the optical connection in packaging photonic devices, has been the poor cousin to transmission fibre and specialty fibre for devices. In general standard transmission fibre has been used and the only attempt to produce specialty packaging fibre to meet the mechanical requirements of packaging was the release of a fibre with 90 |^m cladding diameter to reduce the tensile and compressive stresses experienced by the fibre within a package [4, 5]. The reliability of optical fibre has principally been studied in respect of durability of cabling,, and the only mechanical test applied to optical fibre in manufacture is the * Corresponding author, Optical Fibre Technology Centre, University of Sydney, 206 National Innovation Centre, Australian Technology Park, Eveleigh NSW 1430. Fax: +612 9351 1911; Email: [email protected]

344

Tensile Behaviour of Polymer Coated Optical Fibres

strength proof test [6] to eliminate sections of fibre containing microcracks. Short lengths of fibre, such as those used in connectorising, are regarded as "strong" in that there is a low probability of a significant microcrack within the length [2]. No discussion has been devoted to the structural mechanics of anchoring fibre in the standard reference on photonic packaging [7] and the only standard pertaining to the durability of the fibre termination is a simple tension test between the device casing and the external cable based on a test developed for connectors [8]. As Trewhella et al. pointed out [9], the conclusions which can be drawn from this particular test are somewhat limited. Understanding the failure modes of a joint or anchor point is a key preliminary to developing more reliable joints, hi this work we carried out a preliminary investigation on the tensile behaviour of a polymer coated optical fibre. The attention was directed to the effects of griping (anchoring) methods on the failure modes. EXPERIMENTAL PROCEDURE The tensile test was carried out in accordance with the American Standard for Test and Measurement ASTM D 3379-75 [10]. An Instron 5567 with a load cell of 10 and 100 N and pneumatic grips was used. Samples were prepared by mounting a single fibre on a pre-prepared paper frame. Two styles of paper frame were tried, one with a diamond cut-out and one with a rounded rectangular cut-out (Figure 1).

FIGURE 1: Two types of paper frame used.

FIGURE 2 Three methods of mounting the fibre.

The length of the cut-out is equal to the gauge length, i.e. the length over which the strain is measured. It was found that the adhesive was more likely to conform to the gauge length when the rectangular cut out was used. A comparison was also made between the use of 2-part epoxy and Acrylate superglue. The former can form a small solid drop after curing, which was found to be more suitable for griping the fibre due to the absence of interaction between the grips and the coating. The fibre tested was a standard commercial single mode fibre with an 8.5 urn doped silica core, 125 |j.m silica cladding and a dual-layer acrylate coating of final diameter 250 |j.m. The fibre was mounted using the epoxy in three different ways, i.e., mounting on the coating directly, mounting only on the bare fibre core after stripping off the coating and mounting on the stripped fibre and the end of the coating, as shown in Figure 2. The fibre was stripped with a mechanical stripper and cleaned with methanol (a common but not optimal method of removing the coating from a fibrefl 1]). Several gauge lengths (10, 25 50 and 100 mm) were used to examine the effect of fibre length on the tensile behavior of this fibre. The same loading rate of 1 mm/min was used for all samples.

Tensile Behaviour of Polymer Coated Optical Fibres

345

RESULTS AND DISCUSSION Gripping on Coating Figure 3 give a typical load-extension curve for the sample with 50 mm gauge length. The load drops after reaching a peak value. An almost constant load is maintained with further increase of the extension. The peak load varies over the range 6~8 N. A similar result has been observed in the samples with 10 and 25 mm gauge lengths. 10

2 0 -2* Extension (mm)

FIGURE 3 Load versus extension curves for the sample with 50 mm gauge length.

FIGURE 4 Tensile stress (CTf) and shear stress (x) at the fibre/matrix interface

Observation of the failed fibres indicated that the fibre was not broken during the test but the polymer coating was stripped from the cladding. Obviously, delamination took place first during the loading. It is interesting to note that the location of the delamination was very close to the gripping points and changed a little among the samples tested. Nairn's stress analysis [11] on an embedded fibre showed that the maximum shear stress (T) is located at a short distance from the loading points, as shown in Figure 4. This is why the delamination always starts from the sites close to gripping points. Consequently, the coating itself breaks as a result of load shift from the fibre to the coating because the load is applied to the coating and the fibre does not bear any loading due to the delamination (Figure 5). In all cases this occurred at or close to the anchor point. Following this the coating is stripped from the fibre with further delamination under an almost constant load.

Tensile Behaviour of Polymer Coated Optical Fibres

346

FIGL'KK 5 Coating dulamination and failure.

The consistency of coating failure indicates that no uniform deformation/strain can be established along the full length of the fibre/coating structure due to the weak interface strength between the coating and the fibre. This implies the sites close to anchoring points of optical fibres can be the potential failure sites in a photonic device. Shorter samples also showed evidence of delamination at the interface between the two coating layers Gripping on Fibre When the gripping point was on bare fibre, the failure mode was dominated by the fibre breaking. The relationship between load and extension is shown in Figure 6 where a typical elastic behavior is observed as expected for a material like silica. Compared with the sample gripped only on the coating (Figure 3), a lower extension but a higher load corresponding to failure point is observed due to the high elastic modulus of silica fibre. 20 15

0 (I

0.5

1

1

-5 Extension (mm)

FIGURE 6 Load vs extension for sample gripped on bare fibre.

Gripping on Fibre and End of Coating In the case where the gripping point (epoxy drop) was over the fibre and end of the coating (Figure 2), the fibre typically failed at one end. Failure occurred in the coated section under the epoxy drop with the fibre stub sliding out of the coating. Examination of the failed samples under the microscope indicated that the failure occurred between

Tensile Behaviour of Polymer Coated Optical Fibres

347

0.5 and 1 mm from the end of the coating (Figure 7). Failure loads were significantly higher than for gripping on bare fibre, as shown in Figure 8. End of Coating

End of Coating

EIVJ

of Fibre

Fibre sliding ou: of anchored coating

FIGURE 7 Failure of fibre under epoxy droplet when gripping over the end of the coating.

One reason is the contribution of coating to the elastic load. Another possible reason is the high constraint imposed by the epoxy drop on the end of the coating, which can increase the load bearing capacity but limit the development of high shear stress for possible delamination. 30 y 25 20' 15 o 10 50 0.5

1

1.5

25

-5 Extension (mm)

FIGURE 8 Load vs extension plot for sample gripped over fibre and end of coating.

Implications for Photonic Packaging Based on above results, the strongest joints for fibre connection in terms of failure load are those where the bond is over the end of the coating although the failure mode is very complex. While anchoring over the coating generally results in delamination close to the anchor point with the fibre left intact, such a failure can have dire consequences both for the optical alignment of a system, and for the durability of the delaminated fibre section (even if the coating does not fail) [12, 13]. hi the case of two anchor points in close proximity (e.g. a fibre end mount and a package feed through) it would appear that significant shear stress can develop on the interface between coating layers for a dual coated fibre. Further work on the effect of mechanical properties of both optical fibre and polymer coating on failure mode is required.

348

Tensile Behaviour of Polymer Coated Optical Fibres

CONCLUDING REMARKS The tensile behavior of polymer coated silica optical fibre was closely associated with how the fibre was gripped. If the fibre was only gripped on the coating, the failure was dominated by delamination between the fibre core and the coating close to the gripping point, followed by stripping of the coating from the fibre. The maximum failure load was observed in the sample when the gripping point (epoxy drop) was over the fibre core and the end of the coating. When the gripping point was on bare fibre the failure mode was dominated by fibre breaking. These results can provide some useful guidelines for packaging design in a photonic system. ACKNOWLEDGEMENTS The authors would like to acknowledge the support of the Australian Government via the ARC and the Australian Photonics CRC. In particular C. Yan acknowledges the receipt of an ARC Australian Research Fellowship. They would also like to acknowledge the support received from their colleagues at the OFTC and the CAMT respectively. Dr Law would also like to thank her daughter for assistance with cutting out numerous paper frames. REFERENCES 1. Suhir, E. (2001). Structural mechanics of polymer coated optical glass fibres: review. First International IEEE Conference on Polymers and Adhesives in Microelectronics and Photonics. Incorporating POLY, PEP & Adhesives in Electronics. Proceedings (Cat. No.01TH8592), 270-275. 2. Matthewson, M J. (1994). Optical fiber reliability models. Proceedings of the SPIE - The International Society for Optical Engineering CR50, 3-31. 3. Gebizlioglu, O.S., Kurkjian, C.R., and Reith, L.A. (1999). Materials issues in the development and use of lightguide fibers, cables, and components. Proceedings of the SPIE - The International Society for Optical Engineering CR73, 68-111. 4. Suhir, E. (1996). Predicted curvatures and stresses in a fiber-optic interconnect subjected to bending. Journal of Lightwave Technology vol. 14, no.2, 144-147. 5. Suhir, E. (1997). Stresses in a partially coated optical glass fiber subjected to the ends off-set. Journal of Lightwave Technology vol.15, no.ll, 2091-2094. 6. TIA/EIA-455-31-C (1999). FOTP-31 - Proof Testing of Optical Fibers by Tension, Telecommunications Industry Association. 7. Mickelson, A.R., Basavanhally, N.R., and Lee, Y.-C. (1997). Optoelectronic Packaging (New York: Wiley Interscience). 8. TIA/EIA-455-6-B (2003). FOTP-6 - Cable Retention Test Procedure for Fiber Optic Cable Interconnecting Devices, Telecommunications Industry Association. 9. Trewhella, J.M., DeCusatis, C , and Fox, J. (1999). Performance comparison of small form factor fiber optic connectors. 1999 Proceedings. 49th Electronic Components and Technology Conference (Cat. No.99CH36299), 398-407. 10. ASTM-D-3379-75 (1982). Standard test method for tensile strength and Young's modulus for highmodulus single-filament materials, American Society for Testing and Materials: Philadelphia. 11. Matthewson, M.J., Kurkjian, C.R., and Hamblin, J.R. (1997). Acid stripping of fused silica optical fibers without strength degradation. Journal of Lightwave Technology vol.15, no. 3,490-497. 12. Hand, R.J., Ellis, B., Whittle, B.R., and Wang, F.H. (2003). Epoxy based coatings on glass: strengthening mechanisms. Journal of Non-Crystalline Solids vol.315, no.3, 276-287. 13. Shiue, Y.S., Matthewson, M.J., Stupak, P.R., and O'Connor, M.J. (2001). Coating additives for enhanced mechanical reliability of fused silica optical fibers: effect on mechanical and optical performance. Proceedings of the SPIE - The International Society for Optical Engineering vol.4215, 129-133.

Statistical Model for Multiaxial Fatigue Behavior of Unidirectional Laminates Xiaoxue Diao* PreciCad Inc. 350 Sharest Est, Quebec, QC, G1K 3H4, CANADA Larry B. Lessard Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 3K6, CANADA

ABSTRACT In this paper a statistical model was developed to simulate the fatigue behavior of a unidirectional composite laminate subjected to multiaxial fatigue loading based on the experimental data of static and fatigue behavior of that laminate subjected to uniaxial fatigue loading and under in-plane shear conditions. The statistical model was applied to evaluate fatigue life and residual strength of the unidirectional graphite/epoxy AS4/3501-6 composite lamina subjected to off-axis fatigue loading Simulation of the S-N curve for a 30° off-axis laminate showed a good agreement with experimental data.

INTRODUCTION Although some models have been proposed to study the biaxial/multiaxial fatigue of composites [1,2], all these models are deterministic in approach. However, The large scatter in residual strength and fatigue life measurements of composite materials is a well-known fact, which should be included in the design of composite structures. In this paper, a statistical approach is employed to study the fatigue failure of fiber reinforced composite lamina subjected to multiaxial loading. The generalized residual material property degradation model developed by Shokrieh and Lessard [3,4] is used to generalize the statistical model for composite lamina under fatigue loading with arbitrary stress ratio.

DEVELOPMENT OF STATISTICAL MODEL Consider a unidirectional lamina under a biaxial state of fatigue stress in longitudinal (an), transverse (022) and shear (012) directions. Sims and Brogdon [5] proposed a fatigue failure criterion,

* Corresponding author. Email: xdiao(3)hotmail.com

350

Multiaxial Fatigue Behavior of Unidirectional Laminates

R22(n,a22,K)J

{Rl2(n,a 12,K)

=1

where Rii(n,crn,K), R22(n,a22,K) and Ri2(n,ai2,K) are the residual strengths in the longitudinal, transverse and in-plane shear directions, respectively. In this research, the equation presented by Harris et al [6] is adopted to describe the degradation of residual strength, R(n,a,K):

^n, a,,

=

K)

flog(n)-108(0.25)]'

where Rs;, a; and b, (i=l 1,22,12) are the static strength and curve fitting parameters. Nfi (i=ll, 22, 12) are fatigue cycles to failure of the unidirectional lamina under uniaxial loading a n , a22 and du, respectively. From Eqs. (1) and (2), the number of cycles to failure can be numerically solved as an explicit function of static strength and stress state. It is also an implicit function of stress ratio by means of the Goodman-type diagram. n = g(R sll ,R i22 ,R J12 ,o 11 ,a 22 ,CT 12 )

(3)

In the statistical description [7], the fatigue strength of a lamina in the longitudinal, transverse and in-plane shear directions is a random variable. Fatigue life of the lamina subjected to multi-axial loading must be determined statistically in terms of distribution functions of the random variables R s n, Rs22, Rsi2It is assumed here that the static strengths in the longitudinal, transverse and inplane shear modes are independent of each other and their distribution functions are of the form of Weibull functions [8], f

'(R-)=f(f!)"rl«PH|i)a},

1 = 11,22, 12

(4)

where i, i (i=ll, 22, 12) are the shape and scale parameters of the Weibull function, which are determined from the experimental data of static strength in three loading modes, respectively. The density distribution function of the random variable n can be calculated based on Eq. (4) if the failure criterion Eq. (1) is utilized [9]. f(n,CT11>a22,CT12) = JdR.» ]dR ffi JdR i .28(n-g(a 11 ,CT H ,CT 12 ,R sll ,R C2) R, 12 )f 11 (R !l ,)f 22 (R a2 )f 12 (R sl2 )(5) 0

0

0

The average fatigue life of the composite lamina under multi-axial loading can be calculated [9] N F ( o n , 0 2 2 , a 1 2 ) = Jnf(n,a11)CT22,a12)dn

/" = JdR,.. jdR,22

.

(6) }dRsl2g(RI11,Rs22,R,,2,an,a22;a12)f1,(R,,1)f22(Rs22)f12(R!l2)

Multiaxial Fatigue Behavior of Unidirectional Laminates

351

The dependence of residual strength on the stress ratio K is reflected by a relationship between number of cycles to failure and the corresponding state of stress in Eq. (2). The generalized relation between the alternating stress ca=(amax-<7miii)/2, tensile strength at, compressive strength a c was presented by Harris [6] based on Adam's model [10-12] as

where a=a a /a t , q=am/at, c=oc/at, and f u, v are curve fitting constants. Experimental results by Harris and his co-workers [6] showed that u can be expressed by a linear function of logarithmic fatigue life Nf, i.e. u = A + BlogNf (8) where A and B are curve fitting parameters. Combining Eqs. (7) and (8) yields U=

ln[(l 1 - ( q)(l ) +q )] =A + B l 0 g N f

(9)

Eq. (9) is fitted with experimental data from different stress ratios so that a master curve for u versus logNf for different stress ratios is extracted, consequently, A and B are found. For a better simulation of the fatigue life of the unidirectional lamina under shear fatigue loading, a modified formulation was proposed [3,4]

hi order to apply the statistical model to predict the fatigue life of a unidirectional lamina under biaxial loading, the following tests must be conducted to characterize the properties of the lamina under uniaxial load in longitudinal, transverse and in-plane shear directions, respectively: 1. tests of static tensile, compressive and shear strength and their deviation for unidirectional lamina, from which the Weibull parameters a; and p\ (i=ll, 22, 12),are determined; 2. tests of residual strength of the unidirectional lamina for determination of strength degradation parameters a\ and fy (i=l 1, 22,12) based on Eq. (2); 3. tests of fatigue life of the unidirectional lamina under different stress ratios (at least two) for determination of curve fitting parameters Aj and Bf (i=ll, 22, 12) fromEq. (9)orEq. (10).

MATERIAL CHARACTERIZATION A unidirectional lamina under biaxial fatigue loading ((Tn=0 in Eq. (1)) was considered. A series of tests were conducted on graphite/epoxy AS4/3501-6 unidirectional lamina under transverse and in-plane shear loading conditions for material characterization. The results of fatigue life of unidirectional lamina under transverse tension-tension (R=0.1) and compression-compression (R=10) fatigue loading [4] are shown in Fig. 1. Similar results are shown in Fig. 2 for the unidirectional lamina under in-plane shear loading with the maximum stress of 40%

Multiaxial Fatigue Behavior of Unidirectional Laminates

352

and 80% of static strength and two different stress ratios 0.1 and 0.0. The results are converted to a relation between the life parameter U22, U12 and logarithmic fatigue life based on Eqs. (9) and (10), shown in Figs. 3 and 4, from which a master curve can be extracted with fitting A; and B; (i=22,12) determined consequently. The parameter/ =1.06 for better fitting to the experimental results [6]. The residual strength of a unidirectional lamina under transverse tension-tension and in-plane shear loading with different maximum stresses [4] are presented in Figs. 5 and 6. The fitting parameters a; and bj (i=22, 12) in the degradation formula of normalized residual strength Eq. (2) are thus determined, shown in Table 1. 1.2

£

1.0

c
0

O In

o .

0.2

0.8

A8DA ^

ISo

OO

O A

O

'g 0.4

OO

o static (T) • static (C) o R=0.1 AR=10

O static O R=0.1 A R=0.0

O

0.0 -

1

0

1

2

3

4

5

6

7

-

1

1

0

1

2

3

4

5

6

7

8

LogNf

LogNf

FIGURE 1 Experimental data of static and fatigue life of unidirectional lamina under transverse loading with different stress ratios.

FIGURE 2 Experimental data of static and fatigue life of [0/90]s laminate undeT in-plane shear loading with different stress ratios.

3.0 CN

u22 = 0.0937LogNf+ 1.0117

2.5

= 0.1785LogNf+ 0.1245

mel

CD

2.0

S3 urv Life

S.

1.5 1.0

O R=0.1 AR=10

0>

0.5

ter

O [0

0-0 0

1

2

2

3

4

5

6

7

8

LogNf

FIGURE 3 Normalized fatigue life curve for a unidirectional lamina under transverse tensile loading conditions.

FIGURE 4 Normalized fatigue life curve for a [0/90]s laminate under in-plane shear loading conditions.

TABLE I. Model parameters obtained from material characterization. Loading Mode (i) Trans. Tension (22) In-plane Shear (12)

Rsi [MPa] 52.56 136.33

OC;

16. 1 3 18. 6 3

P.

[MPa] 54.31 139.42

Ai

Bj

ai

bi

1.011 7 0 .124 5

0.093 7 0.178 5

9 .628 7 0 .160 0

7 .968 1 9.110 0

Multiaxial Fatigue Behavior of Unidirectional Laminates

353

1.2

6

i

£ 1.0 •a 2 $ 8

£ 0.8

1

<"

8

o static 0 60% A 40%

">,

0 ^

E ra

o-S0'6 a: 0.4 0.2

a22=9.6287 b22=0.1255

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.2

Normalized Cycles

0.4

0.6

0.8

1.0

Normalized Cycles

FIGURE 6 Normalized residual strength curve for a [0/90]s laminate under in-plane shear loadin

FIGURE 5 Normalized residual strength curve for a unidirectional lamina under transverse tensile loading.

STATISTICAL EVALUATION With all the model parameters obtained from materials characterization in Table 1, the statistical model can be applied to calculate the S-N curve of a lamina under a 30° off-axis loading. The calculated residual strength of the laminate subjected to 30° off-axis fatigue loading with maximum of 70% static strength is shown in Fig. 7. Similar calculations can be made for other applied stress levels. These results are normalized and shown in Fig. 8. If the normalized residual strength of unidirectional laminates with off-axis angle 9 is of the same form as Eq. (2): R e (n,q e ,K)-CT e

•[-

log(n)-log(0.25) f

(11)

vlog(Nffi)-log(0.25)j

where Rse, Re(n,ae,K) and OQ are the off-axis static strength, residual strength and applied stress, the value of parameters ae and be (9=30°) are determined to be 3.272 and 1.346, respectively. Therefore, if the fatigue life of an off-axis laminate under different applied stress levels is known, the normalized residual strength of the laminate can be determined based on Eq. (11). The fatigue life of unidirectional laminate with 30° off-axis angles is calculated from Eq. (6), shown in Fig. 9, which shows a good agreement with experiments [4].

E" 1S0 CD

Maximum Applied Stress - FVediction 95% - 1 0

1

2

3

4

5

6

LogN

FIGURE 7 Residual strength of [30] 16 offaxis laminate under an applied stress with maximum of 70% static strength.

0.2

0.4

0.6

0.8

Normalized Cycles

FIGURE 8 Normalized residual strength of [30] i6 off-axis laminate.

354

Multiaxial Fatigue Behavior of Unidirectional Laminates 1.0 I 0.8 0.6 0.4 •

n0.8

0.2 •

A 0.7 O 0.6

X0.5 0.0 i 0.0 0.2

§ ^l jF at i 0.4

i 0.6

i 0.8

Td 1.0

Normalized Cycles FIGURE 9 Calculated S-N curve and deviations for [30]]6 off-axis laminate.

SUMMARY 1) The residual strength and fatigue life of an off-axis laminate can be determined from the statistical model if the fatigue behavior of unidirectional lamina under longitudinal, transverse and in-plane shear loading are known through material characterization. 2) The normalized residual strength of an off-axis laminate against normalized fatigue cycles for different applied stress levels converges to a master curve, which can be used to determined the residual strength of the laminate under any applied stress levels if the corresponding fatigue life is known. 3) The fatigue life calculated for the unidirectional laminate with off-axis angle 30° agrees well with experimental data, indicating the usability of the statistical model. REFERENCES 1.

Garud, Y. S., 1981. "Multiaxial Fatigue: A Survey of the State of the Art", Journal of Testing and Evaluation, JTEVA, 9:165-178 2. Found, M. S., 1985. "A Review of the Multiaxial Fatigue Testing of Fiber Reinforced Plastics", Multiaxial Fatigue, ASTM STP 853, K. J. Miller and M. W. Brown, Eds., American Society for Testing and Materials, Philadelphia, pp.381-395 3. Shokrieh M. M. and L. B. Lessard, 1997 "Multiaxial Fatigue Behaviour of Unidirectional Plies Based on Uniaxial Fatigue Experimental: Part I. Modeling", International Journal of Fatigue, 4. Shokrieh, M. M. and L. B. Lessard, 1997, "Multiaxial Fatigue Behaviour of Unidirectional Plies Based on Uniaxial Fatigue Experimental: Part II. Experimental Evaluation", International Journal of Fatigue, 5. Sims, D. F. and V. H. Brogdon, 1977. "Fatigue Behavior of Composites Under Different Loading Modes", in Fatigue of Filamentary Composite Materials, ASTM STP-636, ASTM, Philadelphia, pp. 185-205 6. Harris, B., H. Feiter, R. Adam, R. F. Dickson and G. Fernando, 1990. "Fatigue Behaviour of Carbon Fibre Reinforced Plastics", Composites, 21:232-242 7. Diao, X.X, Lin Ye and Yiu-Wing Mai, 1995. "Statistical Prediction of Fatigue Failure of Fibre Reinforced Composite Materials", Applied Composite Materials, 2:153-173 8. Weibull, W. 1951. "A Statistical Distribution Function of Wide Applicability", Journal of Applied Mechanics, 18:293-297 9. Melsa, J. L. and A. P. Sage, 1973. An Introduction to Probability and Stochastic Processes, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 10. Adam, T., G. Fernando, R. F. Dickson, H. Reiter and B. Harris, 1989. "Fatigue Life Prediction for Hybrid Composites", International Journal of Fatigue, 11:233-237 11. Adam, T., R. F. Dickson, G. Fernando, B. Harris and H. Reiter, 1986. "The Fatigue Behaviour of Kevlar/Carbon Hybrid Composites", IMechE Conference Publications (Institution of Mechanical Engineers), 2:329-335 12. Fernando, G., T. Adam, B. Harris and H. Reiter, 1994. "Life Prediction for Fatigue of T800/5234 Carbon-Fibre Composites: I Constant-Amplitude Loading", International Journal of Fatigue, ' 16:523-532.

Part VII

FEM/Simulation

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Simulation of Three-dimensional Flow in Compression Resin Transfer Molding by the Control Volume/Finite Element Method Akbar Shojaei* Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran Davood Boorboor and S. Reza Ghaffarian Polymer Engineering Department, Amirkabir University of Technology, Tehran, Iran

ABSTRACT In compression resin transfer molding (CRTM), resin injection and mold closing occur during the mold filling stage. In this paper, numerical simulation of threedimensional flow in compression resin transfer molding (CRTM) is presented. Numerical method is based on the control volume/finite element method (CVFEM) and the numerical algorithm to update the flow front at each time step is based on quasi-steady state approach. Numerical scheme presented in this article can be used to predict the flow progression, pressure distribution, mold clamping force in full threedimensional mold. Numerical example provided in the paper demonstrates the effectiveness of the developed numerical simulation in analyzing the CRTM process.

INTRODUCTION Due to advantages of Resin transfer molding (RTM), it increasingly becomes an important processing technology to fabricate net-shape polymer-matrix composites, ranging from nonstructural components with simple shapes, to structural parts with complex geometries. Despite various advantages of the RTM process, there are still some problems in the fabrication of part with large dimensions or high fiber content, including long mold filling time and presence of considerable void content in the final product. In order to overcome the above mentioned problems, various methodologies have been presented to modify the conventional RTM process. One important improvement in RTM is to combine the compression into the resin transfer molding. This process is called compression resin transfer molding (CRTM) and consists of resin injection and mold clamping or compression during the filling stage. Numerical simulation is known as effective tool to analyze filling stage in CRTM. Recently, numerical simulation of the CRTM process has been addressed in literature [1-4]. But, all of these simulations are restricted to two-dimensional flow in the CRTM mold. In some practical applications, two-dimensional flow assumption is no longer valid, and then three-dimensional simulation is needed to estimate the processing parameters accurately. Corresponding author. Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran 11365-9465, Iran. Fax: +98-21-6022853. Email: [email protected]

358

Three-dimensional Flow in Compression Resin Transfer Molding

The objective of the present article is to propose a numerical method for the full three-dimensional simulation of filling stage in the CRTM process. First, the current mathematical model of CRTM process, continuity equation, is extended to threedimensional domain. Then the control volume/finite element method (CV/FEM) is used to solve the governing equation. Various capabilities are provided in the computer code, permitting prediction of the flow front progression in threedimensional domain, pressure distribution and clamping force. Finally, application of three-dimensional simulation is demonstrated by providing a numerical case study. THEORETICAL MODELING During filling stage in the CRTM process, the liquid resin flows through the fibrous reinforcement. This can be assumed as flow through porous media. Mathematical models governing filling stage for pure injection process, namely RTM, have been well documented in literature [5]. Resin flow for both RTM and CRTM can be modeled by Darcy's law, but the continuity equation for CRTM needs to be modified for considering the mold closing effect. Resin flow through porous media described by Darcy's law is given as follows in three-dimensional domain: dP - dx xz dP yz (1) dy zz dP

Eq. 1 can be rewritten in tensor notation as:

=-~[K].\

(2)

where v is the superficial velocity vector with three components v, u and w in x, y and z directions, respectively, [K] represents the permeability tensor, Ky are its components, P is the pressure and u. is the resin viscosity. The general continuity equation for a deformable medium is given as follows: V.v=—L-^

dV dr

(3)

where dV is the infinite small elemental volume at time t and the term d(dv)/dt represents the rate of deformation of this elemental volume. This deformation rate depends on the mold closing speed and fiber preform deformation behavior. Eq. 3 had been first derived in soil mechanics [6,7], then it was rederived by Pham et al. [2] for CRTM in which the fiber deformation may be large. Substituting Darcy's law into Eq. 3 leads to single equation for pressure as: dV dt

(4)

Three-dimensional Flow in Compression Resin Transfer Molding

359

Eq. 4 is a general form of governing equation for three-dimensional flow in the CRTM process. By solving Eq. 4 with the aid of appropriate boundary conditions, one can obtain the pressure field in saturated zone and consequently estimate the flow front progression during filling stage. The total force exerted on the mold is composed of two components, including the resin pressure in saturated region and fiber bed stress. The total force may be estimated by the following model [2,4]: PdS

(5)

where Ftoal is total force exerted on the mold, S the surface area of the mold, P the resin pressure in saturated zone and af the fiber bed stress. NUMERICAL METHOD In the present formulation, control volume/finite element method (CV/FEM) is used to discretize the governing equation, i.e. Eq. 4. The volume of mold cavity is first divided into eight-node three-dimensional elements and then control volumes are constructed around a node as shown in Fig. 1.

^<>" -« '/:••

/

/-

J. /FIGURE 1 An eight node element and its subcontrol volumes used in this study

In order to track the flow front progression, a scalar parameter, /, called nodal fill fraction, showing the status of each control volume, is used. The fill fraction for each control volume represents the ratio of occupied volume by the resin to its total pore volume. During the filling stage, each control volume may have three different statuses:/= 1 for main region,/= 0 for empty region and 0
icA »

)

icv. dV

dt

=

dV = dt\['c.v.

(6)

360

Three-dimensional Flow in Compression Resin Transfer Molding

where S and V represent the control surface and control volume, respectively, C.S. and C.V. are the subscripts that denote integration over the control surface and control volume, respectively, n is the unit normal vector of the control surface and V is the rate of volume change of a control volume. Eq. 6 is valid for a complete control volume and can be applied for all control volumes within the domain. In the present paper, the global stiffness matrix is constructed based on element by element assembling procedure. The parameters available in the left hand side of Eq. 6 are identical to parameters in the numerical formulation of pure RTM [8], but major concern in the numerical formulation of three-dimensional flow in CRTM is to establish a correlation between rate of volume change of a SCV, i.e. SCV , and upper mold closing speed. In the present work, the following relation is proposed to calculate 'SCV for a SCV based on the rate of volume change of relevant element: SCV, =

^

Ve

(7)

where Ve and Vscv are volumes of element and SCV, respectively, and Ve is the rate of volume change of an element. This is an important point from the viewpoint of numerical scheme, because according to Eq. 7, SCV is directly calculated based on elemental deformation rate. For an element which is compressed only in the thickness direction, we propose the following relation between Ve and Un as: Ve=SnUn

(8)

where Un is the normal component of the preform deformation rate through the thickness of the part, and Sn is a characteristic surface area of an element. According to Eq. 8, Ve can be obtained if Sn is known for an element. For three-dimensional elements, calculation of Ve is not straightforward and it is dependent on the geometry of the element. Based on the numerical formulation presented, an algorithm is developed to simulate the filling process of CRTM in full three-dimensional space. A computer code is written in FORTRAN computer language based on the numerical algorithm and the validity of the numerical algorithm was checked with analytical solution of 1dimensional flow. NUMERICAL RESULTS AND DISCUSSION In order to demonstrate the effectiveness of the numerical algorithm used in this study, numerical simulation of CRTM is performed for a mold cavity whose shape and finite element mesh is shown in Fig. 2. The resin injection and the mold closing are performed simultaneously throughout the mold filling stage.

Three-dimensional Flow in Compression Resin Transfer Molding

361

I Mold closing direction

100 Time (sec)

150

FIGURE 3 Flow front positions at three different times during filling stage; (a) t=50s, (b) t=100s, (c) t=150s and (d) Force exerted on the mold wall during filling process

362

Three-dimensional Flow in Compression Resin Transfer Molding

The mold closing speed is 5><10"5 m/s. The resin is injected through an inlet gate located at top of the flat section of the mold under the constant flow rate of 4.485 xlO"5 m3/s. The flow rate is set so that a final fiber volume fraction of 0.65 is met at the end of filling stage. Other parameters are: jx= 0.1 Pa.s, kx=k/=kz = 5><10"12 exp(6<£) and P = 2A06VJ531 where J^is the fiber volume percentage and cp is the porosity. It is assumed that the reinforcement deforms elastically during the compression process. Figures 3(a)-3(c) show the flow front positions at three different times during the mold filling stage. As shown in Fig. 3, fluid progresses radially from the injection port and then it becomes flat in the inclined section. The simulated mold filling time is 196 sec. Comparison of this simulation result with analytical value, i.e. 200 sec, shows a 2% error in filling time. As the injection process holds throughout the filling stage, analytical filling time can be simply calculated by dividing the final pore volume of the cavity to the injection flow rate. Fluid pressure force, reinforcement force and total amount of force exerted on the top of the mold calculated by the present numerical scheme are shown in Fig. 3(d). As seen in the figure, contribution of resin pressure force on total force exerted on the mold wall is negligible in comparison with fiber compaction force at early stage of mold filling. However, when the flow front reaches to the mold wall and flow front reaches to the inclined section of the mold, resin pressure force is considerable. This is reasonable, because at latter stage of mold filling, flow length and resistance against flow increase, needing a high pressure to hold a constant flow rate at the inlet port. CONCLUSION Numerical simulation based on the CV/FEM is presented to analyze the isothermal three-dimensional flow in the CRTM process. The numerical formulation for flow progression is based on the concept of quasi-steady state approach. The numerical scheme developed in this study provides necessary information for filling stage such as flow front progression, pressure distribution, and mold clamping force. This information is helpful in designing the optimum processing conditions before the mold is actually built. Numerical example provided shows the effectiveness of the numerical algorithm developed in this paper. REFERENCES 1.

2.

3. 4. 5. 6. 7. 8.

Phelan, Jr. F. 1996. "Analysis of Injection/Compression Liquid Composite Molding Process Variants," ASME International Mechanical Engineering Congress and Exhibition, Atlanta, GA, pp. 1-10. Pham, X. T., F. Trochu, and R. Guavin. 1998. "Simulation of Compression Resin Transfer molding with Displacement Control," Journal of Reinforced Plastics and Composites, 17:15251556. Han, K., J. Ni, J. Toth, L. J. Lee and J. P. Greene. 1998. "Analysis of an Injection/Compression Liquid Composite Molding Process," Polymer Composites, 19:487-496. Kang, M. K. and W. I. Lee. 1999. "Analysis of Resin Transfer/Compression Molding Process," Polymer Composites, 20:293-304. Shojaei, A., S. R. Ghaffarian and S. M. Ff. Karimian. 2003. "Modeling and Simulation Approaches in the Resin Transfer Molding Process- A Review," Polymer Composites, 24:525-544. Taylor, D. W. 1948. Fundamentals of Soil Mechanics. John Wiley & Sons, New York. Bear, J. 1971. Dynamics of Fluids in Porous Media. American Elsevier. Shojaei, A. S. R. Ghaffarian, and S. M. H. Karimian. 2002. "Numerical Simulation of ThreeDimensional Mold Filling Process in Resin Transfer Molding Using Quasi-Steady State and Partial Saturation Formulations," Composites Science and Technology, 62:861-879.

Modeling of Two-Dimensional Cellular Solids with Two Types of Imperfections K. Li, X.-L. Gao* Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA

ABSTRACT The Voronoi tessellation technique and the finite element method are utilized to investigate the microstructure-property relations of two-dimensional cellular solids having irregular cell shapes and non-uniform cell wall thickness. Twenty finite element models are constructed for honeycomb samples (specimens) to obtain the mean values and standard deviations of the effective elastic properties. Spatially periodic boundary conditions are applied to each specimen. The simulation results indicate that the Young's moduli increase as cell shapes become more irregular, but decrease as cell wall thickness gets less uniform. The Poisson's ratios are insignificantly affected by the presence of these imperfections. The effect of the interaction between the two types of imperfections appears to be weak. In addition, it is found that such imperfect honeycombs can be regarded as isotropic.

INTRODUCTION Cellular solids (foams) are prevalent in nature and ubiquitous in engineering applications. A successful model that links the observed properties to the complex microstructures of foams can help us to understand how the microstructures affect the mechanical properties and enable us to optimize the microstructural parameters for a given application. Although unit cell-based models [1-3] can provide important results, they are significantly limited by their inability to account for microstructural imperfections inherent in most real cellular materials, whose cell structures are typically non-periodic, non-uniform and disordered. Thus, more complex, statistical models are necessitated to obtain improved predictions. Efforts have been made to investigate the effects of imperfections, such as irregular cell shapes, non-uniform cell wall thickness, wavy cell walls, and missing or fractured cell walls, on mechanical properties of cellular materials; most of these studies are based on the finite element method (FEM) [1, 4-7]. However, in each of the existing studies, only one type of imperfections was included at a time. In general, two or more types of imperfections are simultaneously involved in the microstructure of a cellular material. Therefore, models incorporating two or more types of imperfections are still in need.

* Corresponding Author, Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA. Tel: +1-906-4871898; fax: +1-906-487-2822. E-mail: [email protected].

364

Two-Dimensional Cellular Solids

, V---{• /----<' •')-—(• y»-/ • \---( • \—(• Vr y _ / • ) — < T v < V ) — < • ) - . { • v < • >- \ • >—< • >—< * >--< • / v

/'

\ Seed 6

, Regular Voronoi cell \

/

\ • }-—\ * ) — < , «

-/ • >—(* v ~ < • \—<" •;—~< * >—< # / — { <

^>--< • y-G}-<' )-< • M • > —( • >—( • )—s i , \—/ • -J

, \ _ - ( . V—< t >—( • ; — ( • ) — ; • } . \

-(.

\ — { . V—< • V - < • •>—( -

x

Delauiiay triangulatioii • Seed 4 Voronoi boundary

. V_y . v_y , V / , y _ / . \ / . v / . v. v_y . V.1/ . FIGURE 1 Voronoi diagram based on regularly packed seeds

FIGURE 2 Coordinate perturbations of the Jthseed(x 1 ',Jj)

The objective of this paper is to address the combined effects of two co-existing imperfections - irregular cell shapes and non-uniform cell wall thickness - on the elastic properties of two-dimensional (2-D) foams. ANALYSIS The Voronoi tessellation technique is often used to capture random features of foam micro structures. When a set of seeds, placed in space simultaneously in a random fashion, grow in all directions with a uniform speed, a 2-D or 3-D Voronoi diagram is formed, depending on the space dimension. The Voronoi tessellation structure is fully determined by the initial locations of the seeds. Using regularly positioned seeds produces regular Voronoi diagrams. The current analysis starts with a reference model, which is a hexagonal honeycomb structure with perfectly ordered, regular cell shapes and uniform cell wall thickness. This reference model can be constructed from a set of regularly packed seeds using the Voronoi tessellation technique, as shown in Figure 1. Perturbations are then introduced to the reference model to generate Voronoi diagrams with irregular cell shapes and non-uniform cell wall thickness. Spatially Periodic Honeycombs with Cell Shape and Cell Wall Thickness Variations There are two methods to construct 2-D random foam models using the Voronoi tessellation technique [8]. The second method, which uses a set of seeds of periodic symmetry [9], is adopted here to construct spatially periodic models. First, a preset number of seeds are generated within a rectangle. Then, the position of each seed within the rectangle is copied to eight identical rectangles adjacent to or sitting at the corners of the original rectangle. Finally, the Voronoi tessellation technique is applied to all of the seeds within the nine rectangles. Part of the resulting Voronoi tessellation that is inscribed by the center (original) rectangle can be taken out as a unique periodic specimen. The irregularity of cell shapes is determined by the irregular distribution of the seeds. The locations of the seeds used to construct Voronoi diagrams with irregular cell shapes are perturbed from a regular lattice of seeds. Figure 2 shows the coordinate

Two-Dimensional Cellular Solids

365

perturbations of a regularly packed seed. The perturbed coordinates of seed i, x\ and x\, may be represented by

=x\ + a(d0 sin 6'. where *,', Xj are the two coordinates of the same seed in the regular lattice, do is the distance between two regularly packed (unperturbed) seeds, 6t (e[0, 2n]) is a stochastic angle (with a uniform distribution) between the x r axis and the line connecting the unperturbed and perturbed seeds,
N

I 7=1

where R is the relative foam density, L\ and L2 are, respectively, the width and height of the foam sample (specimen), /, is the length of cell wall j , and N is the total number of cell walls. To this end, each cell wall is assigned a random thickness given by

(a)

(b)

(c)

FIGURE 3 Honeycomb samples with varying a: (a) a = 0, (b) a = 0.5, (c) a = 1.0

366

Two-Dimensional Cellular Solids j

0)

j

where b (e [0, 1]) is the amplitude used to quantify the non-uniformity of cell wall thickness, y/j (e [-1, 1]) is a random variable with a uniform distribution, and c, called the normalizing factor, is defined by N

to ensure that the relative density (R) remains unchanged with the variation of the cell wall thickness. Given R, a, b, 9i and
j

r

hzxL2

£2=—^-, vI2=—^K '

Z

f

r

'

l

hE2Li

Z

r

v2, = - - ^ - , '

£jL2

Zl

r

(5) '

\

/

E2L-l

where h is the thickness of the honeycomb, F\ and F2 are, respectively, the total reaction forces along x\ and xi directions on the prescribed boundary, and u\ and ui are the lateral displacements (extensions) perpendicular to the loading directions x2 and x\, respectively. Also, biaxial strains £\ = 0.001 and £2 = - 0.001 are applied simultaneously along the two orthogonal directions to determine the effective shear modulus Gn, defined by G12 = Tnlyn, as

_FJL2-F2ILX 12

~

2/,(se)

;

(6)

Two-Dimensional Cellular Solids

367

Note that F\ and Fi in Eqs. (5) and (6) are obtained from the finite element analysis. In modeling uniaxial or biaxial loading tests, displacement boundary conditions are usually used [1,4-6]. However, since the specimen is cut out of an infinite structure that can be regarded as periodic, spatially periodic boundary conditions need to be applied to ensure that the predicted properties of the specimen are representative of those of the honeycomb [12]. Before proceeding to model honeycombs having irregular cell shapes and nonuniform cell wall thickness, a mesh sensitivity study is performed, which reveals that the appropriate number of cells to be included in a specimen is 360 [8]. RESULTS AND DISCUSSIONS Isotropy of the Effective Properties A total of 29 cases with different combinations of the three controlling parameters a, b and R are analyzed here. The maximum and minimum mean values of three ratios, i.e., E\IEi, vnlvii and G\ilGyi, are evaluated. Here, GuT is calculated using G\i = i?i/[2(l+vi2)], which is the shear relation required for material isotropy. Numerical results indicate that the mean values ofEi/E2, vu/vn and GulG\2T are very close to unity for all cases [8]. Therefore, it can be concluded that the elastic response of the honeycombs studied is isotropic regardless of changes in cell shape irregularity, cell wall thickness non-uniformity, and relative density. Effects of Cell Shape Irregularity The effects of irregular cell shapes on elastic properties are analyzed for honeycombs having a fixed relative density R = 0.01 and some uniform cell wall thickness (i.e., b = 0). For each value of a, twenty independent lists of random variables 6>,- and #>,- (z e{l, ..., M}) are used to generate twenty honeycomb samples, each of which has a unique arrangement of cell walls. Finite element analyses are then conducted on the twenty samples, and the mean values and standard deviations of the effective properties, i.e., the Young's moduli and Poisson's ratios, are obtained. Figures 4 and 5 graphically show the predicted elastic properties at different values of a. From Figure 4 it is observed that, on average, the Young's moduli increase considerably with a. Poisson's ratios, however, are insignificantly affected by the cell shape irregularity, as shown in Figure 5. The strong dependence of the Young's moduli on a may be attributed to the changes in the microstnicture as cells become less regular. In addition to hexagons, other types of polyhedrons, such as pentagons, quadrangles, and triangles, appear in the microstructure, as shown in Figures 3(b) and 3(c). The stiffness of each of these fewer-sided polyhedrons is higher than that of a hexagon, thereby leading to a significant increase of the Young's moduli. 40

0.9998 -, < 0.9996

~ 30 LU

•^ 0.9994

,,f 25 i

*

20

0.9992 0.999

0.2

0.4

0.6 a

0.8

1

0

0.2

0.4

0.6 a

0.8

368

Two-Dimensional Cellular Solids 1.002 i

-a = O 40 n a

30

'

S

*

= 10

'

1001

^

! 0,991

uj

J 20 J

0.998 0.997

10

0.996 0

0.2

0.4

0.6

0.8

1

b

FIGURE 6 Young's moduli

0

-a = 0 -a=1.0 02

0.4

0.6

0.8

1

b

FIGURE 7 Poisson's ratios

Effects of Cell Wall Thickness Non-Uniformity For 2-D foams, the influence of cell wall thickness variations on the elastic properties is still unclear. The regular honeycomb (a = 0) and the completely irregular honeycomb (a = 1.0) with non-uniform cell wall thickness are therefore analyzed here. Four values of the thickness non-uniformity amplitude, i.e., b = 0.2, 0.5, 0.8 and 1.0, are used for each of the two values of a. When b - 1.0, cell wall thickness variations are completely random. For each pair of a and b, twenty honeycomb samples are modeled using independent lists of random variables i (i E { 1 , ..., M}) and y/j (J e{l, ..., N}). The relative density R remains to be 0.01 for all of the samples. The predicted effective elastic properties are shown in Figures 6 and 7. Figure 6 reveals that the Young's moduli significantly decrease in a monotonic fashion as b increases for both values of a considered, while Poisson's ratios are insignificantly influenced by the varying values of b, as shown in Figure 7. Furthermore, it can be seen that the differences between the mean values of the Young's moduli for the honeycombs with a = 1.0 and those with a = 0 are insignificantly affected by varying b. This implies that the effect of the interaction between the cell shape and cell wall thickness variations on the elastic properties is weak. A further examination of Figure 6 shows that the Young's moduli are affected more by the cell wall thickness nonuniformity than by the cell shape irregularity. This follows from the fact that the Young's moduli for the case with a = 1.0 and b = 1.0 are smaller than the corresponding ones for the case with a = 0 and b = 0 (i.e., honeycombs without imperfections), although the two Young's moduli are found to increase as a rises (for fixed b) and to decrease with the increase of b (for fixed values of a), as discussed earlier. Moreover, for the special cases without the interaction (i.e., with a or b being zero but the other one varying), it is found that the maximum gain of moduli is 45% as a varies from 0 to 1.0 with the cell wall thickness being uniform (i.e., b = 0), while the maximum loss of moduli is 47% as b changes from 0 to 1.0 for a regular honeycomb. ACKNOWLEDGEMENTS The work reported here is partially funded by a grant from the AFOSR (Grant # F49620-03-1-0004) and by a contract from L & L Products. These supports are gratefully acknowledged. The public access to the Qhull program initially made available by the Geometry Center at the University of Minnesota - Twin Cities is also thankfully appreciated.

Two-Dimensional Cellular Solids

369

REFERENCES 1.

Silva, M. J., W. C. Hayes, and L. J. Gibson. 1995. "The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids," Int. J. Mech. Sci, 37: 1161-1177. 2. Gibson, L. J. and M. F. Ashby. 1997. Cellular Solids: Structures and Properties, 2nd edition. Cambridge: Cambridge University Press. 3. Li, K., X.-L. Gao, and A. K. Roy. 2003. "Micromechanics model for three-dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano's second theorem," Compos. Sci. Tech., 63: 1769-1781. 4. Simone, A. E. and L. J. Gibson. 1998. "Effects of solid distribution on the stiffness and strength of metallic foams," Ada. mater., 46: 2139-2150. 5. Simone, A. E. and L. J. Gibson. 1998. "The effects of cell face curvature and corrugations on the stiffness and strength of metallic foams," Acta. mater., 46: 3929-3935. 6. Silva, M. J. and L. J. Gibson. 1997. "The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids," Int. J. Mech. Sci., 39: 549-563. 7. Chen, C , T. J. Lu and N. A. Fleck. 1999. "Effect of imperfections on the yielding of twodimensional foams," J. Mech. Phys. Solids, 47: 2235-2272. 8. Li, K., X.-L. Gao, and G. Subhash. 2003. Manuscript submitted for publication. 9. Nygards M. and P. Gudmundson. 2002. "Micromechanical modeling of ferritic/pearlitic steels," Mat. Sci. Eng. A, 24: 435-443. 10. ABAQUS Theory and User's Manuals, Version 6.3. Pawtucket (RI): Hibbitt, Karlson and Sorenson, Inc., 2002. 11. Li, K., X.-L. Gao, and A. K. Roy. 2003. "Micromechanical analysis of three-dimensional open-cell foams using the matrix method for space frame structures," in: Proceedings of the 14th International Conference on Composite Materials (ICCM-14), July 14-18, 2003, San Diego, CA. 12. Laroussi, M., K. Sab, and A. Alaoui. 2002. "Foam mechanics: nonlinear response of an elastic 3Dperiodic microstructure," Int. J. Solids Struc, 39: 3599-3623.

Finite Element Modeling of Fine Structure of Natural Plant Fibers for Statistical Characterization of Their Tensile Strengths Kohji Suzuki Chiba Institute of Technology, Department of Mechanical Engineering Science, Japan Isao Kimpara Kanazawa Institute of Technology, Advanced Materials Science R&D Center, Japan Kunio Funami Chiba Institute of Technology, Department of Mechanical Engineering Science, Japan

ABSTRACT Natural plant fibers can be environmentally-preferable industrial raw materials owing to their renewable, biodegradable and carbon-neutral features. However, those natural plant fibers have not yet been fully examined from the standpoint of engineering, and hence are hardly said to have acquired any credentials in the field of structural applications. Furthermore, the plant fibers, made up of numerous plant cells (elementary fibrous cells) glued to each other with the inter-cell material, may exhibit a certain unique statistical characteristics regarding the physical and geometrical properties reflecting their unique internal fine (cellular) structures. In this study, first the biologic internal fine structures of natural plant fibers were carefully discussed about mostly using the optical microscopic images of kenaf (Hibiscus cannabinus L.) bast fibers. After that, a simple but well-devised numerical, i.e. finite element, modeling framework was proposed for the stress analysis and strength simulation of natural plant fibers. By using the proposed numerical modeling, probabilistic simulations of tensile strength of natural plant fibers were conducted with the Monte Carlo direct method invoked, which was followed by a few statistical treatments to the simulation results. The statistically-treated results foretold importance of considering the shear stresses induced in the inter-cell material as well as the axial stresses in the elementary fibrous cells for estimating the fiber breaking loads. INTRODUCTION Fibers extracted from the natural fiber-producing plants such as jute, bamboo, flax, ramie, sisal, abaca and kenaf are cheap, easy to handle, biodegradable and renewable, non-petroleum and carbon-neutral, and hence considerably environmentally-preferable and harmless-to-human-body cellulose-based natural resources, and now are seeking use which can be counted on ever-growing mass production as well as profitability for reducing the environmental burdens to Earth. For instance, kenaf (Hibiscus cannabinus L.) bast fibers are currently looked upon as a promising reinforcing agent for the biodegradable polymers such as poly L. lactic acid (PLLA) in the automobile and house-hold appliance industries. The plants and the fibers shown in Fig.l were actually grown by the first author in the year of 2002 [1]. However, when one tries to put this kind of plant biomass into the mainstream in the industry, especially in the fields of structural * Correspondence Author, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016, JAPAN fax number: +81-(0)47-478-0261, email: [email protected]

Fine Structure of Natural Plant Fibers

371

4/N 9

•• f | ''i • **-.

r

(a)

(b)

(c)

FIGURE 1 (a) Fully grown-up kenaf plants, (b) kenaf fibers in the bast layer and (c) air-dried kenaf fibers.

composite materials, he surely encounters one serious problem, i.e. the issue of assurance of strength reliability and quality. Natural plant fibers are not rigorously-quality-managed products but essentially botanical and agronomy things and by nature they do not fit in engineering ways of thinking so well. Therefore, some careful treatments to these natural resources should be employed toward their practical applications to the industries [2]. In this study, in order to investigate the actual fracture process commonly occurring in the natural plant fibers and the resulting phenomenological tensile-strength statistics, the authors will advocate the merit of numerical modeling in an engineering finite element manner for the fine (cellular) structure of natural plant fibers with kenaf fibers chosen as a typical example. The authors will propose a numerical modeling methodology for fine (cellular) structures of a plant fiber, which are actually a kind of composite material by itself and made up of numerous elementary fibrous cells and inter-cell material (binder gluing elementary fibrous cells together). Beam elements will be used for modeling elementary fibrous cells while solid elements for inter-cell material. By using the finite element models of plant fibers, probabilistic simulations based on the conventional Monte Carlo direct method [3] will also be invoked to obtain some useful numerical statistics in terms of the fiber strength. The validity and benefit of the present framework of numerical modeling and probabilistic simulation will be partly shown by a preliminary case study. INTERNAL FINE STRUCTURE IN NATURAL PLANT FIBERS Figure 2 (a) and (b) respectively show a general illustration and a cross-sectional view of a kenaf (Hibiscus cannabinus L.) bast fiber as an example of plant fiber anatomy. As can be seen in these figures, the natural plant fibers are definitely not a monolithic and homogeneous single fiber with a circular cross section but rather a bundle or a composite with an elliptic or polygonal cross section consisting of several fibrous plant cells which are approximately 10 urn wide and 3mm long in the case of kenaf and can be compared to

Plant Fiber (Technical Fiber) Elementary Fibrous Cells Inter-C»ll V .:• -i.-l

Elementary Fibrous Cell

-

^

- ~

Lumen Secondary Cell Walls

l_/^_,

(a)

Kenaf Bast (Technical) Fiber

(b)

FIGURE 2 Internal fine (meso-scopic and cellular) structures of natural plant fibers, (a) a schematic of a plant fiber, (b) a cross-sectional view of a plant (kenaf) fiber and (c) cell wall fine structure.

372

Fine Structure of Natural Plant Fibers

tiny spindle-shaped hollow structures or macaroni fibers with their both ends capped. In this study, those ultimate plant cells are to be called "elementary fibrous cells". One of the most prominent features commonly seen in the morphology of those elementary fibrous cells is the open hole at the center, so-called "lumen". Note also that, once the elementary fibrous cells are separated from each other through a certain specific series of chemical and mechanical processes, then they will be called "pulp" and, notoriously, have been used as an important raw material for paper. In fact, as shown in Fig.l (c), the past researches have revealed that the elementary fibrous cells themselves are filament winding composite pipes with cellulose micro fibrils (CMF), which are helically winding in the cell wall and give stiffness and strength to the wall, as the reinforcement, and the mixture of the other non-cellulose substances such as pectin, hemi-cellulose and lignin as the matrix resin. Generally speaking, plant fibrous cells have a thick and stiff secondary cell wall, which can be further divided into three layers, Si, S2 and S3 as shown in Fig. 1 (c). Above all, the winding angle of CMF in the thickest S2 layer has a strong positive relation to the cell's physical properties such as stiffness, strength, elongation at break and so on. In addition to the elementary fibrous cells, the inter-cell material, which glues the elementary cells together, is also an important constituent of the plant fiber. It is a kind of binder a few Lim thick filling the space between the neighboring elementary fibrous cells. This adhesive material is primarily made up of non-cellulose polysaccharides such as pectin and hemi-cellulose, and occasionally including a small ratio of lignin. Since there is scarcely any cellulose content in this material, its stiffness and strength are by two or three orders of magnitude smaller than those of materials reinforced by CMF. Although its stiffness and strength are considerably small compared to those of elementary cells, almost all of the loads from one elementaryfibrouscell to the others will be carried via the shear stresses in this interfacial region, and hence the mechanical properties of this binder can govern the overall mechanical performance of the plant fibers. For instance, the present authors have already obtained several evidences that fractures in the plant fibers can be initiated as shear failures in the inter-cell material regions. Figure 3 (a) is a cross sectional view of a fractured plant fiber in which cracks in the inter-cell regions can be clearly seen longitudinally running through along the elementary fibrous cells just like the transverse matrix cracks often seen in the unidirectional fiber-reinforced plastics. Since that fractured fiber could hardly experience any tensile load in transverse direction, those "transverse cracks" might be driven by "shear stress concentrations around adhesive rich regions". This hypothesis is indirectly but quantitatively supported by the dependence of the frequency percentage of the two typical fiber fracture patterns on the fiber gauge length as schematically shown in Fig.3 (b). Thefracturepattern, A, is for the shear failure in the inter-cell material, on the other hand, the latter pattern, B, is for the axial tensile breakage of the elementary fibrous cells. When the fiber increases in gauge length from 3

* \H\. * • Transverse Cracks

(a)

G.L. = 2mm G.L. = 3mm G.L. = 6mm pattern percentage pattern percentage pattern percentage 47.1% A A 30.0% A 58.8% 52.9% B B B 70.0% 41.2% 100% total 100% total total 100%

(b)

FIGURE 3 Some evidences on fractures arising from the inter-cell material, (a) a cross-sectional view of one of the fractured fibers with transverse cracks, (b) the two typical patterns of fiber fracture and the dependence of those fracture patterns on the gauge length of fiber tensile specimens.

Fine Structure of Natural Plant Fibers

373

to 6 mm, then the pattern, A, also increases in frequency from 30.0% to 58.8%. This fact implies that fiber fractures are more easily initiated as a shear failure in the inter-cell material than as a tensile breakage of an elementary cell as long as the gauge length is large enough for shear stress concentrations in resin rich regions to occur at a sufficient frequency which may depend primarily upon the averaged length of elementary cells. FINITE ELEMENT MODELING In this study, after all the discussions about the internal fine structure and failure mechanisms of the plant fibers previously made and also about another anatomical observations in terms of longitudinal cross-sectional morphologies as shown in Fig.4 (a), the following numerical modeling with a combination of beam and continuum solid elements as schematically shown in Fig.4 (b) are proposed for the stress analysis and strength simulation of this natural biomass. Each of the elementary fibrous cells is to be modeled with beam elements. Cross sectional figurations and areas of the elementary fibrous cells can vary, so they will need to be statistically measured and then modeled with a mean, a coefficient of variation (CV) and a most plausible type of the probabilistic distributions. Otherwise, they might be idealized as an ellipse or a rectangle with an open-hole (lumen). Note also that, in the cases that only the axial forces are mainly concerned with, the shape and moduli of the sections are redundant. Similarly, the allover fiber length and flaw density along fiber length (nearly equal to axial tensile strength assigned to each of the beam elements) should be allowed to probabilistically vary. Spatial arrangements of elementary fibrous cells packed in the fibers are randomly generated. On the other hand, the inter-cell material regions are to be meshed with continuum solid elements. As already mentioned, the major ingredients of this cementing material are polysaccharide fractions such as pectin and hemi-cellulose. There is no observation on an existence of cellulose contents, in this interfacial regions, and therefore its stiffness and strength will be very small compared to those of elementary cells reinforced with CMF. A strength data sampled from an appropriate probabilistic distribution representing the strength properties of the elementary cells or the inter-cell material should be assigned to each element. Overall fracture of the plant fibers will be judged at the first moment when the actual stress of a certain element exceeds its strength. The component of stress and strength for that comparison is the axial tensile component for the beam elements (i.e. the elementary fibrous cells) and the shear component for the solid elements (i.e. the inter-cell material). Thisfracturejudgment is fairly applicable to brittle materials and the load-elongation curves of the kenaf fibers experimentally obtained by the present authors clearly indicated the nature of brittle facture in natural plant fibers. Elementary Fibrous Cells

Inter-Cell Material

43Beam Elements for Elementary Fibrous Cells ec n ar;

ell

alls

Kenaf Bast (Technical} Fiber (a)

Solid Elements for Inter-Cell Material (b)

FIGURE 4 (a) longitudinal section of kenaf fiber, (b) the present finite element modeling for plant fibers.

374

Fine Structure of Natural Plant Fibers

NUMERICAL EXAMPLE By using the proposed finite element modeling of natural plant fibers, a preliminary probabilistic simulation for statistical evaluations of their tensile strength were conducted with the Monte Carlo method invoked [3]. The simulation flow was charted in Fig.5. The finite element code, ANSYS 7.0, was used as the mesh generator, the solver and the result visualization tool. Probabilistic Design System (PDS), one of the ANSYS program extensions was also utilized to conduct the present probabilistic simulation. The key tasks up to the point of simulation execution are, (a) to construct a complete set of deterministic finite element analysis in the form of batch files written in APDL (ANSYS Parametric Design Language), (b) to define geometrical or physical parameters as "random input variables" and to specify their statistical data such as mean, standard deviation, and probabilistic distribution, and then (c) to select the resulting output parameters of interest. hi Table 1, the problem description, the dimensions and material properties of the plant fibers, the elementary fibrous cells and the inter-cell material are respectively shown. For the purpose of examining how the fiber strength depends on its gauge length, twelve different cases of the gauge length, L, from 0.1 to 40mm were simulated, hi order to eliminate the so-called "end effects", the numerical fiber models were so created that their length will always longer than the gauge length by the average length of the elementary fibrous cells. In Fig.6 (a), a typical finite element meshes (both of the entire and the zoomed-up views) are shown. On the other hand, Figure 6 (b) shows the shear stress distribution in the inter-cell material at one of the simulation steps. In that distribution are clearly seen the shear stress concentrations which can be a starting point offiberbreakage. TABELI The problem description and the simulation input data. Model dimension Total number of simulation samples

Monte Carlo direct simulation (ANSYSPDS) jrandomnumber generation ana then ''random input variable sampling

Problem Descriptions

i

20

at least 30 Elementary fibrous ceils are generated based on spatially uniform random distribution. The generated cells are dlscretlzed by 2D beam elements. Intercell materials are modeled by 2D plane-stress solid elements. Length, cross-sectional area and axial strength for each of the elementary fibrous cells are assumed to have normal (Gauss) distributions. Fiber strengths are calculated by using an axial reaction force for the first failure of the cells and averaged fiber cross-sectional area.

• modify the APDL file (rased on the | snput variable sampling results ana j prooiem solution ana evaluation of j output parameters tor this step

Gauge length : L [mm] Fiber Cross section height: H [mm] Max. numbers of elementary fibrous cells per cross section Mean of cell length : /_mean [mm] Standard deviation of cell length : STDevJ [mm] Length of beam elements : /_beam [mm] Elementary Mean of cross^ectional area i A mean [mm J Fibrous Cell Standard deviation of cross-sectional area : STDev__<4 [mm1] Young's modulus ; E Cell [N/mm1] Mean of cell axial strength : X_Cell [N/mm2] Standard deviation of ceil axial strength : STDev X [N/mm2]

inter-Cell

FIGURE 5 The simulation flow.

(a)

Young's modulus : E mat [N/mm2] Poisson's ratio : nu mat Mean of shear strength : S_Cell [N/mmJ] Standard deviation of shear strength : STDev S [N/mm2] Thickness: b [mm]

0.1,0.3,0.5, 1,2,3,4,5,6, 10,16,25,40 0.1 11 3 0.6 0.1 0.0001 0.00005 70000 1000 100 10000 0.3 60 12 0.01

(b)

FIGURE 6 (a) Typical FE mesh (Z=6mm) and its zoomed view, (b) shear stress in the inter-cell material.

