Stress Determination for Fatigue Analysis of Welded Components

The International Institute of Welding

Edited by Erkki Niemi

ABI NG TO N P U BLISHI N G Woodheod Publishing LId in association ",;th The; Weldin/t Institute

The International Institute of Welding

Stress Determination for Fatigue Analysis of Welded Components IISIIIW-1221-93

(ex

doc XIII-1458-92, XV-797-92)

Edited by Erkki Niemi

ABINGTON PUBLISHING Woodhead Publishing Ltd in association with The Welding Institme Cambridge England

Published by Abington Publishing, Abington Hall, Abington, Cambridge CB 1 6AH, England www.woodheadpublishing.com First published 1995, Abington Publishing © 1995, The International Institute of Welding

Conditions of sale All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein.

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN-13: 978-1-85573-213-1 ISBN-lO: 1-85573-213-0 Printed by Victoire Press Ltd, Cambridge, England

CONTENTS PREFACE NOMENCLATURE ABSTRACT .......... ............. .......................... .... ... ...... .................... ... ..... .... o INTRODUCTION.. .................................. ........... ........ ... ............... 1 SCOPE AND FIELD OF APPLICATION ...................................... 2 STRESSES CONSIDERED IN FATIGUE ANALYSIS .. .... ........... 2.1 Stress categories ............................................................... 2.2 Stress range ...................................................................... 2.3 Static stress.......................... .... ............................ ... ...... .... 2.4 Loads and load combinations ............................................ 2.5 Multi-axial stress states .... ..................... ................. ........... 3 STRESS RAISERS ..................................... ..... .......... ...... .......... .... 3.1 Effects of macro-geometry and concentrated load areas .... 3.2 Effects of structural discontinuities .................................. 3.3 Effects of local notches ...... .................................. ............. 3.4 Special case: joints between structural hollow sections..... 4 FATIGUE ANALYSIS APPROACHES ........................................ 4 .1 Nominal stress approach ................................................... 4.2 Hot spot stress or strain approach ...................................... 4.3 Notch stress/strain approaches ........................................... 4.4 Fracture mechanics approach ............................................ 4.5 Summary.......................................................................... 5 GUIDELINES FOR THE CHOICE OF FATIGUE ANALYSIS METHOD ................................................... .................................. 5 .1 Nominal stress approach ................................................... 5.2 Hot spot stress approach ................................................... 5.3 Notch stress/strain approaches .......................................... 5.4 Fracture mechanics approach ............................................ 6 GUIDELINES FOR FINITE ELEMENT ANALYSIS .................... 6.1 General notes .................................................................... 6.2 Element types ................................................................... 6.3 Boundary element analysis ............................................... 6.4 Resolution of nominal stresses ......................................... 6.5 Resolution of hot spot stresses ......................................... 6.6 Resolution of nonlinear stress peaks ................................ 6.7 Superposition of the effects of macro-geometry and and structural discontinuity ............................................... 7 EXPERIMENTAL DETERMINATION OF STRESSES ...............

1 1 2 3 3 6 7 8 9 12 12 14 15 17 19 19 19 22 23 24 25 25 25 26 27 28 28 29 32 33 34 50 51 53

7.1 General ............................................................................ 7.2 Introduction to strain gauge technology ............................ 7.3 Applications of strain gauges ............................................ 7.4 Configurations for various criteria..................................... 7.5 Application examples ........................................... ............. 7.6 Stress spectrum and cumulative fatigue damage ................ 8 CONCLUDING REMARKS .. ................ ............... ..... .... ............ .... REFERENCES .........................................................................................

53 53 55 56 59 64 65 66

PREFACE This document has been prepared as a result of an initiative by Commissions XIII and XV of the International Institute of Welding (IIW). An editorial group was established in 1991, consisting of the following members: Prof E Niemi, Finland (Chairman) Mr R Bent, Canada Mr M Huther, France Mr G Parmentier, France Prof H Petershagen, Germany Prof D Radaj, Germany Mr D R V van Delft, The Netherlands Dr R Jaccard, Switzerland I would like to thank all members for their valuable support and contributions. Furthermore,

acknowledged are many constructive comments and suggestions given by: Dr W Fricke (Germany), Dr S J Maddox and Mr R Scothern (United Kingdom), Professor Jaap Wardenier, Dr A M van Wingerde and Dr Ram Puthli (The Netherlands), Dr P W Marshall (USA), Professor M Matoba (Japan), Dr Matti Hakala and Mr Teuvo Partanen (Finland). Dr John Ion and Dr S J Maddox have been of great help in proof reading and correcting the manuscript. Erkki Niemi Lappeenranta University of Technology PO Box 20 SF 53851 Lappeenranta Finland