Fine Structure of Natural Plant Fibers

375

TABLE II Means and CV of the strengths obtained by the simulation and percentage of the shear fracture. L

Q

(mm)

(MPa)

0.1 0.3 0.5 1 2 3 4 5 6 10 16 25 40

817 602 537 513 412 369 350 319 311 261 239 202 184

cv,, (%>

o DL=0.1mm e GL=0.5mm a GL=2.Qmm • GL=3.0n x GL=4.0mm • GL=16mm + GL=4Qmm

T «lit( ojnean) a percentage of inter-cell material fracture

percentage of shear fracture in inter-cell material

0.0

19.5 21.6 20.4

20.0 30.0

16.2 18.5 25.5 17.2 23.0 25.5 27.2 33.2 31.1 32.0

51.7 38.5 50.0 57.4 72.0 58.0 56.0 54.0 56.0 70.0

-2.0

-1.0

0.0

(a)

1.0

2.0

3.0

4.0

(b)

FIGURE 7 (a) Mean strengths and percentages of cases of fracture initiation in the inter-cell materials, (b) Weibull plots of the strengths.

In Table 2, as the simulation results, the means, the coefficient of variations and the percentage of the specimens which were broken by the shear failure in the inter-cell material regions, are summarized against the gauge length, hi Fig.7 (a), the means of strengths and the percentages of cases of fracture which initiated in an inter-cell material region are simultaneously plotted against the gauge length. Generally, as the gauge length increases, the fiber strength tends to decrease and the percentage of occurrence of shear failure increases, which, as previously mentioned in this paper, foretells importance of considering the shear stresses which will occur in the inter-cell material of plant fibers, as well as the axial stresses in the elementary fibrous cells, for the estimation of the fiber breaking loads. Finally, Weibull plots of the strengths of different gauge lengths are shown in Fig.7 (b). Some of the gauge length cases, e.g. G.L. = 0.5, 2.0 and 4.0mm, are seen to make not straight but kinked lines, which implies that strength characteristics of natural plant fibers are not necessarily represented by the classical two-parameter Weibull distribution. This is probably because of the multiple seeds of fracture, that is, the axial tensile breakage of the elementary fibrous cells and the shear failure at the stress concentrations in the inter-cell material regions. CONCLUDING REMARKS A numerical modeling with a combination of beam and continuum solid finite elements for stress analysis and strength simulation of natural plant fibers has been newly developed after carefully discussing about the internal fine (cellular) structure of kenaf (Hibiscus cannabinus L.) bast fibers. By using the present numerical model, Monte Carlo probabilistic simulations for statistical characterizations of tensile strength properties of natural plant fibers were also carried out, and the preliminary simulation results in a general case of natural plants partly indicated importance of considering the shear stresses which will occur in the inter-cell material regions in plant fibers, in addition to the axial stresses in the elementary fibrous cells, for the estimation of the fiber breaking loads. REFERENCES 1. Suzuki, K. 2004. "Research Report on Test Growing Kenaf', Report ofChiba Institute of Technology, 51, (in press). 2. Suzuki, K., Kimpara, L, Funami, K. and Kageyama, K. 2003. "Natural Bast Fibers with Large Variations in Geometrical and Mechanical Properties", Proc. 8th Japan International SAMPE Symposium (JISSE-8), pp. 139-142. 3. Suzuki, K., Funami, K., Kimpara, I and Kageyama, K. 2003. "The Stochastic Finite Element Analysis of Natural Fiber Reinforced Composites with Large Variations in Geometrical and Mechanical Properties", Proc. the 14th International Conference of Composite Materials (ICCM-14), CD-ROM pp.1-10.

Multilayered and Selective Higher-Order-Deformable Sandwich Finite Element Modeling for Numerical Accuracy Improvement Kohji Suzuki Chiba Institute of Technology, Department of Mechanical Engineering Science, Japan Isao Kimpara Kanazawa Institute of Technology, Advanced Materials Science R&D Center, Japan ABSTRACT Multilayered, higher-order-deformable and hybrid treatments are keys to numerical accuracy improvements of finite element analysis of composite and sandwich structures. In this context, the conventional displacement-based equivalent-single-layered and first-order-shear-deformable isoparametric shell finite element models are quite powerless for the multilayered composite and sandwich structures. This is especially true when one needs to numerically analyze composites and sandwiches in unusual states such as considerably severe transverse shear deformed situations and delamination-like damage states. In this study, new multilayered and higher-order-deformable finite element models will be proposed for accurate displacement and stress analysis of structural sandwich composite materials. The proposed model employed the flexible and versatile displacement assumptions for each of the three layers in sandwich-type constructions. The displacement assumptions for the core layer should be higher-order-deformable since this intermediate layer is thick and low modulus, while those of the upper and lower layers can be modeled as lower-order-deformable, such as first-order-shear-deformable, since they are thin and stiff. In the present finite element formulation, the displacement continuity constraints at the layer interfaces are enforced by invoking the penalty function method, in which the adhesions between the adjacent layers can be achieved with the penalty parameter virtually set to be infinitely large. In addition to the finite element formulation and then the program coding, a numerical example of a square sandwich plate subjected to uniformly distributing load were also shown, which showed, for the displacements of the core layer to be accurately modeled, the higher-order-deformable model should be used.

INTRODUCTION Sandwich structures have long been served as high-performance structural parts in many industries such as aerospace, marine and sports, and the demands for this sort of structural component won't be diminished for years to come. A sandwich-typed plates and shells are usually realized by facing the both surfaces of the intermediate core layer with the upper and lower skin layers. The upper and lower skin layers are most commonly formed with very thin but very stiff laminated composite materials like carbon fiber reinforced plastics (CFRPs), while the intermediate core layer with relatively thick, * Correspondence Author, 2-17-1 Tsudanuma, Narashino, +81-(0)47-478-0261, email: [email protected]

Chiba

275-0016, JAPAN;

Fax:

Multilayered and Selective Higher-Order-Deformable Sandwich

377

considerably low-modulus with a minimum transverse-shear resistance and light-weight porous materials like polyurethane foam and aramid honeycomb. This fact leads to a suspicion of multilayered (ML) deformations through the thickness. Apparently, for thick and soft-core sandwich structures, equivalent-single-layer (ESL) models [1-3] are not applicable and instead more-than-three-layered, i.e. ML, models considering the jumping discontinuity through the thickness in terms of the material properties and the kinematical assumptions will be probably indispensable if one wants to numerically model fairly accurate layer-by-layer displacements and in-plane stresses and then inter-laminar stresses in those structures. However, the conventional ML models [4-5] employ lower-order displacement fields for each of the three layers, in spite of the fact that the geometrical and mechanical properties of skins faces and the core are quite different from each other and hence there is possibility of some higher-order-deformable (HOD) states in the structures. This is especially true when one needs to numerically analyze composites and sandwiches in unusual states such as in transversely-shear-deformed situations, in delamination-like damagings, and so on. hi this study, a new multilayered and higher-order-deformable (ML/HOD) model will be proposed for accurate numerical analysis of structural sandwich composite materials, which can selectively consider ML and HOD assumptions in a flexible and versatile manner, hi addition, by using the proposed sandwich modeling, a few different finite elements will be developed and applied to a case of a square sandwich plate. FINITE ELEMENT FORMULATION The multilayered (ML) and higher-order-deformable (HOD) finite element model will be presented herein. For preserving its generality, summation conventions are implied for repeated subscripts in the mathematical formulae. hi the present finite element formulation, the three displacement components in each discrete layer are assumed to be expressed with power series expansions in terms of the thickness coordinates, xf), as follows:

where the superscript'T' denotes either of the upper skin (U), the core (C) or the lower skin (L) layers, and U\kp are the unknown coefficients in the series expansions. The geometric configuration of a laminate and the deformation of the typical layer "&" are respectively shown in Fig.l. Geometrically, U{^, Uf^ and Uf^ are the translational components i n ^ , x2 and x3 directions, respectively, while U\k) and Uf^ respectively stand for small rotations about x2 and —xl axes. The rest of the coefficients of power series expansions are higher-order influences such as warping of the cross-section and elongation of a transverse normal. The series in Eqn.(l) can be truncated at a proper order of expansion (practically at most up to the third order), however, at this moment, the orders of truncation is not yet determined for preserving the generality and flexibility of the present theory. For conceptual sake, when the orders of the series for k^ layer areiVf', JV<*> and N™ f o r < \ uf and uf\ respectively, the notation (N[k) N™ N\k)) will be used to express the order of displacement assumptions, and the notation,

Multilayered and Selective Higher-Order-Deformable Sandwich

378

^ir
\j. M • rotation

Upper

Lower face

~-h(k>/2 Ui P (P > 2).- higher-order terms

(a) through-the-thickhess configurations

(b) Deformation of the layer' k'

FIGURE 1 Sandwich plate element, notations and displacement assumptions.

[(Af> A f > Nlv) ) (Af > N(2C) A f > )(Af > Af } A f >)] will also be used for the entire sandwich laminate. Note that the brackets are for the entire sandwich and three columns of parentheses within the brackets, respectively from the left side to the right, denote the upper skin (U), the core (C) and the lower skin (L) layers. Three integers in each of the parentheses denote, respectively, the order of truncation of the polynomial series of three displacement components. Based on the small deformation elasticity, the strain-displacement relations are expressed in the following expansion forms:

ey=-2{

dXj

ax, )

V

*

3

J

'

^i/P^

•

i'

2)

(2, j = 1,2,3; i < j and P = 0,1,2, • • •, max (Af>,

(2) Nf))

where Efl are general strain components. Physically, E^ are strains at the middle plane of the &* layer, and Ef? are curvatures of that layer. E\k)0 stand for the first approximations of transverse shear strains. When E\k\ are set equal to zero, then the same displacement / strain assumptions as the classical plate (CP) theory are modeled in the kth layer (not in the entire laminate). On the other hand, when these terms are set non-zero, then the first-order-shear-deformable (FOSD) theory, i.e., Reissner-Mindline assumption, (110), are assigned in that layer. The rest of the general strains are higher-order components corresponding to the higher-order-deformable (HOD) displacements. Obviously, the orders of through-the-thickness variations of strains depend upon the displacement orders ( A f ' A f A f J ) . For instance, when the displacement assumption (332) is adopted, then cubic variations of in-plane strains, parabolic variations of transverse shear strains and linear variations of transverse normal strain can be modeled. The aim of the HOD assumptions is placed on an optimization in the numerical modeling of displacement and strain variations over the thickness of the laminates and sandwiches as close to the actual as possible. Appropriate and practical orders of displacements should be determined in accordance with the actual sandwich configurations to be modeled. After assuming the higher-order-deformable (HOD) displacements in each layer, next comes assemblage of layers to form the entire sandwich. In the present formulation, the

Multilayered and Selective Higher-Order-Deformable Sandwich

379

displacement continuity constraints at the perfectly adhered interfaces between the k01 and the (k + l)'h layers are given as follows: fr(k)(x i ) - « ( i t I ) \x x Si

\X1>X2) ~Ui

x

\iX2-:

(3)

(z= 1,2,3 and/> = 0,1,2,---, hi order to consider above constraints, the following modified potential energy functional with displacement continuities relaxed at layer interfaces will be utilized,

where the first two terms are the potential energy in the system obtained after summing the ones stored in all the three layers without interface constraints. 7] andwj, respectively, denote mechanical and geometrical boundary conditions on the upper and lower exterior surfaces of the sandwiches. On the other hand, the last term is the auxiliary energy term due to the interfacial displacement constrains, and Xt stands for each of the three components of the so-called inter-laminar stress, and, in this formulation by the penalty method, can be estimated by, Ajk) - a^k)gjk), in which a\k) are called the penalty parameters. When each a\k) for each layer interface is set virtually infinite, then the displacement continuities will be approximated and the auxiliary energy term will vanish, hi the present finite element formulation, the allover domain of a sandwich plate will be discretized into Ne elements such that: (5) The generalized displacement vector 5 are defined as a collection of each sub-vectors for those in the Ar"1 (k = U, C or L) layer:

Finally, taking the first variation of the functional in Eqn.(5), and then collecting the contributions from all elements yields the following equilibrium equation system: 5

0

^> ^

[K + K J d = f

(7)

55

in which K is the global stiffness matrix without displacement constraints and K a , on the other hand, is the interface constraint stiffness portion including the penalty parameters, d and f are respectively the assembled nodal displacement and force vectors.

Multilayered and Selective Higher-Order-Deformable Sandwich

380

y l

-V2-

simply supported conditions for all four edges

0 (a) the problem definitions

1/2

I

x

(b) top view of the plate

FIGURE 2 A simply-supported CFRP/honeycomb-core sandwich plate to be analyzed.

NUMERICAL EXAMPLE hi order to assess the degree of improvement of the accuracy and convergence properties of the finite element modeling by HOD assumptions, comparative results are presented in the case of a simply-supported CFRP/honeycomb-core sandwich plate subjected to an uniformly distributed load over the whole area of the upper face surface as shown in Fig.2. The dimensions and the material properties and the load intensity applied used in the numerical analysis are as follows: for the entire sandwich plate; / = 200mm, h = 9.6mm, q0 = 1 .OMPa for the faces; = £ , = 560GPa,

£ z =91.7GPa

vxy =0.0813, vYz= 0.450, v z x = 0.0237, G xy =259GPa,

Gyz = Gzx = 29.5GPa

and for the core of aluminum honeycomb with the following properties;

F=8.0mm, Ex=0.5lGPa, Ey=0.63GP&, £z=14.1GPa vxy = 0.83, vyz = 0.015, v2x = 0.34, Gxy = 0.49GPa, Gyz = 2.46GPa, Gzx = 3.03GPa Three different types of sandwich elements, that is, [(110)(110)(l 10)] element, [(110)(332X110)] element and [(332)(332)(332)] element based on the selective formulations shown in the previous section were used for the analysis. As a baseline for numerical accuracy, a detailed 3-D continuum solid element model was also generated using the general purpose finite element package MARC (version k-5) with the use of 20-node isoparametric 3-D continuum solid elements. The total number of nodes in the 3-D solid FEM model was 15236, and the total number of elements was 3125. The variation of the central deflection (normalized with the result by 3-D solid FE) against square mesh refinement is shown in Fig.3. It is observed that, as the degrees of freedom are increased in number, every of the present FEs' solutions are converging to the constant value a little bit smaller than the result obtained with the detailed 3-D continuum solid FE. It is also observed that [(110)(332)(110)] and [(332)(332)(332)] element, the results obtained by which were almost identical, gave more accurate results than [(110)(l 10)(l 10)] did. On the other hand, the other analytical models, all of which are

Multilayered and Selective Higher-Order-Deformable Sandwich

381

[(110)(110)(110)] FE solution [(332)(332)(332)] or [(110)(332)(110)] FE solution

1.1 3-D solid FE solution 1,(0.982) '(0.951) Allen's analytical solution (0.841) HOT of Reddy (0.773) FOSDT (0.694) CLT (0.609)

10

15

20

25

Number of elements FIGURE 3 Central deflections against square mesh refinement.

based on the existing classical and equivalent-single-layered (ESL) theory, without any exception, provided poor (too stiff) results. CONCLUDING REMARKS Some accurate FE models for sandwich plates were presented, based on the selective multilayered and higher-order-deformable (ML/HOD) assumption, i.e. [(110)(l 10)(l 10)], [(110)(332)(H0)] and [(332)(332)(332)]. The numerical example on a square sandwich plate with uniform distributing load clearly illustrated that those ML/HOD models proposed in this study were more accurate than the ESL-based models such CLT, FOSDT, which showed, for the displacements of the core layer to be accurately modeled, the higher-order-deformable models should be used. In addition, since the numerical accuracy of [(110)(l 10)(l 10)] model was slightly inferior to the other two models, i.e. [(110)(332)(110)] and [(332)(332)(332)] and also from the view point of computational efficiency, the optimum numerical model will be [(110)(332)(110)] among the three models taken into consideration in this study. REFERENCES 1. Yang, P.C., Norris, C.H. and Stavsky, Y. 1966. "Elastic wave propagation in heterogeneous plates", Int. J. Solid Struct, 2, pp.665-684. 2. Lo, K.H., Christensen, R.M. and Wu, E.M. 1977. "A higher-order theory plate deformation. Part 2: Laminated plates", J. Appl. Meek, 44, pp.669-676. 3. Reddy, I N . 1984. "A simple higher-order theory for laminated composite plates", J. Appl. Meek, 51, pp.745-752. 4. Mau, S.T. 1973, "A refined laminated plate theory", J. Appl. Meek, 40, pp.606-607. 5. Ferreira, A.J.M., Barros, J.A.O. and Marques, A.T. 1991, "Finite element analysis of sandwich structures", Proc. 8th Int. Conf. Compos. Mater. (ICCM/8), Honolulu, 3A2.

Adhesion Measures of Elasto-plastic Thin Film via Buckle-driven Delamination Qunyang Li and Shouwen Yu* Key Lab .of Failure Mechanics of MoE, Tsinghua University, Beijing 100084, China

ABSTRACT Indentation test is becoming increasingly used to quantitatively assess the thin film interfacial adhesion for its simplicity and ability to mechanically probe the smallest of solids. The conventional technique is based on the analysis of Marshall and Evans which is a combination of Linear Elastic Fracture Mechanics (LEFM) and simplified post-buckling theory. In this paper a full post-buckling response of elasto-plastic thin film is investigated by FEM calculation; the contributions plastic buckling to the indentation test is discussed. The results show that plasticity is a significant factor for those films with low yield stress and must be taken in account in adhesion measurement. INTRODUCTION Thin films have a wide range of applications in microelectronics and magnetic recording industries. Because of the importance of thin film adhesion, there are more than 200 different methods [1] to measuring interfacial adhesion at present, suggesting them to be material, geometry and even industry specific. While many of these tests are semi-quantitatively measurements and are useful for functional or comparative purposes [2-5]. For brittle, weakly bonded films, indentation can be used to delaminate the films from the substrates, thus measuring the thin film interfacial strength [1]. During this process, the thin film experiences five stages of deformation from elastic contact and dislocation nucleation to film decohesion and buckling [6]. This indentation technique is mainly based on the pioneer works of Marshall & Evans [7] and Evans & Hutchinson [8] which gave the theoretical analysis for the conical indentation-induced thin film delamination. Consider an indentation-induced interface crack in a residually stressed film, shown in Fig.l. The film has a thickness t and stick on a semi-infinite substrate, loaded by a hard angular indenter which leaves a permanent impression, and the residual stress is assumed to be aR. The strain energy release rate G is obtained as follows [6,8].Denote V, E as Poisson ratio and elastic miduli, <7Q = 2?(a7a)/(l- V), <JC express the critical buckling stress of the plate,we have

G = t(l - v) {(1 - cc)aR2 + <x02 [(1 + v) / 2 - (1 - a)(l - ac I
(1)

Correspondence Author, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China, Fax: ++86 10 62781824, E-mail: [email protected]

Adhesion Measures of Elasto-plastic Thin Film

383

Film , T.1 *• T Substrate Crack Plastic Zone FIGURE 1 Schematic of indentation-induced delamination at the interface of a thin film and substrate

where a—radius of delamination, a'—increment of radius a induced by plastic deformation, a = 1 for <JO+CTR <<JC (no buckling) or a = (1 + 1.207(1 + v))

for

ao+crR > <7C (buckling). After measuring the strain energy release rate G, the interfacial adhesion between the thin film and substrate can be calculated. The equation (1) is only valid for initial stage of post-buckling, and the assumption of the buckling of plate is taken without considering the plastic behavior of thin films. Experiment of Kriese et al. [9] found that during indentation the interfacial fracture toughness was reproducibility high for shallow indents, 8-10 J/m 2 , but dropped to a fairly steady 0.7-1.2 J/m2 for deeper indents. It is hard to explain these experimental data via conventional analysis. As we know, the plasticity of materials will greatly affect the buckling process; can it be a reason for this phenomenon? In the paper, we will emphasize on some aspects of thin film bucking and their influences to the indentation test. Based on finite element method (FEM) code ABAUQS, the full post-buckling responses of thin films are obtained .The material plasticity are taken into consideration and their contributions are discussed. LARGE DEFORMATION BUCKLING FOR THIN FILM DELAMINATION Model for FEM Analysis A circular delamination at a film/substrate interface is considered, as shown in Fig.2(a), with a uniform biaxial compression a exiting in the film. For this axisymmetric problem, only one cross-section of the buckled film (i.e. the buckled film disc) is modeled, shown in Fig.2(b). The film disc has a thickness t and a radius a, and is subject to uniform biaxial compression a on the perimeter (BC2). Boundary conditions are applied, such that the perimeter (BC2) is always fixed in r direction while the film center (BC1) is fixed in r direction for single-buckling case FEM Results of Full Single-buckling Response The procedure of 'Eigenvalue Buckling Prediction' in ABAQUS is used to obtain the critical buckling stress. For various values of tl a, using the non-dimensional stress uc = 12(1 - v2 )
tV with k = 14.3876, which coincides the theoretical Euler buckling stress A; = 14.68 very well. To calculate the film response when a > <JC , RIKS procedure is used to perform post-buckling analyses :For the case of tl a = 1/20, the edge stress a as a

384

Adhesion Measures of Elasto-plastic Thin Film

function of displacement A for this film disc is plotted in Fig.3. The Fig.3 gives the full post-buckling response of the elastic thin film, from which we can clearly observe the whole process of buckling and the stiffness of the film (i.e. the slope of the curve) is greatly reduced after the critical point of buckling.

(a)

BC2 Film

BC1

(b)

FIGURE2 (a) Circular delamination at a film/substrate interface; (b) Model for FEM calculation

1

"i

— • — Single-buckling ) 4 3 2 1

-

•

n 12

16

A/A

FIGURE 3 Plot of edge stress <J as a function of inward displacement A (Uc

and Ac are the

critical stress and displacement for single-buckling)

The FEM results of the initial slope well fit the theoretical prediction, which is provided by Evans & Hutchinson [8] and assumed to be a = (l +1.207(1 + v))~l. But from Fig.5, it can be seen that the slope of the post-buckled brunch goes down as the increase of inward displacement. To consider the deviation from the initial slope value, we assume the slope a has the following form a = aa-/3

—

(3)

where a0 is the initial slop value and p is fitted from the FEM data to be around 0.01973 for different values of v. Thus the equation of energy rate is modified as .1 + v G=-^)2]} (4) c £ ^ " 2 ° c RJ where a , ft are determined by equation (3).

Adhesion Measures of Elasto-plastic Thin Film

385

POST-BUCKLING OF ELASTO-PLASTIC THIN FILMS All the discussion above is based on the assumption of elastic deformation. But because of the large deformation during the post-buckling stage, it may be very helpful if we take the plasticity of the film into consideration to investigate its influence, especially for the film with low value of yield stress ay. This section will carry out the FEM analysis on the effects of plasticity to the single-buckling process. Model for FEM Analysis The schematic of the model is similar as Fig.2, but the thin film is modified as an elasto-plastic material which obeys the power hardening law a

=

(5) o\,

where ay and sy are the initial yield stress and yield strain, and n is the hardening exponent. FEM Post-buckling Analysis for Elasto-plastic Films First, we calculate the case of ay IE = 2xlO~3, i.e. ac Iay * 1.7 .From Fig.4, the energy release rate decreases significantly when considering the film plasticity. For the perfect plastic case, the energy release rate decreases to one half of the elastic one when a » ac, to 20% when a « 2<xc and to less than 5% when a » 3ac (it should be noted that the result is not yet valid and only serve a qualitative analysis when the stress reaches such a high value, such expressed in Fig. 5.

Elastic 1.5

O

n=3 n=7 n=20 Perfect plastic

/

y /

1.0

0.5

nn 0

/*

"^ 1

2

3

4

5

a la

FIGURE 4 Energy release rate for elasto-plastic films with different values of hardening exponent n (<Jcla*

1.7)

386

Adhesion Measures of Elasto-plastic Thin Film 2.0 Elastic

/

n=2 n=3 n =7

''""""" ^

1.5 \

Perfect plastic

1.0 • \

'•

\

\ \ '

0.5 •

\ \v

0.0

0

1

2

3

4 cr/cr

5

6

7

I

FIGURE 5 Energy release rate for elasto-plastic films with different value of hardening exponent n «Jc/ay*0.3)

As we has been mentioned above, experiment of Kriese et al.[9] found that during indentation the interfacial fracture toughness was reproducibility high for shallow indents, but dropped to a fairly steady value for deeper indents. If we assume that the radius of the buckled film increases from 30 um for shallow indent to 100 um for deeper indent, the value of ac I ay for deeper indent will reduce to about one tenth of the shallow one. According to the discussion above, the influence of the film plasticity will be a dominant factor for shallow indent, so it must be included to interpreter the results correctly. This might be one of the reasons for the discrepancy between shallow and deeper indent. CONCLUSION An investigation on the post-buckling of thin film is carried out by FEM calculation. Some of the important factors, such as the material plasticity, are discussed in this paper .The results show that for the case of a < 3<7C, the asymptotical solution is satisfactory with a relative error less than 10%.The plasticity has significant influence on the post-buckling responses and should be considered in interpreting the indentation test results. The greater the value of ac/ay, the more contributions of the plasticity. The abnormal experimental results of Kxiese [9] can be explained by this calculation. We can say that if the conventional method of indentation test is considered, the deeper indent the more precise of the results. ACKNOWLEDGEMENT This project is supported by NSFC (10172050) and SRFDP 3064, Key grant project of Chinese MoE-No-0306. REFERENCES 1

Volinsky, A.A., N.R. Moody,and W.W. Gerberich. 2002. Interfacial toughness measurements for thin films on substrates. Acta Materialia., 50:441-466.

Adhesion Measures of Elasto-plastic Thin Film 2

3 4 5 6 7 8 9

387

Jindal, P.C., D.T. Quinto, and GJ .Wolfe. 1987. Adhesion measurements of chemically vapor deposited and physically vapor deposited hard coating on WC-Co substrates. Thin Solid Films, 154:361-375. Rickerby ,D.S. 1988.A review of the methods for the measurement of coating substrate adhesion. Surf. Coat. Tech., 36:541-559. Steinmann PA, and H.E. Hintermann. 1989.A review of the mechanical tests for assessment of thin film adhesion. J. Vac. Set TechnoX. A, 7:2267-2272. McCabe ,A. R., A.M. Jones, and S.J. Bull. 1994. Mechanical properties of ion-beam deposited diamond like carbon on polymers. Diamond and Related Technol, 3:205-209. Gerberich, W.W., and D.E. Kramer, et al.1999. Nanoindentation-induced defect-interface interactions: phenomena, methods and limitations. Ada. Mater, 47(15):4115-4123. Marshall, D.B., and A.G. Evans. 1984. Measurement of adherence of residually stressed thin films by indentation. I. Mechanics of interface delamination. J. Appl. Phys,, 56(10):2632-2638. Evans, A.G., and J.W. Hutchinson. 1984. On the mechanics of delamination and spalling in compressed films. Int. J. Solids Structures, 20(5):455-466. Kriese ,M.D., D.A. Boismier, N.R. Moody, and WW Gerberich. 1998. Nanomechanical fracture-testing of thin films. Engineering Fracture Mechanics, 61:1-20.

Evaluation of Intra-ply Shearing Stiffness for a Plain Weave Fabric Prepreg Xiaobo Yu , Lin Ye School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney, NSW 2006, Australia Damian McGuckin Pacific Engineering Systems International Ltd 22/8 Campbell St., Artarmon, NSW 2064, Australia

ABSTRACT It has been found that forming simulations give poor predictions of the formability of simple cup shapes during double-diaphragm forming of fabric prepreg stacks. In response, this study evaluated the available test results, as well as test set ups, for intraply shearing stiffness measurement. Parametric studies using multiple simulations indicated that the effective intra-ply shearing stiffness of a plain weave prepreg may be more than ten times higher than currently available experimental data indicates. This finding is supported by a modelling analysis that attempts to predict the effect of compaction pressure on the intra-ply shearing stiffness.

INTRODUCTION Carbon fibre reinforced epoxy composites are well accepted in the aerospace industry. A typical aerospace composite part is assembled from 3 to 60 plies of carbon fabric impregnated with epoxy resin (prepreg) [1]. Traditionally, it is formed by successive hand lamination of individual plies. This is appropriate and efficient for small production runs, but makes composite parts expensive for high-volume production [2]. To achieve automation and reduce manufacturing costs, aerospace industries and research institutes around the world have been developing alternative manufacturing approaches in the last decade. In Australia, diaphragm forming has been identified and developed by the Cooperative Research Centre for Advanced Composite Structures (CRC-ACS) to be the leading solution to automated preforming of a large variety of aerospace parts [2]. Numerical simulations on diaphragm forming are also in development [3-6] for the purpose of establishing a virtual prototyping approach to quickly identify optimum forming parameters. So far, better numerical simulations have been achieved by a number of improvements including the better understanding of diaphragm material properties, improved finite element treatment of intra-ply shearing stiffness [3-4], more accurate experimental data and simulation of inter-ply friction [5], and the awareness of, and a remedy to, an intra-ply shear locking problem [6]. With all these improvements however, as will be demonstrated in this paper, it still remains a

f

Correspondence author, fax: +61 2 9351 3760, e-mail: [email protected]

Intra-ply Shearing Stiffness for Plain Weave Fabric Prepreg

389

challenge to accurately predict forming quality based on given forming parameters and available material properties. The present study was investigated following poor predictions of wrinkling in benchmark simulations of double diaphragm forming of a simple cup. The study evaluated the reasonableness of available test results for intra-ply shearing stiffness, by means of parameter studies and modelling analyses. Even with all the efforts of a more accurate and repeatable measurement of intra-ply shearing stiffness, for example [7-13], the present study gives rise to the suspicion that the effective prepreg intra-ply shearing stiffness encountered during double diaphragm forming cannot be reproduced in a test set up without prepreg compaction. BENCHMARK SIMULATIONS CRC-ACS has performed a number of experimental studies on double diaphragm forming of a simple cup shape, using stacks of CF/EP plain weave fabric prepreg, to investigate the effects of various forming parameters [14]. The current benchmark simulations consider two of the tests. One was a 3-ply [±45/0,90/±45] simple cup where the part was formed without wrinkles. The other was a 6-ply [±45/0,90/±45]s simple cup where significant wrinkles developed in the flange of the part. Except for the number of prepreg plies, the two tests were performed under identical set up (see Figure 1) and forming conditions. The 2002 version PAM-FORM software [15] was used for the benchmark simulations. The diaphragm was modelled by membrane elements degenerated from Type 107 shell elements. The diaphragm material properties were measured from uniaxial tension tests. The stack of prepreg was modelled following the concept described in Figure 2. Each ply was discretized individually and was connected to its neighboring plies by a Type 13 segment-to-segment large sliding contact. The inter-ply friction was calculated considering compaction pressure and sliding velocity within a user subroutine using non-linear functions determined by ply pullout tests [5]. The transition from static (high) to dynamic (low) friction was ignored. By using static friction, the benchmark Stack of prepreg-—,.

Top diaphragm

1 J

Bottom diaphragm 1

Dimensions: Box: diameter = 420mm, depth = 100mm; Tool: diameter = 100mm, height = 80mm; Stack of prepreg: diameter = 140mm.

FIGURE 1. Schematic section showing the test set up for double diaphragm forming of a simple cup.

Inter-ply friction

Intra-ply shearing stiffness

Out-of-plane bending stiffness

FIGURE 2. Illustration showing how a stack of woven fabric prepreg is decomposed in a PAM-FORM simulation.

390

Intra-ply Shearing Stiffness for Plain Weave Fabric Prepreg

simulations produce conservative, or more likely to wrinkle, predictions. Type 140 shell elements were used to model each ply of woven fabric. The fabric was decomposed into two directions according to their orientations. Each was assigned an axial stiffness that represents the equivalent Young's modulus of the prepreg along the fibre direction, and an out-of-plane bending stiffness that was scaled by a bending factor to correlate with ply self-weight tests [16]. The prepreg also had an intra-ply shearing stiffness to resist trellis deformations. The intra-ply stiffness was determined from bias extension test results [17] using the improved Ideal Fibre Reinforced Fluid (FRF) model [4]. To implement the improvement on the FRF model, each Type 140 shell element was overlapped by a Type 107 shell as reported in [3]. It was known that the IFRF model, in spite of being improved, may still be not as accurate as desired, and might induce up to 70% error in reproducing experimental data [4]. However, as will be demonstrated later, this error may be minor compared to those from other sources. Figure 3 shows the meshes used in the benchmark simulations. Triangle elements were used to avoid warping and hourglass mode deformations. For each triangle element, two of its three edges were aligned with fibre directions. The aligned mesh was introduced to avoid so-called intra-ply shear locking, a phenomenon of numerical overestimation of intra-ply stiffness [6]. The aligned mesh differentiates the present simulations from most previous ones. Based on the aforementioned modelling and material properties, the 3-ply forming simulation predicted no wrinkles, in agreement with the test result. However, the 6-ply forming simulation predicted no wrinkles as well, in contrast to the experimental result. The inaccurate simulation could be attributed to a number of possibilities, including misinterpretation of forming mechanisms, inappropriate implementation in finite element codes and incorrect material properties. A couple of these possibilities were checked. Altering the diaphragm material properties within a large range had little effect on predicted forming quality in this particular case. The inter-ply friction has been found to be an important parameter for wrinkle development. However, it was calculated in a user friction subroutine that accurately reproduced reliable test results. In addition, static friction values were used, so that the inter-ply friction value used was more likely to predict wrinkles. The fibre out-of-plane bending stiffness can affect wrinkle development in a single ply but it has little effect on a stack of plies connected by interply friction. It was found that no wrinkles developed even if the fibre out-of-plane bending stiffness was set to zero. In comparison, there appeared to be considerable inaccuracy when the IFRF model was used to describe the intra-ply shearing stiffness. Furthermore, it is suspected that the effective intra-ply shearing stiffness of a prepreg ply in diaphragm forming cannot be accurately measured in a bias extension test without compaction pressure. In view of these, parametric simulation studies were performed to "back-calculate" a more likely intra-ply shearing stiffness. 0/90 ply

± 45 ply

FIGURE 3. Aligned meshes used in the benchmark simulations, (only a quarter of the full model is shown for clarity)

Intra-ply Shearing Stiffness for Plain Weave Fabric Prepreg

391

A wide range of intra-ply shearing stiffness was tried. Figure 4 shows force versus displacement relationships when three representative intra-ply shearing stiffness properties were applied in bias extension test simulations. The force responses corresponding to A, B and C are approximately 30, 20 and 10 times as high as the test result [17]. When applied to simple cup forming simulations, the intra-ply shearing stiffness A appears too stiff because wrinkles developed in the 3-ply forming simulation as well. Intra-ply shearing stiffness B seems appropriate as the simulations of 3-ply and 6-ply forming, as shown in Figure 5, both agree with the experiment. In the case of intraply shearing stiffness C, wrinkles predicted in the 6-ply forming are not as pronounced as in the experiment.

10

20

30

Displacement {mm)

FIGURE 4. Force versus displacement relationship in bias extension test simulations.

•V FIGURE 5. Benchmark simulations based on intra-ply shearing stiffness B.

MODELLING OF INTRA-PLY SHEARING STIFFNESS The parametric studies suggest that the intra-ply shearing stiffness needs to be scaled up by more than 10 times from the current experimental data in order to get the benchmark simulations to make the correct predictions. The increase required is thought to be far greater than the possible inaccuracy in the IFRF model or experimental randomness. The authors suspect that the intra-ply shearing stiffness of a prepreg ply during diaphragm forming may not be measured by a bias extension (or picture frame) test which does not include the effect of the compaction pressure experienced by the fabric stack during diaphragm forming. As further evidence for this concern, a modelling analysis is presented as follows. As explained in [18], we assume that the intra-ply shearing stiffness is mainly caused by the viscous friction at fibre cross-over and between neighboring tows contacts. It is noted that due to differences in fabric structure, the conclusion of [18], stating that the friction at fibre cross-over is negligible, does not apply to this study. As shown in Figures 6(a) and 6(b), the adjacent tows in a plain weave fabric are separated at the top

392

Intra-ply Shearing Stiffness for Plain Weave Fabric Prepreg

and bottom halves of a ply thickness. The friction at fibre cross-over therefore plays a predominant role on intra-ply shearing stiffness. This study goes one step further to incorporate the effects of compaction pressure. It is assumed that the friction over a unit area can be described by a function ^(q, v), where q and v are local compaction pressure and sliding velocity, respectively. Introducing the virtual work principle, the pulling force of a bias extension test, F(p, u), under nominal compaction pressure p and pulling velocity u, can be calculated by Eq. (1), where the integration calculates energy rate over a single cross-over, and "2" sums up the energy rate of all cross-over points. We further assume the q and v effects can be decoupled [5] so that function *¥(q, v) takes the form of Eq. (2). Substituting Eq. (2) into Eq. (1) and considering Figure 6(c), Eq. (3) can be obtained for a given pulling velocity (M) and deformation, where Sd is the tow width. Now the effect of compaction pressure can be examined. Assume that the pressure dependency of inter-tow friction takes the pattern of inter-ply friction as shown in Figure 6(d). The slight difference caused by the local and nominal pressure was ignored. It can be seen that when the compaction pressure increases from zero to the range of 60 to 100 kPa, f(q) increases to approximately nine times as much. When combined with 10%, 15%, or 20% Sd increment due to tow flattening under compaction pressure, the pulling force increases to approximately 12, 13.5, or 15.5 times as much, even if the cS"d term in Eq. (3) is ignored. If cSd is included, Eq.(3) predicts a larger pulling force. ,v)dA

(1) (2) (3)

No compaction Individual test data -Averaged test data

Compaction Normal Pressure (kPa) b

( )

FIGURE 6. (a) A woven fabric; (b) Tow flattening due to compaction pressure; (c) A fibre cross-over; (d) The pressure dependency of inter-ply friction.

FINAL REMARKS AND SUGGESTIONS The previous simulations show that the intra-ply shearing stiffness needs to be increased by more than ten times the measured figures to obtain good results. The implication that the current intra-ply shearing stiffness is incorrect is supported by a modelling analysis that incorporates the effect of compaction pressure. These two analyses suggest that a bias extension test or a picture frame test performed without compaction pressure may significantly under-estimate the effective intra-ply shearing stiffness of a plain woven prepreg ply during double diaphragm forming. The present work highlights the necessity to clarify the effect of compaction pressure experimentally. As a starting point, a diaphragm packaging method as reported in [19] is suggested as a possible test for measurement of intra-ply shearing stiffness. This approach is currently being investigated by the authors.

Intra-ply Shearing Stiffness for Plain Weave Fabric Prepreg

393

ACKNOWLEDGEMENTS This work was supported by the Australian government under the ARC-Linkage Project Scheme, and the Auslndustry R&D Tax Concession/Offset Scheme, and ESI Group who provided a copy of the PAM-FORM software. The ongoing and underlying support of the Cooperative Research Centre for Advanced Composite Structures Ltd is also gratefully acknowledged. The help given to the authors by their colleagues Allen Chhor and Bruce Cartwright of Pacific ESI was invaluable.

REFERENCES 1.

2. 3.

4. 5.

6.

7.

8.

9. 10. 11.

12.

13.

14. 15. 16.

17. 18.

19.

Paton, R., G. Clayton, P. Falzon and D. Do. 2000. "Automated manufacture of advanced composite aerospace components," 8th International Conference on Manufacturing Engineering, Sydney, Australia, August 2000, Paper Number 62. Young, M. 2003. "Diaphragm forming guidelines," CRC-ACS TM 03016. Yu, X., B. Cartwright, L. Zhang, Y.-W. Mai and R. Paton. 2000. "Finite element simulations of the diaphragm forming process," presented at 15th Annual Technical Conference of the American Society for Composite. Texas, USA, 2000. Yu, X., L. Zhang and Y.-W. Mai. 2003. "Modelling and finite element treatment of intra-ply shearing of woven fabric," Journal of Materials Processing Technology, 138(1-3): 47-52. Cartwright, B., A. Chhor, S. Howlett, D. McGuckin, R. Paton, L. Ye and X. Yu. 2003. "Industrially robust modelling of viscous friction effects in composites," presented at EuroPAM 2003, October 1617, 2003. Mainz, Germany. Yu, X., B. Cartwright, D. McGuckin, L. Ye and Y.-W. Mai. 2004. "Intra-ply shear locking in finite element analyses of woven fabric forming processes," submitted to Composites Science and Technology. McGuinness, G.B. and C.M.O. Bradaigh. 1997. "Development of rheological models for forming flows and picture-frame shear testing of fabric reinforced thermoplastic sheets," Journal of NonNewtonian Fluid Mechanics, 73(1-2): 1-28. McGuinness, G.B. and C.M.O. Bradaigh. 1998. "Characterisation of thermoplastic composite melts in rhombus-shear: the picture-frame experiment," Composites Part a-Applied Science and Manufacturing, 29(1-2): 115-132. Wang, J., J.R. Page and R. Paton. 1998. "Experimental investigation of the draping properties of reinforcement fabrics," Composites Science and Technology, 58(2): 229-237 Nguyen, M., I. Herszberg and R. Paton. 1999. "The shear properties of woven carbon fabric," Composite Structures, 47(1-4): 767-779. Harrison, P., M.J. Clifford and A.C. Long. 2002. "Shear characterisation of woven textile Composites', presented at 10th European Conference on Composite Materials, 3-7th June, Brugge, Lebrun, G., M.N. Bureau and J. Denault. 2003. "Evaluation of bias-extension and picture-frame test methods for the measurement of intraply shear properties of PP/glass commingled fabrics," Composite Structures, 61(4): 341-352. Peng, X.Q., J. Cao, J. Chen, P. Xue, D.S. Lussier and L. Liu. 2004. "Experimental and numerical analysis on normalization of picture frame tests for composite materials," Composites Science and Technology, 64:11 -21. Young, M. and R. Paton. 2001. "Investigation on the forming of a simple cup," CRC-ACS TM01003. ESI Software. 2002. PAM-FORM 2002 Solver Reference Manual. Young, M., B. Cartwright, R. Paton, X. Yu, L. Zhang and Y.-W. Mai. 2001. "Material characterisation tests for finite element simulation of the diaphragm forming process," presented at ESAFORM 2001 Conference. Wang, J., R. Paton and J.R. Page. 1997. "Forming properties of thermoset fabric prepregs at room and elevated temperature," CRC-ACS TM 97028. Harrison, P., MJ. Clifford, A.C. Long and CD. Rudd. 2002. "Constitutive modelling of impregnated continuous fibre reinforced composites micromechanical approach," Plastics, Rubber and Composites, 31(2): 76-86. Nestor, T.A., and CM. O'Bradaigh. 1995. "Experimental investigation of the intraply shear mechanism in thermoplastic composites sheet forming," Key Engineering Materials, 99-100: 19-36.

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Part VIII

Fracture

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Initial Fracture Behaviour of the Weft-Knitted Textile Composites Having Welt-Knit Architectures Omar Khondker*, Tatsuro Fukui, Asami Nakai and Hiroyuki Hamada Advanced Fibro-Science, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto, 606-8585, Japan

ABSTRACT Initial fracture behaviour of the weft-knitted glass/epoxy composites was investigated to study their dependence upon the welt-knit architectures with varying structural parameters, such as the length of the non-loop welt-stitches and the lineal density of held-stitches within the welt-length. Strain gages were bonded onto the test specimens at different locations of the structural unit-cell. Knee points of the stress-strain curves were closely studied in order to characterize the first onset of local failure. Postfailure examination was carried out on the test specimens using stereo-optical and scanning electron microscopy to analyze their microscopic fracture behaviour. No significant changes were recorded in the stiffness and strength values with increasing welt-lengths and number of held stitches, in either test directions. In general, crack propagated almost normal to the direction of the two principal loading axes. According to the SEM micrographs, fracture plane for the wale-tested specimens coincided along the length of the welt-stitches and continued through the fibre crossover regions of the same course, whereas for the course-tested specimens, fracture plane ran along the fibre crossover regions transverse and adjacent to the length of the welt-stitches. Initial fracture modes in either test directions combined transverse and debonding cracks, inside and between the fibre bundles, respectively. These observations agreed well with the knee point responses obtained from the local stress-strain curves.

INTRODUCTION Considerable research [1-11] has been directed on the macro-mechanical properties of textile composites, such as their static tensile, bending and fatigue properties with regard to their overall fracture behaviour, hi textile composites, several modes of micro fractures, such as transverse cracks inside the fibre bundles, delamination at the fibre cross parts, matrix and filament failure occur and accumulate before final rupture of the composite. The initiation of micro fracture termed as 'initial fracture' is particularly important, in order to carry out a precise investigation on the overall mechanical properties of textile composite materials. Knitting is ideally suited for the cost-effective production of intricately-shaped composites. Lack of comprehensive investigation on the initial fracture behaviour of knitted composites towards understanding their overall mechanical properties, still acts as an impediment to the wider acceptance of these materials and, hence, expanded application. In an earlier work [12,13], initial fracture * Correspondence Author, Advanced Fibro-Science, Kyoto Institute of Technology, Matsugasaki, Sakyoku, Kyoto 606-8585, Japan Phone: (81-75) 724 7844 Fax: (81-75) 724 7800 Email: [email protected]

398

Initial Fracture Behaviour of Weft-Knitted Textiles Composites

behaviour of the weft-knitted glass/epoxy composite having a plain architecture was investigated. The effects of lengths and locations of the strain gages on the knee point stress-strain behaviour were investigated. Strain gage with a small gage length (up to 3 mm) was recommended and used for this study to measure the strain values at the local areas of the plain-loop architecture. It was concluded that for the plain weft-knitted composites, initial fracture mode was primarily dictated by a transverse crack inside the fibre bundle within the loop head in the wale direction, and a fibre bundle debonding at the fibre crossover regions in the course direction. Fractographic observation agreed well with the knee point responses obtained from the stress-strain characteristics. The present work concentrated on various welt-knit architectures and their effects on the initial fracture behaviour of the welt-knitted glass/epoxy composites. A typical loop configuration of a plain knit architecture, as shown in Figure 1, creates heterogeneous type of structure at unit-cell level, consisting of four major parts namely loop head, fibre cross part, slant loop and resin rich area. This heterogeneous loop-structure causes local variation in the strain values, and is believed to have an important effect on the overall fracture behaviour of knitted composites.

' '

FIGURE 1 A typical plain knitted loop

Held-stitch

' '

Non-loop welt-stitch

' '

FIGURE 2 Schematic of the welt-knitted architectures

EXPERIMENTAL Materials, Manufacture and Mechanical Test Weft-knitted fabrics from D-Glass fibre of density 2.17 gm/cm3 (D B450 1/2 4.4S Y23, Nippon Electrical Glass Co., Ltd.) were produced as the reinforcements and Bisphenol-A type epoxy resin (Epikote 828, lapan Epoxy Resin Co., Ltd.) was used as the matrix. The fabric materials under investigation comprise of three different welt-knit architectures such as (2,2,2), (2,4,2) and (2,6,2). Figure 2 represents schematic diagrams of these welt-knit structures. Welt-stitch, also known as non-loop float-stitch, can be defined as the length of yarn, not received by the needle(s), and which connects two other loops (not adjacent to each other) of the same course. The loop which, having been pulled through the loop of the previous course, is retained by the needle(s) during the knitting of the welt-stitch, can be defined as the held-stitch. Through manipulation of welt and held stitches, various welt-knit architectures can be created in the fabric structure, by changing the length of the non-loop welt-stitches and the number of heldstitches within the welt-length in a unit cell. The expression for welt architecture, for example (2,2,2), (2,4,2) or (2,6,2) in Figure 2, implies the number of wale-stitches ahead of the non-loop welt-length (1st numeral), the lineal density of the held-stitches within the welt-length (2nd numeral) and the number of courses between the non-loop weltstitches (3rd numeral). 1 ply composite panels, having 1 mm nominal thickness, were fabricated by hand lamination method. The average fibre volume fraction was estimated as 16.4% for all the three types of welt-knit structures under investigation. The composite panels were cured at room temperature for approximately 48 hours, followed

Initial Fracture Behaviour of Weft-Knitted Textiles Composites

399

by a two-hour postcure at 100°C to optimise resin properties. Tensile tests were conducted on an Instron universal testing machine (type 4206) under a nominal test speed of 1.00 mm min"1 in both wale and course directions. Deformation and fracture behaviour at each loop component were expected to be different. Strain gages with 1 mm gage length, were bonded onto these different loop segments of the welt-knit structural unit-cell to measure the local responses at these points. It is noteworthy that strain gages were deliberately avoided in the resin rich areas where knee stresses were found to be much higher than any other location in the entire knit structure [12]. Post-failure examinations were carried out on the selected test specimens using a scanning electron microscope (SEM) to study the fracture behaviour of composites at micro-level. RESULTS AND DISCUSSIONS Macro-Mechanical Properties Figures 3a and 3b show typical tensile stress-strain characteristics and tensile properties of welt-knitted composites in either test directions. It should be noteworthy that, contrary to the case of the course specimens, the wale specimens were able to maintain loads over a relatively larger strain interval before ultimate failure occurred, hi the current study, knee point is defined as the measure of the initial micro-fracture and was identified by a simple statistical approach [14].

a 5 M 4 1 3 c. Wale

1

d Wa e p 10 H

0

8

s,6

Strain (%)

Ss

S

Tensile Modulu

Strain (%)

«60

° e. Course

J

g-

2 S

S.50 Sij40 2 20

«u

f. Course

FIGURE 3 Stress-strain characteristics and tensile properties of welt-knitted composites

As shown in Figures 3c to 3f, both modulus and strength values were improved in the course direction than in the wale direction for each type of the welt-knit structures. This was attributed to the simple fact that the straight lengths of the non-loop weltstitches have their yarn orientation in the course direction only. Manipulation of weltlength and held-stitch density appeared to have noticeable effects on the tensile properties of welt knitted composites, in either knitting directions. Both modulus and strength values slightly decreased with the increase in welt-lengths and held-stitch densities for the wale-tested specimens, whereas the course-tested specimens exhibited an opposite trend. A closer observation on the wale-tested specimens reveals that 2,2,2 specimens have the orientation of non-loop welt-stitches (with shorter lengths) at a denser proportion in the cut-out test specimens as compared to other welt structures (2,4,2 and 2,6,2). This also resulted in a slightly higher fibre content in 2,2,2 wale specimens as compared to other welt counterparts. Hence, while tested in the wale

400

Initial Fracture Behaviour of Weft-Knitted Textiles Composites

directions, the fracture path of 2,2,2 specimens had a better chance to get bridged intermittently by the un-fractured fibre bundles as compared to 2,4,2 and 2,6,2 structures, so that load could be re-distributed to the fibres to delay the final rupture by improving fibre loading efficiencies. The slightly higher modulus value for the wale-tested 2,2,2 composite specimens was attributed to their higher fibre content as compared to 2,4,2 and 2,6,2 specimens. On the contrary, while-tested in the course direction, the fibre orientation of non-loop welt-stitches behaved like course-inserted fibre tows, and the proportion of these straight fibres obviously increased in 2,6,2 specimens than 2,2,2 and 2,4,2 specimens. This has resulted in the increased strength value in 2,6,2 composites. In the course direction, the slightly higher modulus value for 2,6,2 composites as compared to 2,2,2 and 2,4,2 composites, was obviously due to their better fibre directionality and higher proportion of straight fibres along the loading direction. Fracture plane for the wale-tested specimens coincided along the length of the non-loop welt-stitches and continued through the fibre crossover regions of the same course, whereas for the course-tested specimens, fracture plane ran along the fibre crossover regions transverse and adjacent to the length of the welt-stitches. In the knit structures, fibre crossover regions are the areas experiencing crucial fibre bending and high stress concentration, and were predominantly considered to be the failure nuclei [15]. Initial Fracture Behaviour The initial fracture behaviour of composites defined more on the local aspects than on the average properties. A knee point was not the intersection between the linear and the non-linear segment of the stress-strain curve. These points were rather defined so as to correspond to the values of the initial fracture stress and strain. A statistical approach [14], was applied to estimate these knee points as a quantitative evaluation of initial fracture - the first onset of failure. Knee point stress values varied at different characteristic locations of the welt loop configurations, and were also affected by the welt knit-structural parameters, in either knitting directions (Figure 4).

Stress at Initial Fracture

Cross (1)

aWale

Cross (2)

Stress at Initial Fracture

(1)

b Course

-

Cross (2)

FIGURE 4 Knee stresses at different characteristic locations of the welt architectures

It was quite noticeable from Figure 4a that, for the wale-tested specimens, the lowest knee stress occurred at the welt loop of 2,2,2 composites and at the cross parts 1 of 2,4,2, and 2,6,2 composites. On the other hand, for the course-tested specimens, the lowest knee stress or the first imtial fracture occurred at the cross parts 1 of 2,2,2 and 2,4,2 composites and at the slant-cross part of 2,6,2 composites, as observed in Figure 4b. Micro-fracture aspects of the welt knitted composites were examined from the photomicrographs taken at the weakest areas of welt architectures, as illustrated in

Initial Fracture Behaviour of Weft-Knitted Textiles Composites

401

Figures 5. As discussed earlier, for the wale-tested specimens, fracture initiation occurred at the welt loops and at the cross parts 1, whereas for the course-tested specimens, cross parts 1 and slant-cross parts were the areas suffering initial fracture. Fracture modes for the wale specimens consisted of a transverse crack inside the fibre bundle of the welt loops and a fibre-bundle-debonding at the cross parts (Figure 5a). For the course specimens, fracture modes were the combination of debonding between the fibre bundles at the cross parts and transverse crack inside the slant-cross loops (Figure 5b). Transverse Crack

Debonding

Debonding

Transverse Crack

*!»'

Welt loop Transverse crack

0

Welt loop

Cross part (1) Fibre Bundle Debonding

WtuaadloV----'

Cross part (1)

Cross part (1) Fibre Bundle Debonding

\MherllniKlk >

Slant-Cross loop Transverse crack

•—y

Cross part (1)

Slant-Cross loop

FIGURE 5 Photomicrographs and the schematic representation of micro-fractures in the welt knitted composites

A closer observation on the cross sections offibrebundles at the welt-stitch revealed that, the width of fibre bundle at the welt loops increased with the increase in the weltlengths and/or held stitches, and so did the aspect ratios of the fibre bundles at the welt loops. The higher aspect ratios in 2,4,2 and 2,6,2 wale specimens, seemed to have resulted in the higher knee stresses at their corresponding welt loops, whereas a low knee stress value at the welt loops of 2,2,2 wale specimens was due to their low aspect ratio at the cross section of the fibre bundles. SUMMARY Manipulation of welt-length and held-stitch density appeared to have noticeable effects on the tensile properties of the welt knitted composites in either knitting directions. Whilst strength is mechanically controlled, modulus is predominantly controlled by factors such as fibre content and fibre directionality. There was a gradual degradation in the tensile properties with the increase in the welt-lengths and held-stitch densities for the wale-tested specimens, while the course-tested specimens exhibited an opposite trend. In the knit structures, fibre crossover regions were believed to have experienced crucial fibre bending and high stress concentration, and due to which, fracture plane for the wale-tested specimens coincided along the length of the non-loop welt-stitches and continued through the fibre crossover regions of the same course. On the other hand, fracture plane in the course-tested specimens ran along the fibre crossover regions transverse and adjacent to the length of the welt-stitches. These observations agreed well with the responses obtained at the knee points of the local stress-strain curves. The knee stresses varied at different characteristic locations of the welt knit architectures, and were also affected by the welt knit-structural parameters, in either knitting directions. The

402

Initial Fracture Behaviour of Weft-Knitted Textiles Composites

initial fracture behaviour of composites defined more on the local aspects than on the average properties. For the wale-tested specimens, initial fracture resulted from the fibre fractures at the welt loops and at the cross parts 1, whereas, for the course-tested specimens, cross parts 1 and slant-cross parts were the areas suffering initial fracture. Fracture modes consisted of transverse and debonding cracks, inside the fibre bundle of the welt loops and at the cross parts for the wale specimens, whereas, for the course specimens,fracturemodes were the combination of debonding between the fibre bundles at the cross parts and transverse crack inside the slant-cross loops. Observations on the cross sections of fibre bundles at the welt-stitch revealed that the higher aspect ratios seemed to have resulted in the higher knee stresses at the corresponding welt loops while comparing the wale-tested composite specimens with regard to their different welt architectures. References 1.

2. 3.

4.

5. 6. 7.

8.

9.

10. 11. 12.

13.

14.

15.

Leong, K.H., Falzon, P.J., Bannister, M.K. and Herszberg, I. 1998."An investigation of the mechanical performance of weft-knit milano-rib glass/epoxy composites", Comp. Sci. and Tech., 58:239-251. Ramakrishna, S., Hamada, H., Cheng, K.B. 1997. "Analytical Procedure for the Prediction of Elastic Properties ofPlain Knitted Fabric-reinforced Composites", Composites Part A, 28:25-37. Wu, W.L., Kotaki, M., Hamada, H., Inoda, M., Maekawa, Z., Kanamaru, R. and Sanae, N. 1992. "Bending Properties of 2.5 Dimensional Warp Knitted Fabric Reinforced Composites", Advanced Composite Letter, 1:197-200. Kitagawa, K., Kankawa, Y., Shimamura, T., Wu, W.L., Kotaki, M., Inoda, M., Hamada, H., Fujita, A., Goto, A. and Maekawa, Z. 1992. "Effects of Surface Treatments on Mechanical Properties of Knitted Structural Composites", Advanced Composite Letter, 1:201-204. Ramakrishna, S. and Hamada, H. 1995. "Impact Damage Resistance of Knitted Glass Fibre Fabric Reinforced Polypropylene Composites", Science and Engineering of Composite Materials, 4:61-72. Hamada, H., Nakai, A., Fujita, A. and Inoda, M. 1995. "Mechanical Properties of Weft Knitted Fabric Reinforced Composites", Advanced Composites Letters, 4:83-85. Wu, W.L., Inoda, M., Hamada, H. and Maekawa, Z. 1993. "Study of Mechanical Properties in Kitted Structural Composites-Computer Simulation of Deformation of Knitted Fabrics", Proceedings of 36th JAPAN Congress on Materials Research, 205-212. Wu, W.L., Inoda, M., Hamada, H., Maekawa, Z., Kanamaru, R. and Sanae, N. 1993. "Influence of Knitted Structure on Mechanical Properties in Knitted Structural Composites", Proceedings of 36th JAPAN Congress on Materials Research, 213-218. Ramakrishna, S., Hamada, H. and Hull, D. 1995. "The Effect of Knitted Fabric Structure on the Crushing Behaviour of Glass-Epoxy Composite Tubes", Impact and Dynamic Fracture of Polymers and Composites, 453-464. Verpoest, I. and Dendauw, J. 1992. "Mechanical Properties of Knitted Glass Fibre/Epoxy Resin Laminates", Proceedings of The 37' International SAMPE Symposium, 369-377. Kameo, K., Haan, J. DE., Nakai, A. and Hamada, H. 1999. "Open Hole Tensile Behaviours of Knitted Fabric Composites", Journal of Reinforced Plastics and Composites; 18(17): 1605-1617. Fukui, T., Osada, T., Nakai, A., Inoda, M. and Hamada, H. 2002. "Initial Fracture Behaviour of Plain Knitted Composites", Proceedings of the Tenth U.S.-Japan Conference on Composite Materials, 1618 September, 2002, 849-858. Osada, T., Nishiyabu, K., Fukui, T., Nakai, A., Inoda, M. and Hamada, H. 2002. "Initial Fracture Behaviour of Knitted Composites", Proceedings of the Third Asian-Australian Conference on Composite Materials, 15-17 My, 2002, 715-721. Osada, T., Mizoguchi, M., Kotaki, M., Nakai, A. and Hamada, H. 2001. "Initial Micro Fracture Behaviour of Woven Fabric Composites", Proceedings of the 13th International Conference on Composite Materials, 25-29 June, 2001, ID 1083. Khondker, O.A., Leong, K.H. and Herszberg, I. 2001. "An Investigation of the Structure-Property Relationship of Knitted Composites", Journal of Composite Materials, 35(6):489-508.

Mixed-mode Fracture of a CF/PEI Composite Material Naghdali Choupani, Lin Ye* & Yiu-Wing Mai Centre for Advanced Materials Technology School of Aerospace, Mechanical and Mechatronic Engineering J07 The University of Sydney, Sydney, NSW 2006, Australia

ABSTRACT This study reports investigation on mixed-mode interlaminar fracture behavior in CF/PEI composite material based on experimental and numerical analyses. Experiments were conducted on modified Arcan specimens using the special test loading device. By varying the angle,oc from 0° to 90°, mode-I, mixed-mode and mode-II data are obtained experimentally. Using the finite-element results, correction factors were applied to the CF/PEI fracture specimen. Based on experimentally measured critical loads and by the aid of the finite-element method, mixed-mode interlaminar fracture toughness for the composite under consideration has been determined. Numerical results indicate that for pure mode-I loading, mode-I stress intensity factor is maximum and as a increases, Ki decreases down to 0 for pure mode-II loading. Stress intensity factor for mode-II loading shows the opposite trend; as the ratio of mode-II to mode-I increases, Kn increases. It should be noted that for loading angles close to pure mode-I and pure mode-II loadings, very high ratios of strain energy release rates are dominant. As expected, it is confirmed that by varying the loading angle of Arcan specimen, pure mode-I, pure mode-II and a wide range of mixed-mode loading conditions can be created and tested.

INTRODUCTION Failures in composite materials occur mainly due to the interlaminar fracture between laminates. This indicates that characterizing interlaminar fracture toughness is the most effective factor in the fracture of composite materials. The critical strain energy release rate, Gc, which is the energy released due to extension of a crack is often used for prediction of fracture, hi recent years, many test methods have been proposed by many researchers to determine interlaminar fracture toughness for each of the three modes of loading (I, II, and III) and also under mixed-mode conditions [1]. The double cantilever beam (DCB) test is the most widely used method for measuring mode-I (opening) interlaminar fracture toughness. The end-notched flexure (ENF) has emerged as one of the most convenient mode-II (sliding shear) interlaminar fracture specimens. A crack rail shear (CRS) specimen has been proposed to determine the mode-Ill (tearing) critical strain energy release rate [2]. However, due to the strong anisotropy of composite structures, the fracture is usually not a result of pure mode-I or pure mode-II loading, and the delamination occurs in the mixed-mode loading conditions. For this reason, the study of the mixed-mode interlaminar fracture toughness is very important.