NOMENCLATURE A area of cross-section E elastic modulus Faxial force I moment of inertia Km stress magnification factor for misalignment effects Ks structural stress concentration factor Kt theoretical notch factor M bending moment Mk function accounting for the effect of nonlinear stress peak in the stress intensity factor R stress ratio, electrical resistance _Re yield strength a depth of a surface crack, or half length of a through-thickness crack e eccentricity t plate thickness y distance from neutral axis E strain 0' normal stress O'b shell bending stress O'hs hot spot stress O'is local structural stress (at sharp corners of gussets etc.) O'm membrane stress O'max maximum value of stress at a point in time O'min minimum value of stress at a point in time O'in local notch stress O'nom nominal stress O'n1p nonlinear stress peak at a notch O'res residual stress O's structural stress O'x, O'y normal stresses in a specified co-ordinate system 0'1 largest principal stress 0'2 second principal stress LlO' range of normal stress (LlO')max maximum range of normal stress 'txy in-plane shear stress in a specified co-ordinate system

1

ABSTRACT This document introduces definitions of the terminology relevant to stress determination for fatigue analysis of welded components. The various stress concentrations, stress categories and fatigue analysis methods are defined. The fatigue analysis methods considered are: nominal stress, hot spot stress, notch stress, notch strain, and fracture mechanics approaches. The document also contains comprehensive recommendations concerning the application of finite element methods and experimental methods for stress determination.

o

INTRODUCTION

Fatigue life prediction of welded components requires appropriate stress analysis adapted to the method of fatigue analysis. It is a generally accepted fact that the main controlling parameter is the stress range, i.e. the difference between (successive) peak and trough values of the fluctuating stress. It may often be difficult to decide on the level of accuracy which should be chosen for a certain stress analysis task. In a welded component there may be several geometric features which act as stress raisers. Such stress raising discontinuities can produce essentially global or local effects and they frequently interact such that very high local stresses can occur. There are four basic approaches to fatigue life prediction of welded components [1]: (i) (ii) (iii) (iv)

the nominal stress approach; the structural hot spot stress or strain approach; the local notch stress or strain approach; the fracture mechanics approach.

The approaches differ in the level of stress and strain analysis used, i.e. the extent to which stress-raisers are taken into account by the analysis. This holds true both for the determination of fatigue properties from the test specimens and for the design calculations. The level of stress analysis in the design phase must match that used in the determination of fatigue strength data. Factors that are ignored in the analysis, are left to the fatigue strength criteria determined empirically, e.g. S-N curve. Particular attention must be paid to the above questions when the stress analysis is made using finite element methods. The stress analyst must possess a clear

2

insight into the type of the fatigue analysis to be made in order to be able to choose correct element types, correct element mesh and appropriate level of idealization for the finite element model of the structure etc.

1 SCOPE AND FIELD OF APPLICATION fu this document a number of approaches to fatigue analysis of welded

components are described, and the various stress categories used in the analyses are defined. Recommendations for the application of the Finite Element Method as well as the use of strain measurements are given. Detailed consideration of the fatigue strength data required in the various types of fatigue analysis is outside the scope of this document This document is intended for fatigue design of common welded structures, such as cranes, excavators, vehicle frames, bridges, ship hulls, offshore structures etc., fabricated from at least 3 mm thick material. In general, attention is focused mainly on weld details which give rise to fatigue cracking from the surface, notably from the weld toe. It is to be considered as a reference document giving general guidelines. It is the responsibility of code writing bodies, or companies and their design offices, to establish appropriate working instructions adapted to the needs of the specific branch ofindustIy. This document primarily considers fusion welded structures with predominantly elastic behaviour. Therefore, cyclic plasticity is assumed to occur at the notch roots only. The so-called low cycle fatigue approaches which consider cyclic plasticity at the structural stress or even the nominal stress level (see Section 2.1) are outside the scope. Moreover, also out of the scope are force-based methods used in the analysis of spot welds, in which the fatigue strength is expressed in terms of the force per weld spot The main purpose of this document is to harmonize the terms, methods and conceptions used by fatigue testing laboratories, designers, finite element analysts, and educational institutions. It is hoped, for example, that this document would help in communication between designers and finite element specialists, such that designers could express their problems correctly and stress analysts could supply correct answers. It is recommended that fatigue analysis reports should be written using the