" Corresponding author. Tel: +61-2-9351 4798, Fax: +61-2-9351 3760, e-mail: ve(oiaeromech.usvd.edu.au

404

Mixed-mode Fracture of a CF/PEI Composite Material

Various attempts have been made to characterize interlaminar fracture toughness under mixed-mode loading conditions, but mostly beam type specimens were used [3-5]. Some of these include: the mixed-mode flexure (MMF) test, the end loaded split (ELS) TABLE I Elastic Properties of CF/PEI composite E,[GPa]

E2[GPa]

E3[GPa]

G12[GPa]

G13[GPa]

G23[GPa]

57.6

57.6

8.7

3.1

2.8

2.8

0.03

Ul3

"23

0.4

0.4

specimen, the single leg bending (SLB) specimen, the crack lap shear (CLS) test, the edge delamination tension (EDT) specimen, and the asymmetric double cantilever beam [3,4]. However, for all these test methods there are problems to create a wide range of mixed-mode ratios which limit their usefulness. The mixed-mode bending (MMB) test, has been proposed by combining the schemes used for DCB and ENF tests, which can produce a wide range of the ratios of mode-I and mode-II components by varying the lever arm of the specimen [4,5]. But in order to obtain reliable results for interlaminar fracture toughness for pure mode-I, pure mode-II, and mixed-mode loading conditions different beam type specimens would be required. In this study, a modified version of Arcan specimen is made for the mixed-mode fracture test of CF/PEI specimens, which allows mode-I, mode-II, and almost any combination of mode-I and mode-II loading to be tested with the same test specimen configuration [6]. Therefore, disadvantages presented in the previous mixed-mode toughness test methods can be avoided. This investigation seeks to extend the understanding of the interlaminar fracture behavior of a CF/PEI composite under mixedmode loading conditions. EXPERIMENTAL PROCEDURES Material In the experiment, a woven plate consisting of 22 plies of CF/PEI prepergs, in order to obtain a plate thickness of approximately 6mm were used. During the lay up prepergs by hand to the required number of plies, a non-adhering film placed between the central plies in order to introduce a starter crack. The composite plates were produced using hot press. The specimens were cut with a diamond wheel and machined to the dimensions of 30x10x6 mm. This composite is similar to the material investigated previously by Kim [7] and elastic constants of plate used in FEM analyses are summarized in Table 1. Test method and setup In Figure 1, the loading device and modified version of Arcan specimen are shown. This specimen is used in order to study the mixed-mode interlaminar fracture toughness of a CF/PEI composite material. The composite strip was attached into aluminum plates using adhesive. For surface preparation of aluminum plates, FPL-Etch method was applied [8]. Composite surface preparation method involved degreasing with methyl ethyl ketone (MEK), rinse and check for water break, hand abrasion with 320 grit aluminum oxide abrasive papers and clean for bonding [9]. The specimens were pinned into the loading device in order to transmit the applied loads. With the application of load P and by varying the loading angle,a from 0° to 90° , pure mode-I, pure mode-II, and all mixed-mode loading conditions can be created and tested. Fracture tests were conducted by controlling the constant displacement rate of 0.2 mm/min and the fracture

Mixed-mode Fracture of a CF/PEI Composite Material

405

loads and displacements were recorded. All tests were carried out using an Instron 5567 testing machine. Tests were repeated 3 times for every loading angle.

i .

t

(a) FIGURE 1 Overview of test rig and set up: (a) Mode-I test; (b) Mixed-mode test; (c) Mode-II test

ANALYSIS OF MIXED-MODE INTERLAMINAR FRACTURE The energy release rates for orthotropic material with the crack in one plane of symmetry can be calculated from the following relationships [2,10]: j-

K,

(1) where Ej and En are effective moduli, and Kj and Kn are mode-I and mode-II stress intensity factors, respectively. It is assumed that the specimens are orthotropic linear elastic material. For plane strain conditions, effective moduli Ei and En are defined as: E - I

T

l

"

E

\b12

+2bi2+b66

1

^ \b22

2bn

(2) +2bn+b66

2bn

where the terms of the constants btj are defined in terms of the following nonzero entries a{j of the orthotropic compliance matrix: b

-a

WJL

(ij = 1,2,4,5,6)

(3)

\Y\Tx FIGURE 2 Finite element mesh pattern of the entire specimen and around the crack tip

406

Mixed-mode Fracture of a CF/PEI Composite Material

The stress intensity factors ahead of the crack tip for a modified version of Arcan specimen were calculated by using the following equations [11,12]: cosaf^alw) wt K,,=

Pc4na

(4)

wt

where Pc is critical load at fracture, a is loading angle, w is specimen length, t is specimen thickness and a is crack length. In turn Ki and Kn are obtained using geometrical factors/J (a/w) and/ 2 (a/w), respectively, which are obtained through finite element analysis of Arcan test specimen. Numerical analyses were also carried out. Figure 2 shows example of the mesh pattern of the specimen, which were performed with ABAQUS 6.2.4 [13]. The entire specimen was modeled using 2424 eight node collapsed quadrilateral element and the mesh was refined around crack tip, so that the smallest element size found in the crack tip elements was approximately 0.25mm relative to the crack length. A linear elastic finite element analysis was performed under a plain strain condition using 1/r0'5 stress field singularity. To obtain a 1/r05 singularity term of the crack tip stress field, the elements around the crack tip were focused on the crack tip and the mid side nodes were moved to a quarter point of each element side. The method used to calculate the stress intensity factor was an interaction method performed in the ABAQUS [13]. The J integral was also calculated, hi linear elastic fracture mechanics, the J integral coincides with total energy release rate, GT=GI+GH. These J values were compared with those obtained by the method mentioned above. RESULTS AND DISCUSSION In order to assess stress intensity factors at fracture, Ki and KD using Equations (4), geometrical factors fx (a I w) and f2 (a I w) for both loading modes were determined. The a I w ratio was varied between 0.3 and 0.7 at 0.1 intervals and a fourth order polynomial was fitted through finite element analysis as:

Loading angle (degree) FIGURE 3 The ratio of mode-II to mode-I Gn/Gi (in logarithmic scale) vs. loading angle,ct

Mixed-mode Fracture of a CF/PEI Composite Material

407

250

15

30

45

60

75

90

Loading angle (degree) FIGURE 4 Energy release rates G,, Gu, GT=Gi+Gn and J integral vs. loading angle,a

= 182.12(a/w) 4 -293.81(a/w) 3 +187.87 (a/w) 2 -51.492(a/w) +6.1137 (5) = -18.622(a/w)4 + 36.753 (a/w) 3 -25.182(a/M')2 + 7.759(a/w) + 0.0944 The energy release rates were calculated using conventional Equations (1). The relationship between the mixed-mode ratios of energy release rates and the loading angles a is shown in Figure 3. For loading angles close to pure mode-I loading, very high ratios of mode-I to mode-II is dominant. The ratios of strain energy release rates close to pure mode-II loading exhibits the opposite trend. As expected, it is confirmed that by varying the loading angle of Arcan specimen pure mode-I, pure mode-II and a wide range of mixed-mode loading conditions can be created and tested. In Figure 4, energy release rates Gi and Gn obtained by Equations (1), the total energy release rate obtained by Gr=Gi+Gn and the J integral are compared for a constant value of the load P=1000 N. It is seen that for loading angles oc<60° the mode-I fracture becomes dominant. As mode-II loading contribution increases, mode-I strain energy release rate Gi decreases and mode-II strain energy release rate Gn increases. For a>75° mode-II fracture becomes dominant. Total strain energy release rate under mixed-mode

12

15

18

Crack length (mm) FIGURE 5 The relation between energy release rate and crack length

21

408

Mixed-mode Fracture of a CF/PEI Composite Material

loading conditions decreases with the loading angle. The results of total strain energy rates values obtained by Equations (1) and the J integral agree with each other very well. Figure 5 shows the changes in energy release rates due to change in the crack length under different loading conditions. Although the mode-I energy release rate value changes largely due to the change in the crack length ratio, the mode-II value does not change markedly. It is also confirmed that as the mode-II fracture becomes dominant, the mixed-mode fracture toughness decreases. In the present experiments, bond failures limited the Arcan test use for tough CF/PEI laminates, especially under pure mode-II and mixed-mode loading conditions. The experimental work is still in progress and will be reported later. CONCLUSION hi this paper the mixed-mode interlaminar fracture behaviour for CF/PEI composite specimens was investigated based on experimental and numerical analyses. A modified version of Arcan specimen was employed to conduct mixed-mode test using the special test loading device. The full range of mixed-mode loading conditions including pure mode-I and pure mode-II loading can be created and tested. It is a simple test procedure, clamping/unclamping the specimens is easy to achieve and only one type of specimen is required to generate all loading conditions. The large scatter of the results was observed and unstable crack growth occurred in all cases, hi the Arcan test configuration, composite specimens were bonded between two metal fixtures that bond failures limited the test use for tough composite materials, especially under pure mode-II and mixed-mode loading conditions. The method of bonding needs improvement and more work is needed for the Arcan test method. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13.

O'Brien, T. K. 1998. "Interlaminar Fracture Toughness: The Long and Winding Road to Standardization," The 4th International Conference on Composites Engineering, July 6-11,1997. Gillespie, J. W. and L. A. Carlsson. 1990. Delaware Composites Design Encyclopedia-Volume 6. Technomic Publishing Co. Inc., pp. 113-119. Rikards, R. 2000. "Interlaminar Fracture Behaviour of Laminated Composites," Computers and Structures, 76:11-18. Reeder, J.R. and J.H. Crews 1990. "Mixed-mode Bending Method for Delamination Testing," J. AIAA, 28: 1270-1276. Ducept, F., D. Gamby, and P. Davies. 1999. "A Mixed-mode Failure Criterion Derived from Tests on Symmetric and Asymmetric Specimens," Compos. Sci. Tech., 59:609-619. Arcan, M., Z. Hashin, and A. Voloshin. 1978. "A Method to Produce Plane-stress States with Applications to Fiber-reinforced Materials," Experimental Mechanics, 18:141-6. Kim, K.-Y. and L. Ye., Private Communication (2003). Glyn, L., L. Ye, Y.-W. Mai, and C.-T Sun. 1997. "The Effect of Adhesive Bonding between Aluminum and Composite Preperg on the Mechanical Properties of Carbon-fiber-reinforced Metal Laminates," Compos. Sci. Tech., 57:35-45. Daghyani, H. R., L. Ye, and Y.-W. Mai. 1996. "Mixed-mode Fracture of Adhesively Bonded CF/Epoxy Composite Joints,"/. Compos. Mater, 30:1248-65. Sih, G. C. andE. P. Chen. 1981. Crack in Composite Materials. Martinus Nijhoff Publishers, pp. 1-9. Yoon, S. H. and C. S. Hong. 1990. "Interlaminar Fracture Toughness of Graphite/Epoxy Composite Under Mixed-mode Deformations," Experimental Mechanics, 30:234-9. Jurf, R. A. and R. B. Pipes. 1982. "Interlaminar Fracture of Composite Materials," J. Compos. Mater, 16:386-94. Habbit, Karlsson and Sorensen, 2001. ABAQUS User's Manual version 6.2.4.

Effects of Molecular Structure on the Essential Work of Fracture of Amorphous Copolyester at Various Deformation Rates H. B. Chen and J. S. Wu Materials Research Group, Department of Mechanical Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong J. Karger-Kocsis Institute of Composite Materials, University of Technology Kaiserslautern, Kaiserslautern, Germany

ABSTRACT The fracture behavior of amorphous copolyesters with different molecular structure was studied with double edge notched tensile loaded specimens (DENT) using the essential work of fracture (EWF) approach. Various deformation rates ranging from 1 mm/min to 1000 mm/min were employed. Amorphous poly(ethylene terephthalate) (aPET) exhibited considerably higher specific essential and nonessential work of fracture than the copolyesters containing either cyclohexylenedimethylene (aPET-C) or neopentyl glycols (aPET-N). At high deformation rates, ductile/brittle fracture transition was observed with aPET-C and aPET-N, while aPET always fractured in ductile mode within the entire deformation rate range. These phenomena were ascribed to the different molecular flexibility and entanglement density of the copolyesters. The specific essential work of fracture of the aPET as a function of deformation rate went through a minimum. The initial decrease in toughness was caused by the hampered segmental mobility due to the increased deformation rate. The subsequent increase in toughness was attributed to the adiabatic heating induced temperature rise in the process and plastic zones.

INTRODUCTION Amorphous linear polyester and its copolymers are widely used in various applications, particularly, for packaging. Amorphous polyesters, such as polyethylene terephthalate) (PET) and polyethylene terephthalate glycol) (PETG), have good optical properties (e.g. high transparency, gloss and low haze) and high ductility. However, some of them are prone to physical aging and crystallization, which result in material embrittlement. To diminish the tendency to crystallization, one can incorporate certain stiff moieties in the PET main chain to violate the regularity of the chain structure to a certain degree, for example, replacing a part of ethylene glycol with 1,4-cyclohexylene dimethylene units (CHDM) or neopentyl glycol [1]. With the above-mentioned modification, the molecular chain flexibility * Correspondence Author, Tel: (852) 2358 7200; Fax: (852) 2358 1543; E-mail: [email protected]

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Essential Work of Fracture of Amorphous Copolyester

and entanglement characteristics of the copolyesters are changed, which must have influences on the mechanical and fracture properties of the materials. Obviously, a good understanding on the mechanical property-molecular structure relationships of the copolyesters will provide useful guidance to R&D practice of the industry. In this work, fracture toughness of three amorphous copolyesters with different molecular structures and entanglement densities were investigated using the essential work of fracture approach. The correlations between the fracture toughness and their molecular built-up were discussed with the hope of making a contribution to a better understanding of the important relationships. Moreover, various deformation rates ranging from 1 mm/min up to 1000 mm/min were employed to study the strain-rate dependent fracture behavior. THE ESSENTIAL WORK OF FRACTURE The essential work of fracture (EWF) is a useful method to characterize the fracture toughness for ductile polymeric materials and is becoming popular due to its simplicity [1-7]. As illustrated in Figure 1, the fracture zone of a double-edge notched tensile (DENT) specimen can be separated into the inner process zone and the outer plastic zone. Accordingly, the total energy, Wf, required to fracture a pre-cracked specimen may be divided into two related components: the essential (We) and nonessential (Wp) work of fracture, corresponding to the energy dissipated in the process zone and plastic zone, respectively. Physically, We is the energy needed to create two new fracture surfaces, thus is proportional to the area of fracture surface; Wp is the energy dissipated in the plastic zone through various deformation mechanisms, thus is proportional to the volume of the plastically deformed zone. Accordingly, the basic equations of the EWF can be written as: wt = we + wp = •

It2

(1)

Wf

(2)

where t the specimen thickness, / the ligament length and /? the shape factor of the plastic zone. The specific essential work of fracture (we) and the specific non-essential work of fracture (wp) can be obtained by plotting wf against /. we is considered a material constant under plane stress conditions, at least for a given specimen thickness. wp, on the other hand, may change with the specimen geometry, gauge length etc.

Process Zone (WJ at2

\

Plastic Zcm ( Wf)

FIGURE 1 DENT specimen used in the EWF study

Essential Work of Fracture of Amorphous Copolyester

411

EXPERIMENTAL Materials Three amorphous copolyesters used in this study were aPET (amorphous polyethylene terephthalate), aPET-C (amorphous copolyester synthesized from terephthalic acid and two diols: ethylene glycol and 1,4-Cyclohexane dimethylene glycol), and aPET-N (amorphous copolyester synthesized from terephthalic acid and two diols: ethylene glycol and neopentyl glycol). All the specimens were in the form of films with a thickness of 0.25 mm. Table 1 shows their basic properties. TABLE I Basic characteristics of the amorphous copolyesters studied. Materials aPET aPET-N aPET-C

I.V. [dl/g] 0.74 0.75 0.70

E-Modulus IGPa] 2.4 2.2 2.1

Yield Strength [MPa] 52.4 48.1 45.5

Fracture Tests The EWF tests were performed on a Zwick 1445 universal testing machine at room temperature. Double edge notched tensile (DENT) specimens with various ligament lengths ranging from 5 mm to 25 mm were employed. The width, gauge length was 35 mm and 70 mm, respectively. For each ligament length, at least three specimens were tested. Various deformation rates, viz. 1, 10, 100, 500 and 1000 mm/min, were applied. Dynamic Mechanical Analysis Dynamic mechanical analysis (DMA) was performed using a TA instruments DMA 983 at the resonance mode with displacement amplitude of 0.2 mm and frequency of 1 Hz. The temperature scanning ranged from — 100°C to the softening point at a heating rate of 2°C/min. RESULTS AND DISCUSSION Validity of Current EWF Tests Before discussing the relationships between the molecular structure and the EWF parameters, the validity of current EWF measurements should be assessed first, particularly at high deformation rate. For a valid EWF test, two basic requirements must be satisfied [8]. One is that the load-displacement curves obtained with samples of different ligament lengths have geometric similarity; the other is that the ligament of the specimen must undergo fully yielding prior to the onset of crack growth. To our best knowledge, there are little EWF tests performed at very high deformation rate, hi this study, to check the validity of the EWF method at high deformation rate, an infrared thermographic camera was employed to monitor the entire fracture process. The observations as illustrated in Figure 2 demonstrate that the fracture process at high deformation rates occurred in the same way that satisfies the prerequisites for a valid EWF measurement.

Essential Work of Fracture of Amorphous Copolyester

412

FIGURE 2 Serial infrared frames reflecting the fracture process of aPET at v = 1000 mm/min.

Fracture Behavior at Low Deformation Rate Table 2 lists the EWF parameters of the copolyesters obtained at a deformation rate of 1 mm/min. Clearly, all the parameters do depend on the copolyester's molecular build-up. The ranking of the specific essential work of fracture is same as the ranking of their yield strength (cf. Table 1), i.e. aPET > aPET-N > aPET-C. TABLE II The fracture parameters of the amorphous copolyesters at a deformation rate of 1 mm/min

v=l mm/min aPET aPET-N aPET-C

P 2

[kJ/m ] 50.6 ± 1 8 46.2 ± 1 5 38.7 ± 2 2

Sic

3

[MJ/m ] 10.6 ±0.2 6.8 ±0.2 7.5 ±0.2

3

[MJ/m 99.5 72.3 76.7

0.107 0.091 0.099

1

[mm] 1.9 1.6 1.4

Theoretically, we in mode I fracture consists of two components [5]: w=d(°

(3)

ade + (*' cr(A, )dA

where (a,e) the true stress/strain, sn and sn the true and engineering necking strains., a and A, the stress and crack tip opening displacement within the fracture process zone. 8]C is the mode I critical value of A[, d is the width of the fracture process zone as illustrated in Figure 3 and is of the order of the specimen thickness. Physically, the first term is the plastic work to necking and the second term refers to the fracture work of the neck. For the samples with same specimen thickness, one can expect that the width of the fracture process zone will be similar. Thus the parameters dictating the value of we will be the stress ( a ) in the ligament and the critical crack tip opening displacement (CTOD) (Slc). S T

Crack

FIGURE 3 A fully developed fracture process zone under mode I loading schematically

Essential Work of Fracture of Amorphous Copolyester To determine the CTOD, the method used by Hashemi et al [9] was adopted. eb=e0+epL

413

(4)

where eb the extension to break for the specimen with a ligament length of L; e0 the extrapolated value of eb at zero ligament length and can be identified to equal to Slc. The critical CTOD results obtained in this way are listed in Table 2, together with the yield stress (<jy) of the tested samples. Apparently, both Slc and ay values are in the order of aPET > aPET-N > aPET-C. If we is calculated using Eq. (3) with the 8lc and ay values in Table 2, the aPET would have the highest we value, followed by aPET-N and aPET-C, this is in agreement with our experimental results. Fracture Behavior at High Deformation Rate Figure 4 illustrates the changes of the specific essential work of fracture of the copolyesters under different deformation rates. The results indicate that we decreased with increasing the deformation rate in the range of 1 mm/min to 100 mm/min. Further increasing the deformation rate, aPET-C and aPET-N failed in a brittle mode, whereas we of the aPET started to increase. This trend suggests that the dominant influence of deformation rate on the fracture behavior of polymers is different at different rate range. At the rate above 100 mm/min, the adiabatic heating ahead of the crack tip due to high rate dominates, resulting in an increase of the temperature in the process and plastic zones. This temperature rise is beneficial to the molecular chain mobility, thus, the fracture toughness. On the other hand, increasing the deformation rate can also lower down the fracture toughness if the chain relaxation cannot response to the loading induced deformation in the time scale at high rate (wellknown as strain-rate embrittlement). The segmental mobility of molecular chains at high deformation rate is seriously hampered so that only a part of the entangled chains may be involved in the stress distribution process and the network deformation is limited [10]. Given the above-mentioned two competing factors, it seems that in the rate rang between 1-100 mm/min, the effect of stain-rate embrittlement has a dominant effect; whereas at higher deformation rates, the effect of adiabatic heating becomes dominant for the aPET. 70.

—•— aPET aPET-C aPET-N

60.

g

50-

u E 40.

s.

in 30.

\ Brittle Failure 1

10

100

500

1000

Deformation Rate [mm/min]

FIGURE 4 Deformation rate dependence of the specific essential work of fracture

In agreement with the changes of EWF parameters against the deformation rate, different failure modes at different rates were also observed. The failure of the aPET was always ductile within the entire deformation rate range studied, whereas two different failure modes, i.e. stable ductile fracture and unstable brittle fracture were

414

Essential Work of Fracture of Amorphous Copolyester

observed with both aPET-C and aPET-N specimens. The onset deformation rate for the ductile/brittle transition was at 500 mm/min and 100 mm/min for the aPET-C and aPET-N, respectively, which reflects again the molecular flexibility of the two samples, as discussed in the following text. Figure 5 shows the dynamic mechanical analysis (DMA) results of the amorphous copolyesters studied. Besides the obvious primary dissipation, i.e. oc-relaxation peak at Tg temperature (about 75°), there is also a broad but distinct secondary dissipation, i.e. P-relaxation peak at about -60°C. When the EWF tests are carried out at room temperature and low deformation rate, the heat generated during tension is not significant and has sufficient time to exchange with the ambient; therefore, the temperature around the ligament of the tested specimens is close to or slightly higher than the ambient temperature. For instance, at v = 100 mm/min, the temperature ahead of the crack tip of the aPET specimen was about 35°C, as recorded by the infrared camera. Therefore, the fracture of the specimen at low deformation rate was completed at a temperature between the arelaxation and p-relaxation, which means that the P-relaxation was activated and achieved to a substantial degree, while the a-relaxation was not activated at all. In other words, only p-relaxation has contributions to the fracture behavior. Furthermore, the peak temperature (PMT) and the peak height (PH) of tan8 represent the characteristics of the molecular chain relaxation. The higher the temperature and/or the larger the tan8 peak, the more flexible is the molecular chain [11]. Though the PMT of the P-relaxation of the three copolyesters in Figure 5 is quite close, the PH of each sample has obvious difference, which indicates that the three copolyesters have different chain rigidity. Based on the peak height, it is obvious that the molecular chain of aPET-N is most rigid. Therefore, the low ductile/brittle transition rate for the aPET-N can be attributed to its lower molecular flexibility. Based on the same DMA argument, the molecular chain flexibility of the aPET-C is better than that of the aPET, which is probably because the cyclohexylene rings in the aPET-C promote the longrange cooperative chain motions in the copolyester, leading to increased chain flexibility [12]. Since the aPET has the highest ductility at high deformation rate, it may suggest that high entanglement density plays a more important role on the stress transfer ahead of the crack tip, as discussed below. t

aPET aPET-C • • -aPET-N

-100

-50

ad' 0

50

100

150

Temperature [°C] FIGURE 5 Loss tangent (tan8) vs. temperature curves of the amorphous copolyesters at 1.0 Hz

It was noted that the brittle fracture occurred only at relatively large ligament lengths. For instance, the DENT specimens of the aPET-N with a short ligament length (e.g. 5 mm) would still fail in ductile manner at v = 100 mm/min. The reason behind this phenomenon may be explained as follows. When ligament length is large, considerable elastic energy will be stored in the tested body when it is loaded. Although the ligament yielding and the formation of the outer plastic zone can

Essential Work of Fracture of Amorphous Copolyester

415

dissipate some of the stored energy, however, at high deformation rate, the energy dissipation due to the plastic deformation of the materials in the plastic zone may not be fast enough for complete release of the stored energy. Therefore, once the crack starts to propagate after the full ligament yielding, the stored elastic energy is suddenly released through fast unstable fracture of the ligament. This brittle fracture behavior should depend strongly on the stress and energy transferring ability of the molecular network. Since the aPET has the highest entanglement density, the applied stress and energy can be transferred to and dissipated efficiently in a relatively large area surrounding the crack tip, leading to a bigger plastic zone and higher toughness. In addition, at high deformation rate, the strain-induced temperature rise makes the temperature of the material ahead of the crack tip and around the ligament of the aPET sample close to or above its Tg, which may activate the primary relaxation and enhance the molecular chain mobility. Therefore, no brittle failure was observed with the aPET. CONCLUSION This work studied the essential work of fracture (EWF) and molecular structure relationships using three amorphous (co)polyesters with different molecular build-up (viz. aPET, aPET-C and aPET-N) at different deformation rates. Based on the results obtained, the following conclusions can be drawn: • Both specific essential and non-essential work of fracture of the (co)polyester films strongly depend on the molecular architecture, particularly the entanglement density. Higher entanglement density will results in greater EWF parameters. • Effects of deformation rate on the EWF parameter were investigated at very high deformation rate up to 1000 mm/min for the first time. It was found that the deformation rate affects the specific essential work of fracture via two competing mechanisms, i.e. strain rate embrittlement and adiabatic heating. The former will results in a decrease in toughness with deformation rate increase, while the latter does the opposite. • Ductile/brittle (D/B) transition was observed with the aPET-C and aPET-N. The offset deformation rates for the D/B transition depends on the molecular build-up of the films. The brittle unstable failure was ascribed to the sudden release of the elastically stored energy in the specimens. REFERENCES 1.

Karger-Kocsis J, in Williams JG and Pavan A, editors, Fracture of Polymers, Composites and Adhesives - ESIS Publ.27, Elsevier Sci., Oxford, 2000, pp.213-230. 2. Mai YW and Cotterell B, Eng. Fract. Mech. 1985; 21(1): 123-128. 3. Mai YW and Cotterell B, Int. J. Fract. 1986; 30(2): R37-R40. 4. Mai YW, Cotterell B, Int. J. Fract. 1986; 32(5): 105-125. 5. Mai YW, Int. J. Mech. Sci. 1993; 35(12): 995-1005. 6. Wu JS, Mai YW and Cotterell B, J. Mater. Sci. 1993; 28(12): 3373-3384. 7. Wu JS and Mai YW, Polym. Eng. Sci. 1996; 36(18): 2275-2288. 8. Clutton, E. in Moore, D. R.; Pavan, A.; Williams, J. G., editors, Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites -ESIS Publ. 28, Elsevier Sci., Oxford, 2001, pp. 177-195. 9. Arkhireyeva A, Hashemi S, Polymer 2002; 43(2): 289-300. 10. Karger-Kocsis J, Czigany T, Polym. Eng. Sci. 2000; 40(8): 1809-1815. 11. Lu SX, Cebe P, J. Appl. Polym. Sci. 1996; 61(3): 473-483. 12. Chen LP, Yee AF, Moskala EJ, Macromolecules 1999; 3.2(18): 5944-5955.

How to Eliminate Buckling in the Essential Work of Fracture Measurement with Very Thin Plastic Films H. B. Chen, S. L. Liu and J. S. Wu Materials Research Group, Department of Mechanical Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong

ABSTRACT When the Essential Work of Fracture (EWF) method is used to evaluate the fracture toughness of ductile thin polymer films, buckling phenomenon is very often observed, which may violate the conditions for data validity. In some cases, buckling is so severe that to perform a valid EWF test is virtually impossible. In this work, we propose an experimental set-up using U-shaped fixture to eliminate the buckling problem in thin film EWF tests with double-edge notched specimen (DENT). The influences of the U-clamp on the yielding, plastic zone development, crack initiation and propagation behaviors of the thin film samples were examined by experiments as well as finite element analysis. The results demonstrate that the use of the newly designed U-clamp has little effect on the fracture behavior of the tested thin polymer films. Therefore, it is an ideal set-up for the EWF measurements with very thin films when buckling is a problem.

INTRODUCTION Essential work of fracture (EWF) method becomes quite popular recently in the fracture toughness characterization of ductile polymer materials [1-8]. This method is particularly useful when the toughness of plastic thin films is under concern. For thin ductile polymer films, due to extensive plastic deformation associated with crack propagation in a toughness test, neither linear elastic fracture mechanics (LEFM) nor J-integral analysis can be applied, because a valid measurement of fracture toughness by the two methods must be conducted under plane-strain condition to ensure small scale plastic deformation at the running crack tip. To maintain the plane-strain condition at a given testing temperature and strain rate, the size, mainly the thickness, of the specimens must be larger than a certain value that is determined primarily by the yield strength of the material being tested as well as specimen geometry. For ductile polymer materials at room temperature, the thickness requirement for a valid LEFM or J-integral test is rather difficult to meet. When fracture toughness of plastic film is required, a valid LEFM or J-integral test of the film is virtually impossible. Thus, the EWF method is an alternative methodology for such an application and being practiced increasingly in the plastic film industry and other industries, for example paper and textile industries. When EWF method is employed in the film toughness tests, a rigid and flat metal clamp is usually adopted to hold the film samples that have a double edge notched " Correspondence Author, Tel: (852) 2358 7200; Fax: (852) 2358 1543; E-mail: [email protected]

Eliminate Buckling in the Essential Work of Fracture Measurement

417

tensile (DENT) geometry. Previous work has proven that the flat clamp works very well as long as the thickness of the film is relatively large, for example, 200 /jm or larger. However, when the thickness of the film is smaller, it is often observed that use of the flat clamp may introduce film buckling during loading, which certainly has effect on the stress distribution and deformation behavior of the material in both the fracture processing zone and plastic deformation zone, leading to measurement errors. An example of the above-mentioned film buckling in the EWF test is shown in Figure 1, which is a HDPE film of about IQ/jm in thickness. The only effort to eliminate the buckling found in literature review was done by Mai and his co-workers [1]. The authors used a semi-circular metal holder to depress the buckling in the tests of a paper sample, hi other published work related to plastic film tests [7-8], the buckling phenomenon was not reported. In the present work, we report the results of our recent effort using a simple Ushaped clamp to eliminate the buckling in EWF tests of very thin plastic films. The effects of the constraint from the U-shaped clamp on the measurement of the specific essential work of fracture and specific non-essential work of fracture were examined experimentally and numerically by final element analysis.

• •-• £

-A

FIGURE 1 The buckling phenomenon in the EWF test

EXPERIMENTAL The materials used were high density polyethylene (HDPE) blown films with a thickness of 12.5 /Mn and isotactic polypropylene (iPP) extruded films with a thickness of 400 /jm . The double edge notched tensile specimens (DENT) were employed for the essential work of fracture tests with different ligament length ranging from 5 mm to 25 mm. The width of the specimen (W) was 50 mm and the length between two clamps is 60 mm. Initial notches were made with fresh razor blades and the ligament lengths were measured with a traveling microscope (Topcon, TMM-130 Z). All the fracture tests were performed on a universal testing machine (Sintech 10/D) with a crosshead speed of 10 mm/min at ambient temperature. ANSYS was used for numerical simulation. The model used was inelastic, rate independent and isotropic hardening mises plasticity. Three stages, i.e. elastic deformation, crack-tip yielded and full ligament yielded were chosen. RESULTS AND DISCUSSION To eliminate film buckling during thin film EWF test, a U-shaped fixture is used in the present work. As illustrated in Figure 2, buckling was not observed when the Ushaped fixture was applied, because the two legs of the U-clamp provided additional lateral constraint to hold the otherwise free edges of the specimen. The entire fracture

Eliminate Buckling in the Essential Work of Fracture Measurement

418

of the thin film took place in a typical and stable way, i.e. crack blunting, initiation and propagation. Figure 3 (a) gives the load-displacement curves of the HDPE blown film obtained using DENT geometry and U-shaped clamp. The geometric similarity of the curves indicates that the tests satisfy the prerequisite of the essential work of fracture approach [9]. The specific essential work and specific non-essential work of fracture are obtained by plotting the specific total fracture work against the ligament length as shown in Figure 3 (b). The linearity coefficient is high and the results are listed in Table 1. It seems that use of the U-shaped fixture may be a suitable measure for elimination of sample buckling in thin film EWF tests.

FIGURE 2 The fracture process of HDPE film with U-shaped fixture

HDPE film DENT specimen U-shape Clamp

HDPEfilm DENT specimen

5 10 15 20 Ligament length [mm]

Displacement [mm]

FIGURE 3 The load-displacement curves of HDPE film (a); Plot of wf against 1 (b) TABLE I The fracture parameters of HDPE film and iPP film with two types of fixture Materials

Fixture

we (kJ/m2)

HDPE iPP

U-shaped Flat U-shaped

70 57 54

^

(MJ/m3) 17.8 9.6 9.8

On the other hand, one may question that since the two legs of the U-shaped fixture impose additional lateral constraint to the specimen, the lateral constraint must have influences on the stress state in the ligament and affect the fracture process and the fracture parameters, particularly the specific essential work of fracture. To investigate this influence, an isotactic polypropylene (iPP) film with a large thickness was tested using both a flat and a U-shaped fixture. The iPP film does not have buckling problem using flat clamp due to its large thickness, as shown in Figure 4 (a). The load-displacement curves obtained in the EWF tests with different fixture geometries are drawn in Figure 5 (a). The shape of the curves is in fact identical, particularly in the region of crack initiation and ligament yielding. The sudden loaddrop corresponds to the full ligament yielding, followed with the crack propagation.

Eliminate Buckling in the Essential Work of Fracture Measurement

419

The similarity of the entire fracture process of the specimen with the two clamps can also be seen in Figure 4 (a) and (b). As a result, the specific essential work and specific non-essential work obtained with two different fixtures are same, refer to Figure 5 (b). This experimental evidence indicates that the clamp geometry has little effects on the measurement of EWF parameters.

(b) FIGURE 4 The fracture process of iPP film with (a) flat fixture and (b) U-shaped fixture 300. Ligament length = 25mm - Flat Clamp U-shape Clamp

i-PP

200-

.i

100

'

* ^

Flat Clamp

*~~^

U-Shape Clamp

& 0j - 3002001005

10

15

Displacement [mm]

05 - 1 0 15 20 Ligament length [mm]

FIGURE 5 The load-displacement curves of iPP with two fixtures (a); Plot of wf against 1 (b)

To confirm the findings from the experimental work, finite element analysis of the two fixtures were performed. The stress distribution and plastic energy dissipation of the specimen at various stages, including elastic deformation, crack-tip yielded and full-ligament yielded, were simulated and calculated numerically. The ligament length used for the simulation is 10 mm and the center of the ligament is set as the origin. Figure 6 (a) and Figure 7 (a) demonstrate the stress distribution along and around the ligament at the elastic deformation stage, respectively. It is clearly that at this stage, the stress distribution ahead of the crack tip and that around the ligament are slightly different with different fixtures due to the different clamp geometries. In the stage of crack-tip yielded as shown in Figures 6 (b) and Figure 7 (b), the same phenomenon is observed but the difference of the stress distribution becomes smaller. Since the fracture parameters of the EWF approach is energy related, the plastic energy dissipated ahead of the crack tip and around the ligament is more interesting and important. Figure 8 (a) gives a picture of the energy contours around the crack tip, which shows that the plastic work distribution around the crack tip is also very similar

420

Eliminate Buckling in the Essential Work of Fracture Measurement

for the U-shaped and flat fixtures, which indicates that the geometry of the clamp does not affect the plastic energy dissipation in the ligament region. Further, in the full ligament yielded stage, as shown in Figures 6 (c) and Figure 7 (c), the full ligament is yielded with a certain width in the loading direction. According to the EWF theory, the specific essential work of fracture is composed with the energy for yielding, necking and breaking the process zone, as expressed with following equation [4]. w=d\

ads+

a(A,)dA,

(1)

where (cr,£) are the true stress/strain, s~n and en are the true and engineering necking strains., a and A( are the stress and crack tip opening displacement within the fracture process zone. 5IC is the mode I critical value of A,; d is the width of the fracture process zone, which is in the order of the specimen thickness. The first item is the plastic work to yielding and necking and the second one refers to the fracture term of the neck. Clearly, the second fracture energy is related to the fracture mechanisms when tearing the neck, which should be less affected by the clamp geometry. On the other hand, some parameters would influence the first terms, including the size of the necked area, the opening displacement of the crack tip (CTOD). From the finite element analysis, the CTOD at the full ligament yielding stage is 0.81 mm for the U-shaped fixture and 0.82 mm for the flat one. Obviously, the discrepancy is negligible. Compared the pictures in Figure 7 (c), the width of the fully-yielded region are also identical for both fixtures. Thus, one can expect that the plastic work to yield and neck the ligament should be comparable for both fixtures. The energy dissipation around the ligament at this stage is shown in Figure 8 (b), which does not show any difference. Therefore, the finite element analysis results confirmed that though the geometry of the fixture influences the stress distribution ahead of the crack tip and around the ligament, the energy dissipation for fracture the materials are not affected. CONCLUSIONS A U-shaped fixture is employed to eliminate the buckling problem when very thin films are tested using the essential work of fracture method. The geometric influence of the U-shaped fixture on the fracture process is examined experimentally and by finite element analysis. The results indicate that the U-shaped clamp does not affect the fracture process and the fracture parameters. Reliable EWF parameters can be easily obtained using this U-clamp without introducing noticeable error. Therefore, the U-shaped clamp designed in this work is an ideal setup for the EWF measurements with very thin films. DENT specimen Liagment iength: 10 rr U-shape Clamp Rat Clamp

DENT specimen Liagment length: 10 mm U-shape Clamp — Flat Clamp

r

r |

DENT specimen Liagmeni length: 10 mm ——— U-shape Clamp Flat Clamp

10. C

>„ Distance [mm]

10

15

Distance [mm]

20 Distance [mm]

FIGURE 6 The stress distribution along the ligament at (a) elastic deformaiton stage; (b) crack-tip yielded stage; (c) full ligament yielded stage

Eliminate Buckling in the Essential Work of Fracture Measurement

421

# (a)

£*

"""I*

(b)

FIGURE 7 The stress distribution around the ligament at (a) elastic deformaiton stage; (b) crack-tip yielded stage; (c) full ligament yielded stage (left: flat fixture; right: U-shaped fixture)

FIGURE 8 The plastic energy around the ligament (a) crack-tip yielded stage; (b) full ligament yielded

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Mai YW and Cotterell B, Eng. Fract. Mech. 1985; 21(1): 123-128. Mai YW and Cotterell B, Int. J. Fract. 1986; 30(2): R37-R40. Mai YW, Cotterell B, Int. J. Fract. 1986; 32(5): 105-125. Mai YW, Int. J. Mech. Sci. 1993; 35(12): 995-1005. Wu JS, Mai YW and Cotterell B, J. Mater. Sci. 1993; 28(12): 3373-3384. Wu JS and Mai YW, Polym. Eng. Sci. 1996; 36(18): 2275-2288. Karger-Kocsis J, Czigany T, Polymer 1996; 37(12): 2433-2438. Hashemi S, Polym. Eng. Sci. 2000; 40(1): 132-138. Clutton, E. in Moore, D. R.; Pavan, A.; Williams, J. G., editors, Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites -ESIS Publ. 28, Elsevier Sci., Oxford, 2001, pp. 177-195.

Fracture Behaviour of Sandwich Laminates Reinforced by Short-Glass Fibres Akbar Afaghi Khatibi* Department of Mechanical & Manufacturing Engineering University of Melbourne, Australia

ABSTRACT The main aim of this work was to develop new sandwich laminates using glass fibre/polyester facings with low density polyurethane foam reinforced by short glass fibres. Hand lay-up and casting techniques were used to manufacture test specimens with different characteristic parameters. Several experiments were then conducted in order to characterise the mechanical properties of sandwich laminates. It was found that reinforcing core material by short glass fibres improves the mechanical properties of sandwich laminates. However, the extension of this improvement depends not only on the length and shape of the short glass-fibre but also the weight percentage of the reinforcement. In addition, it was concluded that the curing temperature plays a significant role on the core-reinforcement alignment and its microstructure. Specimens cured at lower temperature (ambient) exhibited improved fracture properties compared with those of cured at an oven.

INTRODUCTION Composite sandwich panels consist of two thin face sheets or skins bonded to a thick and lightweight core. The faces are typically composite laminates or metals, while the core could be cellular foam, metallic and non-metallic honeycombs, balsa wood or trusses. The concept of these sandwich laminates is very suitable for lightweight structures with high in-plane and flexural stiffness. In compare with traditional stiffened panels, sandwich laminates offer many advantages such as high flexural rigidity and strength, ease of manufacture, improved stability and ease of repair [1]. There are a large number of papers and publications on the behaviour of sandwich structures. The basic principles of sandwich construction and reviews of analytical and computational methods can be found in references [2, 3, 4]. The structural performance of sandwich laminates depends not only on the properties of skins, but also on those of the core, the interface bonding between the core and the skins, and the geometrical dimensions of the components. Cellular foams are increasingly being used as core materials in conjunction with high strength skins, to produce strong, stiff and lightweight sandwich structures for aerospace and marine applications. Due to their higher impact resistance and energy absorbing capability, cellular foams are being also used extensively in automobile applications. The * Correspondence Author, Department of Mechanical & Manufacturing Engineering, The University of Melbourne, VIC 3010 Australia, facsimile: +61(0)393478784, email: [email protected]

Sandwich Laminates Reinforced by Short Glass Fibres

423

mechanical behaviour of foam depends on the structure of the cell and the density of foam. The focus of this work was to investigate the fracture behaviour of sandwich laminates constructed with and/or without short-fibre-reinforced core. The impact and flexural behaviour of sandwich laminates with short-fibre-reinforced core is characterised and compared by those with un-reinforced core. The effects of corereinforcement length and curing temperature were studied in detail. MATERIALS AND EXPERIMENTAL PROCEDURE Sandwich panels were manufactured from 300 mm by 300 mm glassfibre/polyester skins and polyurethane core. Hand lay-up and casting techniques were used to manufacture test specimens with different characteristic parameters such as short-fibre volume fraction, short-fibre length, and etc. Two individual wet layers of glass-fibre/polyester were placed on the mould's internal walls and premixed agents of polyurethane foam (Polyol and Isocyanate), with or without reinforcement were then cast into the mould cavity. Two types of short glass fibre were used as reinforcement for the foam, namely milled and chopped fibres. The length of milled and chopped short glass fibres was 0.8 mm and 6 mm, respectively. Curing of skins and core occurred simultaneously under ambient (18°C - 20°C) and/or oven (85°C) temperature. No adhesive was used between skins and the core. The completed sandwich panels were cut into different coupon sizes, using a diamond saw. A "XYYZ" notation was used to categorise specimens, where X: Curing temperature, R for ambient or O for oven YY: weight percentage of short-glass fibre reinforcement in the core Z: type of core reinforcement, M for milled or C for chopped short glass fibre For example R05C refers to a sandwich panel cured at the room temperature with its core has been reinforced by 5% (weight) of chopped short-glass fibres. The mechanical characterisation tests were conducted to determine the compression strength (ASTM C365-00), bending moduli and strength (ASTM C39300 and D790-96a) and impact strength of sandwich specimens. All compression and flexural 4-point bendmg tests were performed on MTS universal testing machine with a constant crosshead rate of 0.5 mm/min and 6 mm/min, respectively at ambient temperature. The load and displacement data were recorded through a computer data acquisition system. To characterise the impact strength of sandwich panels Charpy test was conducted using a drop-down pendulum. At least four specimens were tested for each individual case.

RESULTS AND DISCUSSION Effect of Fibre Length Typical load-displacement curves for sandwich panels under four-point bending tests are shown in Figure 1. For all fibre weight ratios studied in this work, a linear (elastic) behaviour is followed by a plateau regime where the load required to crash the sandwich remains nearly constant. In this regime, some foam cell walls are compressed until they buckle, while others are stretched until they crack [5]. When additional load is applied, cell walls are compressed against neighbouring cell walls and the stiffness of the material increases as it is compressed into the lock-up regime.

Sandwich Laminates Reinforced by Short Glass Fibres

424

15%

0

10

20

30

40

50

0

Displacement [mm]

10

20

25%]

30

40

50

Displacement [mm]

(b) (a) FIGURE 1 Effect of core-reinforcement weight percentage on load-displacement curves under four-point-bending: sandwich laminates reinforced by (a) chopped- and (b) milled-glass fibre.

The level of plateau value, however, depends on the core-reinforcement length. It can be seen that the reinforcement of the core with chopped-glass fibres (6 mm in length) had significant effect on the plateau value and increased it by up to 35%. Contrary to this, adding milled-glass fibres with only 0.6 mm length decreases this value by 30%. The failure mode was also different for laminates reinforced by chopped- and milledglass fibres. Extensive delamination between core and skin was observed for the later. The effect of core-reinforcement-fibre length on flexural strength and modulus of specimens cured at room temperature is shown in Figures 2a and 2b, respectively. Although adding 5% reinforcement to the core decreases both bending strength and modulus to some extent, however, increasing the reinforcement weight ratio to 15% and/or 25% improves both mechanical properties. This phenomenon is more 0 -— Chopped — -• —

Milled

14

r

y12

11! 1. °

^

^ ^

^

0 - — Chopped — •• — Milled

r I

1000 "re1 1.

S. - "

r"

[ !

""*

800 •

1 1 s

600 '

3 X

•1

400 -

a 4

1

2

6

L

200 • 2 •

1 ' ' ' 0 •

10

t • ' • • I ' • ' '

15

20

Fibre Weiglh %

0 •

10

15

20

Fibre Weight %

(a) FIGURE 2 Effect of core-reinforcement weight percentage on (a) flexural strength and (b) bending modulus for sandwich laminates reinforced by chopped- and/or milled-glass fibre.

Sandwich Laminates Reinforced by Short Glass Fibres

425

significant with chopped-short-glass fibres with 6 mm length, hi this case, an increase up to 23% in flexural strength and 43% in bending modulus was observed. Reinforcing the core with milled-short-glass fibres with 0.6 mm length did not contribute to the flexural strength of sandwich panels and had an inverse effect, as shown in Figure 2a. The positive effect of milled fibres on bending modulus was observed only for specimens with 25% reinforcement. The effect of reinforcement length on impact strength of sandwich panels cured at room temperature is depicted in Figure 3a. For the laminates reinforced by choppedglass fibres an increase up to 15% was observed in impact strength. However, reinforcement by milled-glass fibres did not contribute to any improvement in impact behaviour. Furthermore, improvements at compressive strength were observed for reinforcement ratios of 15 and 25%, as shown in Figure 3b. Effect of Curing Temperature In order to investigate the effect of curing temperature on mechanical properties of sandwich laminates specimens were manufactured using two different curing temperature, namely ambient (18°C - 20°C) and oven at 85°C. Experimental results, as reported in Table I, indicate that curing temperature plays a significant role on the engineering properties of sandwich laminates. As it can be seen from Figure 4, all specimens cured at room temperature exhibit higher bending modulus and flexural strength compared with those of cured at higher temperature. This increase was up to 100% for bending modulus and 65% for flexural strength, as shown in Figure 4. These improvements in mechanical properties can be contributed to the microstracture of sandwich laminates. Since the microstructure of the reinforced-foam depends on the curing temperature, it's observed that specimens cured at high temperatures have got more porosities than those cured at room temperature. Although the manufacturing time was longer for specimens cured at room temperature but much more uniform structure was achieved in these specimens.

• Chopped QMilled

„

• Chopped DMilled

„

80

T T

:

.£.:£

_rh •I:

T

L .1-

-

:

•

!

r

FiT - ;i

•

_ I"

1 1.5-

if]

ill

r •

I 2]

-§1 -X

3,T

3-

s

a.

1 0.50

5

15

Fibre Weight %

(a)

5

15

Fibre Weighty.

(b)

FIGURE 3 Effect of core-reinforcement length on (a) impact and (b) compressive strength of sandwich laminates.

426

Sandwich Laminates Reinforced by Short Glass Fibres — • - — Room

—

m

—

O v e n

f

14-

i1 12-

2 ^ ^

i

c 10 3)

! 5

8-

< Q)

i.

4

2 0 -

10

15

1 •'

10

20

Fibre Weight %

15

'• i

'

20

Fibre Weight %

FIGURE 4 Effect of curing temperature on bending modulus and flexural strength.

TABLE I Experimental data

Sample R00 R05S R15S R25S R05M R15M R25M OOO O05S O15S 025 S O05M 015M O25M

Flexural Strength [MPa] Mean A 0.38 11.08 10.00 0.46 11.96 0.45 13.68 0.66 0.36 8.81 8.73 0.58 0.41 10.08 9.99 0.49 0.26 7.69 7.19 0.55 0.52 8.75 7.20 0.07 7.67 0.27 6.25 0.38

Bending Modulus [MPa] Mean A 83.54 618.91 601.13 37.58 95.39 738.78 885.70 68.90 541.23 61.16 604.54 69.79 827.52 52.89 54.20 550.08 364.56 29.55 369.12 36.80 414.64 45.38 398.24 27.45 478.97 57.86 51.26 553.79

Impact Strength [kJ/m2] Mean A 44.85 4.20 43.33 23.64 53.03 5.25 51.21 10.86 3.64 46.67 44.09 5.76 37.58 4.64 44.09 5.76 47.12 7.77 47.73 4.78 45.91 3.44 49.55 2.12 46.67 3.64 33.94 4.85

A: Standard deviation

CONCLUSIONS The effect of core-reinforcement in sandwich laminates was investigated. The core was reinforced by using milled- and chopped-glass fibres with 0.6 and 6 mm length, respectively. After conducting extensive experiments it was found that the length of core-reinforcement plays a significant role in fracture behaviour of sandwich laminates. The sandwich specimens with their core reinforced by chopped-glass fibres, exhibited 23% and 46% increase in flexural strength and bending modulus, respectively, compared with those of specimens without any core reinforcement. Furthermore, it was concluded that curing temperature is also affecting the engineering properties of the sandwich laminates. Specimens cured at lower temperature (ambient) showed higher fracture properties.

Sandwich Laminates Reinforced by Short Glass Fibres

427

REFERENCES 1. 2. 3. 4. 5.

Saporito J. 1989. "Sandwich structures on Aerospatiale helicopters" in Proc. 34* Int. SAMPE Symp and Exhibition, Reno, Nevada, pp. 2506-13. Zenkert D. 1995. "An introduction to sandwich construction" London: Engineering Materials Advisory Services. Noor AK, Burton WS, Bert CW. 1996. "Computational models for sandwich panels and shells" Applied Mechanics Reviews; 49: 15-199. Reddy JN. 1997. "Mechanics of laminated composite plates: theory and analysis" Boca Raton, FL: CRC Press. Neilsen MK, Krieg RD, Schreyer HL. 1993. "A constitutive Theory for Rigid Polyurethane Foam" in: MD-Vol 46 Use of Plastics and Plastic Composites: Materials and Mechanics Issues. ASME, New Orleans, Louisiana, pp. 181-194.

Analytical and Numerical Simulations of Plastic Zone at Crack Tip in Anisotropic Solids 'Hong-Xin Liu, 2Zhi-Ming Ye* ^ept.of Mechanics, 2Dept.of Civil Engineering, Shanghai University 99 Shangda Road, Shanghai, 200436, P.R.China 3

Hong-Yuan Liu Centre for Advanced Materials Technology (CAMT) School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW 2006, Australia 3

ABSTRACT This paper presents analytical and numerical studies on fracture behavour of anisotropic materials. A theoretical model was developed to characterize the plastic zone size and shape at crack tip in anisotropic solids. Several cases of anisotropic materials will be discussed by using uni-axial stress and bi-axial assumptions. Additionally, numerical results of finite element analysis are applied to examine the theoretical models. The method developed by this work is expected to provide a useful tool towards a better description of the crack-tip field in those materials.

INTRODUCTION Composites, whether fibre reinforced polymer, ceramic, metal, or steel reinforced concrete, are often considered as orthotropic or anisotropic materials [1]. It has been widely recognized that crack propagation in such type of materials should be appropriately governed by mixed mode models [2]. Since the early studies the stress and displacement fields of crack tip by Sih and Liebowitz [3] and Wu [4], considerable attention has been given to this problem in ideally brittle isotropic materials. However, there was little research which focused on the mixed-mode crack propagation of orthotropic or anisotropic materials. Development on those problems were made by Saouma et al (1987) [5], Ye & Ayari (1994, 1995) [6, 7], in which the classical fracture theories were extended to anisotropic solid cases. But, one important characteristics shape and size of the plastic zone at crack tip in anisotropic solids was not showed in literatures. Based on the earlier work on the characterization of plastic zone by Ye (1995/6) [8], this paper presents analytical and numerical estimations of fracture plastic zone size and shape at crack tip in anisotropic solids. Some models of anisotropic materials will be discussed by using uniaxial stress and biaxial assumptions. For uniaxial stress assumption, three models will be presented for softening models. For biaxial stress * Correspondence Author: Fax: 86-21-66134021, email: zmve(«!yc.shu.edu.cn

Simulations of Plastic Zone at Crack Tip

429

assumption, Hill's yield criterion (see Ref. [1]) is adapted to seek the shapes of plastic zone. A finite element technique was also applied to verify the theoretical model.

ANALYTICAL AND NUMERICAL SIMULATIONS ON CRACK TIP FIELD hi this section, instead of the single component, ay, a biaxial state of stress around the crack tip will be considered. As such, the near crack tip stress field is substituted into the expression of a yield function, which is appropriate to anisotropic solids. Then the yield radius can be solved as a function of the polar angle 6 and the ratio Ku I Kj = m . This approach is very similar to the uniaxial Irwin's first order approximation. The only difference is that a surface, as plastic zone ahead of the crack tip, should be sought to determine the shape of the plastic zone using one of the appropriate yield surfaces to anisotropic solids. For this purpose, an approximate general yield function is taken as the form of following quadratic function: F{ay -azy+

G{az -ax}r2x + H{CTX -ay}

+ 2Lz2y2 + 2MT2X + 2Nr2xy =1

(1)

where. F, G, ..., N are the constants of materials. Equation (1) was utilized by Hill (1948) and was applied, in Hill (1950), to a number of technological problems. Also, the yield function can be expressed by the principal stress. First, we note that, in general, when the reference axes are principal axes, the shear stress components vanish and Eq. (1) can be written in the form of F(a2 -aj+

G(<73 -
(2)

If X, Y and Z are the tensile strengths in the principal directions, the Eq. (2) predicts 0)2=l

(3)

or G + H = l/X2

(4)

H+F = l/Y2

(5)

F+G = l/Z2

(6)

Similarly,

The principal stress field at the crack tip can be obtained. For plane problem, the principal stresses are

430

Simulations of Plastic Zone at Crack Tip

and the following expressions could be obtained

m

-FIy-mFIlyJ

+4^

+

mFIIJ (8)

Plane Stress State Here, we consider a case in plane stress state firstly. In this case, the stresses are in the conditions: az = %zx = ryz = 0, in which, az is one of the principal stresses, of + a2 - [2R /(l + R)\j,a2 = Y2

(9)

where, R = 2{z IY)2 -1. Substitute the principal stresses given by Eq. (8) into Eq. (9), then we can get the following expression, which presents the boundary of the plastic zone, as a function of 8, that is

^

^

{

^

(10)

in which

+ mFm + Fiy

+ >»FIIy

F.-rnF, ryy+4{Fby+>r

F,J

Plane Strain State In the same way, we have

r = r(9) =

AnY2

'+

2

(12)

here,

r n=4A 2 2

(13a,b,c)

r i =A 2 + (l-2v)A 1 ' and k = HY2. Parametric Study Three assumptions are used in the following analyses: i) The crack is aligned in direction 1 and assumed to correspond to one of the two major planes of elastic symmetry (corresponding to an ortho tropic case); ii) The crack tip is subjected to a mixed mode loading, I-II mode;

Simulations of Plastic Zone at Crack Tip

431

iii) To simplify the numerical calculation, we assume a polar variation of the toughness of the form:

*± = Ef

(14)

^

(15)

and a modulus G12 given by G12=

E1 + E2 +2vl2E2

The characteristic equation is given by [6,7] s4+(l + El/E2)s2+El/E2=0

(16)

which would yield s = ±i if El = E2. If we assume n

K m = — K,n— , n = •E.

(17a,b,c)

Dx = cos 8 + n sin 9 and 0< w< 10 and 0.1<w<10, m = 0 represent a pure mode I case, m = \0 represents an approxamte pure mode II case (numerically this assumption is very close to similarly pure mode II loading), and m-\, represents a mixed mode I-II case. A large number of engineering materials, e.g. roller concrete for dams, etc, was observed in conjunction with their tabulation of elastic properties with fifteen different anisotropic parameters [1-7] and should be considered as under mixed mode I-II.

NUMERICAL EXAMPLES OF PLASTIC ZONE SHAPES Numerical examples of this model are shown in Fig. 1 in which the shapes of plastic zone for different values of the ratio Kn I Kl and different material parameters, were obtained under plane stress conditions with Hill's yield criterion. A finite element technique for 2-D problem was applied to verify the estimated plastic zone shape. Here, the quarter point singular element model proposed by Barsoum in [9] and Hill's yield model were also adapted to seek the boundary line between elastic and plastic zones. Similarly, the parameters of models were the same as the ones of previous analysis, i.e. the orthotropic cases. The numerical simulations of plastic zone shapes at crack tip in orthotropic solid were shown in Figs. 2(a) and 2(b). It was found that there were similar characteristics between analytical and numerical estimations. It is of interest to notice that those kinds of plastic zone characteristics carried out the effects of fracture toughness measurements experimentally in the condition of the linear-elastic fracture field.

Simulations of Plastic Zone at Crack Tip

432 G

-

-

n-IO

\

A

B-O.l 10

i Crack

5

2 V

2

'f\

/m=IO

1

-5

Craot'

H. /

•

ft'

V, 1

4

10

-

6

-15

-10

IS

-5

-15

(a)

- 1 0 - 5

0

5

10

15

(b)

FIGURE 1 Numerical simulations on the shape of plastic zone at crack tip by present analytical model in which (a) n=10 and (b) n=0.1, respectively.

(a)

(b)

FIGURE 2. Numerical simulations on the shape of plastic zone at crack tip by finite element analysis, in which (a) n=10 and (b) n=0.1, respectively.

ACKNOWLEDGMENTS The financial support of Sciences Fund of Shanghai Education Committee for Scholars, is gratefully acknowledged. REFERENCES [1] H. Liebowitz, Fracture, An advanced treatise, Vol. II, Academic Press, New York & London, (1968). [2] F. Erdogan and G.C. Sih, J. Bos. Engng., 85, 519-527, (1963). [3] G.C. Sih, Int. J. Fracture Mech., 10, 305, (1974). [4] E.M. Wu, Composite Materials Workshop (Edited by Tsai, Halpin and Pageno), 20-43, Technonic Press, Stanford, CT (1968). [5] V. E. Saouma, MX. Ayari & D. A. Leavell, Engng. Fracture Mech., 27, 2, 171-189, (1987). [6] Zhiming Ye & M.L. Ayari, Engineering Fracture Mechanics, 49, 6, 797-808, (1994). [7] M.L. Ayari, & Zhiming Ye, Engineering Fracture Mechanics, 52, 3, 389-400, (1995). [8] Zhiming Ye, International Journal of Fracture, 74, 1, R3-R10, (1995/6). [9] R.S. Barsoum, Int. J. Num. Meth. Eng., 10, 25-38, (1976), 11, 85-98, (1977).

Application of Essential Work of Fracture Methodology to Polymer Fracture Kai Duan, Xiaozhi Hu School of Mechanical Engineering University of Western Australia Perth, Australia Yiu-Wing Mai Center for Advanced Materials Technology School of Aerospace, Mechanical and Mechatronic Engineering University of Sydney, Australia

ABSTRACT The applicability and limitation of the essential work of fracture model originally proposed for double-notched polymer and metal specimens with full ligament yielding prior to failure are studied using two sets of ABS polymer results measured with threepoint-bend specimens without full ligament yielding. The model is then extended and related to a simple fracture mechanics model on the local fracture energy distribution, which is originally developed for quasi-brittle fracture of concrete-like materials. Both models lead to the conclusion that the height of the crack-tip plastic zone controls the fracture toughness of materials, and the specific fracture energy dissipation along a crack path.

INTRODUCTION The essential work of fracture (EWF) model [e.g. 1,2] has been successfully used to analyze the specific fracture energy of double-notched polymer and metal specimens with full ligament yielding prior to failure. Recently, EWF has also been used to the plane strain fracture of ABS three-point-bend (3-p-b) specimens [3] that clearly do not satisfy the full ligament yielding condition prior to the final failure. In this paper, we are going to discuss the applicability and limitation of EFW, and show why EFW can still be used even if the full ligament yielding is not satisfied. The key argument is that the specific fracture energy Gf dealt with by EWF can always be determined experimentally regardless the ligament condition. SPECIFIC FRACTURE ENERGY Gf Interestingly, the quasi-brittle fracture of concrete-like materials is also frequently characterized by the specific fracture energy Gf as used for yield failure of polymers and metals. RILEM has set up a standard for Gf measurements of concrete [4]. Similar to the case of EWF for polymers and metals, a stable load (P) and load-point displacement •"Corresponding author, Fax: 61-8-9380-1024, Email: [email protected]

434

Application of Essential Work of Fracture Methodology to Polymer Fracture

(S) curve is required so that G/ can be evaluated from the total energy consumption over the initial ligament area.

where B is the specimen thickness, W is the width and a is the initial crack (or notch) length. In the case of a double-notched specimen, the total width (2W) and the total crack length from two notches (2a), as commonly denoted, should be used. Clearly, the specific fracture energy Gf as used by RTLEM and EWF is only an average fracture energy measurement, which is equivalent to assuming a constant fracture energy distribution over the entire fracture area. Such a simplified assumption has to be limited to special material and specimen conditions. To extend the applicability of the specific fracture energy G/ adopted by RILEM and EWF, a local fracture energy distribution concept has been proposed [5,6]. The local specific fracture energy gf is used to describe the energy dissipation along the crack path, over the fracture area of B-(W-a). Both G/and g/are related according the energy conservation principle. 1

W-a

If the local fracture energy distribution gyis indeed constant over the crack path, 0 < x < W-a, as assumed, then G/=gf= constant, and the RILEM definition which is also used by EWF is valid. Clearly, the local specific fracture energy concept extends the applicability of the RILEM definition and EWF. EWF: THE RELATIONSHIP BETWEEN G/AND LIGAMENT A typical double-notch specimen used by EWF is shown in Figure l(a). For the deep notch geometry, a circular plastic zone with the radius of (W-a) prior to fracture is adequate. EWF shows that the following linear relationship exists for polymers and metals. Gf = go + constant -(W-a)

where go is the essential work of fracture corresponding to zero plastic zone size. The non-essential work of fracture, gp, is related to the plastic zone size, which can be evaluated from the volume of the plastic zone for a constant plastic work density pp. _ 8p

(thickness • length • height | Pp

{

thickness-length (

J plasticzone

B-(2W-2a)-(2W-2a)]

= pn • constant p I

LA

-

B-(2W-2a)

v

v

= p • (constant • height) ^P

y

5

= constant -(W — a)

-plastic zone

...

l

) , t. '

' plastic zone

(4) '

K

Application of Essential Work of Fracture Methodology to Polymer Fracture

(a)

435

(b)

(a) Full yielding due to deep-notch influence (b) Full yielding due to specimen back-face influence

FIGURE 1 (a) Common EWF specimen showing the influence of deep double notches on the plastic zone and then Gf, and (b) deep single notched EWF specimen showing the influence of specimen back-face on the plastic zone and then Gf.

As shown by equations (3) and (4), the linear relationship between Gf and ligament 2-{W-a) actually proves that Gf is directly related to the crack-tip plastic zone height measured by 2-{W-a). The yield condition shown in Figure l(a) can also be satisfied by a single edge notched specimen either under direct tension or bending (e.g. 3-p-b) as illustrated in Figure l(b), where the full ligament length is given by (W-a) and equations (3) and (4) are still valid. Obviously, the full ligament yield can only be achieved for a very deep notch or crack. In this case, the crack-tip condition can also be considered under the strong influence of the specimen back-face boundary. When the boundary is far away from the crack tip, full ligament yield is not possible. However, it has been shown that EWF could still be used to ABS 3-p-b specimens without full ligament yield [3], which shows EWF can be extended to cases without full ligament yield. BOUNDARY EFFECT MODEL AND LOCAL ENERGY DISTRIBUTION Recognition of the boundary influence from Figure l(b) is important. The classic EWF can be considered modeling the specimen back boundary influence, a case dealt with frequently for quasi-brittle fracture of concrete-like materials. Similar to Gf of polymers and metals modeled by EWF, Gf of quasi-brittle materials like concrete is also found to be ligament and specimen size dependent. The fracture process zone (FPZ) in front of a crack tip in a quasi-brittle material like concrete is similar to a crack-tip plastic zone in a ductile polymer or metal. If a concrete specimen has a deep notch or crack as shown in Figure l(b), FPZ covers the whole ligament showing the strongest back boundary influence. If a crack tip is far away from the specimen back-face boundary, a fully developed FPZ without any back-face boundary influence is expected. The RILEM Gf definition does not require the condition that FPZ has to cover the entire ligament area. A simple boundary effect model has recently been developed [7-9], based on the local fracture energy concept proposed by Hu and his colleagues [5,6]. The full ligament region in a specimen with a single edge notch or crack has been separated into the inner and boundary zones illustrated in Figure 2(b). In the inner zone, the crack-tip FPZ is far away from the specimen back boundary, and can thus remains constant or shows no boundary effect. In the boundary zone, development of the crack-tip FPZ is restricted by

436

Application of Essential Work of Fracture Methodology to Polymer Fracture

the ligament as FPZ is too close to the specimen back-face boundary. This is akin to the full ligament yield in a polymer or metal specimen modeled by EWF. (a)

W-a Inner Zone

; Boundary Zone, a^

(b)

11'/

I-IV.

FPZ

W-a FIGURE 2 Separation of inner and boundary zones by a/* in a specimen of width W and crack a. (a) Corresponding bi-linear local energy gf distribution in comparison with the RILEM Gf as the average fracture energy, (b) Variation of FPZ and its height hFpz in the inner and boundary zones.

If a linear function is assumed for the local specific fracture energy gf as shown in Figure 2(a), it can be obtained from equation (2) that: (W-a) 2a\

W-a
•a'i

2(W-a)

W-a>a]

where GF is the maximum stable specific fracture energy in the inner zone. For a large specimen with a crack-tip away from all the specimen boundaries, GF is identical to the critical strain energy release rate G/C. The transitional ligament length a* is used to separate the inner and boundary zones as illustrated in Figure 2. Clearly, in the boundary zone where {W-a) < ai, equation (5) is identical to EWF or equation (3). Therefore, the linear relationship between Gf and ligament (W-a) as proven by EWF implies a linear local fracture energy distribution over the ligament area. ANALYSIS OF ABS 3-p-b RESULTS The specific fracture energy Gf of ABS-740 was measured using 3-p-b specimens [3]. The span is 56 mm, depth Wis 14 mm, and thickness B = A and 7 mm respectively. Two testing temperatures were 20 and 80 °C. The 20 °C results were measured using only the specimens with thickness B = l mm, and are shown in Figure 3(a). Even after excluding the two solid points that were questionable as discussed by the original authors, the relationship between Gf and (W-a) is clearly not always linear. Applying equation (5) to the results, it is found that g0 =

Application of Essential Work of Fracture Methodology to Polymer Fracture

437

3.35 N/mm, GF = 20.6 N/mm, and the transitional ligament length a* separating the inner and boundary zones is 5.8 mm. The curve from equation (5) is also provided. It should be noted the saturated specific fracture energy GF is higher than the experimental Gf values.

T = 80 °C B = 4mm 5

W-a (mm)

10

W-a (mm)

FIGURE 3 The comparison of the Gf predicted using Eq. (5) with experimental data [3]. The solid and dashed curves in (b) and (c) are obtained using different g0 values and an identical g0 value as listed in Table 1.

The 80 °C results were measured using the specimens with thickness of 4 and 7 mm, and are shown in Figures 3(b) and 3(c). Again, the relationship between G/and (W-a) is clearly not linear for the results in Figure 3(b). Two slightly different approaches are adopted in the present study. First, the two sets of experimental results with B = 4 and 7 mm can be used separately to determined their own go and GF values. Second, the same go can be assumed for both sets of experimental results if both specimens with B = 4 and 7 mm satisfy either the plane stress or strain condition at the same time. The results from equation (5) are listed in Table 1. The saturated GF is almost identical for both approaches for a given thickness of either 4 or 7 mm. The essential work of fracture go estimated appears to be thickness dependent if we assume the specimens with B = 4 and 7 mm are influenced by the plane stress condition. A higher go for the specimens with thickness B = A mm is consistent with the well-known plane stress fracture toughness behavior. The thickness dependence of GF is also consistent with the explanation. The single go assumed to be applicable to both specimens of B = 4 and 7 mm is 5.96 N/mm, between the two separate go values of 4.97 and 6.48 N/mm. The curves from equation (5) are plotted in Figures 3(b) and 3(c) for the two different approaches.

438

Application of Essential Work of Fracture Methodology to Polymer Fracture TABLE I 80 °C results from Equation (5) Identical g0

Different go 5 (mm) go (N/mm) GF(N/mm) d[ (mm)

7 4.97 13.80 3.50

4 6.48 15.12 7.82

7

4 5.96

14.06 4.40

15.11 7.27

DISCUSSIONS AND CONCLUDING REMARKS The non-linear Gf measurements of ABS polymer following the EWF methodology have been explained by introducing the concept of local fracture energy gf distribution, which extends the applicability of EWF. As a result, the full ligament yield in a polymer specimen prior to final failure is no longer necessary. A linear Gf and ligament (W-a) relation described by EWF implies a linear local fracture energy gf distribution in the specimen back-face boundary region, which is directly related to the plastic zone height at the crack tip. The conclusion that the crack-tip plastic zone height controls the fracture energy dissipation is significant, as the same linear Gf and ligament (W-a) relation can also be taken as the Gf and plastic zone height relation. This conclusion has led to a simple fracture mechanics model [10] recently proposed for the adhesive thickness effect on fracture toughness of adhesive joints, which is a case where the crack-tip plastic zone height is identical to the adhesive thickness. ACKNOWLEDGEMENTS The financial support from the Australian Research Council (ARC) through a Discovery Projects grant is acknowledged. REFERENCES 1.

Cotterell, B. & Reddell, J.K. 1977. "The Essential Work of Plane Stress Ductile Fracture," Int. J. Fract, 13: 267-277. 2. Atkins, A.G. & Mai, Y.W. 1985. Elastic and Plastic Fracture: Metals, Polymers, Ceramics, Composites, Biological Materials. Ellis Horwood Ltd., Chichester. 3. Luna, P., Bernal, C , Cisilino, A., Ftontini, P., Cotterell, B. and Mai, Y. -W. 2003. "The Application of the Essential Work of Fracture Methodology to the Plane Strain Fracture of ABS 3-Point Bend Specimens," Polymer, 44: 1145-1150. 4. RILEM TC-50 FMC, 1985. "Determination of the Fracture Energy of Mortar and Concrete by Means ofThree-Point Bend Tests on Notched Beams," Mater. Struct, 18:287-90. 5. Hu, X. Z. 1990. Fracture Process Zone and Strain Softening in Cementitious Materials. ETH Building Materials Reports No.l, ETH Switzerland. (AEDIFICATIO Publishers, 1995). 6. Hu X.Z, Wittmann F.H., 1992. "Fracture Energy and Fracture Process Zone," Mater. Struct. 25: 319326. 7. Duan, K., Hu, X.Z., Wittmann, F.H. 2002. "Explanation of Size Effect in Concrete Fracture Using Non-Uniform Energy Distribution," Mater. Struct., 35:326-331. 8. Duan, K., Hu, X.Z., Wittmann, F.H. 2003. "Boundary Effect on Concrete Fracture and Non-Constant Fracture Energy Distribution," Eng. Fract. Meek, 70:2257-2268. 9. Duan, K., Hu, X.Z., Wittmann, F.H., 2003. "Thickness Effect on Fracture Energy of Cementitious Materials," Cem. Concr. Res., 33(4):499-507. 10. Duan, K., Hu, X.Z., Mai, Y.W. 2003. "Substrate Constraint and Adhesive Thickness Effects on Fracture Toughness of Adhesive Joints", J. Adhesion Science and Technology, in press.

Three-Dimensional Micromechanics Analysis of Strain Energy Release Rate Distribution along Delamination Crack Front in FRP Hiroshi Tanaka and Yoshikazu Nakai Department of Mechanical Engineering, Kobe University, Japan

ABSTRACT The effect of fiber/matrix interfaces on the distribution of local strain energy release rates along crack front was studied by using a three-dimensional inhomogeneous model of a unidirectional FRP. For a crack with a straight crack-front line perpendicular to fibers, the local strain energy release rate along the crack front takes a maximum value at the crack-front point closest to the fiber/matrix interface. This result suggests that a crack with a straight front line starts to grow at the nearest crack-front point to interfaces and the crack growth in the region far away from interfaces follows behind.

INTRODUCTION Crack growth along fibers is one of the most prevalent failure mechanism for fiber-reinforced plastics (FRP). Most of researches on crack growth in FRP were on the basis of the macromechanics where FRPs were regarded as homogeneous orthotropic materials. However, to analyze damage processes in FRPs, a micromechanical analysis of the local stress state around crack tip is important. For cracked FRP plates, two-dimensional analyses by periodically layered models [1-2] and three-dimensional analyses by using a model containing cylindrical fibers [3-4] have been carried out by several researchers, but little attempt has been made to investigate the three-dimensional elastic stress state around crack tip. hi the present study, the elastic stress analysis of continuous fiber-reinforced plastics containing a crack parallel to fibers was conducted by using a three-dimensional inhomogeneous FRP model, and the effect of fiber/matrix interfaces on the distribution of the local strain energy release rate was discussed. ANALYSIS Problem Statement The three-dimensional elastic analysis of a unidirectional FRP plate with a uniform thickness as shown in Figure 1 was conducted. Figure l(a) shows a mode I problem for a center-cracked plate with a width of 2PF=4mm subjected to tensile stress, a. Figure l(b) shows a mode II problem for an edge-cracked plate with a width of W=2mm where the *Corresponding author, Department of Mechanical Engineering, Kobe University, 1-1, Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan, Fax: +81-78-803-6107 e-mail: [email protected]

Analysis of Strain Energy Release Rate Distribution

440 a

r tT 111111

'7, V ~ t ' «?I^* •'

o

u

o

o

o

c;

(;

z

Crack \

Crack

a=2mm

<

a=1mm

Fiber direction

W=2mm

<

(a) Mode I problem

1

>

Fiber direction

Umim 2W=4mm

A

>

(b) Mode II problem

FIGURE 1 Mode I and mode II problems

lower end is fixed and the upper end is subjected to uniform tangential displacement, w, as shown in the figure. The crack has a length of a=lmm (a/W=0.5) and is parallel to the fiber direction (z-direction) for both mode I and II problems. Inhomogeneous FRP Model We consider an inhomogeneous FRP model as shown in Figure 2(a) where circular cylindrical fibers are arranged in a square array with a pitch of £>=9.14um. The fiber diameter is d=8\xm and the fiber volume fraction is 60%. For all analyses in the present study, the crack plane is parallel to fibers and the crack-front line is perpendicular to the fiber axis, that is, z=constant. For a homogeneous orthotropic plate, the strain distribution along crackfrontis nearly uniform except near the plate surfaces. Therefore, in view of symmetry, an interior region with a thickness of D/2 containing only half of each fiber as shown in Figure 2(b) was analyzed under plane strain condition. The inhomogeneous FRP region contains every two fibers in the upper and lower sides of the crack plane. This region containing the crack tip has a length of 0.4 W in the fiber direction and is surrounded by homogeneous FRP as

Matrix

A Inho Tiogeneous FRF

x=DI2

(a) Arrangement of fibers (b) Inhomogeneous FRP (c) Model for analysis FIGURE 2 Arrangement of fibers in inhomogeneous FRP model

Analysis of Strain Energy Release Rate Distribution

441

illustrated in Figure 2(c). The height of the cracked matrix layer, t, is defined as shown in Figure 2(b). When tl{D-d)=\, t is equal to the height of other matrix layers. Finite Element Analysis The finite element analysis was carried out by the MARC software. For mode I loading, the right half of the FRP plate shown in Figure l(a) was modeled because of symmetry. The finite element model used is composed of 8000-10000 quadrilateral solid elements for both mode I and IT problems. The strain energy release rate was calculated from the modified crack closure integral method [5]. The matrix corresponds to isotropic epoxy with the Young's modulus of £'m=3.5GPa and the Poisson's Ratio of vm=0.35. The fibers are transversely isotropic graphite with the elastic constants of £3=295GPa, £i=17.5GPa, G3i=15GPa, v3i=0.3 and vi2=0.5. The elastic constants of homogeneous FRP were determined from the relationship between mean stresses and mean strains calculated by using the inhomogeneous FRP model without cracks. RESULTS AND DISCUSSION Distribution of Local Strain Energy Release Rate Figure 3 shows the distribution of the local strain energy release rate along crack front for tl{D-d)=\, where the crack is placed on the midplane between adjacent fibers. The abscissa is the x-coordinate of points on the crack front defined as illustrated in this figure. In the case of homogeneous FRP, the local strain energy release rate is constant along crack front. On the other hand, in the case of inhomogeneous FRP, the local strain energy release rate takes a maximum value, GmaX) at the crack-front point closest to the

^°- 2 F

^0.8

Model C,7 D 0.6

x=o

i

CD

x=DI2

0)

0.4

cp P

Homogeneous FRP 0.2

"8

I

i

)

/ x=0

\ ro

I

Mode II

V

0.1

Homogeneous FRP

u

x=DI2

'

/tetoaxtn

Inhomogeneous FRP~

e=0 f/(D-d) = 1.0 II 0.0 0.2 0.4 0.0

-a I 0.6

(D N

I

0.8

1.0

Location along crack front, x/(D/2)

Inhomogeneous FRP e=0 t /(D-d) = 1.0 II I I

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Location along crack front, xl(DI2)

(a) Mode I (b) Mode H FIGURE 3 Distribution of strain energy release rate along crackfront

Analysis of Strain Energy Release Rate Distribution

442 Large 6

K—\ //* 1

X

Fatigue crack

Small G

-Large G

-•>

Crack-

\( \ (a) Distribution of strain energy release rate for cracks with straight front

(b) Front shape of a real fatigue crack observed on fracture surface (mode II).

FIGURE 4 Front shape of real crack

fiber/matrix interface (x=Q) and decreases as x increases away from fibers for both mode I and II cracks. This result suggests that a crack with a straight front line as illustrated in Figure 4(a) starts to grow at the nearest crack-front point to interfaces and the crack growth in the region far away from interfaces follows behind. Therefore, a real crack has a bow-shaped front line as shown in Figure 4(b). Effect of Height of Cracked Matrix Layer Figure 5 shows the ratio of the maximum energy release rate along crack front Gmax (at to the minimum rate Gm;n (atx=D/2) as a function of the height of the cracked matrix layer, t/(D-d). The value of Gmax/Gmm decreases with the increase of the height of the cracked matrix layer and the strain energy release rate along crack front is nearly uniform for t/(D-d)>7, that is, t>d (the height of the cracked matrix layer is more than the fiber diameter).

JC=O)

3.0

1

1

1

D

1

o Mode 1

2.5

•

Mode II

on

2.0 1.5 -

-

B

-

CP

Q

1.0 0.5 0.0 0

-

o

9

CftlQjO O_

V, = 60% e=0 1

1

I

1

2

4

6

8

10

Normalized height of cracked matrix phase, t /(D-d) FIGURE 5 Effect of matrix-phase height on Gmax IGmm .

Analysis of Strain Energy Release Rate Distribution

443

Effect of Crack Eccentricity A three-dimensional analysis of an eccentric crack away from the midplane between adjacent fibers was also conducted. An eccentric crack may be under a mixed-mode state microscopically, even if it is under macroscopically pure mode I or II condition. Figure 6(a) shows the shape of the eccentric crack in the section perpendicular to the fiber axis. For 2elt<\, the eccentric crack is a plane crack, while for 2elt>\, a part of the eccentric

0.8

1

1 2e/( = 0 2e/t = 0.613 2e/t = 2.065 -

o

CD

•

0.6>», 0.4 -

x=DI2

8

0.2 ~tl(D-d)= 1.0 Macroscopic

2e/t < 1

1

0.0 0.0

2e/f > 1

mode 11

1

0.2

0.4

I

I

0.6

0.8

1.0

Location along crack front, xl{D/2)

(a) Definition of e

(b) Distribution of total strain energy release rate FIGURE 6 Distribution of total strain energy release rate along front of eccentric cracks

2.0

tl{D-d) = 1.0

2.0 Macroscopic mode I 2e/f=0.613

cf

Macroscopic mode I 2e/t= 2.065

1.5

c|

1.5 Interface

Matrix

I.OmDDDDDDDDDDDDDDO CD

CD D

qo = 1S 0.5

o

0.0

0.2

0.4

C3,/GT

d

O G,,/GT

1 0.5

•

CD

0.6

6,,,/G,

0.8 1.0

Location along crack front, xl(DI2)

G,,/GT 0.0' 0.0

0.2

0.4

0.6

0.8 1.0

Location along crack front, xl{DI2)

(a)2e/< = 0.613 (b) 7e/t = 2.065 FIGURE 7 Change of rrode ratio along front of eccentric crack

444

Analysis of Strain Energy Release Rate Distribution

crack is an interface crack and the remaining portion is a matrix crack. Figure 6(b) shows the distribution of the total strain energy release rate, Gj, along the front of the eccentric crack under macroscopically mode I condition. For 2e/tl, the value of Gj increases locally near the boundary between the interface and matrix region. Figure 7 shows the mode I, II and III components of the strain energy release rate for eccentric cracks under macroscopically mode I condition. For 2e/t<\, there are little mode II and mode III components at the front of eccentric cracks. For 2e/t>\, the mode II and III components are generated in the neighborhood of the boundary between the interface and matrix region. CONCLUSIONS (1) For a crack with a front line perpendicular to the fiber axis, the local strain energy release rate takes a maximum value at the crack-front point closest to the fiber/matrix interface and decreases with increasing distance from fibers under both mode I and II loading. (2) For an eccentric crack, a part of which is an interface crack, the mode II and III components of the strain energy release rate are generated in the neighborhood of the boundary between the interface and matrix region, even if the crack is under pure mode I condition macroscopically. REFERENCES 1. 2. 3.

4. 5.

Kimachi, H., H. Tanaka and K. Tanaka. 1999. "Transition from Small to Large Interlaminar Cracks in Fiber-Reinforced Laminated Composites," JSME Int. Journal, Series A, 42(4):537-545. Jha, M. and P. G. Charalambides. 1998. "Crack-Tip Micro Mechanical Fields in Layered Elastic Composites: Crack Parallel to the Interfaces," Int. J. Solids Struct., 35(1-2):149-179. Crews, J. H., Jr., K. N. Shivakumar and I. S. Raju. 1992. "A Fibre-Resin Micromechanics Analysis of the Delamination Front in a Double Cantilever Beam Specimen," in Phase Interaction in Composite Materials, A. Paipetis and G. C. Papanicolaou, eds. Oxon: Omega Scientific, pp. 396-405. Dubois, F. and R. Keunings. 1997. "DCB Testing of Thermoplastic Composites: A Non-Linear Micro-Macro Numerical Analysis," Comp. Sci. Tech., 57:437-450. Rybicki, E. F. and M. F. Kanninen. 1977. "A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral," Eng. Fract. Meek, 9:931-938.

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour during Mode I Fracture in Glass Fibre Composites S. Feih*, B.F. S0rensen Materials Research Department, Ris0 National Laboratory, Denmark

ABSTRACT The mode I fracture toughness of glass fibre reinforced composites is studied by measuring the effect of fibre cross-over bridging in DCB specimens under pure bending moment. Bridging laws were obtained by simultaneous measurements of the crack growth resistance and the end opening of the notch end. For a given composite system, the constants of the bridging law depend on the interfacial properties of the fibre/ matrix interphase. A micromechanical model is used for relating the microscale parameters, such as the interfacial fracture energy, to the macroscopic bridging law. The microscale parameters are determined from investigations in the environmental scanning electron microscope.

INTRODUCTION Interfacial properties of glass fibre composites are controlled by the sizing, which is applied to the glass fibres during manufacture. For the same matrix system, a change of sizing results in changes of these properties, thereby influencing the mechanical properties such as strength and fracture toughness. The concept of strength is used for characterising crack initiation in composite design, while fracture toughness determines crack growth and damage development, hi this article, the influence of the interfacial properties on the crack growth parallel to the fibres during mode I fracture is investigated. PRINCIPLE OF MEASURING BRIDGING LAWS The approach for the measurements of bridging laws is based on the application of the path independent J integral [1], and has been used recently to determine the bridging characteristics of unidirectional carbon fibre/ epoxy composites [2] and glass fibre composites [3]. A symmetric DCB specimen is loaded with pure bending moments M (FIGURE 1). This specimen is one of the few practical specimen geometries, for which the global J integral (i.e. the integral evaluated around the external boundaries of the specimen) can be determined analytically [1]: M b H^3 E n 2

(

1

)

'Corresponding Author, Materials Research Department, Ris0 National Laboratory, P.O. Box 49, 4000 Roskilde, Denmark, Tel: 0045 4677 5787 / Fax: 0045 4677 5758, E-mail: [email protected]

446

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour

En is the Young's modulus referring to the material directions, V13 and v3i are the major and minor Poisson's ratio, b is the width and H the beam height.

2H

M' FIGURE 1 DCB specimen with pure bending moment

Now consider the specimen having a crack with bridging fibres across the crack faces near the tip. The closure stress a (x2-direction) can be assumed to depend only on the local crack opening 8, i.e. the crack grows in pure mode I. The bridging law a = a(8) is then taken as identical at each point along the bridging zone. Since fibres will fail when loaded sufficiently, we assume the existence of a characteristic crack opening So, beyond which the closure traction vanishes. Shrinking the path of the J integral to the crack faces and around the crack tip [4] gives p,

(2)

where JtiP is the J integral evaluated around the crack tip (during cracking Jtip is equal to the fracture energy of the tip, Jo). The integral is the energy dissipation in the bridging zone and 5* is the end-opening of the bridging zone at the notch root. The bridging law can be determined by differentiating equation (2) [4].

Thus, by recording JR and the end opening of the bridging zone 8*, the bridging law can be determined. This approach models the bridging zone as a discrete mechanism on its own. Contrary to crack growth resistance curves (R-curves), the bridging law can be considered a material property and does not depend on specimen size [4], EXPERIMENTAL METHODS Composite specifications We investigated two commercial E-glass fibre systems with the same fibre diameters (~l7\im ± 2|xm), but different silane-based sizings. Sizing A is described as multi-purpose compatible, while sizing B is epoxy compatible. A detailed chemical analysis of the two fibre sizings, which clearly showed differences regarding the surface groups, can be found in [5]. The two resin types consist of a bisphenol Abased epoxy resin and an orthophthalic polyester resin. An in-house developed resin transfer moulding technique was applied for the composite manufacture. The epoxy

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour

447

resin was cured at 120°C for six hours, and the polyester resin was cured at 50°C for 24 hours. The nominal fibre volume fraction was 55%. Crack bridging tests The specimen width b was 5 mm with a beam height of H=8 mm (FIGURE 1). The length of the specimen was 145 mm. The notch, cut with a 0.7mm diamond saw for a length of 36 mm, was parallel to the fibre direction and perpendicular to the plane of the plate. The subsequent crack growth was therefore intralaminar. At least 5 specimens of each fibre/ matrix type were tested. Extensometers were mounted at each face of the specimens just at the end of the notch to record 6 as a function of the applied bending moment. The crosshead displacement was kept at 2 mm/min, which corresponds to 0.15mm/min for the end opening rate d8*/dt (t denotes time). EXPERIMENTAL RESULTS With increasing applied moment, crack propagation took place. Fibre cross-over bridging developed in the zone between the notch and the crack tip. FIGURE 2 shows the bridging fibre ligaments for the different systems at the end of the test. With increasing opening, the bridging fibres eventually broke at the end of the notch for the epoxy systems. This point represented the start of the steady state cracking, where the bridging length remained approximately the same, and the bridging zone moved forward with the crack tip advancing into the specimen. The behaviour is nearly identical for the other epoxy composite. For the polyester resin systems, crack bridging was considerably more extensive.

(a) sizing A/ epoxy

(b) sizing B/ epoxy

(c) sizing A/ polyester

(d) sizing B/ polyester

FIGURE 2 Crack bridging behaviour of composite systems

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour

448

JR is calculated according to equation (1). Assuming that the unidirectional composite is transversely isotropic, the following elastic composite data were applied for equation (1) as previously measured: EnjepOxy= 41.5 GPa, E33= 9.2 GPa, En, polyester = 42 GPa, E33, pOiyester= 10 GPa and vi3=0.3 (assumption). The function 1/2

for8*<8 n

<(§*)= Jo

(4)

was found to fit all experimental data curves well, resulting in curve fits for the crack growth resistance JR as shown in FIGURE 3(a). Jo is the initial value of the experimental curve and equal to the fracture energy of the tip during crack growth, while AJSS, which is equal to (Jss-Jo), is the increase in crack growth resistance. S0rensen and Jacobsen [2] found that the same function fit the data of carbon fibre composite systems well. 6000 -•—A/ epoxy -"- B / epoxy —*-A/polyester ~»--B/ polyester

I 2

4000

E 1

2000

f

—•—A:/ epoxy -•- Bi/ epoxy -*-A'l polyester --•—Bi/polyester

£5

o

2 4 6 Crack opening [mm]

CO

^•^—f-"*—•0

8

MM*—ft—m-

2 4 6 Crack opening [mm]

(a)

(b)

FIGURE 3 Comparison of (a) crack growth resistance and (b) resulting crack bridging laws

The experimental values for the bridging laws are given in TABLE I. The starting value Jo indicates the point of crack growth initiation and can easily be determined during the experiment. The highest value of 355 J/m2 was observed for the sizing B/ epoxy system. The crack initiation value is significantly lower for the sizing B/ polyester system with 115 J/m2, which also relates to a significantly lower transverse strength of not more than half the transverse strength of the other composites [3]. TABLE I Experimental bridging law parameters for the different fibre/matrix systems Composite system sizing A/ epoxy sizing B/ epoxy sizing A/ polyester sizing B/ polyester

Jo [J/m2] 300±40 355±15 170±20 115±45

AJSS [J/m2l 4000±1000 3700±500 -3800 >4100

So [mm] 2.0±0.2 2.0±0.2 -5.5 >5.0

X [kPa m1'2] 44.7 41.4 25.6 29.0

The end opening value 5o at the onset of steady-state cracking was determined to be 2 mm for the epoxy systems. For the sizing B/ polyester system, steady-state cracking could not be determined with the present specimens, as the fibres continued to bridge

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour

449

the whole length of the crack after the maximum measurable end opening of 5 mm was obtained. Since no upper bound was found for AJSS, this bridging behaviour was termed 'infinite toughening'. Differentiating equation (4) according to (3) results in the bridging law

The bridging laws for the different fibre systems are compared in FIGURE 3(b). The bridging law can be considered a material property [6,7] and is in an accessible form for implementation in finite element codes with spring elements or cohesive elements. MICROMECHANICAL DISCUSSION Smaller DCB specimens (H=4 mm, b=5 mm) were loaded in a similar fashion within the environmental scanning electron microscope to study the crack development. FIGURE 4 shows the difference between two systems.

(a) sizing A/ epoxy

ISOum — C ' l OOum (b) sizing B/ polyester FIGURE 4: Micromechanical differences in fibre bridging for strong (a) and weak (b) interphase

For the strong composite, moderate fibre bridging is observed, where the ligaments mostly consist of around four fibres. These bridges tend to break at higher loads. For the weak composite, on the other hand, extensive bridging can be seen. With increasing crack front, the bridging ligaments separate and multiple crack fronts develop. Like for previous SEM results [2,7], the model in FIGURE 5 appears to provide a reasonable description of fibre bridging. The bridging ligaments are considered as short beams of rectangular section, capable of deforming in shear and bending. During loading, they peel away by overcoming an interfacial fracture energy, Fj. For single fibre bridging, this value is the fibre/ matrix interfacial fracture energy, while it must also include some fracture energy of the matrix itself if multiple-fibre ligament bridging is present.

450

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour

FIGURE 5 Cantilever beam used for micromechanical modelling of ligament bridging

The displacement relationship is derived in [7]. Neglecting shear deformation, the crack bridging stress can be related to 5 as [2] _1.373N(El) l/4 (wr i ) 3/ ~

(6)

gl/2

The bridging stress is a function of the number of bridging ligaments per unit area N (#/area), the ligament modulus E, width w and thickness 2t (resulting in a second moment of area I), and the interfacial fracture energy IV The micromechanical bridging law has a similar form as the measured experimental bridging law. Comparison of macro-equation (5) and micro-equation (6) leads to AJS • = 1313N{EljH{wT f"=X. i

(7)

The material parameter A, is constant for each composite system (see TABLE I). TABLE II summarises the micromechanical parameters. From the micrographs in FIGURE 4, the parameters 2t and n can be determined, where n is the number of ligaments for a given length. The width w of the ligament is assumed, and the number of ligaments per unit area N is extrapolated with the values of w and n by presuming evenly distributed ligament density. TABLE II Micromechanical parameters and predicted interfacial fracture energy Ligament parameters Modulus E [GPa] Ligament width w [\un] Ligament height 2t [|im] Number of bridging ligaments n [#/mm] Number of bridging ligaments N [#/mz] Interfacial fracture energy Fi [J/m2]

Sizing A / epoxy 41.5 -100 100 2/2 1E7 690

Sizing B / Polyester 42 -100 150 (before separation) 5/4 1.25E7 190

The interfacial fracture energy Fj is calculated from equation (7). The values are rather large with 690 J/m2 and 190 J/m2, as the literature reports values of around 100 J/m2 [8]. However, TABLE assumes that the surface observations from FIGURE 4 represent the internal bridging state. 3D tomography is currently undertaken to estimate the number of bridging ligaments in more detail. The micromechanical

Influence of Fibre/Matrix Interphase on Crack Bridging Behaviour

451

model, however, results in a reasonable difference of the interfacial fracture energy of the two composite systems. CONCLUSIONS The article emphasises that the characteristics of the interphase between fibre and matrix have a strong impact on the fracture toughness of a given composite material. Bridging laws were derived for four different composite systems from DCB specimens with mode I crack growth parallel to the fibres. These bridging laws can be considered material parameters and can easily be implemented in finite element codes. The article furthermore investigates micromechanical parameters during the development of bridging ligaments by studying in-situ micrographs. The interfacial fracture energy is linked to the ligament geometry. It is shown that a sufficiently small interfacial fracture energy can then lead to 'infinite toughening', where no upper bound can be found for the crack growth resistance as fibres continue to peel away from the composite material without fracture.

REFERENCES 1. Rice, J. R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of applied mechanics. 1968, 35, 379-386. 2. S0rensen, B. F. and Jacobsen, T. K. Large-scale bridging in composites: R-curves and bridging laws. Composites: Part A. 1998, 29A, 1443-1451. 3. Feih, S., Wei, J., Kingshott, P. K., and S0rensen, B. F. The influence of fibre sizing on strength and fracture toughness of glass fibre reinforced composites. Composites: Part A. 2003, submitted. 4. Suo, Z., Bao, G., and Fan, B. Delamination R-curve phenomena due to damage. Journal of Mechanics and Physics in Solids. 1992, 40(1), 1-16. 5. Wei, J., Feih, S., and Kingshott, P. K. 2003, to be submitted 6. S0rensen, B. F. and Jacobsen, T. K. Crack growth in composites: Applicability of R-curves and bridging laws. Plastics, Rubber and Composites. 2000, 29(3), 119-133. 7. Spearing, S. M. and Evans, A. G. The role of fibre bridging in the delamination resistance of fiber-reinforced composites. Acta Metallica Materials. 1992, 40(9), 2191-2199. 8. Kim, B. W. and Nairn, J. A. Observation of fiber fracture and interfacial debonding phenomena. Journal of composite materials. 2002, 36(15), 1825-1858.

Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures Ashraf T. Mohamed* Professor, Production and Design Department, Faculty of Engineering, Minia University, Minia 61111, Egypt ABSTRACT Monolithic carbon, carbon/carbon composites, discontinuous fiber carbon/carbon composites, continuous fiber carbon/carbon composites and three different surface treatments silicon carbide/alumina composites has been tested at temperature ranges from 20°C to 1650°C. The tested specimen results are compared at various specimens orientations using two notch shapes. Two-dimensional three-point-bend SENB specimens, with both chevron-and straight-notch configurations were used to evaluate the resistance to crack initiation and crack propagation, in different orientations with respect to the reinforcement. The effect of temperature, elastic properties, weight loss by oxidation on the fracture process variables is carried out and investigated. INTRODUCTION Metal matrix composites are a new class of materials which find several industrial applications and form a new generation of materials. They are difficult to machine mechanically due to the presence of a hard ceramic phase. Shirakashi and Obikawa [1], discussed the transition condition of the machining mechanism from a brittle mode to a gentle one from the view-point of the size effect of brittle fracture using FEM simulation. Quan and Ye [2], concluded that the residual stress maybe released due to structural defects at the surface of composites reinforced by coarse SiC particles, for composites reinforced by fine particles there is a tendency for compressive residual stress in the surface. Cutting with a larger removal rate increases the possibility for tensile residual stress in the machined surface layer. The fracture toughness of the composites were much lower than that of the unreinforced alloy. Mohamed et al. [3] investigated the effect of hard reinforcements on the Al composites, also Mohamed et al. [4-6] developed a model to describe the densification mechanisms in isostatic pressing of the aluminium composites, discussed the effect of particle size on the composites properties and illustrated the relation between the elastic constants and the particle deformation of these composites. Oleszak [7], focused on the influence of consolidation methods and parameters on the density and final microstructures (crystallite size). Sima et al. [8], performed the MA process with Al-matrix powders reinforced by the hybrid mixture: SiC + Graphite in a high-energy ball mill in argon atmosphere, the influence of the graphite particles on the sintering response of the hybrid composite powders is discussed. Besterci [9], prepared dispersion strengthened aluminium compacts with dispersed ceramic particles by powder metallurgy. Carbon transformation to carbide AI4C3 is characterized. Over the recent years, there has been an increasing interest in using fiberreinforced composite (FRC) materials because of their superior properties such as high strength, low weight and high corrosion resistance [10]. Development of Al • Corresponding author. Email: [email protected]

Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures

453

alloys has led to materials which can challenge many other engineering materials in terms of specific strength. To compare failure events in different types of brittle materials, this research addresses two composite types, carbon fiber/carbon matrix composites with both continuous and discontinuous fibers, and a series of silicon carbide whiskers/alumina matrix composites differing by the nature of whisker/matrix interfacial film. The discontinuous fiber carbon/carbon material will be fully characterized in terms of fracture parameters. The fracture characterization includes measurements of the plane strain fracture toughness (Kic) and computations of the crack growth resistance curves (R-curves). The influence of temperature, elastic properties, weight loss by oxidation on the fracture process is investigated. EXPERIMENTAL PROCEDURES Materials A monophase commercial polycrystalline graphite material has been used to determine its fracture properties. The average grain size of 5 to 10 urn and the density was 1.795 g/cm3. The material was received in the form of plates [7]. The discontinuous fiber carbon/carbon composite material was developed for use in aircraft brake components. The 6-7|am diameter fibers are pyrolyzed from a polyacrylonitrile (PAN) precursor. Their outer surfaces have ridges running parallel to the fiber axes with 1.54 g/cm3 density and a total porosity of 16%. The fiber volume fraction is 40%. The two-dimensional woven continuous fiber carbon/carbon composite (ACC4) has a density of 1.68 g/cm3, and the fiber volume fraction is 45%. Three types (A, B and C) plates with 10 mm thickness of silicon carbide whisker reinforced alumina matrix composites were examined, they comprise of 25% of SiC in volume in the form of high aspect ratio whiskers. The density of A12O3 composites is 3.77g/cm3. Type A and B materials differ only by the surface chemistry of the whiskers. Type C material, the whisker/matrix interface chemistry was less controlled than for type A material. Type A whiskers material were subjected tocleaning heat treatment and chemical treatment, which removed the surface carbon layer and left a surface with siliceous elements. The type B whiskers remained coated with 10A thick film of carbon residues that promotes whisker pullout during fracture by lowering the frictional stresses. Fracture Tests The Young's modulus, fracture toughness, strength values, as well as crack growth resistance curves have been obtained for various specimen orientations, up to 1650 °C. Fracture testing was carried out on a screw-driven, displacement-controlled load frame having a room temperature compliance of 0.03 |im/Kg, with a 10000 kgf load capacity. A 200 Kg self-identifying load cell was used for all tests, which allowed simple calibration and balancing. Modulus of Elasticity (E) and Modulus of Rupture (MOR). For a measured load, P, and a displacement, u, both Young's modulus, E, and strength (modulus of rupture), Op, are; u = (PL3 / 48 El) (1) E = (P/u) (L3 / 4BW3), and (2)

454

Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures CTF = (3/2) * (Pmax * L) / (BW2).

(3)

R-Curves and Fracture Toughness. The calculated stress intensity factor K is equal to the crack growth resistance parameter KR when the load Pj reaches its maximum, Pmax, the critical fracture toughness is obtained by; Kic = P max Y ac ,/BVW. (4) Where Yact is the geometry correction factor obtained through the fracture parameters calculation sequence at the point where Pmax occurs. In this last case, since the R curve analysis starts at Pmax , the Kic data point is also the first point of the KR curve [7]. RESULTS AND DISCUSSIONS Moduli of Elasticity and Rupture Figure 1 shows the temperature effect on the elastic modulus of the monolithic carbon and alumina, Kobe C/C, ACC4, AlaCVSiC (type A). The essential role of the carbon fiber reinforcement in the improvement of elastic properties will be shown to be 4 to 6 times greater by fiber addition. They are representative of the range of stiffness of the carbon matrix phases in the carbon/carbon composites. The monolithic alumina and A^C^/SiC show a gradual decrease of elastic modulus with temperature up to 1000 °C and a rapid decrement at higher temperatures due to the silica-based grain boundary phase and the material softening. The composite elastic modulus trend is higher due to its higher strength. Figure 2 shows that the L-T (the first letter refers to the specimens length direction normal to the crack plane, and the second letter indicates the crack propagation direction) and T-L orientations tests consistently outperform their respective L-S and T-S orientations, by approximately 20%. This difference shows that the in-plane (LT) isotropy is not experimentally verified. This unexpected anisotropy will also be confirmed by a similar trend observed for the toughness. The L-T and T-L orientations are stiffer and stronger than their respective L-S and T-S orientations, in consistent with the composite laminar nature. The elastic properties follow the same trend as the strength data shown in Figures 3 and 4. The observed decrease of the elastic modulus and strength with increasing temperature is inconsistent with the mechanical behaviour of carbon materials, which indicate stiffening and strengthening at high temperatures [6]. This is attributed to weight loss by oxidation. Moreover, oxidation has been reported to degrade the material in a 150 |jm thick surface layer. This results in increasing the maximum flaw size and decreasing MOR strength values. Oxidation of The Carbon/Carbon Composite. As shown in Fig. 5, the minimum relative weight loss remains near 13% for a maximum argon flow of 18cf/h. This graph evidences the beneficial influence of an inert atmosphere to avoid degradation of carbon/carbon materials. For maximum thermal protection of the furnace, the minimum final weight loss has been to be 4.5%. This value is high compared to 0.5% weight loss measured under vacuum, but is nevertheless representative of realistic environmental service conditions. This level of oxidation must be taken into account to compensate mechanical properties deterioration.

Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures

455

Load/Displacement (LPD) Relation Fig. 6 shows the LPD of monolithic graphite for L-S and L-T orientation at different temperatures. The curves are remarkably unchanged over this range of test temperatures as opposed to the case of monolithic alumina and AI2O3 composites shown in Figs 7 and 8. This suggests that the temperature-independent mechanical behaviour of graphite over this range result from stable interfacial characteristics not available from the glassy intergranular phase of alumina. For Kobe C/C composite, the load-point-displacement (LPD) results for typical chevron-notch fracture tests of both L-T and L-S orientations are presented respectively in Fig. 9 from 20 to 1650°C. The L-S and T-S curves are characterized by frequent load drops which correspond to run-arrest crack propagation, which is also consistent with the fracture surface appearance. These load drops are associated with the massive fiber groups failure as crack advances through the layered structure. Deviation from linearity of LPD curve observed prior to Pmax, accentuated for L-S specimens attributed to matrix cracking. This results in increasing subcritical crack growth experienced by the L-S over that of L-T specimens. A comparison of the composites load-displacement plots obtained at 1400°C are shown in Fig. 8, type A supports much more load than the two other types. The behavior of type A, consistent throughout the entire tests compared to type B and C. A slightly higher softening temperature of the type A glassy interface, enhancing the friction at the whisker/matrix interface be the cause for such improvement. Crack Growth Resistance (KR). The fracture surface energy, GR, VS. dimensionless crack length for monolithic graphite and cobe C/C are shown in Fig. 10. The slopes of each of the L-S curves exceed those of the respective L-T orientation specimens by a factor of about two. This fracture behaviour is consistent with the relatively large area under the corresponding LPD curves, and reflects the increased energy consumed by local delamination, greater fiber pullout, and more extensive matrix damage associated with this crack orientation. Critical Stress Intensity (Kic) and Notch Shape Effect. Fig. 11 presents the K K data as a function of test temperature for the L-T and L-S orientations. The toughness of this material is lightly rising with temperature, the difference between the L-S and L-T orientations signifies that the crack encounters more resistance to propagate through the thickness of the material, in the compaction direction (S). Fig. 12 presents the variations of KIC data with temperature, for each of the specimen notch configurations tested in both the L-T and T-L orientations. The chevron-notch "Kic" values fall between 8.0 and 11.6 MpaVm, and increase slightly with slightly with increasing test temperature. The Kic values for both notch types of the L-T orientation specimen are 10 to 20% higher than the corresponding T-L values, and the L-S KIC values consistently exceed those of the T-S orientation. CONCLUSIONS 1. The fracture behavior of monolithic graphite, carbon/carbon composites, monolithic alumina (AI2O3) and three SiC whisker-reinforced alumina composites (A^Oa/SiCw) has been carried out successfully at the temperature range of 20°C to 1400°C. 2. In all AI2O3 /SiCw composites, it was found that the whiskers and test temperature enhance both the fracture toughness and crack growth resistance compared to the monolithic A12O3.

456

Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures

3. The whisker surface treatment has a remarkable effect on the composite properties. 4. The notch shape has a prominent effect on the composite fracture toughness and the crack growth resistance. The chevron notch effect is better than the straight notch. 5. The Kobe C/C composite exhibited an increase stress intensity factor with crack length, demonstrating the existence of commutative toughening mechanisms. REFERENCES 1.

Shirakashi, T. and T. Obika. 2003. "Feasibility of gentle mode machining of brittle materials and its condition," J. of Mat. Processing Technology., 138/1-3: 522-526. 2. Quan, Y. and B. Ye. 2003. "The effect of machining on the surface properties of SiC/Al Composites, "_J. of Mat. Processing Technology., 138/1-3: 464-467. 3. Ashraf, T.M., Y.M. Ismaiel, T.M. Salem and K.A. Khaliel. 1995. "An Investigation Into The Production of Al/Fe and Al/SiC Composites Using The Compaction Technique," The 4th AlAzhar Univ. Eng. Int. Conf, Nasr City, Cairo., December 16 - 19, 1995. pp. 155-166. 4. Chen, Y.C., T.M. Ashraf, H. Rahman and K. Salama. 1998. "Powder Densification Mechanism of Metal Matrix Composite Materials," The Fifth International Conference on Composite Engineering ICCE/5, Nevada, USA, July 5-11, 1998. pp. 791-792. 5. Ashraf, T.M., M.H. Rahman, Y.C. Chen and K. Salama. 1998. "Relationship Between Elastic Constants and Particle Deformation in Metal Matrix Composites," Review of Progress in Quantitative NDE,, Snowbird, Utah, USA. July 19-24, 1998. pp. 20-29. 6. Rahman, M.H., A. T. Mohamed, Y.C. Chen and K. Salama. 1998. "Ultrasonic Velocity Measurements Applied to Process Control of Metal Matrix Composites Densification," Review of Progress in Quantitative NDE, Snowbird. Utah, USA. July 19-24, 1998. pp. 40-49. 7. Oleszak, D. 2003. "Intermetallic Matrix Composites Reinforced with Alumina Prepared by Reactive Milling and Consolidation of The Powders,"_The 4th Int. Conf. on Mechanochemistry and Mechanical Alloying (INCOME 2003). Braunschweig, Germany. 7-11 Sept., 2003. p. 43. 8. Sima,G., O.Gingu and M. Mangra. 2003. "Sintering Response of the Mechanically Alloyed Hybride Composite Powders Al/SiC+Graphite," The 4th Int. Conf. on Mechanochemistry and Mechanical Alloying (INCOME 2003). Braunschweig, Germany. 7-11 Sep.,2003. p. 133. 9. Besterci, M. 2003. "Kinetics of Mechanical Alloying, Microstracture and Properties of A1-A14C3 System," The Fourth International Conference on Mechanochemistry and Mechanical Alloying (INCOME 2003). Braunschweig, Germany. 7-11 September, 2003. p. 73. 10. Ashraf, T.M. 2000. pp. 714-720. "The Reinforcement Surface Treatment Influence on The Fracture Bending of The Ceramic Composites" "I", Proceedings of The ACUN-2, Int. Conference: Composites in The Transportation Industry, Sydney, Australia, pp. 714-720. 450 400

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Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures

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FIGURE 6 Load/displacement relation of monolithic graphite at L-S and L-T orientations.

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Behavior of Brittle Reinforced Composites Fracture at Elevated Temperatures

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Part IX

Impact

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Non-woven Fabric Reinforced Cellular Textile Composites with Improved Energy Absorption Capacity S.W. Lam1*, X.M. Tao ', and T.X. Yu 2 "^Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong 2 Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Hong Kong

ABSTRACT Flat-topped grid-dome cellular composites made of non-woven PET fabric reinforcement with polypropylene (PP) matrix were subjected to quasi-static axial compression and impact conditions. The mechanism of deformation and the energy absorption characteristics of the cells were studied. Based on the observations of the cell deformation mode, analytical expressions were formulated to find the mean peak value and thus the energy absorption capacity of the cellular structure. The results obtained are in good agreement with the experimental results.

INTRODUCTION Textile materials to be designed specifically to form three-dimensional structure may absorb large amounts of energy with light-weight. Tao and Yu [1-3] investigated a range of cellular textile composite structures in terms of energy absorption behavior under both quasi-static compression and impact conditions, including circular and square tubular knitted, multi-layer 3D woven, non-woven spun sponded and grid-domed cells projected from knitted fabric. They have identified that the grid-domed cellular structure possesses the highest specific energy absorbing capacity among all the cell configurations, which is also greater than that of polyester foams of identical density, hi their studies, knitted fabrics were used to fabricate the cellular textile composites due to its excellent drapability with acceptable mechanical properties [4]. Replacement of the fabric reinforcement by non-woven fabric has shown the improved performance on the energy absorption capacity under dynamic response with more beneficial during manufacturing [5]. hi the present study, flat-topped grid-dome composite cells made of PET non-woven fabric reinforced in PP matrix were subjected to quasi-static axial compression and impact conditions. By observing the deformation mode during the compression process, an analytical model is proposed to predict the energy absorption capacity of the flat-topped grid dome cellular composites with isotropic reinforcement.

Lam S.W., Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Fax: (852) 2773 1432, Email: [email protected]

Non-woven Fabric Reinforced Cellular Textile Composites

462 EXPERIMENTAL

Specimens and Experiments The cellular composites comprised a commercial PET non-woven fabric and polypropylene films were fabricated by compression molding. The number of non-woven fabric layers and PP matrix films for molding the composite depends on the fibre volume fraction required. Fabrication was detailed described in [5]. Figure 1 shows the dimension details of the cellular structure. Grid-dome cellular samples made of pure PP material, having the same dimension as described in the compression-molded samples, were prepared by injection molding. The quasi-static compression test was performed on the cellular composites and the pure PP cellular samples using the MTS Universal Material Tester with a crosshead speed of 5 mm/min. Each specimen containing four conical cells was used the test. The deformation mechanism of the cellular composites was observed on a single cell only. The impact tests were conducted on a Dynatup Drop Weight Impact Tester (Model GRC8250). The mass of a drop weight (6.61 kg) included a plate striker of 120 mm X 120 mm X 12 mm, which was normal to the plane of the samples. The selected impact velocity was 6.0 m/s by adjusting the height of the drop weight and the air pressure of the pneumatic assist. Specimens were put on the supporting base of the testers and were impacted by a flat steel plate. 18mm

15 mm : 1 6

Centre distance: 23 mm

FIGURE 1

Schematic geometry of the grid-dome sample

RESULTS AND DISCUSSION Quasi-static Compression and Impact Tests Typical load-displacement curves of the cellular samples (ranged from 0 to 0.38 fibre volume fractions) under axial compression and impact conditions are shown in Fig. 2. With the increase of the fibre volume fraction in non-woven PET samples, the energy absorption capacity reduces by approximately 30 % at 38 % fibre volume under quasi-static compression. However, it is shown that pure PP matrix is brittle under impact. Increase in fibre volume fractions in non-woven composites has shown the improvement on the material ductility and a significant reduction on the peak load.

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Observation on the Cell Deformation It is observed that both the isotropic pure PP and the non-woven PET/PP cellular samples deformed in the same pattern as a ring on the cell walls, which is different from the previous study by Xue et al [6] on the cellular composites with knitted fabric reinforcement that deform into a two-lobe diamond pattern. Figure 3 shows the deformation process: (1) the flat top was bent inwards during the large deformation process; (2) the flat-topped conical shell plastically collapsed inwards to form a ring pattern; (3) circumferential hinge lines were observed when the loading plate was removed.

ft* FIGURE 3 Deformation process of a cell made of pure PP material under quasi-static compression at a loading speed of 5 mm/min.

Prediction of the Energy Absorption Capacity Figure 4 shows a flat-topped grid-dome cell of semi-apical angle (/) , cell height L, diameters D and d, collapsed inwards during axial compression. The assumptions are made for our model: (1) the cell wall collapses internally with a circular plastic hinge between the top and bottom; (2) the top circle remains unchanged during deformation; (3) the effect of the cell top deformation is negligible; (4) the values of xi and X2, the length variables referring to Fig. 4, are the same as those measured from the experiment.

Non-woven Fabric Reinforced Cellular Textile Composites

464

FIGURE 4

Deformation mode of a flat-topped conical cell forming internal convolution

Let (j> represent the semi-apical angle of the conical shell. After deformation, sides AB and BC will deviate from the original position with angles/? a n d # , respectively. The geometry relations for an increment d8 of the deflection can be obtained: x2 sin {6 + (ft) = (x, + x 2 ) sin (j> + xx sin (/? - (fi)

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(3;

(4;

w=wb+wm The corresponding mean post-buckling load is

V3 To verify the theoretical model, two sets of samples, i.e. the pure PP and non-woven PET/PP samples were made possessing the same cell parameters: semi-apical angle=16°, cell height Z=15mm, Z>=10mm, cf=18mm, while little difference on the cell wall thickness measured were £pp=1.15mm and />jw=1.0mm,

(5)

(6)

Non-woven Fabric Reinforced Cellular Textile Composites

465

respectively. The mean peak load and the energy absorption capacity predicted by the theoretical model are obtained and compared with those obtained from experiments, as summarized in Table I. The deviation comes up with 5.5% for the prediction on the PP samples, but only 2% on the non-woven PET/PP samples. The difference between the predicted and the experimental results may be attributed to the negligence of the deformation of the cell top, the non-uniformity of the non-woven fabric reinforced composites and the experimental measure errors on the deformation mode. TABLE I Sample PP FV3

Measured and predicted energy absorption capacity for a single . Buckling load (KN) Mean Maximum peak P (kNmm 2 ) load (,Pmax) Theor. Exp. 0.03365 1.310 1.130 1.071 0.670 0.02338 0.957 0.684

cell until collapse Energy absorption capacity (J) Exp. Theor. 11.78 12.43 7.52 7.37

CONCLUSION The cellular composites with non-woven PET fabric reinforcement in polypropylene matrix behave differently under quasi-static compression and impact conditions. A theoretical model is presented and it is able to predict the mean peak load and energy absorbing capacity of a cell during plastic collapse. The theoretical predictions for pure material or non-woven reinforced composite are all in good agreement with the experimental results, so it could provide a basis for the effective design of similar material systems.

ACKNOWLEDGMENT Miss Lam would like to acknowledge the postgraduate scholarship from The Hong Kong Polytechnic University Research Grants. REFERENCES 1. 2. 3. 4.

5. 6.

Yu T.X., Tao X.M., and Xue P. The energy-absorbing capacity of grid-domed textile composites. Composites Science and Technology. 2000; 60: 785-800. Tao X.M., Yu T.X., Ngan K.M., and Ko F.K. Energy absorption of cellular textile composite under quasi-static compression. In: Proceedings of ICCE-4. Hawaii, USA, July, 1997. p.981-2. Yu T.X., Tao X.M., and Wu K.Q. Energy absorption of cellular textile composite under impact. In: Proceedings of ICCE-4. Hawaii, USA, July, 1997. p.1099-100. Ramakrishna S., Hamada H., Cuong N.K., and Maekawa Z. Mechanical properties of knitted fabric reinforced thermoplastic composites. In: Proceedings of ICCM-10. Whistler, Canada, 1995. p.245-252. Lam S.W., Tao X.M., and Yu T.X. Comparison of different thermoplastic cellular textile composites on their energy absorption capacity, Composites Science and Technology, in press. Xue P., Yu T.X., and Tao X.M. Flat-topped conical shell under axial compression. International Journal of Mechanical Sciences. 2001; 43(9): 2125-2145.

Energy Absorption Properties of Braided Composite Tubes Masanori Okano, Kenichi Sugimoto, Asami Nakai* and Hiroyuki Hamada Kyoto Institute of Technology, Japan

ABSTRACT In this paper, the influence of material properties with respect to the middle-end-fiber inserted into braided composite tube on the energy absorption characteristic was investigated. The static compression tests by using three types of braided composite tube were carried out and crushing mechanisms based on precise cross-sectional observation of crush zone were discussed. It is considered that the energy absorption capability depends on the rupture elongation of the middle-end-fiber. Because the fiber is broken easily in the case of the fiber with small rupture elongation, it is considered that the energy absorbed by bending of fronds is very low. Thus, the energy required for fiber fracture is low and the energy absorption properties become low because of the low bending energy.

INTRODUCTION An important aspect of the crushing performance of a material is its specific energy absorption value which is much greater for polymeric composites than for conventional metallic materials. Many researches have studied the energy absorption characteristics of polymer composite materials [1-3]. It was clear that crushing mechanism and specific energy absorption of composite tubes depend on hoop-to-axial ratios for a fiber arrangement. Textiles such as weaving, knitting and braiding, have often been used as reinforcements of composite materials. Figure 1 shows a schematic of a triaxial braided structure. Multiple yarns are intertwined on a mandrel to form tubular shape. The triaxial braiding consists of three types of fiber orientation, 0°, +6° and -6°. In particular, the braiding has the characteristic that fibers are oriented continuously. Braiding yarns make braiding angles (±0°) with axis of the braided fabric. 0° yarns named middle-end-fiber can be inserted into braided fabric. It is easy to vary mechanical properties in the hoop direction and in the axial direction by arranging braiding angle and types of fibers. In previous study, it was not proven how the energy absorption capability was affected by middle-end-fiber. Hence this necessitates development of a design methodology of braided composites. In this paper, it was investigated how the energy absorption characteristic was influenced by the material properties of the middle-end-fiber. Hence the static test by using various braided composite tube were carried out and crushing mechanisms based on precise cross-sectional observation of crush zone were discussed. * corresponding author: Gosyo-kaidoucyo, Matsugasaki, Sakyo-ku, Kyoto, 606-8585, JAPAN FAX: +81-75-724-7800 E-mail: [email protected]

Energy Absorption Properties of Braided Composite Tubes

467

Braiding angle

-e . +e

Braiding fiber

Middle-end-fiber

Longitudinal direction

Trsnswse direction

FIGURE 1 Schematic illustration of circular braided fabric

MATERIALS AND EXPERIMENTAL METHOD In this study, three types of the fiber; T700, T1000 and XN60 were chosen as the middle-end-fiber. Table 1 shows the material properties of T700, T1000 and XN60. Here, T1000 fiber is called the high strength fiber in which the tensile strength has higher than T700 fiber and XN60 fiber is called the high modulus fiber in which the tensile modulus has higher than T700 fiber. At first, the three-point bending test was performed to clarify bending properties of three types of the fiber. Three types of the specimen were fabricated by using only T700, T1000 and XN60 respectively. Epoxy resin was employed as matrix. The specimens for the bending test were cut along the longitudinal direction of the fiber. Geometry of the specimen was 2.0mm in thickness and 15mm in width. A span length was 80mm. The tests were performed by INSTRON testing machine at a cross-head speed of 2.0mm/min. Secondarily, three types of braided composite tubes were manufactured by inserting T700, T1000 and XN60 into braided tubes as the middle-end-fiber. Table 2 lists the specifications of the fabricated tubes. The type of braided yarn in all the tubes was carbon fiber, T700. Epoxy resin was employed as matrix similarly. Filaments of fiber bundles for the middle-end-fiber were adjusted to achieve the minimum differences in percentage of total fiber volume fraction of 0° yarn in each tube. Laminated structures were used to achieve the required thickness. Two braiding angles were used, which were 60° for the innermost layer and 30° for other layers. The fiber volume fraction was approximately 50% in each tube. The inside diameter was 50mm and the thickness was approximately 3.2mm. The height of specimen for static test was 100mm. In order initiate progressive crushing, 45° chamfer was made at either end of the specimens. The compression tests were performed by using INSTRON testing machine at a constant cross-head speed of 5.0mm/min.

468

Energy Absorption Properties of Braided Composite Tubes TABLE I. Material properties of the T700, T1000 and XN60 fiber

Type of fiber Tensile strength [MPa] Tensile modulus [GPa] Elongation [%]

T700|T1000|XN60 4900 6370 3530 230 294 590 2.1 2.2 0.6

TABLE II. Specification of the braided composite tubes Name of specimen Number of ply

Normal High strength High modulus 8 8 8 30° T700 T700

30°

30°

T700 T1000

T700 XN60

Fiber volume fraction of total middle-end-fiber [%]

22.9

24.3

24.3

Inside diameter [mm] Outside diameter [mm] Thickness [mm]

50.0 56.5 3.25

50.0 56.6 3.29

50.0 56.4 3.18

Layer

Braiding angle Braided yarn Middle-end-fiber

BENDING TEST Figure 2 shows the results of the load-deflection curves and Table 3 shows the results of the bending strength and bending modulus for each specimen. From the 1-d curves, it was shown that the maximum load of T700 fiber and T1000 fiber was higher than that of XN60. And also, the bending strength of T700 fiber and T1000 fiber were about 2.5 times as high as that of XN60 fiber. In respect to bending modulus, XN60 fiber showed the highest value of all specimens. On the other hand, comparing the T700 fiber with T1000 fiber, there was no almost difference of the bending strength between T700 fiber and T1000 fiber. CRUSHING TEST Typical load-displacement curves obtained from static testing of three tubes are shown in Figure 3. For the normal specimen and the high strength specimen, two curves showed a similar tendency. Initially, the load decreased rapidly drastically after the rapid increases of the loads. After the gradual increase of the load, the load kept a high value. However, for the high modulus specimen, the value of the load was very lower than that of two others. The results of mean crush load and specific energy absorption value, or Es value of each specimen are given in Table 4. The values of the loads of normal specimen and high strength specimen were almost same value. On the other hand, the value of the mean crush load of high modulus specimen was very lower than that of two others. Es values of normal and high strength specimens showed almost same and 1.5 times as high as that of high modulus specimen.

Energy Absorption Properties of Braided Composite Tubes i

469

.\J

T700 T1000 XN60

0.8 _ 0.6 0.4 -

TABLE III Results of bending strength and bending modulus

A y\

/ y^

0.2

5 10 Deflection [mm]

15

Type of Bending strength Bending modulus specimen fGPal [MPal T700 98 1368 130 T1000 1287 XN60 255 539

FIGURE 2 Load-deflection curves in bending test

100 - The high strength specimen

TABLE IV Results of mean crush load and specific energy absorption value

The normal specimen

igh modulus specimen

Type of specimen

20

10 20 30 Displacement [mm]

40

normal high strength high modulus

Specific energy mean crush load absorption value P[kN] Es [kJ/kRl 71.7 60.8 60.2 71.8 47.6 38.3

FIGURE 3 Load-displacement curves in static test

In order to investigate the crushing mechanism, detailed photographs and schematic illustrations of cross sections cut through the crush zones parallel to the axis of each specimen are shown in Figure 4 and Figure 5 respectively. For the normal specimen, the fronds spread inwards and outwards with central crack and many fragments were observed. A debris wedge was seen between fronds. For the high strength specimen, the fronds spread out toward inner and outer side with central crack similarly and many fragments were observed. A debris wedge was observed between fronds. For the high modulus specimen, the fronds spread out toward both sides with central crack. With respect to the central crack, the length of the central crack of the normal specimen was almost the same as that of the high strength specimen. However, the central crack of the high modulus specimen was shorter than those of two others and the curvature of fronds and the fragment were also small compared with those of two others. A clear debris wedge was not seen.