terminology defined in this document

2

insight into the type of the fatigue analysis to be made in order to be able to choose correct element types, correct element mesh and appropriate level of idealization for the finite element model of the structure etc.

1 SCOPE AND FIELD OF APPLICATION fu this document a number of approaches to fatigue analysis of welded

components are described, and the various stress categories used in the analyses are defined. Recommendations for the application of the Finite Element Method as well as the use of strain measurements are given. Detailed consideration of the fatigue strength data required in the various types of fatigue analysis is outside the scope of this document This document is intended for fatigue design of common welded structures, such as cranes, excavators, vehicle frames, bridges, ship hulls, offshore structures etc., fabricated from at least 3 mm thick material. In general, attention is focused mainly on weld details which give rise to fatigue cracking from the surface, notably from the weld toe. It is to be considered as a reference document giving general guidelines. It is the responsibility of code writing bodies, or companies and their design offices, to establish appropriate working instructions adapted to the needs of the specific branch ofindustIy. This document primarily considers fusion welded structures with predominantly elastic behaviour. Therefore, cyclic plasticity is assumed to occur at the notch roots only. The so-called low cycle fatigue approaches which consider cyclic plasticity at the structural stress or even the nominal stress level (see Section 2.1) are outside the scope. Moreover, also out of the scope are force-based methods used in the analysis of spot welds, in which the fatigue strength is expressed in terms of the force per weld spot The main purpose of this document is to harmonize the terms, methods and conceptions used by fatigue testing laboratories, designers, finite element analysts, and educational institutions. It is hoped, for example, that this document would help in communication between designers and finite element specialists, such that designers could express their problems correctly and stress analysts could supply correct answers. It is recommended that fatigue analysis reports should be written using the

terminology defined in this document

3

2 STRESSES CONSIDERED IN FATIGUE ANALYSIS Stresses used in fatigue analysis are those resulting from live loads, dead weights, snow, wind, waves, acceleration, vibrations etc. Secondary stresses, such as bending stresses in rigidly-jointed trusses, or fluctuating thermal stresses must also be included, if relevant.

2.1 STRESS CATEGORIES In fatigue analysis the following stress categories are used: (i) nominal stress; (ii) structural (hot spot) stress; (iii) notch stress. The choice of stress category depends on the method used to express the fatigue strength data which will be used in the fatigue assessment.

2.1.1 Nominal stress In general, nominal stresses are those calculated using the simple formulae found in elementary text books:

(1) where

F is axial force; A is area of cross section; M is bending moment; I is moment of inertia of the cross-section; y is distance from centroid to the point considered.

An example of nominal stress in a beam-like component, established according to Eqn. (1), is shown in Fig. 1. When fatigue at the welded attachment is considered, the nominal stress is calculated in the region containing the weld detail, but excluding any influence of the attachment on the stress distribution. However, in practice it might also be necessary to include in the nominal stress the effects of certain macro-geometric features, as well as stress fields in the vicinity of concentrated loads and reaction forces, as discussed further in Section 3.1.

4

Weld

)Fig. 1 An example of nominal stress in a beam-like component.

2.1.2 Structural stress

Structural stresses include both nominal stresses and the effects of structural discontinuities, see Section 3. It is not generally feasible to determine them using analytical methods. Stresses in plate and shell structures which are established by FEA based on the theory of shells are structural stresses, (j's. Structural stress is linearly distributed across the plate thickness and consists of two parts: membrane stress and shell bending stress, Fig. 2. Membrane stress, (j'm, is the mean stress across the plate thickness, and shell bending stress, (j'b, is one half of the difference between the. values of structural stress at the top and bottom surfaces.