470

Energy Absorption Properties of Braided Composite Tubes

ENERGY ABSORPTION DURING CRUSHING The total energy (UT) absorbed during crushing is given by equation (1). UT=Uff(

Ubend ( Uic))+ Usf+ Ufr + others

(1)

where Uic is the energy required for longitudinal cracking of the pipe wall, USf is the energy absorbed by the splitting of fronds into beams, Ubend is the energy absorbed by bending of fronds, Uff is the energy required for fiber fracture and Ujr is the energy associated with frictional heating. In addition to these five main mechanisms, there are other fracture processes, such as splitting of the pipe wall into fronds along the circumference of the pipe, which contribute to the overall energy absorption. And Uff( Ubend ( Uic)) means that Ubend is function of C//c and Uff is function of UbendIf the crack which propagates in initial stage is short, the energy absorbed by bending of fronds is high. Subsequently, many fiber fractures are generated because of the increase in bending energy for the spreading of fronds. On the contrary, if the crack which propagates in initial stage is long, the bending energy of the. fronds is low. Therefore, less fiber fracture is generated due to the low bending energy. As it is considered that the energy Uff required for fiber fracture contribute to the total absorbed energy UT greatly, it had better increase the energy Uff. The Es value of the high modulus specimen was the lowest of all the specimens in static test. It is considered that the Es value might be related to rupture elongation. The elongation of the XN60 fiber was smallest of all specimens. If the rupture elongation is small, the fiber would be broken immediately without bearing of the axial load. Hence, it is considered that the energy Ubend absorbed by bending of fronds was low. Although the fiber fracture was generated, the energy Uff required for fiber fracture might be low.

(a) The normal (b) The high strength (c) The high modulus FIGURE 4 Detailed photographs of cross section of crush zone in static test

Wedge

' /Central i \ crack 1 .fragment

\r (a) The normal (b) The high strength (c) The high modulus FIGURE 5 Schematic illustration of cross section of crush zone in static test

Energy Absorption Properties of Braided Composite Tubes

471

CONCLUSIONS In this paper, it was investigated how the energy absorption characteristics were influenced by using three types of the braided composite tube with different middle-end-fiber. The specific energy absorption value of the high modulus was lowest of all specimens. The influence of the middle-end-fiber on energy absorption properties depends on the rupture elongation of the fiber. In the case of the small rupture elongation such as the XN60 fiber, it is considered that the energy Ubend absorbed by bending of fronds is very low. Because the fiber would be broken currently without bearing the axial load in the initial stage, considering the result of three-point bending test. Thus, it is considered that although the fiber fracture is generated, the energy U// required for fiber fracture is low. REFERENCES 1. P. H. Thornton, "Energy Absorption in Composite Structures", J. COMPOSITE MATERIALS, Vol.13, 1979, pp247-263 2. H. Hamada, S. Ramakrishna and H. Satoh, "Crushing mechanism of carbon fibre/PEEK composites tubes", COMPOSITES, Vol.26, Numberl 1, 1995, pp749-755 3. H. HAMADA, J. C. COPPOLA, D. HULL, Z. MAEKAWA and H. SATO, "Comparison of energy absorption of carbon/epoxy and carbon/PEEK composites tubes", COMPOSITES, Vol.23, Number4, 1992, pp245-252

Characterization of Damage Resistance and Damage Tolerance of Composite Materials Zhen Shen*, Shengchun Yang Aircraft Strength Research Institute of China, P. R. China Shaoyun Fu Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P. R. China Lin Ye Centre for Advanced Materials Technology, School of Aerospace, Mechanical & Mechatronic Engineering. The University of Sydney, Australia

ABSTRACT A lot of experimental data showed that CAI was an ambiguous physical quantity, and could not to guide development of material systems and selection of materials during structural design. The research by authors showed that the damage resistance behavior and damage tolerance behavior of composite systems are corresponding to the design requirements of durability (against impact) and damage tolerance of composite structures, respectively. They can be characterized using the maximum contact force of the static contact force ~ dent depth curve, i ^ x and the threshold of the dent depth ~ compression failure strain curve, CAIT (Compression failure strain After Impact Threshold), respectively.

INTRODUCTION Aircraft integrity requirements usually include static strength, stiffness, durability and damage tolerance requirements. In order to meet these requirements it is necessary to establish corresponding material properties for material scientists to develop new materials and for structural designers to predict structure performance. There have been available material properties for metallic structures. In comparison with metallic structures composite structures have some peculiar contents in durability and damage tolerance requirements. The main difference is impact resistance and impact damage tolerance. ASTM D6264-98 [1] stated that the damage resistance is quantified in terms of a critical contact force associated with a single event or sequence of events to cause a specific size and type of damage in the specimen. But it is not so clear to definite a physical quantity characterizing damage resistance behavior in the standard. Recently MIL-HDBK-17-1F [2] stated that CAI obtained by NASA test standard or SACMA SRM 2R-94 method could be accepted as the

'Corresponding author, P O Box 86, Xi'an 710065, P R China, fax:+86-29-8214765, email: shenzhen@pub .xaonline. com

Damage Resistance and Damage Tolerance

473

characterization of damage tolerance behavior of composites. But a lot of research has showed that CAI was an ambiguous physical quantity. Authors have ever proposed that the threshold of impact damage failure curves by the impact under compression method could be assigned as the compressive impact damage tolerance allowable of composite laminates. In fact this value had been considered as the characterization of damage tolerance behavior of composite laminates. So far the research on the characterization of damage resistance and damage tolerance of composite materials is still under progression. In the paper Authors proposed two new physical quantities to characterize them based on our experimental study. SELECTION OF DAMAGE PARAMETER OF COMPOSITE LAMINATES Whichever of damage resistance and damage tolerance need to choose a suitable damage parameter to describe damage state before choosing the suitable physical quantity to characterize them. The available commonly-used damage parameters include damage area, damage width, and dent depth. All of the three parameters can be the alternative damage parameter used in measurement of damage resistance and damage tolerance behavior. According to the physical meaning of damage resistance (i.e. damage size for a given impact force), the most measurable impact force is impact energy. Fig 1 shows the relationships between impact energy and different damage geometrical quantities for two composite systems with different toughness. Among them E (impact energy) ~ 8 (dent depth) curves distinguish mostly the difference in toughness even though all of these curves could reflect their difference. Fig 2 shows the relationship between E (impact energy) and 5 (dent depth) for 7 composite systems. The rank of damage resistance of these composite systems is obvious. Composite system A and B belong to brittle composites and the others belong to toughened composites. The appropriate damage parameter should meet the following requirements: • For the same impact event (or impact force) the response of composite systems with different toughness (or damage resistance) should be significantly different; • It should be consistent with the parameter describing the damage state in the damage resistance and damage tolerance requirements of the aircraft structure design specification; • The damage parameter should be easily measurable. According the criterion stated above the dent depth is chosen as the damage parameter used in characterization of damage resistance and damage tolerance behavior of composite systems. PHYSICAL QUANTITY CHARACTERING DAMAGE RESISTANCE The available research has shown that impact damage can be produced by the quasi-static indentation (QSI) method instead of the drop-weight method. Fig.3 shows the contact force ~ dent depth curves for two different carbon/modified BMI by QSI method. The conclusion is nearly the same as that obtained from the drop-weight method, hi comparison with the drop-weight method QSI method can obtain the more obvious knee point and is much simpler. Actually, there exists the maximum contact force at the knee point. Repeatability of the contact force ~ dent depth curves of the same composite system is quite good. The definition of damage resistance in ASTM D 6264 is: in structures and structural materials, a measure of the relationship between

474

Damage Resistance and Damage Tolerance

the force, energy, or other parameter(s) associated with an event or sequence of events and the resulting damage size and type. According to this definition the maximum contact force Fmm at the knee point of the dent depth ~ contact force curve of the typical composite laminates is assigned as the physical quantity characterizing the damage resistance behavior of the composite system in this paper. It reflects the maximum capability of resin matrix and fibers near the surface in this composite system as a whole to withstand foreign object impact.Table 1 gives out the Fmax and CAI values for 4 different composite systems. It could be found that the order of both of Fmax and CAI is the same. It means that Fmax can characterize the damage resistance behavior of composite systems instead of CAI. 35

600 | to E

30

J.25 I 20

-400

S £300 00

I

1200

100

> Carbon/Brittle Epoxy

- V

10h > Carbon/Brittle Epoxy

5 0

5 10 15 Impact energy, J

20

0

0

5 10 15 Impact energy, J

20

0

5 10 15 Impact energy, J

20

• • Carbon/Toughened Epoxy • * • • •

Impact energy, J

FIGURE 1 The relationship between impact energy and different damage parameters for carbon/epoxy

3.0

•

2.5 g 2.0 • 1.5

4 Carbon/modified BMIA • Carbon/modified BMI B O Carbon/toughened BMI C ^ Cartran/toughened BMI D O Carbon/toughened BMI E A Carbon/toughened BMI F X Carbon/toughened Epoxy G A

A 1.0 0.5

AD

&

O

a

A m

A

°

0.0 20

40

60

80

100

120

140

Impact Energy, J

FIGURE 2 Impact energy ~ dent depth curves for 7 composite systems

Damage Resistance and Damage Tolerance

475

TABLE I F max and CAI for 4 composite systems Fmax[kN/mml 1.09 1.12 0.98 2.75

Material system Carbon/Modified BMIA Carbon/Modified BMI B Carbon/Brittle Epoxy Carbon/Toughened Epoxy

CAIfMPa] 171 177 151 >200

PHYSICAL QUANTITY CHARACTERING DAMAGE TOLERANCE Fig.4 shows the typical impact damage failure curve of composite laminates (including compression after impact and impact under compression). It is well-known that there exists a horizontal part, e.g. a threshold for all of the impact damage failure curves. The key issue of the damage tolerance requirement of composite structures is that the structure with impact damage meets the specified residual strength and the initial impact damage size assumption is that damage from a 25.4mm diameter hemispherical impactor with that kinetic energy required to cause a dent 2.5mm deep. All of test data show that the compressive failure strain approaches its threshold as long as the dent depth is deeper than 1.0mm. Based on the test data and the damage tolerance requirement of composite structures the CAIT ( Compression After Impact Threshold ) of the impact damage failure curve of a composite system with a specified lay-up under the specified impact condition is used as the physical quantity characterizing the damage tolerance behavior of the composite system. The quantity represents the damage tolerance of the structures with assumed initial defect/damage CONCLUSIONS • The maximum contact force F max obtained from the typical laminates by QSI method can be used as characteristics of the damage resistance behavior of a composite system. • The CAIT (Compression After Impact Threshold) can be used as characteristics of the damage tolerance behavior of a composite system. • In order to characterize damage resistance and damage tolerance behavior of a composite system the effect of a variety of parameters on Fnmx and CAIT should be investigated theoretically and experimentally so that the test standards on Fmiix and CAIT can be established.

Carbon/Modified BMI A

Carbon/Modified EMI B

»

i

F-2 F-3

H-2

\ •

-

a

-

F-5

-

M

'H-4

W

- - —H-5 :•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:].]. g

0.0

0.2

0.4

0.6

0.8

1.0

Contact force, fcN/mm

Contact force, kN/mm

FIGURE 3 Repeatability of test data of contact force -dent depth for multi-specimens

Damage Resistance and Damage Tolerance

476

Impact energy or dent depth

FIGURE .4 Typical impact damage failure curve of composite laminates

ACKNOWLEDGEMENTS Authors would like to thank their colleagues in ASRIC: Liu J S and Chen P H for their contribution in experimental work and helpful discussion. Also authors are grateful to the National Key Laboratory Fund (00JS49. 3. 1.HK53O1) and Aeronautical Science Fund of China (ASFC)( 01B23001) for their financial support. REFERENCES ASTM Standard D6264-98. Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer-Matrix Composite to a Concentrated Quasi-Static Indentation Force. 1998. Department of Defense. MIL-HDBK-17F Composite Materials Handbook. Vol 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials. 17 June 2002

Simplified Prediction Method of Impact Response on Composite Laminates Sung Joon Kim and In Hee Hwang Korea Aerospace Research Institute, Korea

ABSTRACT A new method for simple prediction of the impact response on composite laminates subjected to low-velocity impact is proposed. The present method is based on mode analysis. The simplified prediction method can be efficiently applied to isotropic or orthotrpoic plates with unknown contact laws as well as composite laminates with no restraint on the material properties and geometrical shape. Predicted impact response using the present method is compared with the numerical ones from the impact response analysis using contact law. And in this paper, to investigate the effect of embedding directional damping material, the low-velociy impact response analysis was performed using the present method. Embedding viscoelastic-damping materials into composites can greatly increase the damping properties of composite structures.

INTRODUCTION Low-Velocity impact problems in composite structures have been a hot issue because damage due to the low-velocity impact might be left undetected and become potentially dangerous. Numerous analytical methods have been developed for solving this impact problem in composite laminates [1]. To determine the contact force from the impact response analysis an experimental indentation law or the modified Hertzian contact law proposed by Yang and sun [2]. The dynamic response analyses using this contact law have provided many numerical results on the impact response. However, these analyses using the finite element method on the impact response of the laminate have been known to require long computation time. Shivakumar et al. did not use the finite element method to analyze the impact response of the laminate but used the spring-mass model to efficiently predict the impact force history [3]. In their study the contact energy due to local indentation as well as transverse shear energy and bending energy of plate are considered, and they reported that the contact energy can be neglected in the impact by relatively low velocity foreign object on a flexible or thin plate. However, their study was restricted to circular laminates with transversely isotropic material properties. Choi et al. proposed the simple prediction method of impact force history on composite laminates subjected to low-velocity impact [4], They neglected the contact energy as it has been in other research [5]. The impact duration is computed from the eigenvalue analysis of lumped mass system in which the mass of an impactor is lumped with the plates, and the impulse-momentum conservation law is used with the concept of the spring-mass model. However, they considered only the first mode of lumped system. They did not consider the higher mode of impact response, m the present study, we propose a new method for Correspongding Author, P. O. BOX 113 YUSUNG TAEJON 305-600 KOREA, 82(42)860-2009, [email protected]

478

Simplified Prediction Method of Impact Response

simple prediction of impact response on composite laminates subjected to low-velocity impact. The impact response is computed from several eigenvalues of lumped mass system. Usually viscoelastic-damping materials behave isotropically so that their damping properties are the same in all directions. In these days, there is a desire to develop viscoelastic-damping materials that behave orthotropically so that damping properties vary with material orientation. These orthotropic damping materials can be made by embedding rows of thin wires within the viscoelastic materials [6]. These wires add significant directional stiffness to the damping materials, where the stiffness variation with wire orientation follows classical lamination theory, m this paper, the loss factor of composite laminate was evaluated based on Ni and Adams' theory [7]. SIMPLE PREDICTION ON IMPACT RESPONSE Impact Force Histories The impact duration determined from eigenvalue analysis may be more accurate than that from a direct analysis of spring-mass model, as shown in Ref. 3 where the effect of the mass of the plate were simplified with the concept of the effective plate mass in the spring-mass model analysis. The contact force history may be assumed to be a sine function as in Eq. (l)-(4). mi.sin^

T

-^f

i = \,-,n

i = 2,-,n

(1)

(2)

Where Fmi is the function of impactor mass, initial velocity and eigenvalues in spring-mass model. And 7} is period of each mode in spring-mass model. Neglecting thermal and acoustic dissipation as well as energy loss due to impact damage and residual vibration of the laminate after impact, the mechanical energy of the impact is conservative. Therefore, we may let the rebound velocity of the impact be equal to the impact velocity. Applying the impulse-momentum conservation to the impact history of Eq. (1). IT

(3)

Where mj is mass of impactor. Tf is period of impact force history, v is impact velocity of impactor. The approximate impact force history can be written be as 2m,v > T, sin ' *-• ' T.

Simplified Prediction Method of Impact Response

479

Impact Response Neglecting the gravity, the acceleration and velocity of impactor can be computed using the equations (5)-(6)

(5)

Mi

(6)

T{

To investigate the vibration characteristics of impact system, the lumped mass system in which the mass of the impactor is lumped with the laminate was solved using the finite element method. The size of laminate to be analyzed is 10x10x0.1 cm and stacking sequence is [0]8 and the material properties of a lamina are shown in Table 1. The boundary condition of plate has four edges clamped. In Figure 1, the simplified impact force histories from Eq. (1) is shown. The contact duration and impact force histories agree well with those from the impact response analysis using contact law. TABLE I Material properties of lamina used for analysis

Item

Ei (GPa)

E2 (GPa)

V

Gl2 (GPa)

(10-3)

(io-3)

AS4 Graphite/Acrylic (Damping Material)

156.0

24.8

0.30

8.1

27.7

1860.0 1310.0 1597.0

AS4 Graphite/Epoxy

122.2

17.9

0.27

6.2

1.84

8.58

(10-3)

9.48

kg/m3

1509.0

Mass ratio (M,/Mp) = 35.0 Impact velocity = 5.0 m/sec

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Time (msec) FIGURE 1 Impact force histories using the contact law and present simplified results

480

Simplified Prediction Method of Impact Response

Damped Impact Force Histories The damped contact force history may be assumed to be a sine function as in Eq. (7).

i = l,---,n Where 7} is period. £. is damping ratio. Ando,. is angular natural frequency of each mode in spring-mass model. The Loss Factor of Composite Laminates In this paper, The overall damping loss factor(^ov) is expressed as fallows. AW

(8)

2KW

Where AW is the dissipated energy and W is the stored energy during a cycle. The strain energy dissipation can be divided into five parts as fallows. The overall damping loss factor for composite laminates embedding directional damping material is analyzed as fallows. The stacking sequence of composite laminates is presented in Figure 2.

Casel Angle

Case 2

Case 3

Mart Angle Mat'l Angle Mat'l [1]

0.0

[1]

0.0

[2]

0.0

[1]

[2]

0.0

[1]

[1] [2]

0.0

Damping Material

0.0 0.0

0.0

[2]

Wires at angle 6

[1]

0.0

[2]

0.0

[2]

Damping material

0.0 0.0

[1]

0.0

[2]

0.0

[2]

[1] [1]

0.0 0.0

[2]

Composite

0.0 0.0

[1]

0.0 0.0

[2] [2]

0.0

[1]

0.0

[1]

0.0

[2]

0.0

Composite

[1]: AS4 Graphite/Epoxy, [2] : AS4 Graphite/Acrylic FIGURE 2 Stacking sequence of composite laminate embedding directional damping Material

Damped Impact Force Histories A comparison of impact force histories with and without damping is shown in Figure 3 ~ 4.

Simplified Prediction Method of Impact Response

481

1400.0 Undamped S

1200.0

,

- - - • Damped

J3

b

r

b

ct Force (

g - 1000.0

400.0 200.0

\

J

\

V

* 0.0

1.0

2.0

3.0

4.0

6.0

7.0

8.0

Time (msec) FIGURE 3 Impact Force Histories for Casel

9.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Time (msec) FIGURE 4 Impact Force Histories for Case3

Conclusion In this paper, a new method for simple prediction of the impact response on composite laminates subjected to low-velocity impact is proposed. This method is based on mode analysis for lumped mass system. The impact duration is computed from the eigenvalue of the lumped mass system, and the impulse-momentum conservation law is used with the concept of the spring-mass model to predict the impact force history. The approximate impact force histories using the present method agree well with the numerical ones from finite element analysis. And to investigate the effect of embedding directional damping material, the low-velociy impact response analysis was performed using the present method. Embedding viscoelastic-damping materials into composites can greatly increase the damping properties of composite structures. The present analysis results show that directional damping material has a great influence on vibration and damping characteristic of composite laminate. Reference 1. Abrate, S., "Impact on Laminated Composite Materials," Applied Mechanics Review, Vol. 44, No. 4 , 1991, pp. 155-190 2. Yang, S. H., and Sun, C. T., "Indentation Law for Composite Material Laminates," Composite Materials : Testing and Design, 6* Conference, American Society for Testing and Materials, ASTM STP 787, Philadelphia, PA, 1982, pp. 425-449 3. Shivakumar, K. N., and Elber, W., "Prediction of Impact Force and Duration Due to Low-Velocity Impact on Circular Composite Laminates," Journal of Applied Mechanics, Vol. 52, Sept. 1985, pp. 674-680. 4. Choi, I. H., and Hong, C. S., "New Approach for Simple Prediction of Impact "AIAA Journal, Vol. 32, No. 10, October 1994, pp. 2067-2072 5. Tan, T. M., and Sun, C. T., "Use of Statistical Indentation Laws in the Impact Analysis of Laminated Composite Plates," Journal of Applied Mechanics, Vol. 52, March 1985, pp. 6-12 6. Biggerstaff, J. M. and Kosmatka, J. B., "Shear Measurements of Viscoelastic Damping Materials Embeded in Composite Plates," SPIE Proceedings, Vol. 3672,1999, pp. 82-92 7. Ni, R. G. and Adams, R. D., "The Damping and Dynamic Moduli of Symmetric Laminated Composite Beams-Theoretical and Experimental Results," Journal of Composite Materials, Vol. 18,1984, pp. 104-121.

Indentation Responses and Damage in Kaolin/CelluloseFibre Epoxy Nanocomposites S. Vaihola, W. Vilaiphand, A. Lopez, I.M. Low* Materials Research Group, Department of Applied Physics, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia

ABSTRACT The nature and degree of indentation responses as well as the deformationmicrofracture damage in the vicinity and below the Vickers contacts in epoxy composites reinforced with cellulose-fibre (CF) and nano-sized kaolin have been studied. The hardness of the nanocomposite is load-independent but is time-dependent as a result of both viscoelastic deformation and extensive microscale damage. A pronounced shear deformation within the CF/epoxy matrix is observed during indentation, indicating microscale quasi-plasticity which can be associated with interfacial sliding, interfacial debonding, and microcracking. However, no contactinduced cracks are observed and the extent of micro-damage distributed within the shear-compression zone around and below the contacts is profoundly suppressed as the thickness of the harder kaolin/epoxy layer increases.

INTRODUCTION There is currently a great interest in polymer-clay nanocomposites as a result of the pioneering work by researchers at Toyota on nylon-6/clay nanocomposites which have demonstrated an improvement in both physical and mechanical properties [1,2]. Because of the nanoscale structure, polymer-clay nanocomposites possess unique properties which include an improvement in mechanical (modulus, strength, toughness), thermal (thermal stability, decomposition, flammability, coefficient of thermal expansion), and physical (permeability, optical, dielectric, shrinkage) properties [3-7], Nanocomposites have been demonstrated with many polymers of different polarities including polystyrene, polycaprolactone, poly(ethylene oxide), poly(butylene terephthalate), polymethylmethacrylate, polyamide, polyimide, polyester, polyether, epoxy, polysiloxane, and polyurethane. Similarly, cellulose and other natural fibres are increasingly being used as reinforcements for enhancing the strength and fracture resistance of polymeric matrices because of their low density, low cost, renewability and recyclability as well as excellent mechanical characteristics that include flexibility, high specific strength and high specific modulus [8-13]. These unique properties are particularly desirable in applications as composite materials for automobiles, armour, sports, and marine industries. Here we describe a novel approach to design nano-hybrid eco-composites, in which micro structural elements are tailored to provide both nano- and fibre-dispersed * Corresponding author. Email: [email protected]

Kaolin/Cellulose-Fibre Epoxy Nanocomposites

483

compositions and generate different modes of strengthening and toughening. The basic idea is to produce an outer epoxy layer dispersed with nano-sized kaolin for strength and wear resistance, and with underlayers of cellulose-fibre reinforced epoxy for toughness and damage tolerance. EXPERIMENTAL PROCEDURE Commercial grade nano-sized kaolin and cellulose-fibre preforms derived from wood were used to fabricate kaolin-cellulose fibre-reinforced epoxy hybrid nanocomposites. Softwood aspen (Pinus radiata) mats in the form of bleached chemithermomechanical pulb (CTMP) were used as reinforcing fibre preforms. Samples were be prepared by casting an epoxy mixture in a greased silicone rubber mould filled with kaolin and cellulose-fibre. Initially, the mould will be filled with a thin layer mixture (0.3-1.0 mm) of kaolin/epoxy. Three sheets of previously epoxy soaked CTMP fibre-mat were then laid down. The fully-soaked samples were cured overnight at room temperature. Figure 1 shows the typical surface and crosssectional microstructures of the samples.

(b) (a) FIGURE 1 Typical microstructures of a sample showing the (a) cross-section and (b) cellulose-fibre layer. (Magnification: lOOx)

Samples for indentation tests were resin-mounted and polished with diamond paste down to 1 \xm with a Struers Pedemat auto-polisher. The Vickers hardness measurements were performed with a Zwick microhardness tester. The lengths of the diagonal (2a) were used to calculate the hardness, determined here as: Hv = P/2a2

(1)

where P is the load used. The variation of hardness as a function of load was performed over the range 10-100 N at an indentation time of 20 seconds. The effect of indentation time (0-720 min) on the variation of hardness at 30 N load was studied to ascertain the viscoelastic nature of this material. The time-dependent strain, e (/), due to creep was calculated from the difference in diagonal lengths (d) between the initial (t0) and continuous specified (t) loading times:

e(t)={d(t)-d(to)}/d(to)

(2)

484

Kaolin/Cellulose-Fibre Epoxy Nanocomposites

Information of subsurface damage during Vickers indentations was also obtained using a bonded-interface specimen configuration [7,10]. This test allows the nature and degree of damage accumulation beneath the indenter to be revealed. Polished surfaces of two half-specimens were glued face-to-face with a thin layer of adhesive under moderate clamping pressure. The top surface perpendicular to the bonded interface was polished for the indentation tests. The test to examine the suburface damage was also performed with a Zwick tester at P = 100 N. The two halves of the indented specimens were then separated by dissolving the glue in acetone, cleaned, and examined using an optical microscope. Details of damaged surface topography at higher magnifications were examined using scanning electron microscopy. RESULTS AND DISCUSSION The size of Vickers indents in both CF/epoxy and kaolin/epoxy layers increased with an increase in the load. Fig. 2 shows the typical indents in both layer types. However, no radial cracks were observed on the surface of the individual layers, even at the maximum load used. The absence of these cracks can be ascribed to both low hardness (Hv) and high critical load (Pc) to initiate cracks (15), where Pc is proportional to (KIC4/HV3). An extensive damage due to interfacial-shear debonding and damage was seen in the CF/epoxy layer but not in kaolin/epoxy layer. +*».

(a)

(b)

FIGURE 2 Typical indentation impressions in the (a) kaolin/epoxy and (b) CF-epoxy layer. (Magnification: lOOx)

Fig. 3 shows the hardness profile of a nanocomposite in cross-section. The higher hardness of the kaolin/epoxy (KE) and CF/epoxy (CFE) layers due to reinforcement by kaolin and CF is evident. Figure 4 shows the variation of hardness as a function of load for KE layer. There is clearly a modest display of load-dependent hardness in the KE layer. In contrast, this phenomenon was not observed for the CFE layer. The amorphous nature of epoxy and the fine dispersion of cellulose-fibres can account for the absence of load-dependent hardness in this system. This loadindependent hardness characteristic can be attributed to a grain-size effect (16,17) or the absence of fibre agglomeration. In contrast, agglomeration of kaolin particles can be readily seen in the KE layer. At small loads, the contact dimension (2a) of Vickers impression is comparable with the size of large agglomerated kaolin and the hardness measures properties similar to those of kaolin; when 2a becomes much larger than the average kaolin size at high loads, the hardness measures the "bulk"

Kaolin/Cellulose-Fibre Epoxy Nanocomposites

485

properties, with more kaolin/epoxy interfaces oriented for deformation by plasticshear and viscoelastic flow. It follows that this phenomenon will disappear in the KE layer if the fine kaolin particles can be uniformly dispersed within the epoxy matrix without formation of large agglomerates. The viscoelastic deformation of KE layer during indentation is clearly revealed in Fig. 5 which shows the creep strain as function of loading time. Over a period of 1 h, strain due to creep has increased by -30% but it leveled off after that. This suggests that during loading, the size of the indent increased with time as a result of viscoelastic flow and relaxation processes. As will be shown later, microdamage in the CFE layer due to prolonged indentation may also contribute significantly to the creep process.

-5-0.5-1 o_

o

u>

o

-a

o

2-0.4-

"0.2-

£ 0.3-

o

Hv (GPa)

0.6

1

o

£0.1CFE

Layer type

> o3

2

4

6

8

10

12

Load (kg)

FIGURE 3 Hardness of the various layers within the nanocomposite.

FIGURE 4 Variation of hardness versus load.

Examination of sub-surface damages in the CFE system revealed a hemispherical shape deformation zone directly below the indenter. The size of the deformed zone and the associated extent of damage increased with load and time. However, there were no radial or lateral cracks formed (Fig 6). A closer examination of the damaged zone reveals an extensive debonding along the CF/epoxy interfaces (Fig. 7). In contrast, no debonding along the kaolin/epoxy was observed. It was further observed the degree of micro-damage within the CFE layer became more extensive as the thickness of the KE layer decreased from 1.0 mm to 0.3 mm. Thus, a thicker and harder KE layer has the capacity to shield the CFE underlayer from the undesirable micro-damage and creep. It is postulated that the pronounced and expanding sub-surface damage due to debonding at the CF/epoxy interfaces may also contribute to the indentation creep process observed in the CFE composite. The presence of CF fillers has acted as sites of stress-concentration and shear-deformation. In effect, the presence of these fillers in large amount has modified the intrinsic viscoelastic property of epoxy resin, rendering it more susceptible to shear-induced deformation at the CF-matrix interfaces. This mode of shear-deformation may impart an improvement in fracture resistance to the otherwise brittle epoxy resin.

Kaolin/Cellulose-Fibre Epoxy Nanocomposites

486

30 •

•ffi

20,

10

O

FIGURE 5 Creep strain of the kaolin /epoxy layer at 30 N.

FIGURE 6 Scanning electron micrograph showing the sub-surface damage at 100 N load

• k

FIGURE 7 A closer view of the sub-surface damage in the CFE layer.

FIGURE 8 Near absence of interfacial damage in the kaolin (k)/epoxy layer.

The study of subsurface damage has clearly revealed the existence of microcracks which are not apparent on the indent surface. The capacity of a thick and harder KE layer in providing shielding against excessive micro-damage in the CFE underlayer is also obvious. However, the mechanism for the apparent absence of any interfacial damage in the KE layer is puzzling and remains unclear. It is postulated that the elastic and thermal expansion mismatch in this layer may be favourable to minimize the formation of any undesirable residual stresses which might cause interfacial debonding. The presence of a KE layer is also expected to impart strengthening to the CF reinforced epoxy composite by virtue of nano-kaolin dispersion in the matrix. Contact damages show characteristics of quasi-plasticity in the CFE underlayer; namely large scale compression-shear deformation and absence of macrocrack systems but presence of extensive microdamage due to interfacial debonding. The deformation is accommodated by the buckling of CF and plastic shear at the CFepoxy interfaces which prevent the nucleation of subcritical voids or microcracks. The damage is observed to initiate in the subsurface region of high compressionshear beneath the contact instead of in the surface region of weak tension outside the contact. The primary stage of damage involves extensive sliding between CF/epoxy interfaces resulting in surface uplift, debonding, and interfacial microcracking.

Kaolin/Cellulose-Fibre Epoxy Nanocomposites

487

Microcracks are facilitated by the presence of a large thermal expansion mismatch and initiated as a result of this sliding process which generates intense stresses. As previous eluded, the expansion or growth of these defects during prolonged contact loading may also account for the observed creep. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13.

14. 15. 16. 17.

Kojima, Y., et al. 1993. "Mechanical Properties of Nylon 6-Clay Hybrid," J. Mater. Res., 8(12): 1185-1190. Usuki, A., et al. 1993. "Synthesis of Nylon 6-Clay Hybrid," J. Mater. Res., 8(12) 1179-1184. Park, J.H. and S.C. Jana. 2003. "The Relationship Between Nano- and Micro-Structures and Mechanical Properties in PMMA-epoxy-Nanoclay Composites," Polymer, 44(7) 2091-2098. Isik, I., U. Yilmazer and G. Bayram. 2003. "Impact Modified Epoxy/Montmorillonite Nanocomposites: Synthesis and Characterization," Polymer, 44 (12) 6371-6378. Ma, J., J. Xu, J-H. Ren, Z-Z Yu and Y-W Mai. 2003. "A New Approach to Polymer/Montmorillonite Nanocomposites," Polymer, 44(10) 4619-46-30. Kornmann, X., H. Lindberg & L. A. Berglund. 2001. "Synthesis of Epoxy-Clay Nanocomposites: Influence of the Nature of the Clay on Structure," Polymer, 42(5): 1303-1308. Fu, X. and S. Qutubuddin. 2000. "Synthesis of Polystyrene-Clay Nanocomposites," Mater. Lett. 42(1): 12-18. Bledzki, A.K. and J. Gassan, 1999. "Composites Reinforced with Cellulose-Based Fibres," Prog. Polym. Sci., 24(1): 221-228. G. Marsh, 2003. "Next Step for Automotive Materials," Materials Today 6(3) 36-41. Low, I.M., P. Schmidt and J. Lane, 1995. "Synthesis and Properties of Cellulose-Fibre/Epoxy Laminates,"/. Mater. Sci. Lett. 14 (1): 170-173. Low, I.M., P. Schmidt, J. Lane and M. McGrath, 1994. "Properties of Rubber-Modified Cellulose-Fibre/Epoxy Laminates," J. Appl. Polym. Sci. 54 (10): 2191-2194. Rowles, M., D. Lawrence, I.M. Low, P. Schmidt and J. Lane. 1999. "Indentation Responses and Micromechanisms of Failure in Cellulose Fibre/Mylar/Epoxy Laminates," Proc. Int. Workshop on Fracture Mechanics & Advanced Engineering Materials, (Eds. L. Ye & Y.W. Mai), 8-10 Dec. 1999, Sydney University, pp.343-50. Lawrence, D., G. Paglia and I.M. Low, 2000. "Indentation Responses and Damage of Polymeric Composites," Proc. Structural Integrity and Fracture 2000, (Ed. G. Heness), 29-30 June 2000, UTS,pp.ll9-127. Low, I.M. 1998. "A Modified Bonded-Interface Technique with Improved Features for Studying Indentation Damage of Materials. J. Aust. Ceram. Soc. 34 (1) 120-126. Lawn, B.R. 1993. Fracture of Brittle Solids, Cambridge University Press, Cambridge. Low, I.M., S.K. Lee, M. Barsaum and B.R. Lawn. 1998. "Contact Hertzian Response of Ti3SiC2 Ceramics." J. Am. Ceram. Soc. 81(1) 225-228. Low, I.M. 1998. "Vickers Contact Damage of Micro-layered Ti3SiC2." J. Europ. Ceram. Soc, 18(10)709-713.

Impact Performance of 3D Interlock Textile Composites J-H Byun , M-K Um and B-S Hwang Composite Materials Lab Korea Institute of Machinery & Materials, Korea S-W Song Department of Materials and Engineering Pukyong National University, Korea

ABSTRACT Impact tests of 2D and 3D textile composites have been carried out in order to identify the superiority of 3D composites. For 2D composites, the plain woven and the 8-harness satin woven composites of different fiber bundle size have been considered. For 3D composites, orthogonal woven preforms of different density and type of through-thickness fibers have been studied. To assess the damage after the impact loading, specimens were subjected to C-scan nondestructive inspection. Compression after impact (CAT) tests were also conducted in order to evaluate residual compressive strength. Under the impact energy of 15J the visible damage was small on the impacted side of the 3D woven composites, whereas the same impact energy caused perforation in 2D woven composites. Thus, the impact performance of 3D woven composites is superior to 2D woven materials, although the direct comparison of quantitative characteristics was not successful in this study.

INTRODUCTION The prepreg laminated composite has been widely used in various composites industry. However, laminated composites are liable to fatal damage under impact load due to the fact that they have no reinforcement in the thickness direction [1]. To overcome the inherent weakness and to widen its application to primary structural parts, three dimensional (3D) textile reinforcements have drawn much interests [2-4]. 3D fibrous preforms can be made by various ways such as stitching, needle-punching, 3D braiding and 3D weaving [5]. The needle-punching has been often used in the fabrication of preforms for carbon/carbon composites such as non-structural parts. The 3D braiding provides tubular type of axi-symmetric shapes. For the planar shape of preforms 3D weaving process is prefered. In the 3D weaving, yarns are interlaced in a manner similar to 2D woven structures, except that warp yarns may penetrate more than one layer of weft (fill) yarns. Many variations in the basic geometry of interlock preforms are feasible, depending on the number of layers interlaced, the pattern of repeat, and the presence of in-laid (stuffer) yarns. In this paper, impact performance of 2D and 3D textile composites has been characterized. For 2D composites, the plain woven and 8-harness satin woven composites Corresponding author, 66 Sangnam-dong, Changwon, Kyungnam, South Korea +82-55-280-3883, [email protected]

Impact Performance of 3D Interlock Textile Composites

489

of different fiber bundle size have been considered. For 3D composites, orthogonal woven preforms of different density and type of through-thickness fibers have been studied. The orthogonal preform has 3D orthogonally (x-y-z) arrangement of fibers. To assess the damage after the impact loading, specimens were subjected to C-scan nondestructive inspection. Compression after impact (CAT) were also conducted in order to evaluate residual compressive strength. EXPERIMENTAL Specimen Preparation Figure 1 shows schematic of 3D woven composites. Staffers and fillers are unidirectional carbon fiber bundles of 12K, and weavers for the through-thickness fibers are of smaller bundle size. Depending upon the density and the fiber type of weavers, three kinds of preforms have been fabricated: 3K carbon weavers of single density (SWC), 3K carbon weavers of double density (DWC) and Kevlar weavers of single density (SWK). Figure 2 shows SWC and DWC. For 2D fabric composites, 6K carbon fiber plain weaves (P6K), 3K carbon plain weaves (P3K) and 3K carbon 8-harness satin weaves (S3K) were used. All the specimens were fabricated by vacuum assisted resin transfer molding process. The epoxy resin and hardener were Kukdo Chemical KBR1729 and KBH1089, respectively. The dimension of the fabricated plate was 320x215x2.5mm. Plates were cut by 150x100mm according to SACMA SRM 2R-94 test specification [6]. The preforms information and the fiber volume fractions are summarized in Table 1. Warp weaver

> . ••

'

. -

=

iniinn B _ • _ *—*—»-^i • • •

t=t=c^jL: i ; : ; ; FIGURE 1 Unit cell of orthogonal woven Preform.

3D Woven 2D Woven

SWC DWC SWK P6K P3K S3K

C12K C12K C12K C6K C3K C3K

(Note) C : carbon fiber ; K : Kevlar fiber.

« »

i;;

FIGURE 2 Surface pattern of SWC and DWC.

TABLE I Specifications of composite specimens

Stuffer (Warp)

i

Filler (Fill) C12K C12K C 12K C6K C3K C3K

Weaver C3K C3K K29 None None None

Volume Fraction 52% 54% 51% 54% 54% 54%

490

Impact Performance of 3D Interlock Textile Composites

Impact Test Samples were subjected to low speed drop weight impact test to examine damage resistance performance. Impact test setup is shown in Fig. 3. The energy levels imposed to the specimens were controlled by adjusting the height of the impactor of fixed weight. The impact energy was kept low to prevent perforation. The impactor weighs 3.605 kg and has a hemispheric tip with a diameter of 15.88mm. The specimen were placed in the test fixture as specified in SACMA and constrained by rubber tip clamps at every corner. During the falling and rebounding, the timing flag passes the timing gate which is placed just above the test specimen, and the impactor velocity is detected from the traveling time passing the timing gate. When the impactor contact with the specimen, the load cell in the impactor reads the impact force change. With the impact load data, the energy imposed to the specimens can be calculated.

Load cell and lf coo lai rts r

impactor lip lest specimen FIGURE 3 Drop weight impact test system.

FIGURE 4 SACMA CAI test.

Compression after Impact Test The compression after impact (CAI) test, which measures compressive strength of the impacted composite specimen was performed to examine the material's strength after exposition to an impact load [7]. The specimens were installed in the SACMA CAI test fixture, and four sides of the specimen were constrained carefully in order to prevent undesirable buckling or local crushing at the bottom. Fig. 4 shows CAI test fixture. The tests were performed at a cross-head speed of lmm/min. RESULTS AND DISCUSSION The impact energy of 15J has been applied on 3D woven composites, and the visible damage was small on the impacted side of the sample. For the case of 2D woven composites, however, the same impact energy caused perforation as shown in Fig. 5. It can be shown that the impact performance of 3D woven composites is superior to 2D woven materials.

Impact Performance of 3D Interlock Textile Composites

491

(a) (b) FIGURE 5 Damage comparison under impact energy of 15J: (a) 3D woven composite; (b) 2D woven composite.

Due to the perforation, impact energy of 7J has been applied for the case of 2D woven composites. Utilizing the different impact energy for these two cases has failed in comparing the impact performance between the 2D and 3D woven composites, quantitatively. Figure 6 shows the load-energy curves of 2D woven fabric laminated composites (P6K) and 3D woven composites (SWC). 3D woven composites reached at its maximum load without sudden load drop. However, 2D woven composites show drastic load drops, which is due to the delamination.

F6K

Load & Energy Histories

SWC

Load & Energy Histories

25006000 2000

/ 4000

1500-

/ 1000

/

/

\

2000

/ / 500

n

1/ t''

.

.

.

\

—

Load Energy

hi

n

Load Energy

\

6 "nm2[ms]

(a) 2D, P6K

"nme[ms]

(b) 3D, SWC

FIGURE 6 Load and energy histories of 2D and 3D textile composites

Table 2 summarizes the results of the impact test, C-scan, and the CAI strength of 2D and 3D woven composites. 2D woven fabric laminated composites show higher energy absorption rate than that of 3D woven fabric reinforced composites due to delamination. Absorbed energy of the 3D woven fabric reinforced composites shows that the specimen of double density weaver absorbed higher energy than the single density weaver. This is because the double density weaver has more resin rich area between stuffer and filler yarns. Among the 2D woven fabric laminated composites, 6K plain weave fabric composites (F6K) absorbed higher energy than the 3K plain weave fabric composites (P3K) because of the larger fiber bundle size. Between the same 3K fabric composites, the 8 harness satin showed higher energy absorption. This is due to the fact that satin

492

Impact Performance of 3D Interlock Textile Composites

weaves have larger area of unidirectional fibers. TABLE II Summary of impact test, C-scan, and CAI test results Impact Energy (J)

Absorbed Energy (J)

Damage Size (mm2)

Residual Comp. Strength (MPa)

3D Woven

SWC DWC SWK

14.8 14.9 14.8

6.0 6.9 5.7

512.7 762.2 454.0

172.3 184.6 164.3

2D Woven

P6K P3K S3K

7.0 7.0 7.1

4.4 2.8 3.0

381.7 197.5 250.2

150.7 172.0 175.4

C-scan results of each specimen are shown in Fig. 7. The damage areas indicate the pile-up images of the damage in the thickness direction. On the surface of the 3D woven fabric reinforced composites, there were small visible damages. However, the internal damage of the 3D woven composites are considerably large. The more the sample absorb impact energy, the bigger the damage size is.

(a) SWC

(d) P6K

(b) DWC

(c) SWF

(e) P3K

(f) S3K

FIGURE 7 C-scanned images of impacted panels.

Residual compressive strengths of the specimens subjected to the impact test were evaluated. Among the 3D woven fabric reinforced composites double density carbon weaver (DWC) specimen showed higher residual compressive strength than single weaver (SWC) composites in spite of its bigger damage area. This is because most of the damage is in the matrix rich area, and higher number of weavers contributed the increased compressive strength. Comparing SWC with SWK, Kevlar weaver composites showed smaller residual compressive strength due to the weakness of Kevlar fibers in the compressive load.

Impact Performance of 3D Interlock Textile Composites

493

Among 2D woven fabric laminated composites, 6K carbon plain woven composite (P6K) showed highest impact damage area and lowest residual compressive strength as can be expected. For the same fiber bundle size, the 8-harness satin (S3K) specimen showed bigger damage area, but has higher residual compressive strength than 3K carbon plain weave composite (P3K). This is due to the fact that satin weaves have more unidirectional fibers that contribute to the improvement of compressive strength. CONCLUSION (1) Under the impact energy of 15J the visible damage was small on the impacted side of the 3D woven composites, whereas the same impact energy caused perforation in 2D woven composites. Thus, the impact performance of 3D woven composites is superior to 2D woven materials. (2) Among the 3D woven fabric reinforced composites, double-density weaver specimen absorbed highest energy and the damage size was the largest. The specimens with Kevlar weavers absorbed lower energy and showed smaller damage size than the specimens of carbon weavers. (3) Among the 2D woven fabric laminated composites, 3K carbon plain weave composites showed smaller damage area than 6K carbon plain weave composite. For the same fiber bundle size, 8-harness satin specimens showed bigger damage area, but has higher residual compressive strength than plain woven composites.

ACKNOWLEDGEMENT This research was supported by a grant from the Center for Advanced Materials Processing (CAMP) of the 21st Century Frontier R&D Program and National Research Laboratory funded by the Ministry of Science and Technology, Republic of Korea. REFERENCES 1 2 3 4 5 6 7

Gao SL, Kim JK. Cooling rate influences in carbon fiber/PEEK composites. Part III: impact damage performance; Composites 2001;32:775-785. Tan P, Tong L, Steven GP, Ishikawa T. Behavior of 3D orthogonal woven CFRP. Part I. Experimental Investigation Composites Part A 2000;31:259-271. Callus PJ, Mouritz AP, Bannister MK, Leong KH. Tensile properties and failure Mechanisms of 3D woven GRP composites. Composites Part A 1999;30:1277-1287. Kuo WS, Fang J. Processing and characterization of 3D woven and braided thermoplastic composites. Composites Science and Technology 2000;60:643-656. Byun JH, Chou TW. Mechanics of Textile Composites. In: Kelly A, Zweben C, editors. Comprehensive Composite Materials. Amsterdam: Elsevier; 2000; chapter 22. SACMA, SACMA Recommended Test Method for CAI Properties of Oriented Fiber-Resin Composites; SRM 2R-94. Ishikawa T, Sugimoto S, Matsusima M, Hayashi Y. Some experimental findings in compression-after- impact (CAI) tests of CF/ PEEK(APC-2) and conventional CF/Epoxy flat plates. Composites Science and Technology 1995:55;349-363.

The Ballistic Impact Behavior of Composites Reinforced by Biaxial Weft Knitted UHMWPE Fabrics Zi-qing Liang Beijing institute of aeronautic material, Beijing 100095, China Guan-xiong Qiu Tianjin polytechnic university, Tianjin 300160, China Xiao-su Yi Beijing institute of aeronautic material, Beijing 100095, China

ABSTRACT Ultra-high Molecular Weight Polyethylene (UHMWPE) fiber is a kind of high-tech fiber proved to be the best bulletproof fiber by far. Because of a good ability of deformation Biaxial Weft Knitted (BWK) fabrics is a possible candidate for some molded bulletproof products such as helmets. The ballistic impact Behavior of Biaxial Weft Knitted UHMWPE composites has been investigated in this paper. It was found that ballistic performances were influenced by the pressing pressure strongly. The composites were manufactured under pressure of IMpa, 2Mpa, 5Mpa, respectively, which results in different matrix contents and ballistic performance. Those samples with higher matrix contents were penetrated by the '51' lead-core bullet fired by the '54' handgun, whereas a sample with lower matrix content arrested the bullet effectively. The ballistic impact responses of penetrated and non-penetrated composites were analyzed comparatively. Both in penetrated and non-penetrated composites, the main failure mode of fiber is cut-out by shear, especially for the penetrated samples, in which there seem to exist a change of failure modes from shear fracture to tensile rupture along the thickness of the target. But for the non-penetrated composites, tensile rupture can be observed only in those layers where the bullets were stopped. Most fibers in the following layers behave in an elastic manner although a 'back bulge' would come into being under ballistic impact. The difference of the delamination in the tow kinds of samples were studied also. Because of the peculiar fabric construction, some special phenomena were observed in the research such as yarn slippage and the fragments of the bonding coils. INTRODUCTION As a novel reinforcement material of bulletproof composites, UHMWPE fiber is a kind of high-tech fiber proved to be the best bulletproof fiber by far [1]. It has been applied in soft bulletproof vests, helmets, insert panels and composite armors successfully till now. hi the process of manufacturing this kind of bulletproof products, the pre-impregnated non-woven or woven fabrics would be laid perpendicular to each other and then pressed on the hot-pressing machine. Especially for some deep-pressed * Correspondence Author, P.O.BOX 81-3, Beijing 100095, Fax:0086-10-62458002, email: zqliang [email protected]

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products such as helmets, these fabrics must be cut into a special with several petals, which will be lapped one after another later. Thus many overlapped seams appear in the final products. The overlapped seams and the potential wrinkles in the helmets would decrease the bulletproof performance. Furthermore, the construction of UHMWPE macromolecule is uniform. There is no side chain and polar group on the main chain. This results in a weak interface bonding between fiber and matrix. The composites will delaminate easily under ballistic impact. The delamination, which will be discussed later, influences the bulletproof performance seriously. Biaxial fabrics were developed in the latest several decades. The load responding speed is faster than that of traditional woven fabrics. Jiang[2] studied the formation of Multi-axial warp fabrics by semi-sphere pressing experiment. He found that the deformation of fabrics depends on the number of lining yarn systems strongly. Those fabrics with fewer lining yarn systems formed well in the pressing process. Compared with warp knitted fabrics, weft knitted fabrics have a better ability of deformation. The lining yarns would slide and twist easily so that the fabrics need not be cut out with petals and the decrease of bulletproof performance due to overlapped seam can be avoid. Another advantage of biaxial weft knitted fabrics is that the bonding coils can limit the slide of lining yarns in a reasonable extent and improve the delamination of composites under ballistic impact. The ballistic impact behavior of Biaxial Weft Knitted UHMWPE composites was studied in this paper. EXPERIMENT MATERIALS The lining warp and lining weft are UHMWPE fibers supplied by Sinotex investment & development co,. LTD, China.(Specification: 400den/60f;Tensile strength: 2.8Gpa;Tensile modular: 81Gpa;Elongation: 3%.) The bonding yarns are high tensile strength polyester filaments with the fineness of 135 denier. Because UHMWPE fiber has a low melt point, the cure temperature of resin should be below 130°C. Herein unsaturated polyester was chosen to be the matrix. SPECIFICATION OF BWK FABRIC The Biaxial Weft Knitted fabrics (see Figure 1) were made by a lining warp and weft-knitting machine, which was developed by the Composites research institute of Tianjin Polytechnic University, China. The lining warp is UHMWPE fiber with 3200den and the lining weft with 1200den. The density of lining yarn is 23.6 warps/lOcm and 80+80 wefts/lOcm. The areal density of fabric is about 340g/m2.

FIGURE1 Morphology of BWK UHMWPE fabric

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496 EXPERIMENT

The fabrics were cut into pieces with the sizes of 20cmx20cm, and then treated with acetone to remove the remaining spin solvent. The initiator and promoter were put into the unsaturated polyester which was stirred after mixing. The prepared resin was coated on the fabrics by manual. Because there is a sandwich construction with one lining warp layer and two lining weft layers in the fabric, these pieces of fabric were laid perpendicular to each other. The preimpragnated fabrics were put on the hotpress and molded at required temperature and pressure. Figure 2 is the photograph of BWK UHMWPE-Reinforced Composites.

(a) (top view) (b) (side view) FIGURE 2 Photograph of BWK UHMWPE-reinforced composites

A "54"handgun and "51" bullets were used in the research. The distance from the gun to the target is 5 meters, which was regarded as the most dangerous distance for a target to be penetrated by this kind of handgun. The shot angle is zero degree. THE BALLISTIC IMPACT BEHAVIOR OF COMPOSITES REINFORCED BY BWK UHMWPE FABRICS The Ballistic Performances of the Composites Reinforced by Bwk Uhmwpe Fabrics In the research three different pressures were used to manufacture the composite target. It was found that ballistic performances were influenced by the pressing pressure strongly. The composites were manufactured under pressure of IMpa, 2Mpa, 5Mpa, respectively, which results in different matrix contents and ballistic performance (see table 1). Those targets with higher matrix contents were penetrated, whereas the target with lower matrix content arrested the bullet effectively, even each target has the same 20 layers of BWK UHMWPE fabrics. The possible reason is that higher matrix contents lead the fibers apt to be failure by shear (see figure3). TABLE I The targets parameters and ballistic results

Target no. 1 2 3

Molding pressure IMpa 2Mpa 5Mpa

Matrix content 40.5% 28.4% 20.0%

Areal density 2

11.43kg/m 9.5kg/m^ 8.5kg/m2

Target thickness 13.02mm 10.96mm 9.78mm

Ballistic results penetrated penetrated Non-penetrated

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FIGURE 3 Section of a penetrated target

The Ballistic Impact Response of Composites Reinforced by BWK UHMWPE Fabrics The ballistic impact response of composites reinforced by BWK UHMWPE fabrics was examined comprehensively. The failure mode of fiber was found to exhibit cutout of a sheared plug. Because of the ovoid shape of the lead-core bullet, the crater aperture is smaller than the diameter of the bullet, and most fibers were pushed aside. A small annulate wrinkle can be observed around the striking point (see Figure 4). The stress wave initiated by ballistic impact spread in the laminate. The longitudinal wave is a kind of compressive wave and the transverse wave is a shearing wave. The former spreads faster than the later. But the transverse wave is main factor on interface debonding. After ballistic impact, a white area similar to rhombus appears on the laminate (see Figure 5). The reason for this phenomenon is that the laminate has different modulus at different direction. The modulus along the filaments is much higher than those at other direction. Another possible reason is that the shock wave will transmit and reflect when arriving at a interface between fiber and fiber or fiber and matrix. Its strength will lower down due to reflection. Along the direction of off-axle, the attenuation of shock wave will be more obviously than that at the direction of axle.

FIGURE 4 The shearing failure of composites under ballistic impact

FIGURE 5 The similar rhombus white area formed by shock wave

Under ballistic impact, some target materials moved with the bullet along the thickness of laminate. A peeling force arose before these materials were sheared. Due to the peeling force, the composite delaminated. The delamination was different with the process of penetration. At the area where the bullet was stopped, the delamination extended to the edge of the laminate (Fig. 6). But for the penetrated panel, there is no obvious delamination can be observed (see Fig. 3).

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The bullet was arrestedhere

FIGURE 6 Delamination of the target. The right side of the black line is the delamination in the target. The white arrow shows the penetration direction.

In fact, a reasonable delamination is helpful for the laminate to arrest the bullet. One, the delamination needs energy. The more important is that when delamination happened, the filaments can embrace the bullet at a certain angle. This is the key for the fibers to utilize its high strength and high modulus. A strong interface bonding will restrain the delamination and the fibers in the laminate tend to be sheared rather than to be stretched. On the contrary, a weak interface bonding will make the fibers slide along the surface of the bullet under ballistic impact, which followed by a unacceptable damage to the bulletproof performance. When the bullet hit the laminate, a unrecoverable deformation occurred to the bullet. The bullet arrested by the laminate looks like a mushroom. From this phenomenon, it can be inferred that the contacting area between bullet and laminate enlarged during the entire penetration. More and more fibers involved in the bullet resistance. The increase of load-bearing fibers combined with the delamination made the energy-absorbing mode changed. At first, most fibers were rupture by shear. With the penetration going on, a 'back bulge' came into being (Fig.7), which is regarded as a evidence of fiber experiencing a tensile load.

FIGURE 7 "Back bulge" of the I.II LV

FIGURE 8 The broken and slid yarns

FIGURE 9 The cracked bonding coils

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The tangential component of anti-penetration force made some filaments on the 'back bulge' slide down to the slope (Fig. 8). A few bonding coils were drawn to break. Those UHMWPE filaments broken by tensile released the deformational energy. They rebounded roughly so that the bonding coils were cracked apart (Fig.9). CONCLUSIONS To meet the bulletproof demand, the area density of composites must be up to a certain range decided by protective level and reinforcement construction. The areal density of the laminate used in the research is about 8.5 kg/m2. Matrix contents is approximately 20%. The ballistic impact response of Biaxial Weft Knitted fabrics reinforced composites was studied in this paper. It was found that the response is familiar with those composites reinforced by other constructional fabrics. However, some special phenomenons were observed in the research. REFERENCES [1], Cunniff, P.M., An Analysis of the System Effects in Woven Fabrics Under Ballistic Impact, Textile, Res. J. [J], Vol.62, No. 9, 509-516(1992). [2], Jiang Ya-ming, Study on the Mechanical and Forming Properties of Multi-axial Warp Knitting Fabrics, Dissertation for Doctor Degree, Tianjin Polytechnic University,(1999). [3]. Lee, B.L., Song, J.W., Ward, J.E., Failure of Spectra Polyethylene Fiber-Reinforced Composites under Ballistic Impact Loading, Journal of Composite Materials [J],Vol.28,No.l3,p p. 1202-1226(1994).

Low Speed Impact Behavior of Aluminum Honeycomb Sandwich Panel Jung-Il Song1*, Sung-In Bae1, Mun-Sik Han2, Kyung-Chun Ham3 Department of Mechanical Engineering, Changwon National University 9 Sarim-dong, Changwon, Kyongnam, 641-773, South Korea 2 Department Mechanical&Automotive Engineering, Keimyung University 1000 Sindang-dong, Dalseo-gu, Daegu 704-701, South Korea 3 Department of Machine Design Information System, Pnha Technical College 253 Yonghyun-dong, Nam-gu, Inchon, 402-752, South Korea 1

ABSTRACT Impact behaviors of Aluminum Honeycombs Sandwich Panel (AHSP) by drop weight test were investigated in this study. Two types of specimens with 1/2" and 1/4" cell size were tested by two impactors with the weight of 5.25kgf and 11.9kgf respectively. Transient, contact and elastic-plastic analyses were performed by finite element method. Impact behavior of AHSP about impact sites appeared nearly the same in low impact energy, but it was different in high impact energy. Face was the strongest about impact and short-edge was the weakest. The damaged area of AHSP was enlarged with the increase of impactor weight that is corresponding to impact energy. After 3-point bending test, fracture modes of AHSP were analyzed with AE counts, lower face sheet was fractured in the long-edge direction first, and then separation between face sheet and core happened. In the short-edge direction after core wrinkled, lower face sheet was torn, impact behavior by FE analysis were increased localized damage in high velocity because the faster velocity of the impact was, the smaller the stress of core was. Consequently, impactor weight had an effect on widely damaged area, while the impact velocity gave rise to localized damaged area.

INTRODUCTION Aluminum honeycomb sandwich panels (AHSP) have been widely used in the fields of aerospace, defense, automotive, railway, marine, communication and sport industry for the merits of light weight, high strength and high stiffness. But AHSP shows it's vulnerable before impact force. McGowan et al.[l] represented that manufacturing defect would happen to AHSP caused by careless impact. This damage almost didn't mark on the face sheet externally but it would cause strength reduction internally. It was also stated that the conditions and degrees of impact damage were variable according to the test methods such as drop weight impact test and air-gun test etc. Santosa et al.[2] compared the impact strength between the honeycomb cell and foam. They found that the aluminum honeycomb could own better impact behavior than aluminum foam under unidirectional loading and a combination load of compressive and bending. Reddy et al.[3]analyzed the impact conformation with the experiential equation derived. Papka et al.[4] evaluated the * Corresponding author, Visiting Professor, Biomedical Engineering Department, The University of Memphis , TN 38152 ,USA, E-mail; [email protected], Fax; 901-678-5281

Aluminium Honeycomb Sandwich Panel

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damage mechanism after impacting by optical analysis and ultrasonic c-scan. Kim et al.[5] found that test frequency is lower than resonance frequency of honeycomb structure by using mechanical impedance method in spite of various ways of finding the debonding honeycomb structure. Kim et al.[6] calculated the elastic modulus, shear modulus, Poisson's ratio, compressive bending strength, shear bending strength and flexibility of the sort of cell. In his research triangular and star cell was weak compressive bending strength and shear bending strength. But it had high flexibility. hi our previous work the variable fracture mode was found corresponding to the increase of impact energy. Goldsmith et al.[7] checked buckling pattern of core and analyzed small elastic energy after AHSP, aluminum core and flex core were impacted. These studies promoted the research of composite honeycomb sandwich panel. But the study of aluminum honeycomb sandwich panel was subject to be developed with consideration of the effect of impact position, weight and velocity. In this study a typical impact fracture mode was evaluated. The analysis of the impact energy caused during the damage of impacted specimens was also stated. Fracture modes of AHSP were analyzed with AE counts according to 3-point bending test. Impact damage area was observed with ultrasonic c-scan. Nonlinear impact analysis is carried Ansys5.5. EXPERIMENTAL METHOD AND FEM ANALYSIS Materials of Specimens Impact behaviors of Aluminum Honeycombs Sandwich Panel (AHSP) by drop weight test are investigated in this part. AHSPs with hexagonal-cell shape are fabricated by A 3003H14 sheet. Bondex is used for adhesive. Mechanical properties of the Aluminum plate (A3003H14) and tup (SS400) are listed in table. 1. Two types of specimens with 1/2" and 1/4" size cell are tested by two impactors with the weight of 5.25kgf and 11.9kgf respectively. Dimension of impact specimen is 100mmxl00mmx6mm. Thickness of upper face sheet is lmm and that of lower face sheet is 0.5mm. The height of core is 4.5mm and thickness of it is 0.0762mm. TABLE I Mechanical Properties of Aluminum Plate (A 3003H14) and tup (SS400)

ou a u (MPa) oys (MPa) e(%) £(GPa) p (g/cm3) A 3003H14 185 150 16 69 2.73 SS400 400 210 235 20 7.85 Experimental Method and FEM Analysis The 3-point bending lest is executed to check the impact mode by using MTS. during the 3-point bending lest, AE signal was analyzed about fracture mode by displacement controls. As shown in Fig. 1, Dynatup GRC8250 drop tower is driven by Instron to finish the impact test, impact behaviors of AHSP are examined according to the parameter changes such as the weight or initial position of the impactor. In Fig. 2, the spherical tup with the diameter of 12.7mm (1/2") is used for impact. AHSP is fixed at the center of the clamp with a 75mm diameter hole. For considering the effect of weight 5.25kgf and 11.9kgf impactors are used with the considering the sum of crosshead and tup weight. Impact sites are chosen at face, long-edge, short-edge and point in order to observe, the impact effects of face sheet and core. AHSP is impacted corresponding to the impact energy of 10J, 19J, 32J and 43J respectively.

502

Aluminium Honeycomb Sandwich Panel

The impact process is simulated numerically using a finite element model by Ansys 5.5 with nonlinear FE code. The meshed model for 1/4 symmetric condition is all constrained except for y direction. AHSP is full constrained because of the fixture of clamp. In contact analysis, the contact pairs are formed by target and contact surface, the upper face sheet of chosen for AHSP Target surface, and the external area of tup is closen for contact surface. Yielding stress and tangent modulus of tup and AHSP are inputted for elastic-plastic analysis. The tup with the weight of 11.9kgf and 5.25kgf contacts AHSP with the initial velocity of v0 = -Jlgh . The commercial program Ansys 5.5 is applied to analyze the relation between the time, stress of face sheet and core and impact energy.

A:face , B: long-edge, C: short-edge, D : point L)long-edge direction, S) short-edge direction FIGURE 1 Specimen fixture of drop weight tester Fig. 2 Impact position and bending direction

EXPERIMENTAL RESULTS AND DISCUSSION Static and Dynamic Behavior According to the AE signals, in the short-edge direction wrinkle of core emitted the low signal at 0-1.5sec. Then several burst signals engenders and debonding is starting at inner face sheet from 1.5~3.5sec. Because of friction between upper and lower face sheet, continuous burst signal appeared at 3.5-5.5sec. Lower face sheet began tearing at 5.5~7.5sec. In the long-edge direction burst signal appeared because of fracture of lower face sheet at 0~1.5sec. Large signal occurred to core tear at 1.5-3.5sec Fig. 2 shows torn specimen observed after impact by naked eye, (a) 34J in face, (b) 21J in long-edge, (c) short-edge, (d) point, damaged at 19J. Thefracturemode of AHSP under stronger impact force is indicated in Fig.2 at the site of face, long-edge, point, and short-edge, respectively

(a)

(b)

(c)

(d)

FIGURE 2 Visible Damage at upper site

(a)

(b)

(c) "

(d)

FIGURE 3 Typical fracture mode

Results in Fig. 3 express the typical fracture modes of honeycomb specimen that is damaged by impact position. After initial tear happens to the point or edge of core at the impact energy of 43J, face sheet begins to be depression as shown Fig.3(a). In 43J penetration happens 6 adjacency cores transmit impact load adequately from the face

Aluminium Honeycomb Sandwich Panel

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Which doesn't tear the face sheet under 10J, 19J, 32J. Fig. 3 (b) and (c) display the damaged specimen of long edge, short edge each in 32J. Fracture mode develops. Core cuts into face sheet when the limit load level is exceeded at the edges and tile fracture is transmitted by linked 4 edges. This certifies that the fracture of edge is the reason of final penetration, furthermore, long edge appears to be stronger under impact than short edge for 4 long edges are linked by 4 short edges. Fig.3(d) illustrates the impact mode at point under impact energy 32J. Embayment and buckling occur in face sheet similarly with Fig.3(b) and (c). While the support load at point exceed the limit, tear happens to face sheet along 3 edges by pinning of the core. Impact load data report that the curve related in hysteresis or impact load-time displays similar tendency to impact load-deflection curve. When U.9kgf impact three is applied to AHSP by 1/2" cell, impulsive load appears increasing tendency with the increases of impact energy (Fig. 4). Result of impact load expressed large difference under 32J, 43 J which is illustrated in Fig.4(a), (b). The impact energy of 10J and 19J cannot give great damage to AHSP. But under 32J and 43J the impact loads create considerable crash at face, long-edge, and point and short edge. After delivering enough shear force by adjacency core face sheet of lower part suffered high impact force from rebounding of the core damage. Buckling occurs to edge and point because of the shear force and upper-part or lower-part face sheet tears by this buckling. 5.5

face long-edge

5.Q

short-edge

4.5 4.0

I35

1.S

0.5

AMK

/K

r,:

7

r-^

" f\

long-edge

-

/v 0

12

14

16

1B

short-edge

20

22

24

26

Time (msec)

(a) 32J (b) 43J FIGURE 4 Impact load of 1/2" AHSP cell corresponding to 11.9kgf impactor

The curves with impact load of 11.9kgf and 5.25kgf are almost similar behavior. The cell size is 1/2". The values of impact load of 5.25kgf and 11.9kgf in equal 1/2" specimen appear to have the similar tendency. But because of the unequal weight and different impact height, the impact is imposed for the increased final speed. For 11.9kgf impact load the speed reaching to maximum impact load is 8.5m/sec for 10J, 8m/sec for 19J, 4~8m/sec for 32J, 4~6m/sec for 43J. For 5.25kgf impact load the impact speed of is 5.5m/sec, 4~6m/sec, 3~5m/sec for 10J, 19J, 32J, 43J respectively, which is much faster than the first case. It invokes larger strain energy and produce bigger damage area. We know the impact energy is the function of speed. But from the data above we can find that the weight is more dominant element of impact behavior than speed. Absorbed Energy The maximum absorption energy is marked as Ea in the absorbed energy curve, which leads to the damage of AHSP. The amount of absorbed energy dedicated to the damage is marked as El, and the remaining elastic energy is marked as Ee. Fig. 5 is the graph of absorption, energy obtained by 32 J impact energy toward 1/2" cell's honeycomb panel with impact tup of 11.9kgf and 5.25kgf, respectively. The elastic

Aluminium Honeycomb Sandwich Panel

504

energy of face and long-edge is shown in Fig. 5(a) under 11.9kgf impact damage. In Fig.5 (b) elastic energy curves of face, long-edge as well as point are illustrated under 5.25kgf. It can be clearly observed that weight has an obvious effect on the impact damage, that is, heavier weight will produce larger damage.

:

face long-edge short-edge point

/

•J

20

22

24

long-edga short-edge point

20

26

22

£4

25

(a)11.9kgf (b)5.25kgf FIGURE 5 Absorbed energy of 1/2"AHSP cell corresponding to 32J

Whole absorption energy curves display similar results regardless of impact position in 10,19J. The impact resistance is increasing by the order of face, long edge, point and short edge in 32, 43J, which can be observed in the cases of existence and nonexistence of elastic energy. The short edge elastic energy appears less than 11.9kgf. This means that the impact energy that the short edge can suffer is lower than 11.9kgf. Ultrasonic c-scan is known as a useful method to observe damage face size after impact. From this figure we can find that the afloat area of 11.9kgf impact force with 32J impact energy in 1/2" cell size's specimen is larger than that of 5.25kgf. This means that heavy impact tup creates big damage face about the same impact energy, which explains that impact experiment data and c-scan image agree well. Finite Elements Analysis Nonlinear analysis about each impact energy that use impact tup of 11.9kgf and 5.25kgf about 1/2" cell is performed by finite element method. From these results we could obtain Von Misses stress of the case of 11.9kgf impact force and 32J impact energy in 1/2" cell specimen. Maximum stress 133.8MPa happens to the face sheet that tup is touched. The maximum in the core is about 58.1Mpa. When impact acts to the face, large stress impose on the edge and joints of edge and the stress is transmitted by contiguity core. 0.12

- o

0.11 0.10 -•-Time • °

V; •••••••

(msec)

\\

-^

v°

"'•••-•'

J l

Time

0.04 20

35

2E

40

Impact Energy (J)

(a)5.25kgt

(b)11.9kgt

FIGURE 6 Stress and time of impact energy by 5.25kgf and 11.9kgf impactor

5

Aluminium Honeycomb Sandwich Panel

505

In Fig. 6, with the increase of impact energy, the maximum stress happens in face sheet. The stress transmitted through the core is decrescent. While the impact speed quickens, stress concentration is happened locally at impact position before damage is transmitted. Comparing Fig. 6 (a) and (b), stress of the core is larger in the case of 11.9kgf than that of 5.25kgf under the same impact energy. This analysis data also agree with the experimental results and c-scan image. Furthermore, the impact tup of 5.25kgf of the faster speed generates yielding stress into face sheet with shorter time. CONCLUSIONS Damage mode at 3-points bending test using AE count is analyzed. By the result, the tear of lower-part face sheet happens while preserve bending forces were applied at the core early in the short-edge direction. After lower-part face sheet of long-edge tears, separation of core and face sheet occur. Therefore, Short edges in the honeycomb structure receive more bending forces. Impact behaviors for various AHSP's positions are similar under low impact energy. However, in high impact energy it is different by the positions such as AHSP's face, long-edge, point and short-edge, Face is strongest to suffer the impact. And thickness is also an important factor to prevent tear of upper-part and lower-part face sheet. Under the same impact energy, heavy impact tup needs more time to reach the maximum impact load than light impact tup. The strain energy is much larger for heavy tup. The wider damage area is engendered which is confirmed by c-scan image. This means that low-speed impact is dominated by the effect of weight. According to finite element analysis of impact behavior, if the speed is the faster, the time that reaches the maximum stress is shortened by increasing the speed. Impact damage increases locally, which explains that the speed is the main variable to generate localized damage. ACKNOWLEDGEMENT This work was supported by grant from the Basic Research Program of the Changwon National University 2001.

REFERENCES 1.

2. 3.

4. 5. 6. 7.

David M. McGowan and Damodar R. Ambur.,"Damage Characteristic and Residual Strength of Composite Sandwich Panels Impacted with and without a Compression Loading", Materials Conference and Exhibit and AIAA/ASME/AHS Adaptive Structures Forum - PART 1, pp. 713-723, 1998 S. Santosa and T. Wierzbicki.,"Crash behavior of box columns filled with aluminum honeycomb or foam", Computers & Structures, Vol. 68, pp.343-367, 1998 T. Y. Reddy, H. M. Wen, S. R. Reid and P. D. Soden., "Penetration and Perforation of Composite Sandwich Panels by Hemispherical and Conical Projectiles," Journal of Pressure Vessel Technology, Vol. 120, pp. 186-194,1998 S. D. Papka, S. Kyriakides and S. Kyriakides., "Experiments and Full-Scale Numerical Simulations of In-Plane Crushing of a Honebcomb," Elsevier Science, Vol. 46, pp. 2765-2776, 1997 M. K. Lim, S. C. Low, L. Jiang and K. M. Liew "Dynamic Characteristics of Disbonds in Honeycomb Structures," Engineering Structures, Vol. 17, pp. 27-38, 1995 7. Beomkeun Kim, Richard M. Christensen.,"Basic two-dimensional core types for sandwich structures,"International Journal of Mechanical Science, Vol. 42, pp. 657-679, 2000 14. Werner Goldsmith and Jerome L. Sackman.,"An Experimental Study of Energy Absorption in Impact on Sandwich plates'lnternational Journal of Impact Engineering, Vol. 12, No.2, pp. 241-262, 1992

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PartX

Industrial Applications

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Thermomechanical Analysis of Water Aged Pultruded Composites Salwan Al-Assafi Composite Materials Research A Division of Pultron Composites Ltd, Gisborne, New Zealand

ABSTRACT Water absorption behaviour of pultruded fibre reinforced plastic (FRP) composites has been investigated in this study. Three resin systems were evaluated in distilled water and salt-water environments. The effect of water absorption on dynamic mechanical properties of the composite was analysed. Results indicate that rate of water absorption was the lowest for the vinylester and the highest for the polyester composite. It was also shown that the vinylester composite reached equilibrium faster than the other composites. Results also showed that changes in storage modulus and loss tangent subsequent to aging varied depending on type of matrix resin.

INTRODUCTION Demand has been growing in the construction industry for alternatives to steel, particularly in harsh environments where corrosion is a major concern. FRP composites can provide the required corrosion resistance, in addition to other advantageous properties such as high specific strength and low thermal and electrical conductivity. However, questions still remain on durability and performance of composites in various environments. Dynamic mechanical thermal analysis has been used in a number of studies to investigate performance and evaluate properties of matrix and fiber/matrix interface under various conditions [1-8]. Chin et al. investigated effects of water and salt solution on polyester and vinylester unreinforced matrix resins. An increase in glass transition temperature (Tg) was detected for both polyester and vinylester and it was attributed to hydrolysis and subsequent dissolution of low molecular weight segments. However, the study found vinylester to be more resistant to hydrolysis than polyester due to the difference in the position of the ester functional groups. Ester groups in vinylester are terminal and shielded by methyl groups, while in polyester they are positioned along the main chain, making them more vulnerable to hydrolysis reaction. Fraga et al. employed dynamic mechanical measurement to study water absorption effects on hand-lay-up polyester and vinylester composites [4]. Results of the study showed after immersion in 40°C water and subsequent drying, neat polyester resin samples exhibited lower loss tangent peak than that for the vinylester neat resin sample. That was attributed to the extraction of monomer. Results also indicated the * Corresponding author, P.O. Box 323, Gisborne, New Zealand. Fax: +64 6 867 8542. email: [email protected]

510

Water Aged Pultruded Composites Secondary Bonding

Tg for polyester matrix increases, while the width of loss tangent peak decreases, due to lower molecular weight distribution. Vinylester neat matrix showed similar behavior, where Tg increases and the width of loss tangent peak decreases, though to a lesser degree compared to the polyester. This study investigates short-term water absorption behaviour of polyester, vinylester and polyurethane pultruded composites. Changes in thermomechanical properties as a result of exposure to elevated temperature distilled water and salt solution are investigated. The results of this study can help in understanding effects of aqueous environments on performance of pultrusions with various resin systems and can assist in the selection of proper characterisation methods for the evaluation of aged composites. EXPERIMENTAL PROCEDURE Samples with a rectangular 19mm x 5mm cross-section were supplied by Pultron Composites Ltd. The samples were produced using the pultrusion process utilising three resin types; vinylester, polyester and polyurethane. E-Glass unidirectional ravings were used as reinforcement for all samples. The same glass volume fraction was used for all samples. All samples were cut to a length of 31mm and then conditioned for 24 hours at 50°C then weighed using an electronic scale with 0.1 mg accuracy to establish dry weight. A set of samples was then immersed in 60°C distilled water. Another set was immersed in a 60cC solution composed of 0.6 mol/L NaCl in distilled water. Samples were kept in the solutions for up to 17 days. Periodically samples were taken out, wiped with a dry cloth and weighed to determine weight gain. The measurement of dynamic mechanical properties was carried out on (5mm x 0.85mm x 31mm) strips in a Rheometric Scientific (New Jersey, USA) DMTA V using a 28mm span three-point bend configuration. The strips were cut from the edge of the 19mm x 5mm specimens. All samples were heated at 3°C/min from 30°C to 300cC and cycled at a frequency of 1 Hz. RESULTS AND DISCUSSION The weight gain for the vinylester, polyester and polyurethane FRP composites in water and salt solution is shown in Figures 1 and 2 respectively, hi both figures, vinylester samples reached equilibrium prior to the end of the trial. Polyester and polyurethane samples continued absorbing water and did not reach equilibrium within the duration of the test. This can be attributed to possible microcracking or crazing which commonly takes place during accelerated aging tests carried out at elevated temperatures2. It is evident that the rate and the final level of weight gain for vinylester are significantly lower than those for polyester and polyurethane. It is also shown in Figures 1 and 2 that the final levels of weight gain are higher for samples immersed in distilled water compared to those immersed in salt solution. This is likely to be a result of sorption retardation due to the presence of salt ions.

Water Aged Pultruded Composites Secondary Bonding

511

0.600 -i 0.500 -

d 0.400 • Vinylester • Polyester A Polyurethane

W 0.300 •

+•«

U)

*

•

'I 0.200 0.100 -

0.000 -T0

.•

•••

100

200

300

400

500

Time (hr) FIGURE 1 Weight gain for vinylester, polyester and polyurethane composite samples immersed in 60°C distilled water.

0.600

n

0.500

d 0.400 c "(5 O 0.300 O)

0.200 0.100 -

M•

•

• Vinylester • Polyester A Polyurethane

•

0.000 0

100

200

300

400

500

Time (hr) FIGURE 2 Weight gain for vinylester, polyester and polyurethane composite samples immersed in 60°C salt solution.

Water Aged Pultruded Composites Secondary Bonding

512 0.07

"Control * 17 days

0.01

50

100

150

200

250

300

350

Temperature (C)

FIGURE 3 Loss tangent plot for the polyurethane control sample and the re-dried distilled water aged sample.

0.07

0.06

"Control •17 days

50

100

150

200

250

300

350

Temperature (C)

FIGURE 4 Loss tangent plot for the vinylester control sample and the re-dried distilled water aged sample.

Water Aged Pultruded Composites Secondary Bonding

513

0.06

0.04

"Control •17 days

0.03

0.02

100

150

200

250

300

350

Temperature (C)

FIGURE 5 Loss tangent plot for the polyester control sample and the re-dried distilled water aged sample.

Dynamic mechanical thermal analysis can provide useful information on changes to the matrix and fibre / matrix interface that are taking place during aging. As shown by Fraga[4], the width of tan 8 peak can give clues on molecular weight distribution of the matrix. Figures 3-5 depict tan 8 plots for the polyurethane, vinylester and polyurethane pultruded samples. It is evident that polyurethane and vinylester samples did not show signs of changes in molecular weight distribution. On the other hand, a significant reduction in the width of tan 8 was observed for the polyester samples (Figure 5). This can be attributed to lower molecular weight distribution caused by monomer extraction or post cure [4], This also resulted in a shift of the tan 8 peak to a higher temperature, indicating a higher Tg for the aged sample. Monitoring the storage modulus (E') during aging can assist in detecting changes in the performance of a composite. As temperature is increased and the sample reaches the glass transition region, E' drops from glass-state level to rubberstate level. A study of E' in the rubber-state can give useful information on polymer molecular structure. High rubber-state E' values correspond to high crosslinking density and low molecular weight between crosslinks [4]. As shown in Figure 6, vinylester and polyurethane composites exhibited no rise in E' in the rubber-state after immersion in distilled water and salt solution for 17 days. On the other hand, polyester samples showed an increase in rubber-state E', which could be attributed to post-cure or monomer extraction.

Water Aged Pultruded Composites Secondary Bonding

514

10000

FIGURE 6 Rubber -state storage modulus for control samples and re-dried distilled water aged samples. All values were recorded at 290°C.

CONCLUSIONS Results presented in this study point to the importance of selecting proper material system for composites employed in wet environments. Sorption tests showed vinylester pultruded composites with the least weight gain in both distilled water and salt solution compared to polyester and polyurethane pultruded composites. Dynamic mechanical analysis of aged samples indicated a drop in molecular weight distribution and an increase in storage modulus of aged polyester samples, possibly due to monomer extraction and post cure. REFERENCES l.J. W. Chin, K. A. Aouadi, M. R. Haight, W. L. Hughes, and T. Nguyen, "Effects of Water, Salt Solution and Simulated Concrete Pore Solution on the Properties of Composite Matrix Resin Used in Civil Engineering Applications", Polymer Composites, vol. 22, no. 22, pp. 282-298, April 2001. 2. S. Zhang, W. Chu and V. M. Karbhari, "Investigation of Environmental Effects on Pultruded EGlass/Vinyl ester Composites", Proc. ACUN-3 "Technology Convergence in Composites Applications", pp. 201-207, NSW, Sydney, Australia, 2001. 3.S. Guionnet and J. C. Seferis, "Water Absorption of Model Phenolic Resin Systems for Composite Applications", vol. 34, no. 3, July 2002. 4. A. N. Fraga, V. A. Alvarez, A. Vazquez and O. De La Osa, "Relationship Between Dynamic Mechanical Properties and Water Absorption of Unsaturated Polyester and Vinyl Ester Glass Fiber Composites", Journal of Composite Materials, 37 (17) 1553 (2003). 5. A. Pegoretti, C. D. Volpe, M. Detassis, C. Migliaresi, and H. D. Wagner, "Thermomechanical .Behaviour of Interfacial Region in Carbon Fibre/Epoxy Composites", Composites: Part A, 27 1067 (1996). 6. S. Keusch and R. Haessler, "Influence of Surface Treatment of Glass Fibres on the Dynamic Mechanical Properties of Epoxy Resin Composites", Composites: Part A, 30 997 (1999). 7. A. Afaghi-Khatibi and Y. Mai, "Characterisation of Fibre/Matrix Interfacial Degradation under Cyclic Fatigue Loading Using Dynamic Mechanical Analysis", Composites: Part A, 33 1585 (2002). 8.V. A. Alvarez, M. E. Valdez, A. Vazquez, "Dynamic Mechanical Properties and Interphase Fiber/Matrix Evaluation of Unidirectional Glass Fiber/Epoxy Composites", Polymer Testing, 22 611 (2003).

Secondary Bonding in the Construction of Large Marine Composite Structures Gary J. Simpson* and Peter J. Burchill Maritime Platforms Division, Defence Science and Technology Organisation, Australia

ABSTRACT An investigation of secondary bond performance of composite systems used in the construction of large marine structures is described. Simple surface preparations were evaluated and materials and techniques that could enhance the strength of the structure and improve through life reliability were investigated. The phenomenon of fibre bridging and the effect it has on the fracture resistance of composite systems is discussed. Simple modifications to the composite systems are suggested that can improve the strength of the secondary bond to beyond that of the original. INTRODUCTION A composite laminate once cured is known as the primary laminate, any subsequent lamination to the primary laminate is known as secondary bonding. If all the constituents are the same as those used for the production of the primary laminate, then the secondary bond will generally prove to be weaker than the primary bond. Glass reinforced polymer (GRP) composites are increasingly being used in the manufacture of large marine structures. The logistics of more complex and extensive construction with composite materials will require wider use of secondary bonding through delayed lay-ups and joining. If the growth in the size of vessels made from composite materials continues at the present rate [1], confidence in being able to achieve effective and reliable secondary bonding will be essential. The through life operational conditions that marine composite structures could experience include damage from shock, impact, fatigue and long-term environmental exposure. For all of these scenarios the use of secondary bonding could be necessary if repair to the damaged composite is required. In addition, it is likely that if fatigue damage repair is required, then the secondary bond would require improved bond strength beyond that of the primary bond since it was the primary bond that can be seen as having failed. In this study, the method used to determine secondary bonding effectiveness is mode I fracture toughness, as measured by the Double Cantilever Beam test (DCB). DCB is a widely used method of evaluating the effectiveness of a composite to resist delamination in terms of interlaminar fracture energies for Mode I (tension failure). Characterisation of the fracture energies, which are seen to propagate these interlaminar cracks, is achieved through linear elastic fracture mechanics (LEFM).

* Corresponding author, Maritime Platforms, DSTO, PO Box 4331, Melbourne, Victoria, Australia, 3001, Australia. 9626 8409, [email protected]

516

Secondary Bonding in the Construction of Large Marine Composite Structures

This allows deduction of the energy release rate (Gi) for the crack growth and hence a measure of fracture toughness. The polyester/E-glass composite chosen for this study is commonly used in marine construction. The secondary bonding systems used were selected to give a reasonable range of the many toughening techniques [2] available rather than for the development of any definitive repair system for this particular marine composite system. EXPERIMENTAL The marine resin used is an unsaturated isophthalic polyester. The fibre reinforcement is a heavy (1400 grams per m2) woven silane sized E-glass roving. The weft fibre is "spun", meaning it is hirsute, which appears to help fracture resistance by increasing the contribution of fibre bridging. Initially the effect of surface preparation on secondary bonding was examined. These secondary bonding surfaces were lightly hand sanded (using A80 grit sand paper), heavily sanded (using a power tool), left unsanded (control), or had a peel ply applied to the wet resin surface. The peel ply is a widely used non-coated polyester available from Advanced Composites®. The most effective surface preparation was then used to prepare secondary bonding surfaces, for the lamination of the toughening systems. A number of the secondary bonding systems used are based on Derekane® 8084. Derekane® 8084 is a widely used vinyl ester that has been internally modified with carboxyl-terminated acrylonitrile-butadiene copolymer (CTBN) to give greater toughness. It is used here as a secondary bonding resin by itself (VE Control) and also blended with both 5% VTBN X33 (VE Toughened A) and 5% Core-Shell rubber (VE Toughened B). VTBN X33 is a vinyl terminated acrylonitrile-butadiene copolymer produced by B. E. Goodrich®, from a group known as reactive liquid rubber. Core-Shell rubber (CSR) can be used as an alternative to toughening with liquid rubbers. CSR's generally have a rubber core, poly (butadiene) in this case, with a more rigid polymer shell, poly (alkyl methacrylate) in this case. The CSR used here was made by Rohm and Haas®. The other systems studied were a toughened version of the original polyester resin, using CSR toughening at 5% (PE Toughened) and the use of a scrim or interweave (PE Interweave). Scrim materials are low cost, continuos filament, reinforcing fabrics, used here as an interply in the interphase region of composite materials. The scrim used here is called Colback®, produced by ColBond®, which is a very thin open weave made from bicomponent polymer filament. The scrim is used with the original marine composite system. All laminates were manufactured using a hand lay-up technique and cured using a peroxide catalyst at room temperature. There was no post-cure. The initial primary bonding sample was prepared as a 4-ply composite. For secondary bonding, 2-ply primary laminates were fabricated. There was a 60-day gap between the initial 2-ply lamination and subsequent secondary bonding to mimic the time gaps between laminations that occur during construction. A teflon ply was inserted, during the primary lamination at the central interphase or, onto the base laminate at the beginning of the secondary lamination. This insert extended 50 mm into the specimen to act as a pre-test crack debond (Ao). For testing, the data analysis method used required specimen thickness (B) to be measured, while load (P), displacement (d), compliance (C) and crack length (a) were measured during the test. These values were subjected to analysis by computer

Secondary Bonding in the Construction of Large Marine Composite Structures

517

spreadsheets to derive a value for Gi. The resulting Gi value has been found by also taking into account the various inconsistencies that can occur with this sort of testing. Hashemi [3] proposed various corrections, as detailed in equation 1. Gi = (F/N)3Pd/2B(a+Zh)

(1)

The value X^ is added to the crack length to correct for the deformation of the beam due to rotation. Correction F allows for the apparent shortening of the beams due to displacement of the beam arms. Corrections N involves minor adjustments made due to stiffening of the specimen by the end blocks. Various methods have been published on the derivation of mode I fracture energies, though from the methods used [3,4,5], very little variation in the final Gi value was observed. RESULTS AND DISCUSSION Effect of Surface Preparation on Secondary Bonding. The following plot details the effect different surface preparations had on the composite system.

1.0

T

Model Fracture Toughness (kJ/m) 0.5-

0.0

Primary bond

No Sand

Light Sand

Heavy Sand

Peel Ply

FIGURE 1 Effect of surface preparation on the Mode 1 fracture toughness of bonded laminates.

The results show a small but significant decrease in secondary bond performance from the best of the series of simple surface treatments when compared to the primary bond. The worst performance was found to be from the use of the peel ply. The weakness appears to be due to the larger resin rich interphase area that occurs with the use of a peel ply. This provided a thicker plane of matrix resin, with relatively poor cohesive forces, through which the crack could propagate. Sanding provided an improvement, though the statistical difference between light hand sanding and a heavy grind using an abrasive power tool did not appear to be significant. For the secondary bonding lay-ups, a medium (80gm) sand paper was used to lightly abrade the bonding surfaces. This was mainly for simplicity than for any advantage in secondary bond strength. No peel ply or chemical surface treatment was used. When comparing the primary and secondary bonding performance of this particular polyester/E-glass marine composite, fibre bridging is an important factor. Fibre bridging has been a widely reported [6,7,8] phenomenon from the early

518

Secondary Bonding in the Construction of Large Marine Composite Structures

seventies and is known to cause an increase in fracture toughness in the form of higher tensile loads needed to propagate the crack front between two plies of the reinforcement. Clumps of fibre strands are attached to either side of the interlaminar crack, mechanically resisting crack growth, as seen in Figure 2. This mechanism will be observed, at least to some extent, in any composite system where the plies of the reinforcement are intertwined or compressed together during the manufacturing process. This intertwining is known as "nesting" and is mainly and most significantly observed with unidirectional reinforcements. The mechanism is also seen [9] to increase crack propagating loads in bi-directional woven reinforcements. While not as extensive as observed in unidirectional composites, it is known to enhance resistance to cracking in woven reinforcements to a significant degree.

.«*,Trw>i Sg

^*~ill^iiiI^^Tif E Ti^'^ l ^ t '''^f ^ '

«»*£?• 15»ii.m rff^jyi ^~ifti •%^'V ^A.

FIGURE 2 Fibre bridging mechanism that increases fiacture resistance in less tougher matrix resins

The spun weft fibre in the reinforcement appears to increase the occurrence of fibre bridging, thus increasing the interlaminar crack resistance. Therefore the subsequent decrease in fracture toughness, normally observed in secondary bonding, is more apparent in this case given the absence of the enhanced fibre bridging in the secondary bond. Delayed lay-up, which occurs in the manufacture of thicker structures, can cause inherent weaknesses due to thicker interply regions. Partial cure of the surface, caused by an overnight stop to the lay-up, will however provide a degree of molecular cross-linking on resumption of the lamination the following day. Given the dependence on fibre bridging that this and other polyester composite system appear to rely on for interlaminar strength, a partly cured resin barrier that result from staged lay-ups prevents the fibres from intertwining causing a potentially weaker final laminate. Furthermore, the absence of fibre bridging during secondary bonding, when laminating critical structural joints or connections, suggests toughened resin systems are vital for obtaining satisfactory structural integrity. Effect of Toughened Composite Systems on Secondary Bonding. The test data obtained for the toughened secondary bonding methods is shown in Figure 3. Major improvements in delamination resistance, above that of both the primary and secondary bond of the original composite, were found for all of the toughening techniques studied. The technique of blending butadiene elastomeric materials has been widely used to toughen epoxy [2] and vinyl ester matrix resins [9].

Secondary Bonding in the Construction of Large Marine Composite Structures

519

The particular blend used is Derekane® 8084 with VTBN, at a 5% loading (VE Toughened A). A previous study [9] has shown this blend to provide much tougher room temperature curing matrix resins with enhanced cohesive and adhesive properties. Similarly, the use of CSR required a blending technique using a highspeed shear stirrer to fully mix the core shell with both resins (PE and VE Toughened B). The immiscibility of various toughening mechanisms with matrix resins is a problem [2] with this sort of technique, though the systems used here are known to be stable for long periods after mixing. 2.0 -r

1.5 --

Mode I Fracture Toughness (kJ/m)

1.0 - •

0.5--

0.0 Primary PE Bond

PE Bond (no sand)

PE Bond (lightsand)

Tough'd PE

PE Interweave

VE Control

TouglVdVE B

Tough'dVE A

FIGURE 3 DCB testing of Primary and secondary bonding systems.

For the toughened secondary bonding systems the observed increased fracture resistance is due to the improved adhesive and cohesive properties of the toughened systems. The failure mechanism of the toughened secondary bond was observed to be more complex than for the failure of the primary bond. The surfaces of the failed secondary bond showed one face mostly devoid of any residual resin, while the other face had a mixture of the primary and secondary bonding resins. An explanation for this is that tough secondary bonding resins adhere much more strongly to the remaining primary resin than the primary resin could adhere to the glass fibre surface. This failure was observed for all of the toughening blends including the VE Control. The tougher the system used, as seen by the Gi result (Figure 3), the more marked this mode of failure would be. The PE Interweave gave a good Gi value considering the matrix resin was the standard polyester. The fracture surfaces showed fibre from the scrim matt on either face, indicating the scrim had a fibre bridging type effect on the crack propagation. The effect would be enhanced given the pliable polymeric materials used in the interweave. This was unexpected as there was residual polyester interphase, unaffected by the interweave scrim, that could have failed at lower loads. There is no obvious explanation as to why the crack would propagate through the tougher scrim interweave region. It appears a value of around 2 kJ/m2 is a maximum achievable limit in secondary bond fracture toughness. This is an acceptable result as it provides a large improvement in mode I fracture toughness when compared to both the primary and conventional secondary bond in the polyester/E-glass composite studied.

520

Secondary Bonding in the Construction of Large Marine Composite Structures

Manufacture of large marine structures using GRP will mean the cost of the two components of the composite will be a large part of the total cost of the structure and in many cases the major reason for the use, or not, of these materials. The use of polyester matrix resins is common, mainly due its low cost compared to other resins such as vinyl esters and epoxies. However the strategic use of the more expensive materials would enhance overall structure integrity and reliability for only minor increases in overall costs. An example of where effective choice of secondary bonding materials could give critical and significant improvement is in the construction of large composite ocean-going vessels. It has been shown [10] that the most likely damage site for heavy impact or shock to such a ship would be in the bulkhead to hull connection. These joints in composite construction generally use an overlaminate method to give the joint strength. Through necessity a large degree of secondary bonding occurs in the various designs of these critical joints. Strategic application of these toughened, more expensive materials could see large increases in initial strength and long-term durability. Improved secondary bonding using the toughened systems studied here would also aid significantly the performance of repairs such as the Scarf repair. CONCLUSION The work detailed in this report shows that secondary bonding problems can be overcome by strategic use of more costly materials in the manufacturing process that would increase resistance to fatigue, impact and shock damage and allow subsequent repairs to be much more effective. When using a secondary bond the inclusion of a toughened system for the first two plies onto a lightly sanded and cleaned surface would enhance the strength and through life reliability of a composite structure. The use of the polyester interweave was also found to be surprisingly effective in improving secondary bond fracture toughness REFERENCES 1. Mouritz A. P., E. Gellert, P. Burchill and K. Challis. "Review of Advanced Composites for Naval Ships and Submarines," Composite Structures, 53 (2001) 21-41, Elseiver Science. 2. Hourston, D. J. and S. Lane, "Rubber Toughened Engineering Plastics," Chapters 8, pp 24359, Chapman and Hall, London, 1994, A.A Collyer ed. 3. Hashemi S., A.J Kinloch and J.G Williams. Proc R Soc Lond, 1990, A427. 4. Carlson L. A. and J B Pipes, "Experimental Techniques in Composite Materials," Elseiver Publications, Chapter 8, 1992. 5. Gdoutos E. E., K. Pilakoutas and C.A. Rodopolous. "Failure Analysis of Industrial Composite Materials," Chapter 4, V. Kostopolous, pp 152-174. McGraw-Hill 2000. 6. Begley J. A. and J. D. Landes. "The J Integral as a Fracture Criterion," Fracture Toughness, Proceedings of the 1971 National Symposium on Fracture Mechanics, Part II, ASTM STP 514, American Society of Testing and Materials, 1972, pp 1-20. 7. Davies, P. and M. L. Benezeggagh. "Interlaminar Mode I Fracture Testing in Applications of Fracture Mechanics in Composites," Composites Materials Series, (K Fredrich ed.), Elsevier Science, Vol 6, pp 81-112. 8. Kardomateas G. A., R. L. Carlson and C. H. Ferrie. "A Micromechanical Model for the Fibre Bridging of Macro-Cracks in Composite Plates," AMD-Vol 196, "Failure Mechanics in Advanced Polymeric Materials," ASME 1994. 9. Simpson G. J., P. J. Burchill and P. J. Pearce. "Tougher Vinyl Ester Resins and their Fibre Glass Composites," Feb 1995 20th Australian Polymer Symposium. 10. Smith C. S., "Design of Marine Structures in Composite Materials," pp 283, Elsevier Science, England, 1990.

Surface Analysis of "Class A" Polymer Composite Substrates for the Automotive Industry P.J. Schubel*, L.T. Harper, T.A. Turner, N.A. Warrior, CD. Rudd University of Nottingham, U.K. K.N. Kendall Aston Martin Lagonda, U.K.

ABSTRACT This work looks at quantifying the level of surface finish needed on a polymer substrate to obtain an acceptable painted finish on a highly visible body panel for use in the automotive sector. A range of materials were investigated with stylus profilometry, light reflectivity and subjective assessment. Results were statistically analysed to produce limits for acceptable surface quality on a bare polymer substrate.

INTRODUCTION The term 'Class A' has been widely used as a classification of surface quality for automotive exterior body panels, however there has been limited work to establish a threshold for identifying a Class A surface. Generally, it is believed that a substrate made of composite material represents a class A surface if its optical appearance is identical to an adjacent steel panel. The market, type segment and brand all influence the definition for a Class A standard [1]. The requirements of a composite body panel for the prestigious automotive sector is generally higher in all aspects compared to mass production vehicles. Emphasis is placed on producing a lightweight panel with a high level of dimensional stability and good surface quality. Polymer matrix fibre composite materials exhibit designer specified mechanical properties and low density, however surface quality is largely dependent on material type, stacking sequence, cure process and mould surface quality. Composite substrates potentially exhibit a range of surface defects which can be attributed to characteristics of manufacture, the application of high gloss coatings (Clearcoat) or a combination of both these factors (see Figure 1). Composite manufacture using liquid moulding may potentially produce porosity and fibre readout as a prevailing surface defect [1]. Porosity occurs as air is entrapped in the surface layers during processing. This can cause an elevation of the coating or destroy the coating layer, creating pinholes due to baking temperatures. Fibre readout becomes more pronounced as the deviation of fibre and resin shrinkage increases during processing as a result of temperature changes. This problem is more evident in thermoplastic processes due to the large temperature drop and high coefficients of linear thermal expansion (CLTE). ""Correspondence Author, ITRC Building, University of Nottingham, University Park, Nottingham, NG7 2RD, England. [email protected]

522

"Class A " Polymer Composite Substrates for the Automotive Industry

Neitzel [1] used surface profilometry to obtain arithmetic mean (Ra) values for a selection of composite surfaces. He observed that glass mat reinforced thermoplastic (GMT) and long fibre reinforced thermoplastic (LFRT) show single filaments, resulting in relatively higher surface roughness. In comparison SMC and RTM both yielded significant improvements in surface quality due to lower CLTE. Laser topography was conducted on both bare and coated (40 urn thick) substrates. Results showed a distinct decrease in surface roughness created by the fabric architecture on the coated substrate. Neitzel concluded that fibre readout and textile induced waviness were considered to be the dominant defects. Wenger [2] and Dickson [3] both used contact stylus profiling to categorise the surface roughness of polymer composite components. These related papers both looked at the effects of tool material, autoclave pressure and fabric lay-up. Wenger stated that the most appropriate parameters for characterising the surface of a composite plaque are Ra, skewness (Rsk) and kurtosis (Rk). The studies were based on an 8-harness satin weave carbon prepreg, moulded on two steel tools of differing hardness. Ra and Rt measurements improved with increased autoclave pressure and skewness increased up to a moulding pressure of 400 kPa but then decreased at higher pressures. Dickson also suggested that there is no immediate difference in surface quality for plain weave and 8 harness satin weave. Halden [4] used a range of amplitudes to categorise the surface of automotive steel body panels and their associated effects on paint quality. He concluded that there was no correlation when comparing the Ra values of steel surfaces to the relative surface tension. Halden [4] also concluded that peak count (Pc) has poor correlation with paint appearance and noted that variation in peak height is one of the critical parameters for paint appearance. Although there have been numerous investigations on automotive related surface quality, studies on the acceptable surface quality limit of a bare polymer substrate are rare. The presented work covers a range of polymer substrates for surface characterization, first by stylus profiling before paint treatment and second by laser diode reflectivity (Wavescan DOI) and subjective assessment after painting. The results are analysed collectively to obtain a quantitative limit for the acceptable surface quality of a bare composite substrate.

Coating

Substrate

Disturbance of coating flow Enclosure of dust particles Colour conformity Roughness, gloss Surface cracking Porosity (coating elevation, blisters, pinholes) Fibre readout, waviness FIGURE 1: Allocation of surface defects on coated substrates [1]

"Class A " Polymer Composite Substrates for the Automotive Industry

523

MATERIALS/ PROCESS The materials used in the study are detailed in Table I, with steel and aluminium being included as reference samples. All mould surfaces were measured to have an Ra of 0.07 um. TABLE I Constituents used in surface quality trials Material

Sample ID Steel Al PD9551E

Twintex

HexMC Sprint

Areal Fibre Mass (gsm)

Resin Type

Mould Process

Scott Bader (resin) Sotira (fibre)

Random mat

3025

RTM

Twintex® commingled Eglass HexMC" carbon

Saint-Gobain Vetrotex

2x2 twill

Ortho UP, 30wt% PVAc, 30wt% CaCO3 Polypropylene

Hexcel

50x8mm strips

Random mat

Sprint" CBS ST85

SP Systems

6

2x2 twill

600

ST86/ S2

Compres sion moulding RFI

ACG

3

2x2 twill 4x4 twill

199 280

VTS263

RFI

SP Systems SP Systems SP Systems/ Hexcel Hexcel (resin) Sotira (fibre) Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Scott Bader (resin) C. Cramer & CO. Hexcel (resin) C. Cramer & CO. Hexcel (resin) C. Cramer & CO. Hexcel (resin) C. Cramer & CO. Hexcel (resin) C. Cramer & CO.

6 12 6

2x2 twill 2x2 twill 2x2 twill Random mat

600 600 300 3025

ST85 ST85 DLS 1554-2 DLS 1648 (epoxy) RT2557 (polyester) RT2557 (polyester) RT2557 (polyester) RT2557 (polyester) PD9749 (vinyl ester) PD9749 (vinyl ester) PD9749 (vinyl ester) PD9749 (vinyl ester) DLS 1648 (epoxy) DLS 1648 (epoxy) DLS 1648 (epoxy) DLS 1648 (epoxy)

RFI RFI LRI RTM

UncoatedFeP04 (0.7 mm) Aluminium6016 (1.2 mm) E-glass preform + E-glass surface veil

3k UP 6k UP

Style 428 carbon

RC300 RC303T RC300LRI 1648E Veil UP

Tow Size (K)

Weave Style

SF95 surfacing film (glass) VTS263 backing layer ZPREG263 surface layer RC300T carbon RC3O3T carbon RC300 carbon LRI E-glass preform + E-glass surface veil Oxidised PAN veil Style 452 carbon Style 452 carbon

Zpreg

Manufacturer

12k UP

Style 424 carbon

VeilVE 3k VE

Oxidised PAN veil Style 452 carbon Style 452 carbon

6k VE

Style 428 carbon

12k VE

Style 424 carbon

Veil EP 3k EP

Oxidised PAN veil Style 452 carbon Style 452 carbon

6k EP

Style 428 carbon

12k EP

Style 424 carbon

Alcan

Continuous 3 3

2x2 twill 2x2 twill

80 200 200

6

2x2 twill

285

12

2x2 twill

660

Continuous 3 3

2x2 twill 2x2 twill

80 200 200

6

2x2 twill

285

12

2x2 twill

660

Continuous 3 3

2x2 twill 2x2 twill

80 200 200

6

2x2 twill

285

12

2x2 twill

660

RFI

RTM RTM RTM RTM RTM RTM RTM RTM RTM RTM RTM RTM

RFI - Resin Film Infusion LRI - Liquid Resin Infusion RTM - Resin Transfer Moulding

Paint Process Half of each test plaque (300 x 210 mm) was painted in an automotive paint process with no excessive abrasion on the surface. The panel was degreased with a degreasing agent, keyed using a 3M® fine grade sanding sponge then degreased again. Two coats of high build primer were sprayed to obtain a film build of 65 um. This was then baked at 80 °C for 20 mins. Once cooled, the surface was lightly sanded with P400 paper and a sealing primer was applied and baked, followed by a light sanding with P400 paper. Two

524

"Class A " Polymer Composite Substrates for the Automotive Industry

coats of solid, dark base paint and two coats of Clearcoat were applied, producing an average total film build of 160 urn. Each Clearcoat was baked at 80 °C for 20 mins. Surface Characterisation Surface roughness was recorded on bare substrates using stylus profiling. A Mitutoyo Surftest SV622 profiler with 5 um stylus and auto drive unit was used to measure an evaluation length of 12.5 mm at a speed of 0.5 mm/s and pitch of 0.8 um. An 'R' profile was applied with a Gaussian filter and cut-off length of 0.8mm to exclude surface waviness. Five traces in both x and y directions were systematically taken from various locations on the sample to obtain an average reading. The surface waviness of the painted substrates was measured using a BYK Gardner Wavescan DOI with built-in laser diode light source and optical camera. A minimum of three scans in the x and y direction was taken over a scan length of 100 mm to obtain an average value. Visual assessment of the substrates was conducted to categorise painted surface quality and relate human perception to machine sensitivity. 15 subjects were used to assess the panels under florescent light to determine the visibility of the defects on the painted surface as a direct result of the patterns seen on the bare substrate. RESULTS & DISCUSSION Subjective visual assessment rated the dedicated body paneling systems (PD9551E and semi pre-pregs), RTM moulded epoxy substrates and the reference steel and aluminium substrates to show no visible defects on the painted surface. Commingled Eglass polypropylene was determined to have the most visible defects on the painted surface, with strong fibre readout caused by high CLTE. Figures 2 and 3 show the samples grouped into three categories in accordance with results obtained from subjective assessment i.e. No visible defects, Visible defects, Highly visible defects. Combined Ford (CF), shortwave (SW) and longwave (LW) readings obtained using a Wavescan DOI (Figure 2), show general trends that match subjective assessment. Linear trendlines fitted to CF, SW and LW results show that substrates classed with having no visible defects are generally within tolerance ranges specified by the original equipment manufacture automotive paint standards for non flattened/polished finishes. Surface roughness measurements were recorded for Ra, Rz, RzDIN, Rq, Ku and Sk. The surface roughness measurements for the bare substrates were analysed using normal (Gaussian) distribution and confidence intervals. The Kurtosis and Skewness of the bare substrates showed no correlation to the resulting paint surface quality, with Rz, RzDIN and Rq showing major discrepancies (results not presented). The arithmetic mean (Ra) of the bare polymer substrate surfaces (Figure 3) best depict the painted surface quality trends measured using Wavescan DOI. Figures 4a,b and c show the normal distribution for the grouped surface roughness data of the bare substrates seen in Figure 3. In each case a normal distribution was assumed and the standard error approximately equalled the standard deviation. Table II shows the resulting 95 % confidence intervals calculated for each of the three categories. From the results it was possible to set a range for acceptable and non-acceptable surface quality for Class A bare polymer substrates. A bare polymer substrate with a Class A surface finish was found to have an Ra equal or less than 0.16 um. Visible defects in the painted surface would be seen on bare substrates above an Ra of 0.16 um and highly visible paint defects would be expected on bare substrates above an Ra of 0.54 um.

"Class A " Polymer Composite Substrates for the Automotive Industry

525

The calculated lower limit of Ra (0.16 um) is comparable to the measured Ra of an aluminium body panel, however a steel body panel measures approximately 1 um Ra. The discrepancy can be attributed to the fine amorphous structure of the steel substrate, which is easily masked under the paint process to produce an acceptable painted surface finish.

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"Class A " Polymer Composite Substrates for the Automotive Industry

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CONCLUSIONS Results show that Wavescan DOI reproduces the human visual perception of an acceptable painted polymer substrate with reasonable accuracy. Assessing surface roughness parameters in relation to Wavescan DOI and subjective assessment results, show that the arithmetic mean (Ra) best represents the expected paint quality from the bare substrate. For the materials presented, it has been shown that an acceptable painted automotive finish is obtainable on a bare polymer substrate below or equal to an Ra of 0.16 um. However, each material has its own unique surface pattern, which adversely affects the final painted substrate. The use of instrumented devices is a useful tool for predicting surface quality, however human visual assessment is still a necessary component in assessing painted Class A polymer substrates. REFERENCES 1. Neitzel, M., et al., Surface quality characterisation of textile-reinforced thermoplastics. Polymer composite, 2000.21(4): p. 630-635. 2. Wenger W., et al., The surface-finish characteristics of composite components. Mat proc tech, 1992. 33: p. 439-452. 3. Dickson G.R. and Mcllhagger R., Assessing the surface finish ofpolymer composite components. J. Mach. Tools Manufact., 1992. 32: p. 51-56. 4. Halden M., Characterisation of steel sheet surfaces in order to predict surface appearance after painting. IBEC, 1997: p. 115-120.

Injection Molding of Silk Composite from Industrial Fiber Waste Teruo Kimura*, Tomohiro Suzuki Kyoto Institute of Technology, Advanced Fibro Science, Japan Seiji Hatta Kyoto Municipal Industrial Research Institute, Japan

ABSTRACT This paper presents a study on injection molding of silk composite from industrial fiber waste. The cut waste of silk textile was pre-treated by opener and card machines and mixed with PP fiber. The sliver-type silk/PP mixture was fed into the injection molding machine directly. As a result, the silk fiber reinforced PP composites were obtained. The mechanical properties of composites were measured and discussed. It is concluded here that the silk waste is good for the reinforcement of composite. The results suggest that the injection molding method described herein shows promise for contributing toward the material recycling of cut waste of silk textile. INTRODUCTION In recent years, the textile industry has taken a growing interest in developing system for recycling waste fibers which result from the process of manufacturing products with the goals of protecting the environment and saving energy. For example, the large amounts of cut wastes of silk textile are discharged from the necktie manufacture factory. However, most of these waste products are destroyed by fire or buried underground. Meanwhile, in the field of composite materials, recent attention has been shifting from glass and carbon fibers to natural fibers because of their renewable nature, low cost, low density and low energy consumption. Application of the cellulosic fibers such as jute, flax and hemp to the reinforcement of composites has been discussed in many papers[ 1-4]. Few papers, however, can be seen about the protein fiber as a reinforcement of composites. Under these circumstances, the present paper discusses the recyclability of cur waste of silk(protein fiber) textile as a reinforcement of fiber reinforced composite. SILK FIBER WASTE Figure 1 shows the cut wastes of silk textile which are discharged from the necktie manufacture factory. As can be seen in the figure, the silk fabrics were dyed in many colors. In this paper, such silk waste was used for the reinforcement. The tensile strength and modulus of silk fiber are about 500MPa and lOGPa, respectively.

* Corresponding author, Matsugasaki, Sakyo-ku [email protected]

,Kyoto 606-8585, Japan, +81-75-724-7863, Email:

528

Injection Molding of Silk Composite from Industrial Fiber Waste

FIGURE 1 Silkfiberwaste

PRE-MOLDING OF SILK/PP SLIVER The cut waste of silk textile was pre-treated by opener and card machines and mixed with PP fiber as shown in Fig.2. Namely, the PP fiber was used as a matrix material of composites.

FIGURE 2 Mixing of silk and PPfibersby using card machine

Figure 3 shows the well-mixed silk/PP sliver. The silk length is about 10 mm in the sliver. The volume fraction of silk fibers was adjusted by regulating the mixing ratio of silk and PP fibers. As the silk fiber waste used in this research was not intended for recycling, PP(density of 0.91g/cm3, graft denaturation rate of 0.30wt%) denaturated with anhydro-maleic acid was used as adhesive resin with silk fibers and non-extended fibers were fabricated using mono-filament solvent yarning device in order to facilitate supplying to the molding machine, as discussed later.

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Figure 4 shows anhydromaleic acid denatured PP fibers (called g-PP hereafter) wound by a bobbin.

Injection Molding of Silk Composite from Industrial Fiber Waste

529

FIGURE 4 Anhydromaleic acid denaturedPP fibers

INJECTION MOLDING METHOD AND MECHANICAL TESTS For molding of silk fiber reinforced PP composite materials, the injection molding method was used. In this case, sliver-type silk/PP mixture was fed into the injection machine directly without forming pellets. With this method, simultaneous supply of woven g-PP is possible. Although g-PP can be supplied in the pellet shape, the supply can be stabilized by yarning. Figure 5 shows an overview of the molding machine used (manufactured by Toyo Machinery & Metal CaLtd., Plaster Ti-30G).

FIGURE 5 Injection molding method

The molding temperature 190deg. was determined as the melting point of PP fiber. The molds were tensile testing specimens whose size followed the JIS K 7133 standard. The specimens for bending and impact tests were cot from the molded specimens. The tensile and bending properties were measured at an ambient temperature using INSTRON (model 4206) according to JIS K7113 and JIS K 7171 standards, respectively. Moreover, impact test was done on an Izod impact tester (model DG-IB) according to JIS K 7110. The specimen dimensions are 80x30x 10 mm. Five samples were tested in each set. RESULTS AND DISCUSSION The sliver of silk/PP fibers used was bitten by the screws of the injection machine by being lightly pushed into the outlet of the machine at the start of molding and automatic continuous molding was possible thereafter. Figure 6 shows the molded tensile test piece. The specimen turned black because of the dyed silk fibers.

Injection Molding of Silk Composite from Industrial Fiber Waste

530

FIGURE 6 Molded test specimen

Figure 7 shows the SEM observations of cross-section of molded specimen without g-PP. The good dispersion of silk fibers can be seen in this figure.

FIGURE 7 SEM observation of cross section (V, =23%)

Figures 8(a) and (b) also show the SEM observation of interface between silk fiber and PP matrix for the specimens with/without g-PP. The lack of adhesion can be seen for the specimen without g-PP. However, the good adhesion can be achieved for the specimen with g-PP.

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FIGURE 8 SEM observation of interface between silk and PP matrix

Attention is now focused on the tensile properties of the molded composites. Figure 9(a) and (b) shows the relation between the volume fraction of silk fiber and the tensile strength and modulus of the composites, respectively.

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The lozenges in the figure are the result without using g-PP. As is seen from these figures, the strength and modulus were improved along with the increase of the volume fraction of silk fiber. Especially, the fairly large strength and modulus can be obtained for the composites with using g-PP. It is believed that such property improvement is due to the improvement of adhesion between the matrix and silk fibers by g-PP as is seen from the cross section photo in Fig.8. Figures 10 (a) and (b) show the bending strength and modulus, respectively. It is cleared from the figures that the bending properties also improved along the increase of the volume fraction of silk fiber.

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The impact value for matrix and composite materials can be seen in Fig. 11. It is seen from the figure that the impact value becomes larger for the larger volume fraction of silk fiber. However, the value for the specimens with g-PP takes a lower value than that for the specimen without g-pp. This fact suggests that the lack of adhesion between silk fiber and matrix is advantage for the impact energy absorption.

Injection Molding of Silk Composite from Industrial Fiber Waste

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CONCLUSIONS The present paper discussed the recyclability of cur waste of silk (protein fiber) textile as a reinforcement of fiber reinforced composite. The molding method in which the cut waste of silk fabrics was pre-treated by opener and card machine as raw material of injection molding was proposed. As a result, it is concluded that the silk wastes used are the good reinforcement of composites. The molding method of composite materials described in the present paper shows promise as a contribution towards the recycling of cut waste silk fabrics generated in the process of manufacturing.

REFERENCES 1. 2. 3. 4.

X.chen, Q.Guo and YMi. 1998. "Bamboo Fiber-Reinforced Polypropylene Composite: A Study of the Mechanical Properties", J.ofApplied Polymer Science, 69:1891-1899. MAvella, L.Casale, RDeU'erba, B.Focher, E.Martusceffi and A.Marzetti. 1998. "Broom Fibers as Reinforcing Materials for Polypropylene-Based Composites", J.ofApplied Polymer Science, 68:1077-1089. Norma EJVIarcovich, Maria M.Reboredo and M.LArangurea 1998. "Mechanical Properties of Woodflour Unsaturated Polyester Composites",J.of Applied Polymer Science, 70:2121-2131. Michael P.Wolcott, S.Yin and Timothy GRials. 2000. "Using Dynamic Mechanical Spectroscopy to Monitor the Crystallization of PP/MAPP Blendin thePresence of Wood",Composite Interface^:3-12.

Test of Full Scale Integrally Stiffened Composite Spoiler Adrian Rispler* Hawker de Havilland, Australia

ABSTRACT An integrally stiffened composite spoiler for a large civil aircraft has been designed, manufactured and tested. The spoiler is a spar and rib dominated design with six hinges and a single central actuator. This paper describes the analysis of the spoiler test set-up and the correlation between the predicted and actual stiffness of a spoiler for a typical large airliner. The aims of this test program were fourfold. Firstly to carry out an assessment of the spoiler's structural strength. Secondly to evaluate the overall stiffness and buckling characteristics of the spoiler. Thirdly to validate the theoretically predicted strength and deformation characteristics from numerical analysis with the actual test results. The correlation of the model allows for the validation of additional technical requirements such as aerodynamic smoothness by means of analysis only. Finally, to validate the manufacturing methodology employed. Three tests were conducted at ambient temperature using the same test article, hi all tests, an enforced displacement proportional to the limit load condition was applied to the spoiler to replicate the wing bending component. The set-up represents the most critical spoiler deployment position. The first test subjected the spoiler below Limit Load and was carried out in order to establish the buckling performance of the spoiler. The second test went up to 1.0 Limit Load with the final test conducted up to 1.5 Limit Load (DUL). Strain and displacement results were recorded throughout the duration of the tests to allow for the correlation of experimental results with the finite element analysis predictions. The test was deemed to be successful as FAR and specific performance requirements were all met. The onset of buckling as well as strain trends for most of the strain gauges showed good correlation between prediction and test results.

INTRODUCTION A co-cured carbon fibre composite control surface demonstrator has been designed, manufactured and tested [1],[2]. The spoiler, shown in Figure 1, is 2.5 metre in span and 1.2 metres in chord is based on a design study for a large civil aircraft. The spoiler is a spar and rib dominated design with six hinges, two of which are nonfunctional and only come into play if one of the functional hinges fail. The spoiler has a single central actuator. Three structural tests were carried out on the same test article. The set-up represents the most critical spoiler deployment position. These tests were conducted from zero Limit Load (DLL) up to design ultimate load (DUL) as described below for the critical deployed configuration: * Corresponding author, Hawker de Havilland, PO Box 30, Bankstown, NSW 2200, Fax (02) 9772-8301, email: [email protected]

534

Full Scale Integrally Stiffened Composite Spoiler

1. 0.8 LL (To ascertain buckling requirements, ie no buckling up to 0.8LL) 2. 1.0 LL (Limit Load case) 3. 1.5 LL (Ultimate Load case) Closing Ribs ^

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The loads applied to the structure consist of aerodynamic as well as wing bending loads. Wing bending loads are applied through enforced displacements at Hinge 1 and Hinge 6 fittings. Aerodynamic loads are applied by the use of hydraulic rams, whose loads are then dispersed through the whiffletree into the spoiler by means of pivoted links and foam pads. This paper describes the analysis of the spoiler under test conditions and correlation of test results with finite element analysis predictions of displacements and strain gage readings for the ultimate load case. EXPERIMENTAL SET-UP Testing was carried out under ambient conditions and the test article was tested at room temperature dry conditions. The test was carried out at the bi-axial test facilities of the University of New South Wales, Solids Laboratory. A schematic of the test article with installed hinges and actuators and the upper and lower whiffletree is shown in Figure 2. Figure 3 shows a front view, looking on the spoiler upper skin, of the actual test set-up. Three tests were conducted using the same test article. In all tests, an enforced displacement proportional to the limit load condition was applied to the spoiler to replicate the wing bending component. Strain and displacement results were recorded throughout the duration of the tests to allow for the correlation of experimental results with the finite element analysis predictions.

Full Scale Integrally Stiffened Composite Spoiler

535

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Full Scale Integrally Stiffened Composite Spoiler

Each hydraulic ram or actuator feeds two articulated form-boards. The load distribution employed during the test replicates the critical load case. The form-boards apply a quasi-uniform spanwise distribution and trapezoidal chordwise distribution. The whiffletree is composed of 6 upper/lower form-boards, which are placed at rib locations. The spoiler is loaded through the upper skin by the foam pads attached to the form-boards through segmented pivoted links. The two-segmented pivoted links per form-board ensure the load is distributed along the full chord top skin. This arrangement is required to accommodate both the pre-stressed shape of the spoiler and its deformed shape under load due to wing bending and chordwise bending under the simulated air load. FINITE ELEMENT ANALYSIS PATRAN/NASTRAN finite element modelling and analysis were employed in all cases to calculate stresses, eigenvalues and deflections of the spoiler under the aerodynamic pressure provided as shown on Figure 4 and under the test load cases to simulate the aerodynamic loading. The model consisted of 4083 Nodes, 4511 CQUAD4 elements, 17 CTRIA3 elements, 216 CHEXA elements, 37 RBAR elements and 2 RROD elements. For the test case (deployed position), the pressure distribution was applied at pivoted links /form-board positions. As each of these foam-padded links was connected to form-boards by means of single pins and spherical bearings; it was assumed that the load was distributed along the full length of each articulated link. The loads to be transferred at each link were calculated from equilibrium equations at each section and area of each link to yield a pressure load. This pressure load was calculated for each link and divided by the load percentage and applied on the QUALM elements where contact existed between foam padded link and top skin of spoiler. Wing bending was super-imposed with the pressure load. The actuator jack position was rotated accordingly for the deployed position. Boundary conditions and pressure loading as employed for the test case (DHL) is shown in Figure 4. SPCs were used to constrain hinge points at Hinges 3 and 4 in the x, y and z directions. MPCs were used to represent the links at Hinges 1 and 6, and for the connection between the actuator hinges and the actuator point. A further SPC was applied at the actuator point in the x, y and z directions. Induced wing bending effects, at 1.0 DLL, were simulated by enforced displacement of 7mm in the upward direction at the link nodes at Hinges 1 and 6. SPCs were also applied at these enforced displacement points to constrain movement in the chordwise direction. These enforced displacements were factored according to the load case being analysed, i.e. for 1.5LL analysis; a factor of 1.5 was applied to the enforced displacement values. When analysing the spoiler to represent the deployed test position, the MPC connecting the centreline between the actuator hinges and the main actuator point was rotated to represent the deployed position about the actuator centreline, hence moving the main actuator point. The enforced displacements at Hinges 1 and 6 were also split into chordwise and out of plane components. Further MPCs were included in the deployed case to connect the hinge fittings to the bottom skin in to prevent the elements moving through each other (in this case there is a pressure between the fittings and bottom skin).

Full Scale Integrally Stiffened Composite Spoiler

537

TEST RESULTS The correlation is applicable for the 1.5LL test and analysis carried out for the critical spoiler deployed position.

efo FIGURE 4 Test pressure loading and boundary conditions

All the available results from the data acquisition system are compared against their finite element prediction by means of graphically representing their discrete values at 10% intervals for each test. Visually no buckling could be detected, although the back to back strain gages show panel instability between 1.0 LL and 1.1 LL (Figures 5,6). There is a marked change in slope occurring almost simultaneously at the outboard and inboard sections (where strain gages were positioned) at 1.1 LL. This lead to the belief that although the onset of buckling occurred at approximately 1.0 LL, the panels where the strain gages were installed undergo post-buckling behaviour at values above 1.1 LL. This can be clearly seen by the diverging plots of back to back strain gauges above 1.1 LL.

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538

Full Scale Integrally Stiffened Composite Spoiler

The front spar close to the actuator location was identified as a critical region and a strain gauge was placed there to monitor the maximum strain. Figure 7 depicts the correlation between predicted and actual critical strain showing that the finite element analysis accurately predicted the strain in this region. Finally, Figure 8 shows the measured strain on the actuator link compared to the predicted one. This strain was monitored to ensure that the test item was subjected to the correct hinge moment. 300.0

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CONCLUSIONS The test was considered to be successful as the design ultimate load (DUL) was slightly exceeded and this load was maintained for over 5 minutes as measurements were recorded. FAR Part 25 Sub-Part C, Sec. 25.305 Strength and deformation (b) requires that "The structure must be able to support ultimate loads without failure for at least 3 seconds". Furthermore, the same directives stipulate that "(a) the structure must be able to support limit loads without detrimental permanent deformation. At any load up to limit loads, the deformation may not interfere with safe operation". No permanent deformation was seen after unloading once the limit load test was completed. This was further corroborated during the third and final test up to 1.5 LL by looking for hysteresis effects on the strain and deflection plots. Therefore regulatory requirements were all met. Furthermore and after unloading of the structure, NDI indicated no failure or delamination between the co-moulded bottom skin and the substructure (ribs & spars). Buckling was not seen to occur under 1.0 LL whereas the technical requirements specified that no buckling should occur up to 0.8 LL. Critical strains correlated well to predicted values. However, actual maximum tip displacement was underestimated by approximately 25 %. ACKNOWLEDGEMENTS The author would like to thank the RMIT Start Grant Team and UNSW staff for their help during the set-up and testing of the spoiler at University of New South Wales. The efforts of Mr Michael Marelli (CRC-ACS) in manufacturing the test rig components well within schedule and budget are greatly appreciated. Thanks are also extended to Dr Ben Qi (CRC-ACS) and Dr Roger Li (UNSW) for their help in setting up the Data Acquisition System. REFERENCES 1. 2.

Rispler, A.R., Raju, J., 2002. "Design and Analysis of a Composite Spoiler", Report No. 180-RSM20002, Issue No. 1, Hawker de Havilland Internal report. Rispler, A.R., Raju, J., Varbola, M., McMahon, C , 2002. "Spoiler Test Analysis and Correlation", Report No. 180-RSM20-003, Issue No. 1, Hawker de Havilland Internal report.