+

Fig. 2 Structural stress in a plate, comprising membrane and shell bending parts. In this document the quantity termed structural stress is not restricted to stresses in curved shells. Structural stress is the sum of membrane and shell bending stresses in any structure consisting of plate elements or their like. It is usually higher than the nominal stress, although far from discontinuities the structural and nominal stresses are equivalent. In order to avoid confusion with the bending stresses in a beam; see Eqn (1), the bending stress component of the structural stress is called the shell bending stress. In many documents dealing with offshore tubular joints, e.g. [2], the structural stress is called the geometric stress, (j'G.

5

2.1.2.1 Hot spot stress A hot spot is the tenn used to refer to the critical point in a structure, where fatigue cracking can be expected to occur due to a discontinuity and/or a notch. Usually, the hot spot is located at a weld toe. Hot spot stress, ahs, is the value of the structural stress at the hot spot. Although the hot spot is located at a local notch, the hot spot stress does not include the nonlinear stress peak caused by the local notch, as will be evident from a comparison of Figs. 2 and 3.

2.1.3 Notch stress Local notch stress, aln, is the total stress located at the root of a notch, such as a weld toe, as illustrated in Fig. 3. This total stress has been tenned peak stress in some countries. Due to its ambiguity, the tenn peak stress is not used in these recommendations. The practical calculation of notch stresses is discussed in Sections 3.3 and 6.6. The nonlinear stress peak, anlp, is the maximum stress in the nonlinear part of the stress distribution, usually across the plate thickness, caused by a local notch, as shown in Fig. 3 and discussed further in Section 3.3. If a refined stress analysis method is used which yields a nonlinear distribution across the plate thickness, the nonlinear stress peak can be separated from the structural stress as shown in Fig. 3. First, the average stress, which is equal to the membrane stress, am, across the thickness, is calculated. Then the shell bending stress is found by drawing a straight line through the point 0 where the membrane stress intersects the mid-plane of the plate. The gradient of the shell bending stress, a b, is chosen (or resolved by calculation) such that the remaining nonlinearly-distributed part is in equilibrium. Its value at the surface is the nonlinear stress peak, anlp.

Local notch stress

Fig. 3 Local notch stress (total stress) at a weld toe, comprising membrane and shell bending stresses and a nonlinear stress peak.

6

2.2 STRESS RANGE The stress range, .6.0' (see Fig. 4), is the main parameter to be determined for fatigue analysis. In the case of constant amplitude loading, the stress range is defmed as: dO" = 0" max

-

(2)

0"min •

Equation (2) can be applied for any of the three stress categories defmed in Section 2.1. In many cases, the stress range cannot be determined directly , but crmax and crmin must be resolved separately from different load cases. In welded structures, variable amplitude loading (Fig. 4 b) is more common than constant amplitude loading. It is caused by the superimposed effects of all nonpermanent actions:

(i) fluctuations in the magnitudes of loads; (ii) movement of the loads along the structure; (iii) changes in the loading directions; (iv) structural vibrations; (v). temperature transients.

(j

(a)

(b)

Time

Time

Fig. 4 Constant (a) and variable (b) amplitude stress histories.

Fatigue analysis is based on the cumulative effect of all stress range occurrences during the design life. A stress range occurrence table is produced from the stress history by a counting method, preferably using Rainflow counting or range pair counting [3]. Design codes for some applications specify standardized stress range spectra (exceedance functions). In such cases the stress analyst needs only to calculate the maximum stress range, (.6.cr)max (see Fig. 4b). It should be noted that the time interval between the maximum stress and the minimum stress may be fairly long.

7

2.3 STATIC STRESS Residual stresses, and stresses caused by pennanent loads, are static stresses. In a structure exhibiting linear behaviour they do not contribute to the stress range, which is the difference between the maximum and minimum stresses. Pennanent loads need to be taken into account in the stress range calculation only in those cases in which the defonnations of the structure are large enough to cause geometrically nonlinear behaviour: Some fatigue analysis methods take into account the effect of mean stress, ( O'max + (Jrrcin)/2, or the stress ratio, R: R = CTmin

(3)

•

CT max

Stress

°

Re

nom

Omax

ores

A~ Or--¥-----r-r+-~-r------

Time

(a)

0

Strain

(b)

Fig. 5 Example ofa nominal stress-time history (a) and the corresponding stress-strain relationship (b) taking the residual stress, o;.es> and the yield strength Re into account. If a fatigue analysis method will be used for which the stress ratio needs to be resolved, the maximum stress, (Jmax, should be detennmed taking into account also the static stresses and all secondary stresses, including welding residual stresses. Therefore, the maximum stress is nonnally assumed to be equal to the yield strength of the material, Re, when as-welded structures are considered. For variable amplitude loading, O'max is assumed to equal yield for the largest commonly occurring load (e.g. annual). The other stress maxima are lower due to the "shake-down" effect, see Fig. 5. Some plastic straining usually occurs due to

8

residual stresses during the fIrst stress cycles, but the subsequent stress-strain behaviour remains predominantly elastic, provided (ilo)max < 2Re.

2.4 LOADS AND LOAD COMBINATIONS The various types of load acting on a structure are called actions in ISO standards. In this document, however, the more familiar tenus load or loading are used. Realistic assessment of the loadings to be experienced by a component or structure in service is a crucial part of the fatigue design process. In some cases, loads to be assumed are specilled in relevant design codes. Otherwise, they are estimated on the basis of the intended operation of the component or structure, or they may be measured on existing or prototype structures under realistic operating conditions. Whatever approach is adopted, it is important to identify the most severe load combinations to ensure that extreme values of stress range are not underestimated. Equally, special attention should be paid to the frequently occurring smaller loads as these often govern fatigue life. It is often useful to calculate the stress components caused by various basic loads as separate load cases. Moving loads have to be located and orientated in different positions in order to find their maximum and minimum effects at the point under consideration. Influence tables or curves are often a great help in finding the critical load locations.

Depending on how the various loads move and fluctuate, the directions of the principal stresses may be constant, or they may vary between different loading events. The former case is called proportional loading (Fig. 6), and the latter nonproportional loading (Fig. 7).

(j

\ ............ /~ 0"2

Time Fig. 6 Example of cyclic principal stresses due to proportional loading

9

-

,----+--, _____~

cr.1~ cry

I

vv

v v ~

---

Time

--=~

Time

Fig. 7 Example ofnon-proportional fluctuations ofstress components at the top of the web ofa crane runway girder during one working cycle.

As Fig. 7 shows, many load combinations at different points in time must be studied in the case of non-proportional loading, in order to establish the extreme values of each of the components. In cases in which standardized stress range spectra are applicable, only two load

case combinations need to be evaluated for each stress component. The maximum stress is calculated as a combination of the basic load cases, taking into account all relevant loads which will increase the maximum stress. The minimum stress is calculated by combining the basic cases such that the stress under consideration attains its minimum value. The appropriate locations and orientations of the moving loads are taken into account. The dynamic stress fluctuations caused by shock loads, and other sources of excitation which increase the maximum stress and decrease the minimum stress, must also be taken into account. The basic load cases can normally be combined easily using FEA. However, it should be remembered that a variety of load combinations may be required if different points in the structure are to be analysed.

2.5 MULTI-AXIAL STRESS STATES Most fatigue design data have been obtained under unidirectional axial or bending loads. However, it is common for details in real structures to experience more complex loading conditions, notably by biaxial or combined (e.g. bending

10

and torsion) loading. Thus, unless the design data were obtained under realistic loading conditions, it is necessary to use them in conjunction with some form of equivalent stress or interaction fonnula.

2.5.1 Proportional loading In some products, the loading is proportional and the degree of multiaxiality is low, Fig. 6. In such cases, quite simple solutions for the equivalent stress have been accepted for use. In some design codes the range of the maximum principal

stress has been chosen. However, problems arise when the directions of the principal stresses are inclined relative to the direction of the weld. The range of the maximum principal stress at the surface of a structure controls the fatigue of welded joints, provided the stress acts predominantly perpendicular to the weld toe, Fig. 8. Therefore, a crack will grow at the weld toe, parallel to it. However, if the maximum principal stress acts essentially parallel to a weld, the smaller principal stress can be dominant due to the higher notch effect in this direction. If in doubt, fatigue caused by both principal stresses should be analysed separately [4]. Some design codes give limit angles for deciding whether a principal stress should be considered as perpendicular or parallel. In many applications, such as joints between structural hollow sections, it is sufficient to determine only the stress component perpendicular to the weld [4].