Study on the Polypropylene(PP) Fiber/Cement Mortar Workability Hui Zhang, Liming Zou, Jianhua Ni, Yimin Wang* State Key Laboratory for Chemical Fibers and Polymer Materials Donghua University, Shanghai, 200051, P. R. China

ABSTRACT The ways to measure polypropylene fiber cement mortar workability are simply discussed in this article. By measuring the flowing extent, the effects of length and content of polypropylene fiber, the ratio of water to cement, mineral additive and the ratio of cement to sand are discussed in this paper. The results show that: 1) the longer polypropylene fiber length and the larger the content, the lower the flow extent of cement mortar; 2) with the increase of the ratio of water to cement, the flow extent is also increased; 3) as the decrease of the ratio of cement to sand, the flow extent of polypropylene fiber cement mortar will be increased; 4). for mineral additive, the addition of fly ash can improve the flow extent of polypropylene fiber cement mortar, while the silica fume can reduce slightly the flow extent of polypropylene fiber cement mortar.

INTRODUCTION The workability of cement mortar is a comprehensive technical target and significant in practice construction, that is because it has something with its mechanical performance such as strength and its efficacy in actual application [1]. However, it's very difficult to find a practical and effective way to predict the workability of cement mortar. Since the workability of cement mortar is markedly affected by flow extent, the general way is to measure its flow extent, and according to the acquired results it is determined whether the cement mortar is fit for practice performance requirement. There are many ways to measure the flow extent, which could be classified into two types: one is to put some external force on cement mortar, generated transmutation value is commended to be the scale of flow extent, and the other is to make cement mortar absorb certain energy to generate transmutation, absorption energy value is the scale of flow extent. The tests include flow cone method and vibrating method or mortar thickness method etc. Polypropylene fiber has many special features such as easy processing, good chemical resistance, high-energy absorption, 100% wet strength retention and low density [2]. Polypropylene fiber has been used as secondly reinforcement in cement material for over thirty years [3] and the studies are still active in ACBM (Advanced Cement * Corresponding author, Donghua University, Tel: 86-21-62379785, Fax: 86-21-62379309, E-mail address: [email protected]

540

Polypropylene(PP) Fiber/Cement Mortar Workability

Based Materials ) , American Northwestern University, American Concrete Institute[4-5] and some Japanese research institutes, Tongji University [6-7] and Donghua University of China etc. [2,8]. Polypropylene fiber can greatly improve cement materials performances such as anti-crack property, toughness [9], impact resistance [10] and permeability [11]. This paper makes use of vibrating method testing flow extent to evaluate the workability of polypropylene fiber cement mortar. EXPERIMENTAL Materials Materials used in this experiments include: 1) Jiaxin 325# common silicate cement produced by Taiwan Jiaxin Cement Group; 2) tap water; 3)mineral additives produced by Shanghai Fulai Zaoxing Material Corporation; 4)standard sand; 5)polypropylene fiber produced by Zhangjiagang Polypropylene Fiber Factory, the features are presented in Table I. Table I The features of polypropylene fiber

Polypropylene fiber Density /g/cm 3 Tensile strength / Mpa Elastic modulus / Gpa Melting point/ °C Wet strength retention / % Acid and alkali resistance

Features 091 400 8.3 160—170 100 very good

Measurements Rationed cement, sand and fiber are mixed in a container, stirred for 5 seconds, and then tap water was fed in slowly, stirred for another 3 minutes. The mixed mortar is fed promptly into the cone for measuring flow extent at two layers. The first layer of mortar is about 2/3-cone height, uniformly pressed, and then the second layer of mortar is put on it, 20mm higher than the cone height, uniformly pressed again. The cone is taken out; the sample is vibrated for 30 times at the speed of once per second. The max diffuse diameter and its upright diameter with the calipers is measured, the flow extent (mm) of cement mortar is attained. The operation must be finished in 5 minutes [12]. RESULTS AND DISCUSSIONS The effects of PP fiber length and content on the cement mortar flow extent The length and content of polypropylene fiber added are two of the most important parameters influencing the properties of cement mortar. The following figures show the effects on the polypropylene fiber cement mortar flow extent. In Figure la, it is noted that with the increase of the length of polypropylene fiber, the fiber crimp in the mortar increases, conglutination of fiber and mortar is higher, and the viscosity of polypropylene fiber cement mortar is therefore enlarged. It leads

Polypropylene(PP) Fiber/Cement Mortar Workability

541

to the decrease of flow extent of polypropylene fiber cement mortar; In Figure lb, it is noted that with the increase of the content of polypropylene fiber, the number of PP fiber is more, the viscosity of polypropylene fiber cement mortar is enlarged and the flow extent of polypropylene fiber cement mortar also goes down.

195-,

220-

190E 200-

— 185|

180180-

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170-

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120 0.0

150 5cm

8cm

15cm

0.3

19cm

0.6

0.9

1.2

1.5

1.8

21

3

PPfiberccntent( kg'm )

FPfiberlergth

FIGURE 1 (a) The effect of PP fiber length on flow extent, (b) The effect of PP fiber content on flow extent

The effects of the ratio of water to cement on the cement mortar flow extent The ratio of water to cement is the most important factor affecting the strength of cement material. Figure 2 shows the relation of flow extent and the ratio of water to cement.

2001 190•§ ISO's' 170-

I 16°-

| 150o) 140o 130120 0.40

0.45

0.50

0.55

0.60

the ratio of water to cement

FIGURE 2 The effect of ratio of water to cement on the PP fiber cement mortar flow extent

Polypropylene(PP) Fiber/Cement Mortar Workability

542

From Figure 2, it is noted that the PP fiber cement mortar flow extent goes down with the decrease of the ratio of water to cement. When the ratio of water to cement goes down to 0.4, PP fiber can't be distributed uniformly and conglobations would be happened in the matrix, which cause stress partly concentrated. The sample surface has much disfigurement and is difficult to mold. Adjusting the ratio of water to cement, which making PP fiber distribute uniformly in the matrix, can therefore control PP fiber cement mortar flow extent. Thus, it is possible to get the predicted mechanical properties of polypropylene fiber cement composites. The effects of the ratio of cement to sand on the cement mortar flow extent

180-| 175-

f. |

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B ISO'S |" 155£ 150-

145

1.0:2.5

1.0:2.0

1.0:1.5

1.0:1.0

the ratio of cement to sand

FIGURE 3 The effect of ratio of cement to sand on the flow extent of PP fiber cement mortar

The ratio of cement to sand is also a very important parameter. Figure 3 shows the relation of flow extent and the ratio of cement to sand. From Figure 3, it is noted that the PP fiber cement mortar flow extent increases slowly with the decline of the ratio of cement to sand. That is because when the amount of sand increases, the viscosity of mortar matrix material will go down, resulting in the increase of polypropylene fiber cement mortar flow extent. The effects of the mineral additive on the cement mortar flow extent There are two functions to add appropriate content of mineral additive. One is to make use of the high fines property of mineral additive, making PP fiber distributed uniformly in the matrix; the other is to improve the compactness of the matrix by adding the mineral additive and modify the interphase behavior of polypropylene fiber and cement matrix, enhancing the strength of the composite.

Polypropylene(PP) Fiber/Cement Mortar Workability

120 0.0

2.5

5.0

543

7.5 10.0 12.5 15.0 17.5 20.0

the quantity of mineral additive( %)

FIGURE 4 The effect of the mineral additives on the PP fiber cement mortar flow extent

In this experiment, two kinds of mineral additives are used: silica fume (SF) and fly ash (FA). The effects of the mineral materials on the PP fiber cement mortar flow extent are shown in Figure 4. From Figure 4, it is noted that the mortar flow extent slightly goes down with the adding of silica fume. The adding of silica fume can fill the vacant space of cement, sand and fibers, with the improvement of compactness of the mortar, the mortar flow extent goes down; whereas when fly ash is added, two things have to be considered [13]. From physical aspect, granule fly ash can act as a lubricator and from chemical aspect, the hydration reaction rate of fly ash is slower comparing to the cement, consequently, the absorption of the water is reduced, which making the whole structure slack, and it can improve the cement mortar flow property. CONCLUSIONS The longer the polypropylene fiber length and the larger the fiber content, the lower the cement mortar flow extent. With the increase of ratio of water to cement, the flow extent is also increased; As the decrease of the ratio of cement to sand, the flow extent of polypropylene fiber cement mortar will be increased. For mineral additive, the addition of fly ash can improve the flow extent of polypropylene fiber cement mortar, while silica fume can reduce slightly the flow extent of polypropylene fiber cement mortar. REFERENCES 1. 2. 3. 4.

Li Wei-wen, Leng Fa-guang, Qi Yun, Xing Feng.2001. "Research and Experiment on Workability of Concrete Incorporated with Cemfiber," Concrete, No.9: 54-58 He Yuan, Liao Xian-ting, Wang Yi-min.1998. "The Application of Polypropylene Stable in Cement Concrete'" Synthetic Technology and Application, 13(4): 36-39 L.Tu, D.Kruger, J.B. Wagener and P.A.B. Carstens.1998, "Surface Modified Polypropylene Fibers for Use in Concrete," Magazine of Concrete, 50(3), 209-217 Ziad Bayasi, Marc Mclntyre.2002. "Application of Fibrillated Polypropylene Fibers for Restraint of Plastic Shrinkage Cracking in Silica Fume Concrete", ACI Materials Journal, 99(4): 337-344

544 5. 6.

7. 8.

9. 10.

11. 12. 13.

Polypropylene(PP) Fiber/Cement Mortar Workability

P. S. Ravanbakhas.1998. "Control of Plastic Shrinkage Cracking with Specialty Cellulose fibers," ACI Materials Journal, 95(4), 429-435 Ma Yi-ping, Tan Mu-hua.2000. "Effects of Polypropylene Fibers on the Physical and Mechanical Properties of Cement Based Composites( I )-Plastic Shrinkage Cracking Resistance," Journal of Building Materials, 3(1): 48-52 Ma Yi-ping, Tan Mu-hua, Wu Ke-ru. 2001, "The Effects of PP Fiber Geometry on Cement Mortar Plastic Shrinkage Cracking Resistance," China Concrete and Cement Products, No.2, 38-40 Liao Xian-ting, He Yuan, Yang Xu-gang, Wang Yi-min.2000, "Interfacial Behavior of PP Fiber Reinforced Cement Composite ( II ) -SEM Observation and Morphological Study on Fracture Surface," Journal of Building Materials, 3(1): 64-67 Victor C. Li & Mohamed M..1996, "Toughening in Cement Based Composites," Cement & Concrete Composites, 18(4): 239-249 A.M.Alhozaimy, P.Soroushian & F. Mirza. 1996. "Mechanical Properties of Polypropylene Fiber Reinforced Concrete and the Effects of Pozzolanic Materials," Cement & Concrete Composites, 18(2): 85-92 Zhu Jiang.2001. "Water Resistance Mechanism of Polypropylene Fiber Concrete (Mortar) and its Application Technique," Architecture Technology, 32(7): 456 Shi Hui-sheng.1999. "Inorganic Nonmetal Materials Experiment," Tongji University Publisher Wu Cheng-zhen.1999. "Influences of Cements and Reduction-Water Agents on Performances of Cement Mortar," Journal of Nanjing University of Chemical Technology, 21(5): 40-41

Hybrid Composites for Engineering Application Faiz Ahmad*, M. Ridzuan A. Latif Mechanical Engineering Dept, Universiti Teknologi PETRONAS 31750 TRONOH, Perak Darul Ridzuan, Malaysia. Harris Nisar Dept. of Aerospace Engineering, College of Aeronautical Eng. PAF Academy, Risalpur, NWFP, Pakistan.

ABSTRACT Composite materials have extensive engineering application where strength to weight ratio, low cost and ease of fabrication are required. Hybrid composites provide combination of properties such as tensile modulus, compressive strength and impact strength which can not be realized in composite materials. Results presented in this paper relate to the development of glass, kevlar49 and carbon woven fibres (WF) reinforced polyester and epoxy based hybrid composites. In our study, a range of composites containing various volume fractions of woven fabric were manufactured by hand lay-up technique and tested mechanically. The results have shown linear increase in tensile strength with an increase in volume fraction fabric for both polyester and epoxy based composites. Hybrid composites have shown up to more than 100% increase in modulus of polyester composites while glass fabric reinforced polyester composites showed high tensile properties.

INTRODUCTION Application of composite materials is increasing due to their lightweight, high modulus and tensile properties. Favourable consideration is given to composite materials over the conventional materials due to ease in fabrication and high strength to weight ratio [1]. The development of glass fibre reinforced composites started in 1940's has revolutionized the materials world. Presently, composite materials have found extensive applications particularly in aviation industry [2], sports, naval [3] and automobiles [4]. The development of hybrid composites [5-6, 12] has led to the application where combination of properties such as tensile strength, tensile modulus [7-8] and impact is required [9-13]. This paper presents results of an experimental work based on woven glass Kevlar and carbon fabric (WF) reinforced polyester and epoxy composites.

* Corresponding author. Mechanical Engineering Dept., Universiti Teknologi.PETRONAS 31750 TRONOH, Perak Darul Ridzuan, Malaysia

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546 MATERIALS

Matrix Materials Polyester and epoxy resin were used as matrix materials for the composites. Polyester resin (civicl99) and hardener (norpol catalyst No. 1)*. Polyester resin was cured at room temperature and curing time was varied between 2 to 4 hrs. Epoxy with hardener for the composites fabricated were cured at 50°C and curing time was varied between 4 to 6 hrs. Fibrous Materials Three types of materials were used as the reinforcement: S-glass woven fabric (WF), Kevlar49 woven fabric and carbon fabric (woven fabric). The properties of matrices and fibres are listed in Table l(a) and (b) respectively.

(a) Resin

Polyesterl99 Epoxy

Tensile strength (MPa) 41.8 83.6

TABLE I (a) Resin and (b) Fibre Properties (b) Modulus (GPa) 2.09 3.83

Fibres

Carbon Glass Kevlar49

Tensile strength (MPa) 4500 2600 2900

Modulus (GPa) 251 73 125

EXPERIMENTAL WORK The following procedure was adopted for manufacture of polymer composites samples of 8X8 inch square plate. This size was selected to manufacture a minimum four test bars for testing mechanical properties of the composite samples. Mould surface was cleaned to remove impurities and was coated with wax for easy removal of the sample. Polyester and hardener was homogenized in the ratio of 100:1. In the case of epoxy based composites the ratio of hardener to epoxy was kept at 9:10. Mixture of polyester was uniformly coated on the mould surface already coated with wax to get an excellent exterior surface finish of the composite. The desired size of fabric was spread on the resin or epoxy and another coat was applied with the help of brush. Similar procedure was repeated to produce multiple layered composites containing various volume fractions of fibres. Finally the samples were left for curing as per requirement. Polyester based composites were named as P-type composites and epoxy based composites were named as E-type composites. P-type Composites The following were produced to study various effects on the P-type composites. P-type composites containing glass (WF) 15, 30, 45, 60% volume fraction were produced to study the effect of increase in volume fraction and directionality of fibres on modulus and tensile strength of composites. A composite reinforced with glass fibre mat, non-woven fabric (NWF) containing 15, 30, 45, 60% volume was produced to compare the effects of volume fraction of fibres on modulus and tensile properties of composites. P-type composites containing 15, 30,45% volume fraction of Kevlar49 (WF) reinforced polyester composites.

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E-type Composites Composites containing 15, 30 and 45% volume fraction of glass (WF) were produced. Composites containing 15, 30, 45% volume of Kevlar 49 (WF) were produced. Three composites were selected due to limited quantity of kevlar49 available. Hybrid Composites Hybrid composites based on polyester and epoxy were called as P-type hybrid and E-type hybrid composites. P-type Hybrid Composites Three types of hybrid composites were produced according to the following stacking sequence: (i) Four alternate layers of glass fibres (WF) and Kevlar 49 (WF) reinforced polyester; (ii) Two layers of glass (WF) and two layers of Kevlar 49 (WF) were reinforced polyester; and (iii) One layer of glass (WF) and one layer of Kevlar 49 (WF) were reinforced in polyester. E-type Hybrid Composites As for the E-type hybrid composites, the following were manufactured: (i) Four alternate layers of glass (WF) and carbon (WF) reinforced epoxy; and (ii) Two layers of glass (WF), one layer of Kevlar (WF) and one layer of carbon (WF) were reinforced in epoxy. Mechanical Testing Tensile Properties Samples of composite material were prepared according to ASTM and test was carried out on computerized Universal testing machine model manufactured in Italy. The results of load vs. strain plot were recorded for each sample and stress was calculated for each composite and hybrid composite samples. RESULTS AND DISCUSSION P-type Composites Figure 1 shows the effect of fibre volume fractions on stress for glass (WF), glass (NWF) and Kevlar (WF) based composites. Stress values found for glass (WF)/ Polyester composites were considerably higher when compared with the stress values for glass (NWF) / polyester composites. Lower values of tensile stress were considered due to randomly oriented fibres in glass (NWF) composite. Results showed that tensile properties of Kevlar 49(WF) composite also increases with volume fraction and this was related to the higher tensile properties of Kevlar 49 compared to glass (WF) and glass (NWF) based composites. The effect of increase in volume fraction of glass (WF) on tensile modulus of Ptype composites is illustrated in Figure 2. It is evident from Figure 2 that tensile modulus of composites is increased with an increase in volume fraction of glass (WF) and this increase is approximately 100% increase within 15 to 30% volume fraction. Further increase in this fibre volume fraction showed approximately 25% increase in tensile modulus of this composite. This was related to isotropic properties of glass (WF) in composite. Similarly, results of glass (NWF) reinforced composites are also

Hybrid Composites for Engineering Application

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shown in Figure 2. Uniform increase in tensile modulus up to 45% volume fraction of glass (NWF) and at 60% volume fraction approximately 100% increase in tensile modulus was observed in accordance with earlier results [7]. It was considered due to anisotropic characteristic of glass (NWF). Kevlar (WF) based composites exhibited higher tensile modulus due to higher properties of Kevlar. 30

1

20 4

a Glass(WF)

300

0Glass(WF)

• Glass(NWF)

250

• Glass(NWF)

m Kevlar(WF)

200

HHKevlar(WF)

150 i

100

s

50 15

30

15

45

30

45

Fibre Vol (%)

Fibre Vol (%)

FIGURE 1 Fibre volume fraction vs. strength of P-type composites.

FIGURE 2 Fibre volume fraction vs. modulus o f p . t y p e composites.

E-type Composites Figure 3 shows the affect of fibre volume fraction on stress of glass (WF) and Kevlar (WF) reinforced epoxy composites. Results showed a considerable increase in stress data for Kevlar based composites. The properties were relatively lower and were considered due to poor bonding between fibres and matrix. Figure 4 represents fibre volume fraction vs. modulus of glass (WF) and Kevlar (WF) based epoxy composites. Results showed that higher tensile modulus of Kevlar-based composites can be achieved with Kevlar (WF) compared to glass (WF) composites.

30

45

Fibre Vol (%)

FIGURE 3 Fibre volume fraction vs. stress of E-type composites.

30

45

Fibre Vol (%)

FIGURE 4 Fibre volume fraction vs. modulus of E-type composites.

P-type Hybrid Composites P-type hybrid composites containing four alternate layers of Kevlar (WF) and glass (WF) were manufactured and their properties were compared with P-type composites as illustrated in Figure 5. Results showed that hybrid composites have higher tensile properties compared to other composites in the P-type category. Higher properties of hybrid composites were due to kevlar (WF) and glass (WF) reinforced in

Hybrid Composites for Engineering Application

549

polyester. A comparison of modulus between hybrid and other composites is illustrated in Figure 6. Results showed that hybrid composite have higher strain compared to other composites, thus resulting lower modulus values. 30 -r a Glass (WF) ED Kevlar (WF) • Glass (NWF) &20

Q Glass (WF) Glass (NWF) DIKevlar(WF) D Hybrid (WF)

300 — 200

t

2 100 -

15

30

45

60

Fibre Vol (%)

FIGURE 5 Comparison of strength of P-type and hybrid composites

FIGURE 6 Comparison of "modulus of P-type and hybrid composites

E-type Hybrid Composites Results of E-type hybrid composites are shown in Figure 7. Hybrid composite consisted of four alternate layers of Kevlar (WF) and carbon (WF) reinforced in epoxy. Three sets of composites were prepared due to limited quantity carbon (WF) available. Hybrid composite containing high modulus carbon (WF) showed high strength and high modulus as illustrated in Figure 8. A comparison of properties of composites prepared and tested is given in Table 2, which summarise the results of both E-type and P-type hybrid composites. TABLE II Properties of hybrid composites compared with P-and E-type composites. Hybrid Composites Lay-up

Multilayered Composites

Tensile Strength (% Modulus increase (% increase or or decrease) decrease)

Kevlar (WF) / Glass (WF) / Kevlar (WF) / Glass( (WF) (P-type hybrid)

4 Layers Kevlar (WF) 4 Layers Glass (NWF) Polyester (P-type)

18% decrease 41% increase

20% decrease 11% increase

Kevlar / Kevlar / Glass (WF)/ Glass (WF) (P-type hybrid) Glass (WF) / Kevlar (P-type hybrid)

4 Layers Kevlar 4 Layers Glass (NWF) Polyester (P-type) 2 Layers Glass (WF) 2 Layers Kevlar Polyester (P-type) 4 Layers Glass (WF) 4 Layers Kevlar Epoxy(E-type).

3% decrease 79% increase

10% increase 22% increase

97% increase 14% increase

123% increase 43% increase

16% increase 72% increase

7% increase 67% increase

58% increase 7% increase

31% increase 87% increase

Glass (WF) / carbon (WF) / Glass (WF) / carbon(WF) (E-type hybrid)

Glass (WF) / carbon / Kevlar / 4 Layers Kevlar Glass(WF) 4 Layers Glass (WF) (E-type hybrid) Epoxy (E-type)

CONCLUSIONS Results showed that tensile strength and modulus of composites are dependent on volume fraction of fibres. The results have shown linear increase in tensile strength with an increase in volume fraction fabric for both polyester and epoxy based

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composites. Hybrid composites have shown up to more than 100% increase in modulus of polyester composites while other hybrid composites have also shown significant improvement in both tensile strength and modulus, signifying that they are suitable and most appropriate for certain engineering applications. It is hoped that future work would include some impact and fatigue studies to further strengthen the suitability of the 'hybrids' for engineering application where a combination of strength and impact resistance is necessary. 300 -, 40 0 Glass (WF)

1200 £150 2 100 50 0

HI Kevlar (WF)

S.30"

• Hybrid (WF)

| 20

23 ii 15

30

a Glass (WF) ED Kevlar (WF)

in

• Hybrid (WF)

I10 45

Fibre Vol (%)

FIGURE 7 Comparison of strength of E-type and hybrid composites.

30

45

Fibre Vol (%)

FIGURE 8 Comparison of modulus of E-type and hybrid composites.

ACKNOWLEDGEMENT We would like to acknowledge Fibre Tech. Lahore and Pakistan Aeronautical Complex, Kamra for their support in terms of supplying research materials. REFERENCES 1. 2. 3.

4.

5. 6. 7.

8.

9.

10. 11. 12. 13.

Ahmad, F. and M. J. Bevis. ISAM-97 P: 32 Islamabad Pakistan Georgi, H. 1979. "Damping Effects in Aerospace Structures," AGARD Conference Proceedings No. 277 , 1979. Davey, A. E. 1994. "GRPC Minesweeper: Pre-production Test Structure with Box Core Sandwich Construction," in Handbook of Polymer Composites for Engineers, Woodhead Publishing Ltd., pp.304. Crivelli-Visconti, I., A. Langella, L. Nele G. Delia Valle. 1990. "Improvement on Composite Connecting Rod Design" presented at the 4Th ECCM, September 25-28, 1990. Stuttgart, Germany, pp.837. Adams, D. F. and A. K. Miller. 1975. "An Analysis of Impact Behavior of Hybrid Composite Materials," Materials Sci. & Eng., 19, pp. 245-260. Summerscales, J. and D. Short. 1978. "Carbon Fibre and Glass Fibre Hybrid Reinforced Plastics," Composites, 9(3): 157-166. Fowser, S., D. Wilson, T. Chou and R. Pipes. June 1986. "Influence of Constituent Properties and Geometric Form on the Behavior of Woven Fabric Reinforced Composites," Progress Report for NASA, Grant No: NAG-1-378. Mohamed, M. H. Z. and L. C. Dickinson. "Manufacture of Multilayer Woven Preforms" in ASME Advanced Composites and Processing Technology, MD-Vol.5 Book No. 00484 , pp. 8189. Beaumont, R. P. W., A. P. G. Reiwald and C. Zweben. 1974. "Methods for Improving The Impact Resistance of Composite Materials" in Foreign Object Impact Behavior of Composites, ASTM STP 568, ASTM, PA., pp. 138-158. Toland, R. H. 1974. "Instrumented Impact Testing of Composite Materials" ASTM STP 563, Philadelphia, PA, pp. 133-145. Toland, R. H. 1978. "Failure Modes in Impact Behavior of Composite Panels," J. Test. & Eval, 6(3):202-210. Broutman, L.J and P. K. Malik. Nov 1974. "Impact Behavior of Hybrid Composites" AFOSR TR-75-0472. YANG, Y. H. 1988. "Aramid Fibre" in Fibre reinforcement for composite materials: Composite Materials Series 2, H.R. Bunsell, ed. Elsevier press.

Development of a Knowledge Warehouse for Intelligent Risk Mapping and Assessment System S. Savci * Hawker de Havilland - Boeing, Australia B. Kayis Mechanical & Manufacturing Engineering, University of New South Wales, Australia

ABSTRACT An Intelligent Risk Mapping and Assessment System is an application of knowledge engineering that involves a combination of case-based reasoning approaches aimed at managing risks. To manage risks, the knowledge' of the different tasks constituting product design, development and delivery must be captured, organised and information on the causes of risks that have a threshold effect on time, cost and performance must be available. The efficiency and reliability of design processes can be improved if risk is taken into account at each phase of design, development and delivery. The System aims to reflect several decision-making factors and criteria to build a conceptually complete model comprised of fundamental engineering knowledge as well as "know-how" from general principles, generic knowledge, specific knowledge and case based reasoning. Forward and backward reasoning methods, along with an informal knowledge association method for building dynamic associations between a starting risk and other risks, based on keyword search have been used to ensure a reliable, accessible and updateable information. This paper primarily details the reasoning and methodology used to populate the Knowledge Warehouse module of the Risk Management and Assessment System which not only will support the decision-making process of the user but also aid the knowledge retrieving, storing, sharing and updating process of manufacturing organizations. This risk assessment tool has been targeted for project manager level education with emphasis on advanced composite manufacturing technology.

INTRODUCTION There are several factors that influence the level of sophistication of a risk mapping and assessment system, namely the scope of the project, the size of the company, the inter-dependency of tasks, multi-site locations of project partners, the type of business and finally the provision for on-going capture of information, what is commonly referred to as intelligence. Over the past several years there have been numerous studies on risk management, but none which address all the aforementioned criteria. Hence a collaborative research between various research institutions and Hawker de Havilland Aerospace was formed for the development of an Intelligent Risk Mapping and * Corresponding author, Hawker de Havilland - Boeing, 361 Milperra Road, Bankstown, NSW, 2200, Australia, Tel: 97728558, Fax: 9772 8482, email: [email protected]

552

Knowledge Warehouse for Intelligent Risk Mapping and Assessment

Assessment System anomalously referred to as IRMAS™. The system is based on the Australian/New Zealand Standard on Risk Management [1]. It provides the basis for identifying, analysing, processing, mitigating and monitoring risks. Furthermore, since the nature of advanced composite structures requires complex technologies as well as concurrent engineering, the system needs to accommodate another dimension of complexity in managing the risk. IRMAS™ aims to cater for a highly technologically demanding field of composite manufacturing. Additionally, it provides a systematic engineering approach to risk management of concurrent product and process development. The knowledge warehouse which interacts with a collaborative environment is built to identify several factors that had an impact on other projects' success and/or failures. The contributions from a collaborative environment can take many forms such as the knowledge distributed over space, time, processes and people. A holistic picture gathered from lessons learnt, case studies, best practices, generic engineering standards and procedures would enhance the validity of IRMAS™ The essence of using knowledge warehouse is to sufficiently identify and detail several critical success factors. Thus, the knowledge warehouse emerges as an appropriate choice of resource to be used for identifying, assessing, monitoring and mitigating risks resulting in measurable benefits. Techniques to support evaluation of case, scenario based systems in a collaborative environment remain as an active topic of research [2, 3, 4, 5, 6 and 7]. It is evident from the review of the literature that the key challenge is to go beyond common assumptions such as "increased collaboration will make a positive contribution to organisational performance" to understand how IRMAS™ features will be used to support the decision-making process of the managers and contribute to projects' unique objectives. IRMAS™ is composed of six modules namely; context establishment, risk identification, risk assessment, risk mitigation, knowledge warehouse and decision support systems. It has been compiled as a web-based portal in Java which also facilitates effective communication between non-geographically co-located project partners. CONTEXT ESTABLISHMENT The risk management system is a model essentially comprising a generic representation of design build (or simply build to print) activities with the aid of cause and effect functions. Causal diagram representation of the inter-relationships between various tasks was used in order to flush out all possible risk items for a manufacturing environment from conceptual design through to delivery. Additionally it simplifies the definition of the risk paths to be used later in the risk assessment component. Every organisation has an inherit culture whereby the influences can be observed throughout the majority of the company. These factors determine the systematic problems which essentially do not change from one project to another. Therefore the initial module for the intelligent risk mapping and assessment system establishes the overall risk profile by assigning a weighting to the infrastructure of the system. The contextual component primarily sets the scene for the organizational nature of the company such as the project objective and management style or company culture. RISK IDENTIFICATION Risk identification focuses on product, project and process specific risks. The tool being developed here takes a more holistic approach to project management than conventional

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techniques. Functional heads such as quality assurance, design, tooling, manufacturing, business development, Research and Development are involved as early as the first phase (i.e. conceptual design) thereby promoting higher levels of communication between various departments and hence reducing theory driven risks. Additionally the data capturing process is based on quantitative analysis of the specific risks with the aim of maximising objectivity and minimising subjectivity. More specifically, the magnitude of the risks identified is a product of its consequence and its likelihood where a 5 point, exponentially increasing scale was employed as the example in Table I illustrates for establishing how the milestones were derived. Furthermore, the questions are structured aimed at optimising success factors. For instance the co-location of team members will dictate the success factor for the location risk category as would logistics with suppliers and customers. TABLE I: An example of quantitative identification of risk likelihood and consequence Likelihood 1. In-house expertise and include reserve time 2. Quantitative based duration (bottom-up) 3. Expert judgement (consultants) 4. Parametric/ simulation technique 5. Analogous methodology (top-down)

Consequence 1. Schedule contingency plan 100% valid 2. Up to 90% valid 3. Up to 70% valid 4. Up to 50% valid 5. Up to 30% valid

Each phase was defined by sub-activities and specific risk items classified by 8 risk types namely schedule, technical, external, organizational, communication, location, resource and financial. The complexities and risks associated with composite technology are primarily covered under technical and resource related risks. For instance technical specification completeness comprises product specification completeness, process specification completeness, level of "know-how". More specifically, it encompasses product performance, design and functional requirements. Additionally technical specification completeness covers quality assurance specifications, understanding of technological area/platform familiarity, process completeness, technical support, material familiarity and regulatory requirements. Plus the resource requirement completeness investigates material, people, equipment and facility related requirements. Furthermore, personnel skills and training requirements are addressed as well as equipment performance, reliability, capacity familiarity and compatibility. The risk identification stage can potentially be extremely large and cumbersome due to the expanse of the scope. For instance major activities such as maintenance, Occupational Health & Safety, design, manufacturing and product life cycle issues have been included. Therefore, customer and supplier profiles were constructed with the aim of increasing inherit intelligence and promoting the user friendly aspect. Similar analysis techniques to the product, project and process risks were used in capturing information on the reliability, expertise, capability, capacity and compatibility of customer and supplier profiles. RISK ASSESSMENT All identified risks with their assigned magnitudes are processed through the risk paths given by the interactions between other risk items. The consequences of the risks are computed using the Analytical Hierarchy Process (AHP) [8] concept while the likelihood of the risks adopts Bayesian Belief Network (BBN) [9] Both techniques will process the risks through the defined paths, capturing concurrency between tasks as well

554

Knowledge Warehouse for Intelligent Risk Mapping and Assessment

as further reducing user related subjectivity. Risk assessment not only provides an automated and reliable mathematical cross reference in calculating the risk magnitude but it is sufficiently flexible to allow the user to also provide a manual assessment of the identified risks. The system thereby is capable of increasing its level of intelligence by building onto the knowledge base via this interactive network.

RISK MITIGATION The risk mitigation module will prioritise the assessed risks and weave an avenue for alternate mitigation strategies. A collaborative environment interacting with the knowledge warehouse may be accessed using a search and retrieval tool. The priority for the mitigation actions will be dictated by the risk magnitude and the threshold value required for that specific risk item. A search facility was developed for access to various components of the knowledge warehouse including case studies, lessons learnt, best practices and generic engineering standards and procedures. Furthermore, other selection criteria governing the mitigation plan will be via associated costs and available resources. Finally, the risk mitigation implemented will feed back into the knowledge warehouse as a "lessons learnt" thereby increasing its intelligence database. RESULTS AND DISCUSSION A comprehensive risk management tool has been developed with a contingency for multi-site concurrent engineering projects. The software systematically integrates an organisation's procedures to identify and assess risks for a scope entailing conceptual design through to product life cycle customer service. The knowledge warehouse collates information captured from generic engineering know-how, lessons learnt (in-depth internal expertise), case studies (internal and external case based knowledge), best practices (external benchmarking) and engineering standards (e.g. Australian/New Zealand Risk Management Standard). The access to such a wealth of knowledge means that the tool is not a mere risk tracking mechanism but potentially a boost forward for the company's success from years of experience from previous projects. Similarly there is a provision for the update of "know-how" which is especially required for dynamic technological areas such as composite manufacturing applications. In other words, it is critical that the intelligence is updated to reflect the current knowledge warehouse if the organisation is to maintain a competitive edge in the market forum. Figure 1 gives a snap shot of the process flow of information within the intelligent risk management and assessment system.

Knowledge Warehouse for Intelligent Risk Mapping and Assessment

Context Establishment

KNOWLEDGE WAREHOUSE

Engineering standards

organizational risks Risk Identification Analytical Hierarchy Process

risk consequence

product, process, project risks Risk Assessment

Belief Bayesian Network

risk likelihood

555

Case studies

Best practices

Lessons learnt

risk magnitude Risk Mitigation

Collaborative Environment

FIGURE 1: Snap shot of Intelligent Risk Mapping and Assessment System

More specifically, the information from the knowledge warehouse may be derived based on criteria such as risk event drivers, resource constraints, type of business activity (e.g. aerospace, automotive etc), project type (design build or build to print) and risk item specifics. The software will automatically access the mitigation strategies associated with the generic risk item identified, however the applicability of the information source needs to be examined before the risk mitigation can be imported into the current project. Hence keyword search facility for various fields was adopted for simplicity and convenience. The knowledge warehouse not only provides the knowledge warehouse for managing the risks but it is additionally a useful tool for educating project managers on the technical aspects of manufacturing without the danger of micromanaging the project. CONCLUSION This study discusses the modules constituting an intelligent risk mapping and assessment system IRMAS™ which also supports concurrent engineering. IRMAS™ is a virtual workbench built as a web-based portal in Java to facilitate multi-site locations. The tool is modelled on the Australian New Zealand risk management standard and it achieves the incorporation of success factors into the management of risks with emphasis on the manufacture of advanced composite structures. This paper serves two purposes, firstly it outlines an intelligent risk mapping and assessment system and it also serves as an educational tool for the purpose of transferring knowledge. In particular, the education of managers has been outlined through a collaborative environment with the use of the knowledge warehouse. The knowledge warehouse captures the wealth of experiences from various sources such as generic engineering "know-how", specific case based knowledge and best practices. Finally, the knowledge warehouse provides the relationship between risk items, risk event drivers and mitigation strategies. In

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Knowledge Warehouse for Intelligent Risk Mapping and Assessment

conclusion, IRMAS™ is capable of integrated product design/development taking a wider holistic perspective in the transfer of knowledge and the management of risks. REFERENCES 1 Anon., "Australian/New Zealand Standard - Risk Management", AS/NZS 4360,1999. 2 Ackerman, M. The Intellectual challenge of Computer Supported Co-operative work: The Gap Between Social requirements And Technical Feasibility. Human Computer Interaction, 15, 179-203,2000 3 Baeza-Yates, R. and Pino, J. A., A First Step to Formally Evaluate Collaborative Work. Proceedings of the International Conference on Supporting Group work: The Integration Challenge, Phoenix, AZ, 56-60, November, 1997 4 Carroll, J.M., Making Use: Scenario-Based design of Human Computer Interactions, Cambridge, MA, The MIT Press, 2000 5 Ross, S., Ramage, M., and Rogers, Y., Participatory Evaluation through Redesign and Analysis, Interacting with Computers, 7 (4); 335-360, 1995 6 Rosson, M.B., Carroll, J.M., Usability Engineering: Scenario- Based Development of Human-Computer Interaction. San Fransisco: Morgan Kaufmann, 2002 7 Stiemerling, O., Cremers, A. B., The Use of Cooperation Scenarios in the Design and Evaluation of a CSCW System. IEEE Transaction on Software Engineering, 24(12), 1171-1181,1998 8 Saaty, T.L., "Decision Making for Leaders - The Analytical Hierarchy Process for Decisions in a Complex World", Ed. 3, RWS Publications, USA, 2001. 9 Press, SJ "Bayesian Statistics: Principles, Models and Applications", John Wiley & Sons Inc., USA, 1989.

Opportunities for Nanocomposites in the Oil & Gas Industry Russell Varley1'* and K. H. Leong2 'CSIRO Molecular Science, Bag 10, Clayton South, VIC 3169, Australia. 2 PETRONAS Research & Scientific Services Sdn Bhd (PRSS), Lot 3288 & 3289, Off Jalan Ayer Itam, Kawasan Institusi Bangi, 43000 Kajang, Selangor Darul Ehsan, Malaysia.

ABSTRACT The use of advanced and more efficient materials are increasingly critical to the oil and gas industry as it strives towards enhanced recovery in marginal and deepwater exploration and production activities. Composites have proved to be extremely advantageous in selected niche applications in the industry, and in recent years they have been identified as an enabling technology for even more demanding requirements, particularly in the upstream sector. However composites still exhibit limitations in certain properties including toughness and fire performance that are impeding the expanded application of the material within the industry. Potentially, the answer to some of these weaknesses could lie, at least in part, with nanocomposite technology.

INTRODUCTION The 21 st century continues to witness an ever increasing need for improved materials which demonstrate significant property enhancements over and above those which already are available. Fibre reinforced polymer (FRP) composite materials are well placed to meet many of these needs due to their excellent strength and stiffness to weight ratios, corrosion resistance and fatigue properties, whilst affording design flexibility. Unfortunately, composites have some serious limitations, including impact properties, cost and fire performance that have inhibited their adoption for more applications and by a wider scope of industries. A new class of materials known as nanocomposites has been shown to have the potential to address these issues, and more, and this has attracted significant interest from the scientific community and industry alike. A nanocomposite is broadly defined as the dispersion of an additive into a matrix where at least the dimension of the additive is of the order of nanometres (10~9). Due to the high aspect ratio of these nano-additives, nanocomposites have the potential to significantly enhance mechanical and physical properties of polymer matrices with minimal impact on cost and processability. This paper reviews some of these enhancements in properties and how they could present opportunities to increase the level of acceptance and application of polymeric based composites in the oil and gas (O&G) industry in its continuing effort to cut costs and to improve operational * corresponding author. Tel: +61 3 9545 2196 Fax : +61 3 9545 2517 Email: [email protected]

558

Opportunities for Nanocomposites in the Oil & Gas Industry

efficiency and safety. In particular, emphasis will be given to the upstream business where the viability of many deepwater and marginal field developments are increasingly dependent on new technologies to remain competitive. Opportunities for downstream businesses of the O&G industry will also be discussed.

NANOCOMPOSITE TECHNOLOGY The most common type of nanocomposites studied today are materials based upon naturally occurring polymeric layered silicate clays which are formed by the intercalation of a polymer into the gallery of the clay. Another additive being actively studied currently is the use of nanofibers such as carbon nano-fibres, nano-tubes or whiskers. These two groups of materials each have their own unique challenges associated with the optimisation of the dispersion within the polymer matrix which is considered to be critical to optimising the transfer of the unique properties of the nano-material to the nanocomposite material. Nanocomposite Formation - Polymeric Layered Silicates Polymeric layered silicates (PLS) consist of stacked layers of lnm thick octahedral silicate layers separated by approximately 10A, as shown in Figure 1. This class of nanocomposite is widely studied due to their availability and their wellknown intercalation chemistry. The use of polymeric layered silicates has been shown to improve mechanical properties, such as moduli, toughness, strength, and heat resistance, while decreasing their gas permeability and flammability in a wide variety of thermoplastic and thermosetting polymer matrices at low additive levels [14]. The fundamental principle of the nanocomposite formation involves migration of the polymer into the interlayer galleries of the layered silicate and pushing apart or swelling the silicate layers. When the polymer is mixed intimately with the clay and the distance between the layers is increased, the clay is said to be intercalated. If the distance between the layers increases such that the layers become completely and randomly dispersed within the polymer matrix, the silicate is said to be exfoliated. Kornmann et al. [5] report that the polymerisation of the epoxy resin is the indirect driving force for exfoliation due to changing polarity of the polymer as the molecular weight increases. Pinnavaia et al. [6] reported that controlling the intragallery polymerisation of the epoxy resin was critical to achieving exfoliation. It was reported that when the intragallery polymerisation was faster or equal to that of the bulk epoxy resin, an exfoliated morphology was achieved. The delicate balance required to achieve the optimum balance of polymerisation between the intragallery cure and the bulk resin is demonstrated by Becker et al. [7] who achieved improved exfoliation at higher cure temperatures and hence higher cure rates. Nanocomposite Formation - Carbon Nano-fibre/nano-tubes The use of carbon nano-tubes or nano-fibers, as shown in Figure 2, holds much promise due to the very extraordinary mechanical properties of the fibres. Their dispersion in polymer matrices is made difficult due to the high degree of entanglement of the fibres. This is a result of the attractive molecular forces such as Van der Waals and the high aspect ratio of the fibres. The dispersion of carbon nanofibers in polymer matrices has been widely investigated using either mechanical or chemical methods. Mechanical methods have focussed upon various ultrasonic and milling techniques [8]. These techniques tend to work well because they reduce the

Opportunities for Nanocomposites in the Oil & Gas Industry

559

length of the fibres, reducing entanglements but also producing large amounts of amorphous carbon, and reducing the benefit of the nano-reinforcement. O

oxygen

©

hydroxyl aluminium and • magnesium o " " silicon

FIGURE 1. Schematic diagram showing the general structure of a polymeric layered silicates (PLS).

l-'ltiLRL 2. LxaiiipL ul i;pu.dl Loibuu Nanofibres commercially available

Chemical methods used to improve dispersion involves activating the surface of the carbon with reactive functional groups enhancing the ability of the nano-fibre/nanotube to transfer its properties to the polymer matrix. This is often performed via an acid treatment method in combination with thermal oxidation or decomposition and tends to significantly reduce the mechanical properties of the nano-tubes. A promising method is to use surfactants which have far less negative impact upon the properties of the carbon nano-fibre/nano-tubes while promoting optimum dispersion. OPPORTUNITIES It has been reported that nano-reinforcements are able to concurrently improve strength, modulus and toughness of neat resins while having minimal impact upon other properties such as Tg and processability [7,9]. Becker et al. [10] demonstrate this for a range of high performance epoxy resin systems which exhibit large improvements in toughness (up to -200%) and modulus (up to 20%). Becker and his colleagues [7] further show the potential of nano-clays to toughen FRP composite materials via a supplementary reinforcement mechanism. Figure 3 illustrates that apart from modulus and strength, the flexural strain-to-failure also increases significantly for a 5wt% clay modified epoxy resin system. More modest improvements are achieved for coefficient of thermal expansion (CTE) and the char yield while Tg is only marginally compromised, but is still around 170°C. These improvements in properties are encouraging since the O&G industry are increasingly turning to composite materials as solutions for not only corrosion problems, but for weight reduction issues so that its superior strength and stiffness to weight ratios are important considerations. This is particularly so as the quest for oil and gas moves towards more demanding conditions, such as deepwater exploration and production. One of the more pressing challenges facing composites development is the need for improved fire performance, preferably with little or no effect upon mechanical and other physical properties, weight, processability as well as cost. Nano-clay and nano-fibre reinforcement has been shown to have great promise in this area. While the most promising improvement in fire performance have been achieved through the addition of nano-clays to thermoplastics such as nylons and polystyrenes, others have also shown that nano-clays are able to significantly improve the fire performance of thermosetting materials. Gillman et al. [12] showed that for a 6wt% addition of a silicate additive approximately a 40% improvement in the peak heat

560

Opportunities for Nanocomposites in the Oil & Gas Industry

release rate was achieved for different epoxy resin systems. For vinyl ester resin systems, a slightly more modest improvement was observed. This improvement was attributed to the clay improving the stability of the char layer and preventing combustible products escaping the condensed phase. However, other studies [13] have found that the addition of clay has little effect upon the fire properties and that the incorporation of phosphorous or silicone based species into the epoxy backbone are far more advantageous. It is expected therefore that a combined approach to fire improvement is expected to provide the solutions required for the oil and gas industries for new materials in this area. 160 -, 135.6

140-

&120-I 0

8 0

-

1 60-

58.4

52.1

S 40 S. 20 -I

21.3

-10.9

0 -20

J

FIGURE 3. Changes in properties for a high performance epoxy resin system due to nano-reinforcement [11].

Magnesium hydroxide nano-particles have been shown to perform better than a corresponding micro-particle for an ethylene vinyl acetate (EVA) composite for peak heat release rate, and carbon monoxide and carbon dioxide emissions, see Figure 4. Whilst the time to ignition is shorter for the microcomposite, the nanocomposite also shows an improvement, and in both cases the degradation temperature and level of smoke emission are improved as well. Other results have revealed the potential use of carbon nanotubes as fire retardants. Kashiwagi et al. [15] found up to a 32% improvement in heat release rate in polypropylene using only 2 vol% of additive. They explained the improvement being a result of an improvement in the mechanical integrity of the protective layer acting as a thermal insulation layer and a barrier for degradation products to the gaseous phase. Another possibility with nano-reinforcement is a significant enhancement of barrier properties. In the O&G industry pressure vessels are used in abundance at a variety of pressure ratings from quite low to extremely high. High pressure vessels are used, for example, in liquid nitrogen gas storage cylinders (downstream) and accumulator bottles (upstream) where operating pressures in the region of 3 OOOpsi are not uncommon. Where polymeric liners are used, sufficient barrier properties are needed to ensure efficient pressure containment. The use of FRP composite materials over metals for pressure vessels is driven by weight savings, as well as corrosion resistance and fatigue performance. The main drawback however is the poor impact properties, which can be significantly lower than metals. The application of

Opportunities for Nanocomposites in the Oil & Gas Industry

561

nanocomposite techniques to this area has considerable potential due to the dual benefit of being able to improve both toughness and barrier properties concurrently. The low level of addition of additive is also advantageous in that it would have minimal effect upon the processing conditions. This is an important consideration for the fabrication of pressure vessels as they are predominantly made via a filament winding process, which is a process that has tight requirements with respect to resin viscosity and reactivity. As we move into the hydrogen era it is anticipated that barrier requirements will be even higher and nanocomposites could well play an important role towards meeting those ever demanding requirements. 140 @Micro5wt% MgOH3

120 -

115

HNano5wt% MgOH3

100 -

Ia.

80

0)

60 -

n c o

40 -

a

20

+•*

57 48 27 15

19

0 Time to ignition

Peak heat release rate

CO release CO2 release

FIGURE 4. Some indicative values of enhanced flammability : comparison between nano- and micro-reinforcement [14].

CHALLENGES For the concept of nano-structure composite materials to be taken to the product development stage the dispersion of these additives needs to be achieved in a manner which is cost effective, reproducible and scalable for manufacturing conditions. When using nano-clays, the chemistry of the organo cation and the processing conditions are critical to the compatibility and dispersion within the polymer matrix. Optimising these factors within a reactive matrix while also ensuring that the fibre matrix adhesion remains unaffected will require a processing and chemical based solutions approach. When using carbon nano-fibres there are significant processing challenges in producing scalable and optimised nanodispersions with no deleterious effects upon the mechanical properties. This suggests that the commonly used approaches such as acid etching and ball milling/ultrasonication may not be sufficient and will require an innovative approach. In addition to technical issues, there is also an urgent need to increase the general awareness and appreciation of "oil men" and "diehard metallurgist" for the potential and abilities of nanocomposites and FRP composite materials. Mathematical models and other techniques with enhanced predictive capabilities, coupled with accelerated testing are needed to address the skepticism of potential users for long-term behaviour thus improving the acceptability of the "new" materials. It is noteworthy that better simulation procedures also contribute towards reducing the cost of certification which is an important element in the viability of adoption of new materials and structures.

562

Opportunities for Nanocomposites in the Oil & Gas Industry

Nevertheless, significant amount of testing is still required to generate a database of properties that will demonstrate the efficacy of composites for O&G operators.

CONCLUDING REMARKS There is evidence, albeit limited at this stage, that nanocomposites has significant potential for the oil and gas industry. They have been demonstrated to enhance fire performance, toughness, barrier properties, strength and stiffness, amongst others, of neat resins that could ultimately be use in advanced FRP composites in the form of matrices. The concept of nano-reinforcement presents an opportunity to improve matrix-dominated properties of FRP composite materials with little cost and weight penalty since they are typically required only in small quantities for a correspondingly large improvement in property or performance. However, enhanced effort in R&D that includes field trials is needed before the potential benefits of nanocomposites and the use of nano-reinforcement in advanced FRP composite materials can be fully realised. The ability to control a uniform dispersion of the nano-particles and the chemical interactions between them and the resin and possibly other additives, plus a full understanding of how the enhanced properties are transferred to an FRP composite material shall be key to engineering the optimum nanocomposite and nano-based advanced FRP composite material. Other issues standing in the way of ultimately seeing the materials in actual applications are not dissimilar to those faced by other new materials - scepticism, cost of qualification and certification, lack of database of properties and experience, etc. - and should be addressed through enhanced capability and effort in testing and modelling, and sound design principles.

REFERENCES 1. 2. 3. 4. 5. 6.

Lan, T. & Pinnavaia, TJ, Chem. Mater., 6, 2216 (1994). Giannelis, E.P., Advanced Materials, 8, 29 (1996). Xu, W.B., Bao, S.P. & He, P.S., J. Appl. Polym. Sci., 84, 842 (2002). Alexandra, M. & Dubois, P., Mat. Sci. Eng., 28, 1 (2000). Kommann, X., Lindberg, H. & Berglund, L.A., Polymer, 42, 1303 (2001). Pinnavaia, TJ. & Beall, T.G., (Eds.), Polymer Clay Nanocomposites 1st Ed., Wiley Series in Polymer Science, Chichester (2000).

7. 8. 9. 10. 11.

Becker, O., Cheng, Y-B., Varley, R.J. & Simon, G.P., Macromolecules, 36, 1616 (2003). Hilding, J., Grulke, E., Zhang, G. & Lockwood, F., J. Disp. Sci. Tech., 24, 1 (2003) Choi, M.H., Chung, IJ. & Lee, J.D., Chem. Mater., 12, 2977 (2000). Becker, O., Varley, R.J. & Simon, Q., Polymer, 43,4365 (2002). Chiefari, J., Gadd, G., Gilbert, E., Kozielski, K., Varley RJ. and Thomson S. manuscript in preparation. Gillman J.W., Appl. Clay Sci., 15, 31 (1999). Hussain, M., Varley RJ., Cheng, Y.B. and Simon G.P., J. Appl. Polym. Sci., 91, 1233 (2004) Okubo, N., Okumura, H. & Okoshi, M., (Proc Conf.) 8th Japan International SAMPE Symposium, Eds. Takeda, etal, SAMPE, 1, 55 (2003). Kashiwagi T., Morgan A., Antonucci J., Harris R., Grulke E., Hilding J. and Douglas J.,, Thermal Degradation and Flammability Properties of Nanocomposites, (Proc Conf.) Nancomposites 2002, September 23-25, 2002, San Diego, USA

12. 13. 14. 15.

Part XI

Interface

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Interfacial Properties of Polypropylene Fibre-Matrix Composites S. Houshyar, R. A. Shanks*, A. Hodzic** Applied Chemistry, RMIT University, GPO Box 2476V, Melbourne, 3001, Australia

ABSTRACT A novel composite consisting of polypropylene fibres (PP) in a random poly (propylene-co-ethylene) (PPE) has been prepared and its properties evaluated. The matrix and fibre components retained their separate melting temperatures. The melting temperature of the polypropylene fibres increased after formation of the composites. The compression moulding of the composites at a temperature below the melting temperature of the fibres caused annealing of the fibre crystals. The mechanical properties of the all PP composites were measured and it was found that by incorporation of long PP fibres into a PPE matrix the flexural and tensile modulus increased. The adhesion between the PPE matrix and PP fibres in the PP composite was characterized using a micro-bond test inspired by the fibre pull out technique. The results show that the adhesion was remarkably increased when polypropylene fibres were substituted for glass fibres in a polypropylene matrix. Nevertheless the thermal processing conditions of the composite materials cause a large reduction in the mechanical behavior of the reinforcement. INTRODUCTION There is a demand for plastics, which requires enhanced performance above which can be achieved with an un-reinforced polymer. Thus, there is much interest in the production of fibre composites in which are oriented polymeric fibres, yarn or woven fabric combined with a lower melting temperature polymer, from the same semicrystalline polymer [1,2]. However, a composite consists of two chemically distinct constituents, which are widely used. Many composites are focused on glass fibres as a dispersed or reinforced phase, are combined with polypropylene. These are used in transport as well as in construction industries [3]. The fibre composite has improved mechanical, thermal and structural properties in comparison with the un-reinforced polymer. In most cases, the density and impact rupture is increased but at present, recycability and low-density composites are of interest in a number of industries especially in the automotive sector [1,4]. Recent research is based on the enhancement of the properties of a base polymer by development of a very high degree of preferred molecular orientation. The composite, which has good stiffness and modulus properties, can be produced by using suitable techniques, but there are problems with recycling and interfacial bonding if the two phases consist of two different polymers [1,2]. This gap in composites can be filled by using the same semi-crystalline polymer in the matrix and reinforcement. A number of techniques has been reported in the * Correspondence Author, Applied Chemistry, RMIT University, GPO Box 2476V, Melbourne, 3001, Australia, Tel and fax: +61 3 9925 2122, [email protected] ** Current address: School of Engineering, James Cook University, Townsville, Australia

566

Interfacial Properties of Polypropylene Fibre-Matrix Composites

literature for production of these composites [2]. Although the majority of publications are on single polymer composites with polyethylene, Loos was the first to investigate the production of PP single fibres, embed in a block of PP matrix [4]. Subsequent work by Poldervaart and Kitayama extended this technique to making unidirectional PP-PP composites using film lamination [5,6]. Other techniques for producing single polymer composites include hot compaction. In the hot compaction method, a major issue is melting of the reinforcement during preparation of the composite, which can reduce mechanical properties of the composite. Recent research has explored the improvement of the sandwich technique for production of single polymer composites. Initial studies showed that the reinforcement of the composite was completely in the matrix, without melting, by using suitable conditions of temperature and pressure [7]. The present work is aimed at preparing all PP composites, which unites the advantages of both PP fibres and PPE matrix, that is a composite material in which both the reinforcement and matrix material are made of PP with significant interfacial interaction between reinforcement and matrix. EXPERIMENTAL The materials employed in this investigation were random poly(propylene-coethylene) matrix (PPE) (density, p = 0.905 gem"3 , MFI = 0.8 dg/min, melting temperature = 147.5 °C, ~ 5 % ethylene) and PP fibres (diameters = 50 urn, tensile strength = 250-350 MPa, tensile modulus = 4.7 GPa and length = 2-3 cm). The fibres were obtained from Melded Fabrics Pty Ltd and the PPE from Basell Australia Pty Ltd. According to differential scanning calorimetry results, the melting temperature of the PPE film and PP fibres was 147 and 165 °C respectively, so that 152-157 °C was selected as the moulding temperature range. A heated press was used. Long PP fibres were distributed randomly on top of a PPE film (with ~ 0.2-0.4 mm thickness) and placed between two Teflon sheets, then pressed at 152 -157 °C for 5-7 minutes. After that, an 11-14 kPa pressure was applied for 8-10 minutes. The fibre volume content of the PP-PPE composites was 50 %. To provide a uniform composite, three layers of composite were laminated together. The composite, fibres and polymers were thermally analyzed using a differential scanning calorimetry (DSC, Perkin-Elmer Pyrisl). Samples of about 3 mg were placed in sealed 10 uL aluminum pans. A constant nitrogen flow of 40 mL/min was used to purge the instrument. The samples were held at 30 °C for 2 min, then heated from 30 to 180 °C at a rate of 10 °C/min, held at 180 °C for 2 min, cooled to 30 °C at the same rate and held for 2 min. Tc was measured from the peak of the exothermic during cooling. The second heating cycles provided results that were more consistent for (Tm) measured from the peak value of the endotherm. For clarity of presentation, successive curves have been shifted by 5 units in Figure 1. The tensile properties of each composite was determined using the average of five specimens for each composite with an Instron Universal Testing machine (Model 4065), following the ASTM standard D 3039-93, with 50 mm/min crosshead speed. Standard tensile specimen shapes with dimensions 57 x 5.9 mm and a gauge length of 57 mm were used. The flexural properties of the composites were measured with a Perkin-Elmer DMA7e in three-point bend mode at 25 °C. The static force was scanned from 100 mN to 8000 mN at 100 mN/min and the samples were cut from the sheets, with dimensions 1x12x5 mm. Specimen for single-filament tests were fabricated by mean of film laminating and process as shown in Figure 2. In this case the geometry of the micro-drop was modified by making cubic matrix samples,

Interfacial Properties of Polypropylene Fibre-Matrix Composites

567

as shown in Figure 2. The strip of matrix was divided into three individual specimens, with one of the two free ends of the roving being cut off in each case.

25 -

5" 13

|

* > •

^

15 -

I ...

12

TemperatureCC)

(a)

Temperature(°C)

(b)

FIGURE 1 DSC (a) and melting (b) crystallization of PP-PPE-composite

The interfacial properties of each composite were determined using the average of ten specimens for all PP composite with a Rheometric DMTA IV. The long fibre end of the specimen was first pulled through the hole in the disc (while observed under a stereo microscope) until the face of disc contacts the matrix cube and is then clamped to the lower tensile fixture.

FIGURE 2 Schematic representation of sample preparation preliminary to the debonding test

In order to prevent slippage of the fibre gripped in the fixture, a thin folded piece of paper was adhered to the fibre end with instant adhesive and placed in the fixture, directly before the experiment was carried out. The experiments were carried out with 100 urn aperture hole diameter. The average gauge length was 6 mm and a forcedisplacement curve was recorded at a pulling speed of 0.001 /s. Prior to the microbond test, the images of the specimen were recorded using a Nikon Labophot 2 optical microscope, which was connected to a digital camera. The images of the specimen after the microbond and tensile test were recorded using an FEI Quantum 200 Scanning Electron Microscopy (SEM) in a low-voltage mode (LVSEM). RESULT AND DISCUSSION Figure l(a) shows that in all PP composites the peak at approximately 150 °C corresponded to the melting of spherulites in the matrix. The second endothermic peak at approximately 165 °C, whose size was determined by fibre volume fraction, was the melting endotherm of the fibres. The distinct melting temperatures of the matrix and fibres confirm that the PP in the matrix and fibres remained as separate phases in the composites. A significant increase of about 1.5-2.0 °C in the melting temperature of the matrix was observed in the composites compared with the pure

568

Interfacial Properties of Polypropylene Fibre-Matrix Composites

matrix PP, Figure l(a). The compression molding of the composites has enabled the matrix to crystallise with nucleation from the fibres. The combined crystallinity of matrix and fibres was greater than that of the separate matrix PPE. This may be attributed to an increased crystallinity in the matrix due to the presence of a transcrystalline interphase in the matrix, or perfection of the matrix crystals after the moulding heat treatment. Figure 1 (b) shows that the crystallisation peak of all composites is slightly shifted to a higher temperature compared with that of pure coPP. This can be explained by the assumption that PP fibres act as a nucleating agent for the matrix, which would increase both the crystallization nucleation and the number of spherulites nucleated in the matrix phase [1,2,6]. Note the PP fibre crystallised separately from the matrix, since there was insufficient time for intermixing of the two components. Figure 3(a) shows characteristics typical of a ductile material, with a maximum in the stress-strain curve, which corresponds to the initiation of necking (yielding). A load drop and subsequent levelling of the stressstrain curve was observed, which corresponds to the initiation of de-bonding of fibre from the matrix in the composites.

PP-PPE composite

U)

20 •

w

e

S5 S t r a i n (% )

10 H 1

2

3

4

5

6

Strain (%) (a) (b) FIGURE 3 Stress- strain curve for all PP composites (a) tensile (b) Flexural mode

It is clear that the addition of fibre reduced the strain to failure of the matrix sharply. This is attributed to the fact that stress concentration at the fibre ends leads to matrix cracking, which ultimately leads to failure when the surrounding matrix and fibre can no longer support the increased load caused by the local failure [8]. The tensile modulus of the composite shows a high value, which is 6 times higher than the matrix, due to the restriction of matrix movement and the effectiveness of the reinforcement. In Figure 4 there is a small amount of fibre pull-out from the matrix. In this case, there exists a tearing of the matrix as well as fibre tensile or shear failure modes. There is considerable fibre rupture during the tensile event that seems to be the dominating failure mechanism.

FIGURE 4 Scanning electron microscopy of fractured sample after tensile fracture

Interfacial Properties of Polypropylene Fibre-Matrix Composites

569

The microbond test described was carried out with as-received polypropylene fibre embedded in PPE matrix. The system with all PP, PP fibres and PPE matrix, is known to develop physico-chemical interaction between two phases. The maximum debonding forces as a function of embedded length are shown in Figure 5. The results display that the load which is necessary for interface debondment for all PP composites are high and greater in comparison with the results for a glass-PP system for a given embedded length, from a literature survey [10]. This can be attributed to the fact that if the interfacial bonding between fibre and matrix is weak, the fibre can be easily separated from the matrix when a load is applied.