Fig. 8 Examples of cracks growing along weld toes due to a principal stress, ~, predominantly perpendicular to the weld toe.

11

2.5.2 Non-proportionalloading In some constructions involving moving loads, e.g. cranes, crane runways and bridges, the various stress components fluctuate in different ways, Fig. 7. The stress components may be out-of-phase and the number of cycles of each stress component may be different. Therefore, it is questionable if a universal equivalent stress criterion could be found [4].

For non-proportional loading, use of the maximum principal stress range can lead to non-conservative life predictions. The equivalent stresses given by the von Mises and Tresca yield criteria are not usually suitable, because the notch effect of the weld varies for different stress directions. Furthermore, the crack will initiate in a certain plane experiencing maximum damage. With a varying principal stress direction the momentary value of the equivalent stress does not necessarily correlate with the damage in that critical plane. These equivalent stresses may be more applicable when local notch stress/strain approaches are used instead of nominal or structural stresses, as discussed further in Section 4.3. The von Mises equivalent stress is a positive scalar quantity. Subtraction of the minimum von Mises stress from the maximum does not generally yield the actual stress range. If the effective von Mises stress range would in some case be used, it should be calculated from the ranges of each stress component. Most pressure vessel design codes, e.g. ASME Code [5] use the so-called stress intensity as the equivalent stress. This is the difference between the highest and lowest principal stresses, which is equal to twice the maximum shear stress. Thus, it derives from Tresca yield criterion. In Ref. [5] a procedure is also given for the treatment of cases of non-proportional loading. The method is applicable only to notch stress components and is, therefo~e, not described here.

2.5.3 Interaction formulae Some design codes, based on the nominal stress approach, rely on interaction formulae instead of defining an equivalent stress. In this method stress components are determined in a co-ordinate system with one axis parallel to the weld. For each stress component, O'x, O'y and 'txy. the fatigue strength is determined separately, depending on the actual detail class and the actual number of cycles. Note that in a general case these are different for each stress component, see Fig. 7. Usage factors, i.e. stress divided by strength, or fatigue damages calculated using Miner's rule are then resolved. The interaction formula can be constructed from usage factors (or Miners's damage sums) in various ways, but the existing formulae are not well-founded theoretically. The draft European standard ENV 1993 [6] has adopted an interaction formula, simply comprising addition of two fatigue damages, the one caused by normal stress and the other caused by shear stress. Actually, the fatigue damage terms are written in

12

terms of m-powers of usage factors where exponent m corresponds the slope of the relevant S-N curve. When new design codes are developed, they should preferably be based on wellfounded interaction formulae. However, only the nominal stress method introduces fatigue strength data for all three components, o"x, O"y and 'txy. The hot spot approach can be applied on the component perpendicular to the weld, whereas the other cases (stress parallel to the weld and shear stress) may be evaluated according to the nominal stress approach. It is worth noting that the structural stress parallel to a continuous weld obtained from FE analysis can be considered as the nominal stress.

3 STRESS RAISERS 3.1 EFFECTS OF MACRO-GEOMETRY AND CONCENTRATED LOAD AREAS Welded structures often contain macro-geometrical forms which are not included in the classified details in design codes. Examples are given in Fig. 9. They alter the stress field calculated using elementary stress analysis formulae.

(e)

..

~

_._-- -

'~'.

'~'~'~'.

(f)

"",1/

- / p\ -- -

~'~.' -.'~.' -.'~.'

-.' -.'

Fig. 9 Examples ofmacro-geometric effects (a) large openings; (b) curved beam; (c) shear lag; (d) flange curling; (e) discontinuity stresses in a shell; (f) bending due to lap jOint eccentricity.

For some macro-geometric effects shown in Fig. 9, analytical formulae are available in the literature which, in combination with elementary stress analysis methods, yield useful solutions for the overall stress distribution across the

12

terms of m-powers of usage factors where exponent m corresponds the slope of the relevant S-N curve. When new design codes are developed, they should preferably be based on wellfounded interaction formulae. However, only the nominal stress method introduces fatigue strength data for all three components, o"x, O"y and 'txy. The hot spot approach can be applied on the component perpendicular to the weld, whereas the other cases (stress parallel to the weld and shear stress) may be evaluated according to the nominal stress approach. It is worth noting that the structural stress parallel to a continuous weld obtained from FE analysis can be considered as the nominal stress.