300

400

500

600

700

600

Embeded Length (microm)

FIGURE 5 Variation of the debonding force of the embedded length for all PP composite

In this case there are no advantages of high strength and stiffness of the fibre. However, if the interfacial bond is too strong between the two phases, the fibre cannot de-bond from the matrix when the fibre is broken by application of a load [6,8]. When a filament is broken, de-bonding to some extent disperses the possibly concentrated stress, and a crack is developed, which results in matrix failure. Figure 6 and Table 1 show the variation of interfacial shear stress (IFSS) as a function of embedded length and type of fibre when a load is applied along the fibre direction. The load will be transferred through interfacial bonding due to its high modulus and low elongation. If the tensile force exceeds the strength of a single fibre, the fibre is fractured and the broken fibre undergoes continuous fragmentation due to the action of interfacial shear stress remaining at the interface and becomes shorter by a specified value. TABLE I Comparison between debonded force and IFSS of all PP composite and glass-PP composite

Sample All PP composite Glass-PP composite Glass-PP composite

Agent for fibre treatment

Designation

-

Cl C2 C3

r-amino-propyltriethoxysilane

IFSS (MPa) 5.18 2.75 2.83

However, if the force is equal to or less than the strength of the fibres; this results in less shorter broken fibres or longer IFSS. An all PP composite has greater IFFS than glass-PP composite. It can be seen from our experiments that the maximum value of IFSS is 5.2 MPa, while the tensile strength of the PPE matrix is about 78 MPa. Hence, normally PPE cannot be stretched to break by only 5.2 MPa at the stress of the broken end of the fibre. However the stress is extended into the matrix when the fibre is suddenly broken similar to an impact test.

570

Interfacial Properties of Polypropylene Fibre-Matrix Composites

300

400

500

600

700

800

Embeded Length (microm)

FIGURE 6 Experimental results and fitting of the average shear stress as a function of the embedded length for all PP composite

CONCLUSION This study revealed a strong nucleation ability of the fibres on matrix crystallization. An increase of melting temperature of the matrix with introduction of the fibres was observed. Incorporation of the fibres gave a considerable increase of the tensile, flexural modulus and strength, due to the efficient reinforcement imparted by the fibre. The adhesion of matrix and fibre has been characterized by using a micro-bond test, essentially a pull out technique. IFSS showed a significant increase for all PP systems, 5.2 MPa, whereas IFSS is about 2.9 MPa for glass-PP system, which leads to the good mechanical properties. This demonstrates the use of PP fibres in all-PP composite application. ACKNOWLEDGEMENTS Financial support of an International Postgraduate Research Scholarship (IPRS) is acknowledged. REFERENCES 1. PJ. Hine, I. M. Ward, N. D. Jordan, R. Olley, D. C. Bassett. 2003. "The hot compaction behavior of woven oriented polypropylene fibres and tapes. I. Mechanical properties," Polymer, 44, 1117-1131. 2. PJ. Hine, I. M. Ward, N. D. Jordan, R. Olley. 2001. "A comparison of the hot-compaction behaviour of oriented high-modulus, polyethylene fibres and tapes," Journal of Macromolecular Science and Physics, 5, 959-989. 3. Z. Xiaodong, L. Qunfang,D. Gance. 2002. "Studies on mechanical properties of discontinuous glass fibre/continuous glass mat/polypropylene composite," Polymers & Polymer Composites, 10, 299-306. 4. J. Loos, T. Schimanski. 2001. "Morphological investigations of polypropylene single-fibre reinforced polypropylene model composites," Polymer, 42, 3827-3834. 5. T. Kitayama, K. Ishikura, T. Fukui, H. Hamada. 2000. "Interfacial properties of PP/PP composites," Science and Engineering of Composite Materials, 9, 67-73. 6. S. Houshyar S, R. A. Shanks. 2003. "Morphology, thermal and mechanical properties of polypropylene fibre-matrix composites," Macromolecular Materials and Engineering, 288, 599. 7. H. Fujimatsu, Y. Ishikawa, H. Usami, Y. Nasu, K. Kajiwara. 2002. ""Formation of adhesive phae onto high strength and modulus PE fibre by PE solution treatment for making PE fibre-reinforced PE composite," Composite Interface, 9, 157-169. 8. A. Zheng, H. Wang, X. Zhu. 2002. " Studies on the interface of glass fibre-reinforced polypropylene composite", Composite Interface, 9(4) 319-333.

Surface Grafting of Nano-SiC with Glycidyl Methacrylate in Emulsion and Its Effect on the Tribological Performance of Epoxy Composites Min Zhi RONG*, Ying LUO, Ming Qiu ZHANG Materials Science Institute, Key Laboratory for Polymeric Composite and Functional Materials of Ministry of Education of China, Zhongshan University, Guangzhou 510275, P. R. China Bernd WETZEL, Klaus FRIEDRICH Institute for Composite Materials (IVW), University of Kaiserslautern, D-67663 Kaiserslautern, German

ABSTRACT To improve the tribological performance of nano-SiC particles filled epoxy composites, surface modification of the fillers is necessary. By means of soapless emulsion polymerization method, graft polymerization of glycidyl methacrylate (GMA) onto the surface of alkyl nano-SiC was carried out. The monomer, polyglycidyl methacrylate (PGMA) is chemically attached to the nanoparticles by the double bonds introduced during the pretreatment with a coupling agent. By analyzing the reaction mechanism, the emulsion polymerization loci were found to be situated at the SiC surface. Besides, the factors affecting the grafting yielding of PGMA on the particles were investigated, including monomer concentration, initiator consumption, reaction temperature, reaction time, etc. Accordingly, an optimum grafting reaction condition was determined. It was shown that the grafted nanoparticles exhibit greatly improved dispersibility in good solvent for the grafting polymer. The primary studies about the tribological performance of epoxy composite showed a positive effect of grafted nano-SiC as expected.

INTRODUCTION hi recent years, there is an increasing trend of utilizing nano-sized powders in various aspects, such as toughening of plastics [1] and tribological performance enhancement of polymers [2]. ha all these applications, establishment of modification technique for the nanoparticles' surface is highly desired to improve dispersibility of the powders in polymer matrices and to tailor the interface interaction. Grafting polymer onto the surface of inorganic particles is a field of great interests. Most of the works were carried out for micron and sub-micron particles in solutions via various chemical processes, including radical, anionic and cationic polymerizations [3]. Besides, a few reports have been devoted to the grafting of polymers onto the particulate surfaces in emulsion rather than in solution [4]. It was suggested that emulsion * Correspondence Author, Dr. Min Zhi RONG, Materials Science Institute, Zhongshan University, Guangzhou 510275, P. R. China. Tel/Fax: +86-20-84114008, E-mail: [email protected]

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Surface Grafting of Nano-SiC with Glycidyl Methacrylate in Emulsion

polymerization offers strong potential advantages for modifying the surface of nano-sized particles. This is because the grafting polymers tend to cover the particles so long as suitable reaction conditions are available, for example, in the presence of functionalized particles or using small amount of surfactant. From both theoretical and engineering points of view, however, the grafting reaction mechanism involved has not been elucidated with satisfaction so far, and most of the grafting polymers attached to the particles do not possess any reactive group that can be used to chemically link the particles to the matrix. In our previous studies [1, 2], the necessity of nanoparticles surface modification in improving the wear resistance of epoxy based nanocomposites was illuminated. To further bring the positive effects of nanoparticles into play in the very area, the authors of the present work plan to introduce grafting polymers containing reactive groups onto nanoparticles so as to build up chemical bonding at the filler/matrix interface during the subsequent composites manufacturing. That is, a fine adjustment of the interfacial interaction in the subsequent composites can be completed by controlling the amount and species of the reactive groups. EXPERIMENTAL Materials The nano-sized SiC particles supplied by Hua-Tai Co. Ltd., China, were in their a-phase, with a specific surface area of 15.2 m2/g and an averaged diameter of 61nm, respectively. A KH570 silane coupling agent (g-methacryloxypropyl trimethoxy silane, provided by Liao Ning Gaizhou Chemical Industry Co. Ltd., China), was employed to introduce the reactive double bonds on the surface of the nanoparticles. Since the ultimate aim of the present work lies in the introduction of grafting polymers on SiC nanoparticles via the methacryloxy groups, a monolayer coverage of silane or a relative thin attachment of KH570 should be beneficial to the subsequent grafting polymerization and the linkage between the particles and the grafting polymers. Therefore, the silane treated SiC nanoparticles containing 1.24wt% KH570 was used in the following grafting reaction. All the materials are commercial products and were used without further purification except GMA monomer, which was distilled under low pressure prior to the grafting polymerization. Emulsion Graft Polymerization The typical graft polymerization experiments were carried out using a four-neck flask (ca. 250cc) fitted with a stirrer. A desired amount of SiC-KH570 and 70ml ammonia were charged into the flask. Then the non-ionic surfactant was incorporated with a dosage lower than the critical micelle concentration (CMC). Having been ultrasonically agitated for 30min, the above mixture was stirred for additional 5.5h under argon atmosphere. The reaction temperature was increased up to 60°C and then the initiator (potassium persulfate) was added. After 35min, the graft polymerization was started when the monomer was filled by drip-feeding. The reaction had to proceed for a period of time (usually 16h), and was stopped by ice cooling. After the graft polymerization, the resultant suspension was filtered, washed and extracted with methanol for 8h to remove the residual monomer. The dried mixture was extracted with acetone for 5 Oh to isolate the polymer-grafted SiC (SiC-g-PGMA) from the absorbed polymers. Then the grafted nanoparticles were dried under vacuum at 50°C. Some of them were transferred to a Shimadzu TA-50 thermogravimeter (TGA) to determine the percent grafting (yg).

Surface Grafting of Nano-SiC with Glycidyl Methacrylate in Emulsion

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Monomer conversion (7C) and grafting efficiency (ye) were calculated according to Ref. [3]. Dispersibility Characterization and Wear Tests The dispersibility of the grafted nanoparticles was characterized by the time dependence of the weight of SiC-g-PGMA suspending in acetone. Unlubricated sliding wear tests were carried out on a pin-on-ring apparatus under a constant velocity of 0.4m/s and pressure of 3MPa, respectively. The carbon steel ring had a diameter of 40mm and an initial surface roughness of 0.1mm. The specimens for wear tests were machined with a geometry of 6 x 10 xl7 mm3, resulting in an apparent contact area of about 5xl0mm2. Prior to wear testing, all the samples were pre-worn to average surface conditions and reduce the running-in period. The actual steady-state test period was set to 3hr. RESULTS AND DISCUSSION Mechanism of the Grafting Polymerization The locus of polymerization is now of prime concern. Normally, the micelles are favored as the reaction sites because of (i) larger surface area of the micelles than that of the droplets by over two orders of magnitude, and (ii) higher monomer concentration (similar to bulk monomer concentration) compared to that in solution. In the presence of nanoparticles, their surfaces become more favorable reaction sites when they have been modified by silane. If the nanoparticles were uniformly dispersed, they possess quite large surface areas (the concentration of the particles is 1013 per milliliter). Besides, the double bonds on the particles surfaces can take part in the initiation reaction to form particulate nucleation. This process is believed to be easier than the formation of polymer particles by micellar nucleation. More importantly, the amount of the introduced monomers remains low at any time and may be fully adsorbed onto the surfaces of SiC nanoparticles due to their hydrophobic surface feature. TABLE I Effect of pre-dispersion time with stirring on the grafting reaction of PGMA (Each reaction was carried out at 60°C for 16h, and the surfactant concentration is 0.0001 mol/L)

Monomer Initiator Weight of Nano-SiC Concentration Concentration [mol/L] [mol/L] [g] 2

0.2

0.003

Pre-dispersion time [h] 7 5 3

Tc [%1

7g

[%1

[%1

64.12 46.07 50.37 30.67 17.24 59.11 13.14 8.03 64.26

The aforesaid analysis receives supporting evidences from Table I. The longer dispersion time for the particles in solution before reaction has a significant effect on the improvement of monomer conversion and percent grafting. Such an improvement can be reasonably related to the increase of the number of the isolated particles with a rise in the dispersion time. The rate of polymerization, Rp, at the stage when only polymer particles exist (free of micelles), is generally given by the following expression [5]:

Surface Grafting of Nano-SiC with Glycidyl Methacrylate in Emulsion

574

*,=

XtfNEk [M]

(1)

where N denotes the particles concentration, n the average number of radicals per particle, and NA the Avogadro number. Evidently, the increase of Nwith longer dispersion time should result in the increase of Rp, and js and yc as well. Effect of Reaction Conditions on the Grafting Polymerization Grafting kinetics of GMA polymerization onto silane modified SiC nanoparticles have been studied. As shown in Fig.l monomer conversion and percent grafting increase with time initially and then level off at about 6h. On the other hand, the grafting efficiency shows the highest value at the beginning of the reaction, and decreases with increasing time. These phenomena imply that the grafting of GMA onto the surface of SiC prefers to take place at the beginning of the reaction. The succeeding polymerization is mainly controlled by the homopolymerization of GMA, because of the blocking effect of the grafting polymers on the subsequent grafting reaction. That is, the surface double bonds cannot be initiated at the latter stage of polymerization as the growing polymer radicals and/or grafting polymer chains block the diffusion of radicals to the particles' surfaces. This is understandable when considering that the grafting PGMA chains must be very close to the particles surfaces in an emulsion system. Besides, the possible hydrogen bonding between SiC and PGMA is also favorable for encapsulation of the polymer around the particles.

100

E 80 A-

_A

a

a

—•— Monomer conversio —O— Percent grafting —A— Grafting efficiency

n |

60

—D— Monomer conversion —0— Percent grafting — A - Grafting efficiency I

.

I

,

10

i

15

.

i

.

i

.

20

Reaction Time [h]

FIGURE 1 Grafting kinetics of PGMA onto silane modified nano-SiC.

0.10

0.15

0.20

0.25

0.30

Monomer concentration [mol/L]

FIGURE 2 Effect of monomer concentration on the grafting polymerization of GMA onto nano-SiC.

Fig.2 shows that the higher monomer concentration, the higher percent grafting and monomer conversion. The values of grafting efficiency exhibit a peak-like dependence on monomer concentration. These results can be attributed to the fact that the polymerization rate increases with monomer concentration. It is consistent with the general law of emulsion polymerization [ 5 ]. With respect to the influence of initiator concentration, it is seen from Fig.3 that with a rise in initiator concentration all the grafting parameters show a significant increase at the beginning. Then, jc and yg keep almost unchanged or decrease slightly, while 7, shows a slight increase at higher initiator concentration. It is known that higher initiator concentration would lead to higher initiation rate, and hence more double bonds on the

Surface Grafting of Nano-SiC with Glycidyl Methacrylate in Emulsion

575

particles' surfaces can be initiated. This accounts for that yc, yg and ye increase evidently with a small rise in initiator concentration at low concentration level. However, a further increase of initiator concentration hardly affects the reaction due to the blocking effect as mentioned above. The decreasing trend of grafting efficiency at higher initiator concentration can be ascribed to the faster bimolecular termination caused by the entry of a second radical into the polymer particles. The effect of reaction temperature on yc, yg and ye is illustrated in Fig.4. Clearly, the proper reaction temperature range should be between 60 and 80°C. When the temperature is lower than 60°C, the rate of radical generation is very slow, resulting in low yc, yg and ye. On the other hand, the initiating rate may be very fast at a temperature higher than 80°C, leading to substantial exhaustion of initiator at the beginning of the reaction and hence low yc, yg and ye. Comparatively, the reaction at 80°C can lead to higher yc, yg and ye than that at 60°C because the overall rate of polymerization increases with increasing temperature. It is similar to the effect of reaction temperature on homogeneous polymerization. A rise in reaction temperature raises the reaction rate by increasing both Kp and N (see Eq.(l)). The increase in N is factually due to the increased rate of radical generation at high temperature.

£,

80

«

I

—D— Monomer conversion —O— Percent grafting —A— Grafting efficiency 0.003

0.006

0.009

0.012

Initiator concentration [mol/L]

FIGURE 3 Effect of initiator concentration on the grafting polymerization of GMA onto nano-SiC.

Reaction temperature [°C]

FIGURE 4 Effect of reaction temperature on the grafting polymerization of GMA onto nano-SiC.

Effect of Grafted Particles on the Dispersibility and Wear Resistance To check the effect of surface treatment qualitatively, the dispersibility of PGMA grafted SiC in acetone was compared with that of the untreated nano-SiC (Fig.5). The results clearly show a remarkable improvement of dispersibility of the former particles originating from the surface grafting. Untreated nano-SiC completely precipitates after a few hours. On the contrary, SiC-g-PGMA gives a stable colloidal dispersion in the solvent. In addition, the grafted SiC nanoparticles with higher percent grafting tend to be less stable than that with smaller amount of the grafting polymers, indicating that excessive grafting polymer chains interfere with the dispersion of SiC nanoparticles due to molecule entanglement. The sliding wear properties of the composites rilled with untreated nano-SiC are shown in Fig.6 as a function of particle content. It is evident that the nano-SiC particles can significantly reduced the wear rate of the composites even at very low filler loading (about 0.3 vol.%). Beyond this value, the wear rate tends to keep unchanged with arisein the fraction of the nanoparticles. On the contrary, the frictional coefficient of the

576

Surface Grafting of Nano-SiC with Glycidyl Methacrylate in Emulsion

composites reduced gradually with the addition of particles, which does not correspond to their filler content dependences of wear rate. Above phenomena, reveal an existing of a special mechanism for nanoparticles filled composites, which may relate with the role of particles as a roller. In case of grafted particles, it was found that the grafted SiC (1.18 vol.%) filled epoxy composites also exhibit improved ws and u, values (0.41 and 2.8x 106 mm/Nm) in comparison with untreated SiC/epoxy composites (0.44 and 5.6xlO6 mrn/Nm) at rather lower percentage grafting (about 10 %). However, at a higher % (40%), both cos and u. values become increasing. The grafting polymer should enhance the interface interaction, but also be detrimental to the particle dispersion by entanglement between the particles. This may explain why the tribological performance tends to decrease at higher yg.

- D - SiC-g-GMA (Tg=52.33%) - O - SiC-g-GMA (y g =27.56%) — A - Untreated SiC

20

30

Time [h]

FIGURE 5 Dispersibility of untreated nano-SiC and SiC-g-PGMA in acetone at room temperature.

1

2

3

4

5

Content of SiC [vol%]

FIGURE 6 Frictional coefficient, jx, and specific wear rate, a>s of neat epoxy and its composites filled with untreated nano-SiC

ACKNOWLEDGEMENTS The financial support by the Volkswagen-Stiftung, Federal Republic of Germany (Grant No.1776645), for the cooperation between the German and Chinese institutes on this subject is gratefully acknowledged. Further thanks are due to the Natural Science Foundation of China (Grant: 50273047) and the Team Project of the Natural Science Foundation of Guangdong, China (Grant: 20003038) for supporting some parts of the chemical works involved in this project. REFERENCES 1.

2.

3. 4. 5.

Zhang, M. Q., Rong, M. Z., Friedrich, K. 2003. "Processing and properties of Non-layered nanoparticle reinforced thermoplastic composites,"In Handbook of Organic-Inorganic Hybrid Materials and Nanocomposites, Volume 2: Nanocomposites; Nalwa, H. S., Ed.; California: American Science Publishers, Chapter 3, pp. 113-150. Rong, M. Z., Zhang, M. Q., Shi, G., Ji, Q. L. Wetzel, B., Friedrich, K. 2003. "Graft polymerization onto inorganic nanoparticles and its effect on tribological performance improvement of polymer composites," Tribol. Int., 36: 697-707. Rong, M. Z., Ji, Q. L., Zhang, M. Q., Friedrich, K. 2002. "Graft polymerization of vinyl monomers onto nanosized alumina particles," Eur Polym J, 38: 1573-1582. Espiard Ph., Guyot A. 1995. "Poly (ethyl acrylate) latexes encapsulating nanoparticles of silica: 2. Grafting process onto silica," Polymer, 36: 4391-4395. Odian, G. 1991. Principle of Polymerization, John Wiley & Sons: New York, pp.335-353.

Influence of Matrix Type and Processing Conditions on the Morphology of the Interface and the Interfacial Adhesion of PE/PE Composites Mahmood Masoomi \ S. Reza Ghaffarian^and N. Mohammadi1 1) Polymer Engineering Department, Amir Kabir University of Technology, Tehran, Iran

ABSTRACT Four different types of polyethylene, high density (HDPE), linear medium density (MDPE), linear low density (LLDPE) and low density (LDPE) have been used to prepare composites with ultra high molecular weight polyethylene (UHMWPE) fibers. PE/PE micro composites were prepared from the above materials and the crystalline morphology of the fiber and matrices interfaces were studied by a polarizing microscope. The interfacial shear strength (IFSS) of UHMWPE fiber with PE matrices was determined by micro bond pull-out method. Thermal behavior of the matrices, the fiber and the prepared hot pressed composites were investigated by differential scanning calorimeter (DSC) analysis. All above specimens were cooled by using two processing conditions, i.e. isothermal crystallization (ISO) and ice water quenching (IWQ). The microscopic images showed a big difference between those samples prepared by HDPE matrix and other matrices that cooled by ISO methods. The ISO cooled sample with HDPE matrix contained a regular transcrystallinity (Tc) region. The intensity of the T c layer in the IWQ cooled samples with LDPE and LLDPE matrix was very poor, hi the micro composites prepared by MDPE and LLDPE as matrix and cooled by ISO method, sever irregular T c region was appeared. The DSC studies revealed that only HDPE had a crystallization condition similar to the melted fibers. The preliminary microbond test results indicated that the IFSS of the ISO cooled samples decreased relative to the IWQ cooled samples.

INTRODUCTION The PE/PE composites are an important group of homopolymer composites possessing interesting and some unique properties. Some of these properties are: toughness, Impact resistance, chemical resistance, lightness, abrasion resistance, weld ability, hydrophobicity, low dielectric properties, acceptable biocompatibility and possible application in cryogenic temperature. Like other composites, interface adhesion is the most influential factor, which affects the mechanical properties of PE/PE composites. Interface adhesion is closely related to interface morphology. This later parameter is itself influenced by processing condition and materials properties. So a good knowledge of the interface morphology and the effects of processing condition and material properties on it is a key factor in controlling the interface * Corresponding author, Polymer Engineering Department, Amirkabir University of Technology, Tehran, Iran, sr_ghaffarian(S).aut.ac.ir.

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Influence of Matrix Type and Processing Conditions

adhesion. The most common morphology in the interface of thermoplastic composites is transcrstallinity (Tc). For the first time, He and Porter [1] observed Tc layer in the interface of HDPE- PE fiber composite. They claimed that T c layer consist of an inner and outer zone. Ishida and Bussi [2] proposed a model to study the Tc growth in the PE/PE composite, by modifying the theory of heterogeneous nucleation. In another work, Teishev and Marom [3] studied the effect of Tc growth on the transverse mechanical properties of HDPE-PE fiber composite. They claimed the Tc growth resulted in a 50% decrease of the transverse tensile strength and strain to failure. Stern et al. [4] found a Tc interface on the fiber surface. They indicated that Tc growth had not effect on tensile strength and modulus of PE/PE composites. This researcher in another work investigated the effect of cooling rate on the crystals morphology of the interface. Also, they extended a model for microstructure of Tc layer by X-ray diffraction. An important and influential factor on the formation and structure of T c region is the type of PE which is used as matrix in the PE/PE composite. With regard to this fact that in the processing and manufacturing of PE-PE composite a surface melting is occurring on the PE fibers, the type of PE, as matrix, can play an important role in the structural morphology of the interface, of these composites. In this article the formation and structure of Tc region when four different types of PEs are used as the matrix have been investigated. Moreover the influence of T c region on the interface adhesion, in the presence of different types of PE as the matrix was studied. EXPERIMENTAL Materials The UHMWPE fiber used in this study was Dyneema SK60 (DSM High Performance Fibers BV). The PE matrix materials were high density polyethylene (HDPE) copolymer grade with narrow molecular weight distribution, trade name of Rigidex HD 5218EA (BP Solvay), linear medium density polyethylene (MDPE), trade name of Rigidex HD 3840UA (BP Solvay), linear low density polyethylene (LLDPE) copolymer grade with narrow molecular weight distribution, trade name of M500026 (Sabic corporation) and low density polyethylene (LDPE), trade name of MG70 (Qapco). Methods Micro-composite samples containing different types of matrix were prepared and analyzed with a Leica polarizing microscope which was equipped with a hot stage crystallization unit and connected to a photo camera. Samples were prepared by laying separately a few monofilaments between two matrix films with 100 |xm thickness and placing the assemblage on a microscope slide, topped with a cover glass, and then placed in the hot stage. The temperature of samples were increased to 137 °C and held for 15 min, thereafter either quenched in the ice water (IWQ) or cooled at constant rate of 1 °C/min to the isothermal crystallization temperature (ICT) and held for 60 min in this temperature, then cooled to the ambient temperature (ISO). The isothermal crystallization temperature for each matrix is different which should be determined e.g. with DSC analysis. To measure the interfacial strength between the fiber and different types of matrices, samples were prepared according to the following procedure. A matrix

Influence of Matrix Type and Processing Conditions

579

ribbon was carefully cut out of a film of that matrix (typically 100 um thick, 500 urn wide and 20 mm long). The matrix ribbon was placed on the middle of a microscope slide. Then a few equally spaced monofilaments were placed on the ribbon in a way that the fibers axes were normal to the ribbon longer side. Finally another matrix ribbon was carefully placed on top of the previous ribbon to sandwich the filaments. The whole assembly was then positioned within the hot stage and the same thermal program as mentioned above was exerted on it. The matrix ribbon was then cut from the middle of the space between the monofilaments; the obtained specimens then were used to determine the IFSS of fiber-matrix by means of pull out test. The test was preformed according to the procedure described by BIRO et al. [5]. In this experiment some length of a monofilament was embedded in a matrix droplet. The upper surface of the droplet was holed against two jaws of a caliper that was mounted on the crosshead of a Zwick tensile machine (type 146460) in a way that the fiber located freely between the jaws. The machine was equipped with a 10 Newton load cell. The crosshead speed was 0.5 mm/min. For thermal analysis, the samples were prepared by molding them in a hot press. The mold pressure was adjusted on 5-7 bar and the molding temperature was controlled with the accuracy of ± 1°C during molding cycle. At the end of molding the mold containing the specimen cooled with two methods: quenching in a mixture of ice and water (IWQ) and isothermal at crystallization temperature for 1 hour (ISO). To investigate the thermal analysis of the prepared composites, a differential scanning calorimeter (DSC) was used. To study the melting and crystallization processes, the DSC analysis was performed in heating and cooling mode. The samples heating and cooling rate was 5 °C /min for all the DSC tests. RESULTS AND DISCUSION One of the criteria in choosing the PEs as matrix was their flow-ability. This parameter is important in the wetting of the fibers. Melt flow index (MFI) is a parameter that quantitatively can express the flow-ability of PEs. Since the processing temperature of PE/PE composites are less than 140 °C, in order to have a proper view of the flow-ability of matrices, the MFI of PEs were also obtained around this processing temperature. TABLE I Physical and rheologieal properties of raw materials. Raw materials UHMWPE Fiber HDPE Matrix MDPE Matrix LLDPE Matrix LDPE Matrix

Density (gr/cm3) 0.975 0.952 0.938 0.926 0.922

Melting peak °C 147, 156 130 126.5 124 104

Crystallization peak °C 117.3 117.7 114.8 109.6 90

ICT °C 121 120.1 116.8 113.8 95

MFI(2.160kg) 190°C 138°C 18 7 4 1.6 50 16 70 9

The DSC curves for UHMWPE fiber and matrices were prepared in order to carefully determine the processing temperature of PE/PE composites. Table 1 shows some of the obtained physical and rheologieal results for the UHMWPE fiber and matrices which were used to select the processing conditions. Melting of UHMWPE fiber in DSC begins at around 127 °C which is due to melting of the low molecular

Influence of Matrix Type and Processing Conditions

580

mass macromolecules present on the periphery of the fibers [6]. The main melting peak, at 147.3 °C, appears with a shoulder at 155.8 °C. Figure 1 and 2 show the DSC curves of the composites produced from four different type of PE as matrix and cooled by ISO and IWQ methods, respectively, hi heating rout of all curves two peaks appeared which the lower one corresponds to the melting of matrix and the other is related to melting of fibers, hi curves la and 2a which belong to a HDPE matrix type composite, only a sharp exothermic peak was seen in cooling, while in other curves two exothermic peaks or a broad peak have been appeared. So it can be deduced that only for the HDPE composite the possibility of co-crystallization of the fiber and matrix in the interface could be conceivable.

100 Temperature 'C FIGURE 1 DSC thermograms of PE/PE composites that cooled by ISO method, a) HDPE, b) MDPE, c) LLDPE and d) LDPE .

100 Temperature °C

200

FIGURE 2 DSC thermograms of PE/PE composites that cooled by IWQ method, a) HDPE, b) MDPE, c) LLDPE and d) LDPE .

Figures 3 and 4 show the microscopic images of composites with HDPE and MDPE matrices that have been cooled by ISO and IWQ methods. The HDPE matrix composite that cooled by ISO method, Figure 3a, have an interface with a uniform thickness which contains of needle like compacted crystals that have been propagated vertically from the surface of fiber. For this system those parts of matrix in the vicinity of the Tc layer have lower crystallinity relative to the bulk of matrix. The MDPE composite which was cooled by ISO method, Figure 4a, have thicker Tc layer compared to other specimens. For this specimen the structure of crystals in the interface is similar to that of the bulk of matrix, but more compacted. Moreover the

Influence of Matrix Type and Processing Conditions

581

compaction intensity of the crystals within the Tc layer along the fiber is variable and in some of, its region reaches the compaction state of the bulk of matrix.

FIGURE 3 Optical micrographs of micro-composite with HDPE matrix (a) ISO and (b) IWQ cooled.

I. FIGURE 4 Optical micrographs of micro-composite with MDPE matrix (a) ISO and (b) IWQ cooled.

Figures 3b and 4b show micrographs of composites with HDPE and MDPE matrix, respectively, that have been cooled by IWQ method. The Tc layer in these samples has variable thickness and the thickness in some region even is near zero. The structure of Tc crystals is the same as the bulk of matrix in both composites. When the composite with LLDPE matrix was cooled by ISO method, a thin Tc layer with variable thickness was appeared. In the IWQ cooled composite with LLDPE matrix, and the composites with LDPE matrix that were cooled by ISO or IWQ methods, no significant Tc layer were observed. Therefore according to these results the Tc layer only appears in the composites with HDPE and MDPE matrix with any processing condition. But for LLDPE matrix the Tc layer was present only in the ISO cooling method. So, both the type of matrix and the cooling process show strong influence on the morphology of the interface in the PE/PE composites. The IFSS, x , can be calculated by using the following equation: Where Fmax is maximum force that was measured from the pull out curve, d is the fiber diameter and L is the embedded fiber length which was determined by an optical microscope. The average IFSS, T , was determined either by the average of 15 to 20 measured values or by evaluating the slop of a best fit linear regression line from plots of Fmax versus embedded area [5]. The maximum value of the IFSS, r max , is

582

Influence of Matrix Type and Processing Conditions

determined when the embedded length reduced to zero [7]. r m a x can be determined by extrapolating the line, which is obtained from plots of r versus the embedded area, to a zero embedded area. Table 2 shows the T and T max of different samples. As can be seen from these results the HDPE and MDPE composites have higher T max with respect to LLDPE specimen. This can be related to the better compatibility between HDPE and MDPE and PE fibers in co-crystallization process at the interface. TABLE II The results of pull out test

r max (Mpa) T (Mpa)

HDPE Composite ISO IWQ 12 9.7 6.2 5.1

MDPE Composite IWQ ISO 14.9 11.1 6.2 7.2

LLDPE Composite ISO IWQ 6.6 5.1 5 4.5

The ISO-cooled HDPE sample showed lower interfacial adhesion in comparison to the ISO-cooled MDPE composite which could be as a result of the needle-like structure of the Tc layer. CONCLUSION Morphology of the Tc layer in PE/PE composites was found to be sensitive to the type of matrix and processing condition. Sample containing HDPE which is cooled by ISO method in contrast to other specimens showed a highly uniform Tc with needlelike structure, which was different from the crystal structures of its bulk. For LDPE composite no obvious Tc layer was observed under the applied cooling methods. The pull out test revealed that the ISO-cooled MDPE composite had the highest IFSS. hi the MDPE composite, the IFSS of ISO-cooled samples was higher than IWQ-cooled samples while in the HDPE composite the results was vice versa. This difference can be related to different Tc structure of HDPE matrix with MDPE matrix. REFERENCES 1.

He, T. and R. S. Porter. 1988. "Melt transcrystallization of polyethylene on high modulus polyethylene fibers," J. of Applied Polymer Science, 35:1945-1953. 2. Ishida, H. and P. Bussi. 1991. "Surface-Induced crystallization in ultra high modulus polyethylene fiber reinforced polyethylene composites," Macromolecules, 24: 3569-3577. 3. Teishev, T. and G. Marom. 1995. "The effect of transcrystallinity on the transverse mechanical properties of single-polymer polyethylene composites," J. of Applied Polymer Science, 56:959966. 4. Stern, T., A. Teishev and G. Marom. 1997. "Composites of polyethylene reinforced with chopped polyethylene fibers: Effect of transcrystalline interface," composites science and technology, 57: 1009-1015. 5. Biro, D. A., P. Mclean and Y. Deslandes. 1991. "Application of microbond technique: characterization of carbon fiber-epoxy interfaces," Polymer Engineering and Science, 37(17):1250-1256. 6. Hsieh Y. and J. Ju. 1994. "Melting behavior of ultra-high modulus and molecular weight polyethylene (UHMWPE) fibers," Journal of Applied polymer Science, 53:347-354. 7. Devaux, E. and C. Caze. 1999. "Composites of ultra-high-molecular-weight polyethylene fibers in a low-density polyethylene matrix II. Fiber/matrix adhesion," Composites Science and technology, 59:879-882.

Filler-Elastomer Interactions: Effect of Ozone Treatment on Adhesion Characteristics of Carbon Black/Rubber Composites Soo-Jin Park , Hwa-Young Lee, Jae-Rock Lee Advance Materials Division, Korea Research Institute of Chemical Technology, P.O. Box 107, Yusong, Taejon 305-600, Korea Byung-Gak Min Department of Polymer Engineering, Chungju National University, Chungju, 380-702 Chungbuk, Korea

ABSTRACT hi this work, the changes in surface and adhesion characteristics of carbon black/rubber compoundings treated by ozone technique are investigated in different treatment times. The surface properties of carbon blacks are studied by contact angle measurement and their adhesion characteristics are determined by crosslinking density and tearing energy (Gmc) of the composites. As a result, it is found that the increasing of the ozone treatment time leads to an increase of the introduction of oxygen-containing functional groups onto carbon black surfaces and to an increase of the polar component (/sSP) of surface free energy (/$), resulting in improving the crosslink density and tearing energy (Gmc) of the composites. The results can be explained by the fact that the polar functional groups of carbon black surfaces by the treatment lead to an increase of the adhesion at interfaces between carbon blacks and polar rubber matrix.

INTRODUCTION Commercial applications of elastomers often require the use of particulate fillers to obtain the desired reinforcement. In the rubber industry, carbon blacks are one of the most important reinforcing filler used to impart specific properties to filler compounds [1,2]. The reinforcement of elastomers by particulate fillers has been studied in depth in numerous investigations, and it is generally accepted that this phenomenon is, to a large extent, dependent on the physical interactions between the filler and rubber matrix, which can determine the degree of adhesion at interfaces. Generally, it is dependent on the active functional groups, surface energy, and energetically different crystallite faces of the filler surfaces [2-4]. Various methods have been used to modify the surface properties of the carbon blacks, such as liquid or gas oxidation, chemical, electrochemical, plasma treatment, and ozone treatment [5,6]. Among them, ozone treatment, one of the most commonly processes used in industry, is used to introduce the oxygen-containing functional groups on carbon black "Correspondence Author. Advanced Materials Division, Korea Research Institute of Chemical Technology, P. O. Box 107, Yusong, Taejon 305-600, South Korea Fax: +82-42-861-4151. E-mail: [email protected]

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surfaces [7,8]. Many authors have reported that ozone treatment of carbon blacks enhances the reinforcement of polar rubber, such as acrylonitrile butadiene rubber (NBR). Chemical reactivity of the polar rubber-carbon blacks is attributed to the presence of oxygen-containing functional groups, including phenol, quinone, carboxyl, and lactone [9]. The main objectives of the present work are to investigate the influence of ozone treatment on surface properties and adhesion characteristics of the carbon black/acrylonitrile butadiene rubber composites. EXPERIMENTS Materials and sample preparation Carbon blacks (N220 noted in ASTM destination) were obtained from Korea Carbon Black Co. and NBR was prepared by Kumho Petrochem. Co., South Korea. The ozone treatment for the carbon blacks were carried out using a ozone generator (LAB 2B, Korea Ozonia Co.) with pure oxygen gas. The ozone concentration was fixed at 30 mg/£ and the treatment time was varied within 0, 10, 30, 60, and 120 min, namely OCB-0, OCB-10, OCB-30, OCB-60, and OCB-120. Prior to measuring the mechanical properties of the composites, the filled rubbers were cured at 1.5 MPa pressure and 160 °C temperature for 60 min. The compounding formulations were reported in Table 1. TABLE I Compounding formulations J- .L Ingredients a

xmr. NBR

Carbon ,, , black

Zinc ., oxide

Loading 100 30 5 (phr) a ./V-Oxydiethylene-2-benzothiazole sulfenamide.

Steanc ., acid 2

. , , = Accelerator 1

„ m Sulfur 2

Measurements Contact angles were measured using the sessile drop method and about 5 /A of wetting liquid was used for each measurement at 20 °C. The test liquids were deionized water and diiodomethane and more than five drops were tested for each of the untreated and ozone-treated carbon black surfaces studied. The degree of swelling was measured according to ASTM D366-82 and calculated using the relation [10,11] (1) where, m0 and m were the masses of the sample before and after swelling (measured using an electric balance of sensitivity 10"5g), respectively. The solvent used in this work was toluene (molar volume 107 cmVmol; cohesive energy density 37.2 (J/citf)05). The tearing energy (Gmc), one of the critical strain energy release rate (Gc), was characterized by trouser beam tests for the mechanical interfacial properties of rubber compounds. Rectangular specimens about 70 X 50 X 2 mm3 thick

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were cut from a sheet that was manufactured by a two-roll mill technique. All tests were conducted at a crosshead speed of 2 mm/min. RESULTS AND DISCUSSION Contact angle and surface free energy Early on, Fowkes introduced the concept of the surface free energy of a solid. The surface free energy as expressed by the sum two components: a dispersive component, "f, attributable to London attraction, and a specific (or polar) component, "f, owing to all other types of polar interactions (Debye, Keesom, hydrogen bonding, and other weakly polar effects) [12,13] 7L

=

7i

+ 7LSF

(2)

where y is surface free energy and superscripts L and SP refer to the London dispersive and specific components, respectively. Figure 1 shows the results of surface free energies of the ozone-treated carbon blacks. The polar component of surface free energy is largely increased with increasing the ozone treatment time, resulting in improvement of the total surface free energy. The results can be explained that the ozone treatment of the carbon black surfaces produces carbon radicals from the hydrocarbon backbone, followed by the formation of unstable hydro peroxides to produce various oxygen functional groups i.e., carboxyl, hydroxyl, lactone, and carbonyl groups by reaction with additional oxygen.

FIGURE 1 Surface free energy of the carbon blacks treated by ozone gas

Crosslink density of carbon black/rubber composites The crosslinking density, Ve per unit volume on a perfect network, is given by the equation [10,11] V =

Mr

(3)

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Filler-Elastomer Interactions

where, pp is the polymer density, NA Avogadro's number, and Mc the average molecular weight of the polymer between crosslinks. Using Eq. (3), the crosslink density, Ve and the degrees of swelling, Q are calculated for the carbon black/rubber composites, as shown in Table 2. As results, the crosslink density is slightly increased and the swelling behavior of the composites is significantly decreased compared to that of untreated one. These results can be expected to diminish the reinforcing ability or network chain density of the composites TABLE II Crosslink density and degree of swelling of the carbon black/rubber composites

Specimen FeX1019 (m"3)

OCB-0/ NBR 4.52 158.5

OCB-10/ NBR 7.63 116.4

OCB-30/ NBR 8.71 107.6

OCB-60/ NBR 9.34 103.1

OCB-120/ NBR 8.87 106.6

Mechanical interfacial properties of carbon black/rubber composites According to Kraus, the degree of adhesion between the filler surface and the rubber can be assessed from the swelling behavior of the sample in a solvent. Therefore, the importance of tearing energy, Gmc; a s a criterion of the interfacial adhesion relationship can be considered. The tearing energy can be considered to be an interfacial behavior of the constitutive elements of a material. The tearing energies (Gmc) are measured by a trouser beam test and are calculated using equation [14]

mc

t

(4)

where F is the applied force and t the width of the tear path after tearing is completed.

OCB-0 OCB-10 OCB-30 OCB-60 OCB-120

FIGURE 2 Tearing energy (Gmc) of the carbon black/rubber composites

Figure 2 shows the tearing energy (Gmc) of the carbon black/rubber composites. As shown on Figure 2, the tearing energies (Gmc) of the composites made from ozone

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treatments are largely increased with increasing the ozone treatment time. It reveals that the polar rubber, such as acrylonitrile butadiene rubber (NBR), shows a high intermolecular interaction with oxygen-containing functional groups of the carbon blacks, resulting in improving the tearing energy (Gmc) of the carbon black/rubber composites. CONCLUSION In this work, the rubber composites filled with the carbon blacks modified by ozone treatments are studied in terms of surface free energetics, crosslink density, and tearing energy (Gmc) for predicting and understanding the mechanical interfacial properties of the composites. The experimental results show that the surface treatment leads to an increase of polar component of surface free energy, and crosslink density, resulting in improving the tearing energy of the carbon black/rubber composites. It is then considered that the ozone treatment of carbon blacks is one of the useful methods in enhancing the degree of adhesion at interfaces between carbon blacks and polar rubber matrix in a composite system. REFERENCES 1. 2.

3. 4. 5. 6. 7. 8.

9.

10. 11. 12. 13. 14.

Donnet, J. B., Bansal, R. C, and Wang, M. J. 1993. Carbon Black Science and Technoogy. 2nd ed. New York: Marcel Dekker. Park, S. J. and Kim, J. S. 2000. "Roles of Chemically Modified Carbon Black Surfaces in Enhancing Interfacial Adhesion between Carbon Black and Rubber in a Composite System," J. Colloid Interface Set, 232:311-316. Frysz, A. and Chung D. D. L. 1997. "Improving the Electrochemical Behavior of Carbon Black and Carbon Filaments by Oxidation," Carbon, 35:1111-1127. Lin, J. H., Chen. H. W., Wang. K. T., and Liaw F. H. 1998. "A Novel Method for Grafting Polymers on Carbon Blacks," J. Mater. Chem., 8:2169-2173. Champman, B. 1980. Glow Discharge Processes. New York: Wiley, pp. 139-173. Donnet, J. B., Park, S. J., and Brendle, M. 1992. "The Effect of Microwave Plasma Treatment on the Surface Energy of Graphite as Measured by Inverse Gas Chromatography," Carbon, 30:263-268. Fu, X., Lu, W., and Chung, D. D. L. 1998. "Ozone Treatment of Carbon Fiber for Reinforcing Cement," Carbon, 36:1337-1345. Rivera-Utrilla, J. and Sanchez-Polo, M. 2002. "The Role of Dispersive and Electrostatic Interactions in the Aqueous Phase Adsorption of Naphthalenesulphonic Acids on Ozone-treated Activated Carbons," Carbon, 40:2685-2691. Park, S. J., Cho, K. S., and Ryu, S. K. 2003. "Filler-Elastomer Interactions: Influence of Oxygen Plasma Treatment on Surface and Mechanical Properties of Carbon Black/Rubber Composites," Carbon, 41:1437-1442. Flory, P. J. 1950. "Statistical Mechanics of Swelling of Network Structures," /. Chem. Phys., 18:108. Gwaily, S. E., Badawy, M. M., Hassan, H. H., and Madani, M. 2003. "Influence of Thermal Aging on Crosslinking Density of Boron Carbide/Natural Rubber Composites," Polym. Testing, 22:3. Fowkes, F. M. 1962. "Determination of Interfacial Tensions, Contact Angles, and Dispersion Forces in Surfaces by Assuming Additivity of Intermolecular Interactions in Surfaces," J. Phys. Chem., 66:382. Israelachivili, J. 1992. Intermolecular and Surface Forces. 2nd ed. London: Academic Press. Griffith, A. A. 1921. "The Phenomena of Rupture and Flow in Solids," Phil. Trans. R. Soc. London, A. 221:163.

Interface End Theory and Fragmentation Test Xing Ji*, Ying Dai Key Laboratory of Solid Mechanics of MOE, Tongji University, Shanghai, China Lin Ye, Yiu-Wing Mai Centre of Advanced Materials Technology (CAJVIT), School of Aerospace, Mechanical and Mechatronic Engineering J07, The University of Sydney, Sydney, NSW 2006, Australia

ABSTRACT Fiber fragmentation test is one of the micro-mechanical test methods to measure the interfacial shear strength in fiber composites. Its result exhibits large discrepancy with those of other three tests (fiber pull-out, micro-indentation and micro-debond tests). It's noticed that there are two questions in the fragmentation test. First, if stress singularity exists at the interface end due to the fiber breaks; second, if de-bonding occurs at the interface end as the critical length is achieved. An axisymmetric model of interface end is used to analyze the stress singularity. With the aid of an asymptotic procedure and variable separation, a characteristic equation is derived to determine the eigen-value of stress singularity. The relation of stress singularity index and Dundurs parameters is presented. It is found that the fragmentation test has the most serious stress singularity at the interface end when compared to the stress singularity indices of these four test methods. This means that the result obtained from the fragmentation test is not exactly the interface shear strength (IFSS), and is not comparable to those determined from the other three methods. The question whether de-bonding at the interface end commences when the critical length is reached is also discussed.

INTRODUCTION Due to their outstanding properties of high strength, high toughness and lightweight, fiber composites have been used for decades as structural materials in aerospace applications and many other fields. Although the mechanical properties of the composites are mostly governed by the properties of the reinforcing fibers and the matrix materials, the interfacial shear strength (IFSS) between fiber and matrix is also a critical factor. Thus, the experimental determination of IFSS has received intensive research interests in the past three decades. The test methods of IFSS may be divided into two categories: macroscopic and microscopic. Macroscopic tests (such as three-point bending) are used to measure the IFSS indirectly. Microscopic test are aimed to measure directly and quantitatively the IFSS. There are four microscopic (single fiber composite) test methods, which have been developed to measure the IFSS: fragmentation test [1], micro-indentation test [2], * Corresponding author, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, China. Fax: +86-21-6598-3267. E-mail address: iixmgl(o>,shl63.net

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pullout test [3] and micro-debond test [4]. In these tests, the specimens with different geometry are used, and a shear force is effectively applied to the fiber-matrix interface. When interfacial de-bonding occurs, IFSS is calculated based on the ultimate shear load and the de-bonded area of the interface. Even though the principle of the test methods seems simple, and many improvements have been made in technique, the results from the four tests often show large discrepancies [5]. Recently, the stress singularities near the interface ends in the pullout, microindentation and micro-debond specimens have been investigated by using the method of asymptotic expansion approach [6]. Due to the differences in their geometry at the interface ends [7], the stress singularity indices of these three specimens are different, even though fiber and matrix materials are the same. Based on the elastic properties of carbon fiber and epoxy matrix given in Ref. [5], the stress singularity values were calculated and compared [7]. Apparently, the stress singularity indices near interface ends can be used to assess the reliability of the test methods. If a stress singularity exists near the interface end, the IFSS result is suspect. If the stress singularity is free from the interface end, the result is not disturbed by the singular stress field, and hence, the test method is acceptable. For completeness, the singularity analysis of the interface end in fragmentation test is given in this paper. A characteristic determinant is derived for the fragmentation test, and the relation between the stress singularity index and Dundurs parameters is obtained. Again, by using the elastic properties of carbon fiber and epoxy matrix in [5], the value of the stress singularity index near interface end for the fragmentation test is calculated and compared with those of the other three tests in Ref. [7]. It is found that the fragmentation test has the most serious stress singularity at the interface end. This means the result from the fragmentation test is not a true IFSS, and is not comparable to those derived from the other three methods. The question if de-bonding occurs at the interface end when the critical length is reached is also discussed. FRAGMENTATION TEST A brief description of the fragmentation test is needed to illuminate the issues in the test method and analysis. As shown in Figure 1, a single fiber is embedded in a tensile specimen of matrix material, and a tensile load is applied to the specimen end, which is transmitted to the fiber via interfacial shear stress. As the stress in the fiber reaches its tensile strength, the fiber breaks. The number of breaks increases with the increase of the applied load, until the number of fiber breaks becomes saturated. Then, the length of each fragment is measured and the average length is called the critical length. Kelly proposed a simple formula to determine the interfacial shear strength with the shear lag theory, T=
FIGURE 1.

Single fiber fragmentation test

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It's noticed that there are two problems in the fragmentation test. First, whether the stress singularity exists at the interface end due to the broken fiber; second, whether debonding occurs at the interface end as the critical length is achieved. STRESS SINGULARITY ANALYSIS NEAR INTERFACE END Usually, the thickness and width of the specimen for fragmentation test are 2 and 4 mm, respectively, and the diameter of the fiber is 0.01~0.001mm. Compared to the diameter of the fiber, the matrix can be considered as an infinite medium, and the load as axisymmetically distributed around the fiber. So an axisymmetric interface end model, shown in Figure 2, is adopted to simulate the single fiber fragmentation test. The fracture in the fiber may be considered as a crack whose tip touches the interface at o, and o is the interface end.

Fiber

Matrix s—Interface

Crack -

A o Fiber

|o\ p j \ Interface End I Matrix

FIGURE 2. Axisymmetric model of fiber fragmentation

Assume that when the number of the fiber breaks is saturated, neither the fiber crack spreads inside the matrix, nor the fiber-matrix interface de-bonding occurs. In practice, there will be a competition between these two processes following a fibre break. This problem has been addressed and analysed by Liu et al [8] and interested readers may refer to this work. In Figure 2, Rf is fiber radius, O-pz is cylindrical coordinates referred to the fiber axis, and o-r6 is polar coordinates referred to the interface end. The cracked surface (z = 0, 0 < p ^ #/) is free from stresses, and the deformation of the matrix is symmetric referred to z = 0, Rf ^p <°°. Along the interface, the stresses and the displacements satisfy the continuity conditions. Assume fiber and matrix are isotropic. hi axisymmetric problems, the governing elastic equations are: dp2 A Ay, =(

p8p

dz2

+ + j) and y/ [9]. For easy representation of the boundary and continuity conditions, components of stress and displacement could be transformed from cylindrical coordinates O-p z to polar coordinates o-rO, whose origin o is at the interface end, Figure 2. Thus the boundary conditions are:

Interface End Theory and Fragmentation Test

= 0,

= 0,

a.

2

up(r,0-) = up(r,0+), ap(r,0') = ap (r ,0+ ),

2

u,(rfi-)

=0

= 0,

uz

2

591

2

=uz{rfi+)

o ^ (r ,0") = a„ (r,0+ )

Eq. (1) should also be transformed to polar coordinates (r, 6) to maintain the consistency of the functions and variances in the analysis. Then, for the condition: — <1, an asymptotic expansion is applied to the transformed equations. If only Rf the stress singularity near the interface end is of interest, the first order asymptotic equation is accurate enough and easy to be solved with method of variable separation. Substituting the solution into the boundary conditions, Eq. (2), homogeneous linear algebraic equations with eight unknown constants are obtained. According to non-zero solutions condition of homogeneous linear algebraic equations, the coefficients of these unknown constants must satisfy the coefficient determinant, simplified below: 2(1 - P)\ (a - P)X7 + (1 + /?)sin2 — I - (1 + a) = 0

(3)

where, X is the eigen value of the determinant, a and p are Dundurs parameters [6]. The stress singularity index Xs (XS=X— 1) of interface end can be obtained from the eigen value X, solved from Eq. (3). The stress singularity index Xs of interface end in fragmentation test only depends on Dundurs parameters a and p. The variation of Xs with a and p is shown in Figure 3. The stress singularity index Xs of interface end equals -1/2, if Dundurs parameters a and /? satisfy: a + p = 0. It means that in this case, the stress singularity index Xs is equivalent to the stress singularity index of a crack tip in a homogeneous medium. For most fiber-epoxy composites, their Dundurs parameters, a and p, are located in the left region of the line: cc+ p = 0 in Figure 3. Therefore, in fragmentation test of fiber-epoxy composites, the stress singularity of interface end is stronger than -1/2. This implies that the stress singularity near the interface end of the fragmentation test will never disappear for any combination of fiber and matrix system. Using the method of singular integral equation, Wang [10, 11] studied the problems of a crack perpendicular to the interface of fiber and matrix. It is equivalent to the case of fragmentation test when the crack in the fiber spreads to the interface in his consideration [10]. If the cracks in fiber and matrix both extend to the interface, this is the case of push-in test [11]. In [10, 11] the solutions are derived analytically. For the problem on solving stress singularity index, the analytical solutions and the asymptotic solutions adopted in the present paper and Ref. [7] give the same results. DISCUSSIONS By using the mechanical properties of fiber and matrix given in [5], the stress singularity index near the interface end of the fragmentation test was calculated, and compared with those of micro-debond, micro-indentation and pullout tests [7], shown in Table 1. The stress singularity indices of micro-debond, micro-indentation, pullout

Interface End Theory and Fragmentation Test

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and fragmentation tests are -0.0002 (wedge angle of resin droplet = 40°), -0.3283, -0.3383 and -0.9290, respectively. Theus, among these four tests, the stress singularity near the interface end of fragmentation test is the strongest one. If the wedge angle of the resin droplet is less than 40°, the stress singularity index near the interface end of the micro-debond test is negligible. Because it is almost free from the disturbance of stress singularity, the results from the micro-de-bond test are most reliable. The specimen used in micro-indentation test is unidirectional composite. The matrix surrounding the indented fiber is strengthened by the neighboring fibers. The stress singularity index near interface end may not be -0.3283. As = -0.3283 is derived from the single fiber model of the micro-indentation test [7]. A further study for the micro-indentation test using composite specimen is needed. It is noticed that the stress singularity near interface end of fragmentation and pullout test [7] never disappears for any combination of fiber and matrix system. The experimental IFSS results from these two tests geometries are always suspect due to the existence of the strong stress singularity at the interface end.

FIGURE 3.

Eigen-value diagram at interface end of fiber fragmentation test

TABLE I Eigenvalue and stress singularity index of specimen in four tests Test Method Pullout Micro-debond (6=60°) (6=40°) Micro-indentation Fragmentation

P

a -0.9857

-0.1949

-0.9857

-0.1949

-0.9857 -0.9857

-0.1949 -0.1949

X 0.6613 0.8786 0.9998 0.6717 0.0710

-0.3387 -0.1214 -0.0002 -0.3283 -0.9290

Another issue of fragmentation test is whether interface de-bonding occurs when the critical length of the fragments is achieved. After the fiber has broken into fragments, fiber cracks will form. There are four cases to be considered. (1) Fiber crack ends at the interface, and does not extend into the matrix. Interface is intact. Stress singularity near the interface end exists, and the stress singularity index equals -0.9290. (2) Fiber crack penetrates through the interface, and spread into the matrix. Interface remains intact. Stress singularity near the interface end exists, and the stress singularity index equals -0.3283, because this is just the case of single fiber model of micro-indentation test.

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(3) Fiber crack ends at the interface, and does not extend into the matrix. Interface de-bonding occurs. The interface de-bonding is influenced by the stress singularity near the interface end, and the stress singularity index is -0.9290. (4) Fiber crack penetrates through the interface, and spread into the matrix. Interface de-bonding takes place. The interface de-bonding is affected by the stress singularity near the interface end, and the stress singularity index is -0.3283. For cases (1) and (2), the IFSS obtained from fragmentation test is suspect, since the interface does not de-bond. For cases (3) and (4), the IFSS evaluated from the fragmentation test is also dubious. This is because interface de-bonding is influenced by the stress singularity near the interface end. ACKNOWLEDGEMENTS Financial supports from the Natural Science Foundation of China (No. 10372072), the Science and Technology Foundation of Tongji University are much appreciated. XJ was Visiting Professor at the CAMT, University of Sydney, supported by the Australian Research Council (ARC) projects when parts of this work were completed. YWM wishes to thank the ARC for the award of an Australian Federation Fellowship tenable at the University of Sydney. REFERENCES I. Kelly, A. and W. R. Tyson. 1965. "Tensile Properties of Fiber-Reinforced Metal: Copper- Tungsten and Copper-Molybdenum," J. Mech. Phys. Solids, 13: 329-350. 2.Favre, J. P. and M. C. Merrine. 1981. " Characterization of Fiber/Resin Bonding in Composites Using a Pull-out test," Int. J. Adhesion Adhesives, 1:311-316 3. Mandell, J.F., J. H. Chen and F. J. McGarry. 1980. "A Microdebonding Test for in situ Assessment of Fiber/Matrix Bond Strength in Composite Materials," Int. J. Adhesives, 1: 40-44. 4. Miller, B., P. Muri and L. Rebenfeld. 1987. "A Microbond Method for Determination of the Shear Strength of a Fiber/Resin Interface," Compo. Sci. Technol., 28: 17-32. 5. Pitkethly, M. J., et al. 1993. "A Round Robin Programme on Interfacial Test Methods," Compo. Sci. Technol., 48: 205-214. 6. Zheng, B. L. and X. Ji. 2002. "Stress Singularity Analyses of Interface Ends in Micro-Mechanics tests," Compo. Sci. Technol., 62: 355-365 7. Ji, X., Y. Dai, B. L. Zheng, L. Ye and Y.-W. Mai. 2003. "Interface End Theory and Re-Evaluation in Interfacial Test Methods," Accepted by Composite Interface. 8. HY Liu, Y-W Mai, L Ye and LM Zhou, "Stress transfer in the fibre fragmentation test: Part III. Effect of matrix cracking and interface debonding", J Mater Sci. Vol 32, 1997, pp 633-641 9.Y. Dai, and X. Ji. 1994. "The Stress Singularity of Axisymmetric Cylindrical Interface Crack," Shanghai Journal of Mechanics, 15(3): 29-39. 10. Wang, Q., X. Ji and Y. G. Wang. 1996. "3D Axisymmetric Analysis of a Cracked Fiber in a Transversely Isotropic Elastic Medium," Mech. Research Communication, 23(2): 171-174. II. Wang, Q., X. Ji and Y. G. Wang. 1998. "Stress singularity near the end of a cylindrical interface and the linear elasticity of push-in tests," Science in China (Series E), 41(5): 471-481.

Stress Singularity Analysis of Interface End and Specimen Design for Fiber Pullout Test Ying Dai*, Xing Ji Key Laboratory of Solid Mechanics of MOE, Tongji University, Shanghai 200092, China Lin Ye, Yiu-Wing Mai Centre of Advanced Materials Technology (CAMT), School of Aerospace, Mechanical and Mechatronic Engineering J07, The University of Sydney, Sydney, NSW 2006, Australia

ABSTRACT Since stress singularity was found at the interface end in current specimen of pullout test, interface shear strength (IFSS) obtained from the tests loses its rationality [2]. But a useful conclusion [2] is that when the wedge angle of the matrix is less than a critical angle, the singularity of stress field at the interface end of the specimen in micro-debond test nearly disappears. Following this conclusion, a conic specimen shown in Figure 1 is presented, in which the wedge angle of the specimen is designed to be less than a critical angle in order to prevent the singular stress field occurred at the interface end. The conic specimen is designed for pullout test to avoid disadvantages inherent in the micro-debond test [3]. An axisymmetric model of fiber/matrix system with arbitrary wedge angles at the interface end is used for the determination of critical wedge angle. With the aid of asymptotic analysis and variable separation, eigenvalue, A,, could be determined by a characteristic determinant. For a given fiber-matrix system, a curve representing the relationship between the stress singularity index and wedge angle could be obtained by solving the characteristic determinant. We define the critical wedge angle, 6cr, as that for a singularity index of-0.005. The design of a conic pullout specimen is also discussed. INTRODUCTION Since fiber-matrix interface plays a main function of stress transfer from the matrix to the fiber in composite materials, the mechanical performance of many fiber composites depends greatly on the properties of the interface. Study on interface properties has been a major driving force to develop various experimental techniques to assess the interface bond quality. The fiber pullout, micro-indentation, microdebond and fragmentation tests are widely used methods to measure the interfacial shear strength (IFSS). Unfortunately, there always exist large discrepancies among the experimental results of these four test methods [1]. Xing Ji et al [2] re-evaluated these Corresponding author. Key Laboratory of Solid Mechanics of MOE, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, China. Fax: +86-21-6598-3267. Email address: [email protected]

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four test methods based on the interface end theory. Singular stress fields were found at the interface ends in all four specimen geometries. This result makes the interface shear strength (IFSS) obtained from the tests loses its credibility. But when the wedge angle of the matrix is less than a critical angle, the singularity of stress field at the interface end of the specimen in micro-debond test disappears [2]. Following this conclusion, a conic pullout specimen shown in Figure 1 is presented, in which the wedge angle of the specimen is designed less than a critical angle to prevent the singular stress field occurred at the interface end. The conic pullout specimen is designed to take advantage of the micro-debond test [2], and to avoid dis-advantages inherent in the micro-debond test [3]. An axisymmetric model of fiber-matrix system with arbitrary wedge angles at the interface end is used for determination of critical wedge angle. With the aid of asymptotic expansion and variable separation techniques [4], eigen-value, X, which has the relation of stress singularity index, Xs, as Xs=X-\, were determined by a characteristic determinant. The contours of eign-value via Durndurs parameters with wedge angles 90° and 60° are shown in Figure 3. It is found that the eign-value contours shift to the right as the wedge angle decreases from 90° to 60°. The relation of stress singularity index and wedge angle of three fiber-matrix systems (listed in Ref [2] ) is presented in Figure 4. It can be seen that the stress singularity index approaches zero as the wedge angle of matrix approaches zero. Hence, for a given fiber-matrix system, there exists a critical wedge angle, below which the stress singularity equals -0.005. Since Xs= -0.005 is a very small singularity and can be ignored in practice, we can define a critical wedge angle, 9cr, with stress singularity index -0.005. Thus, a conic specimen for pullout test with non-singularity at the interface end could be designed. SINGULARITY ANALYSIS OF INTERFACE END An axisymmetric model shown in Figure 1 is used here to investigate the stress singularity at the interface end. O-pz is a set of cylindrical coordinates referred to the fiber axis, and o-rO is a set of polar coordinates referred to the interface end. a and b are wedge angles from interface to the free surface of fiber and matrix, respectively. The test methods can be identified by different combinations of the wedge angles a and b, Viz., (a=n, b=7d2); {a=7d2, b=7tl2) and (CF^K, b<7tl2) corresponding to the

pullout, micro-indentation and micro-debond tests, respectively. In axisymmetric problems, the governing elastic equations are expressed by Papkovich-Neuber functions cp and y/, dp2 d2 dp2

p dp Id p dp

dz2 d2 dz2

Stress Singularity Analysis of Interface End

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1

Fiber Matrix

Holder

FIGURE 1. Sketch of conic pullout specimen FIGURE 2. Axisymmetric model of interface end

where g> and y/ are harmonic functions. The displacement and stress components can be expressed in terms of