3 STRESS RAISERS 3.1 EFFECTS OF MACRO-GEOMETRY AND CONCENTRATED LOAD AREAS Welded structures often contain macro-geometrical forms which are not included in the classified details in design codes. Examples are given in Fig. 9. They alter the stress field calculated using elementary stress analysis formulae.

(e)

..

~

_._-- -

'~'.

'~'~'~'.

(f)

"",1/

- / p\ -- -

~'~.' -.'~.' -.'~.'

-.' -.'

Fig. 9 Examples ofmacro-geometric effects (a) large openings; (b) curved beam; (c) shear lag; (d) flange curling; (e) discontinuity stresses in a shell; (f) bending due to lap jOint eccentricity.

For some macro-geometric effects shown in Fig. 9, analytical formulae are available in the literature which, in combination with elementary stress analysis methods, yield useful solutions for the overall stress distribution across the

13

structure. For example, shear lag and flange curling effects on the longitudinal stress can be analysed using beam theory if suitably defined effective flange widths are used. Macro-geometric effects usually cause a significant redistribution of the membrane stress field across the whole cross section. Similar effects occur in the vicinity of concentrated loads or reaction forces, as illustrated in Fig. 10. Significant plate bending stresses may also be generated, as in curling of a flange . or distortion of a box section. The stresses caused by macro-geometric effects, or stress fields in the vicinity of concentrated loads and reaction forces, must be taken into account in all stress categories, even when nominal stresses are determined. It is very important to remember this when the fatigue analysis is based on nominal stresses since, according to the definition, these effects are not included in the fatigue strength based on simple test pieces. The aforementioned does not apply for geometries for which S-N curves have been established.

p

p

Fig. 10 Examples of local nominal stresses in the vicinity of concentrated loads a) transverse stresses in a web below a load; b) warping stresses in a box section due to distortion. Although there is no doubt that specimens tested to generate fatigue design data will have contained some misalignment, in general it has not been quantified. Consequently, it is normally assumed that the design data are only applicable to aligned joints, or perhaps to joints containing very small amounts of misalignment. It should not be assumed that the fabrication tolerances on misalignment bear any relation to fatigue and, in general, all expected or detected misalignment should be assessed and the corresponding extra bending stresses included when calculating the nominal stress. For an offset misalignment the structural stress can be estimated approximately using the following stress magnification factor, Km [7,8]:

14

K

m

= 1+3·-et '

(4)

where e is eccentricity, and t is plate thickness. More solutions for various misalignment cases are found in Ref. [7]. Webs and stiffeners parallel to the stress can change the stress concentration. Their effect on Km caused by misalignments are studied in Ref. [9].

(b)

Fig. 11 Offset (a) and angular (b,c) misalignments as examples ofmacrogeometric discontinuities which are not designed into the structure

3.2 EFFECTS OF STRUCTURAL DISCONTINUITIES Fig. 12 shows several structural discontinuities which may cause a local concentration in the membrane stress field as well as local shell bending stresses. These structural discontinuities differ from macro-geometric ones, since: (i) the stress field discontinuity is relatively local; (ii) such local discontinuities are normally included in welded fatigue test specImens. The extra membrane and shell bending stresses caused by structural discontinuities are not included in the category of nominal stress. Instead, they belong to the category of structural stress. In general, analysis of structural discontinuity effects is not possible using analytical methods. Therefore, FEA is often applied, in spite of the time and cost required. There is a need for suitable parametric formulae, established by FEA or strain measurements, to relate geometry and hot spot stress. At present, relatively few structural details have been considered in the literature in this respect. However, for tubular joints such formulae are already available, see Section 3.4.

15

It should be noted that the presence of a weld on only one side of an axiallyloaded plate, as in Fig. 17, causes not only nonlinear stress peaks but also some amount of shell bending (see also Fig. 3.)

Fig. 12 Structural discontinuities and their effects (a) gusset plate; (b) variation in width;(c) cover plate end; (d) stiffener end, (e) variation in plate thickness.

3.3 EFFECTS OF LOCAL NOTCHES Fig. 13 shows typical local notches found in most welded components. A local notch does not alter the structural stress, i.e. the membrane and shell bending stresses.

Fig. 13 Typical notches in a welded component (a) gusset (a) transverse weld reinforcement; (b) weld bead roughness or blow holes in a longitudinal weld; (c) ripples on aflame-cut edge.

16

The main effect of a notch is to produce a nonlinearity in the stress distribution, usually in the thickness direction, Fig. 14. The nonlinear stress peak lies within a radius of approximately 0.3t to O.4t from the notch root [10].

Nonlinear stress eak Total stress

Fig. 14 Stress distributions across the plate thickness and along the suiface in the vicinity ofa weld toe.

A nonlinear stress peak is one reason why a surface defect located at a notch is more dangerous than an embedded defect, which is usually located in an area of lower stress (Fig. 15). Edge notches and small drilled holes cause similar nonlinear stress peaks, but with different orientations.

Fig. 15 Nonlinear stress peak, anIpo caused by a transverse weld reinforcement, making a suiface crack (depth = aJJ more dangerous than an embedded crack (depth = 2a~

The notch stress, a In, is usually calculated by multiplying the hot spot stress by a stress concentration factor, or more precisely the theoretical notch factor, Kt • In

17

many cases the result will exceed the yield strength of the material. Thus, elasticplastic behaviour is to be expected, and the calculated stress should be considered as a pseudo-elastic stress. When no solution for Kt is available, FEM can be used for the detennination of notch stresses. However, because of the small notch root radius and the steep stress gradient in the case of a weld, a very fine element mesh is needed. Therefore, it is not practical to solve notch stresses by means of the same finite element model used for detennination of the structural stresses. A separate local model, often a 2-D model using plane strain elements, is more suitable. Another possibility, which is often a· better solution, is to use the boundary element method, BEM [11] (see Section 6.3). The geometry of the local notch at the weld toe varies significantly along a weld and between different welds. In spite of specified minimum requirements for the weld profile, the exact geometry is unknown. Therefore, the nonlinear stress peak has a random value. A specific feature of the nominal stress approach, and also the hot spot stress approach, is that the effect of this random variable is implicitly included in the test results, and it is reflected in the scatter band of the S-N curves. Therefore, nonlinear stress peaks need not be calculated when these two approaches to fatigue analysis are used. On the contrary, they must be excluded from the calculated or measured nominal or hot spot stress.

3.4 SPECIAL CASE: JOINTS BETWEEN STRUCTURAL HOLLOW SECTIONS Large tubular joints are used in offshore structures. For this reason they have been the subject of extensive research. Special recommendations for the detennination of hot spot stress have been published [2, 12-19]. This document is intended for more general application and does not, therefore, cover all the special problems of tubular jOints. Tubular joints, Fig. 16, like other similar shell structures, contain significant geometric effects. The brace forces produce high membrane and shell bending stresses in the chord shell. Fatigue cracking usually occurs at a point along the weld toe, where the structural stress range perpendicular to the weld attains its highest value. This hot spot is predominantly located on the chord side of the weld due to the high bending stresses in the chord shell. However, if the brace is relatively thin-walled, the hot spot may be located in the brace. The secondary bending moments in the members, resolved by structural analysis, assuming rigid or semi-rigid joints, are interpreted as macro-geometric effects. The more local geometric effects in the joint area are interpreted as structural discontinuity effects.

18

Parametric fonnulae for stress concentration factors, literature [12-19], which yield the hot spot stress, a hs : (j hs

=

Ks,

can be found in the

(5)

Ks· (jnom,

where (jnom is usually defined as the axial membrane stress in the loaded member, brace or chord, caused either by axial force or bending moment, and calculated using elementary stress analysis.

Possible crack initiation sites

Fig. 16 Examples a/tubular joints. In practice, the stress concentration factors must be detennined separately for different loading cases: axial loading, in-plane bending, and out-of-plane bending acting in certain members at a time. In a combined loading case the hot spot stress can be estimated by superimposing the results of different cases. However, the superposition is usually possible only for certain special points, e.g. saddle and crown points, see Fig. 16, and requires that stress concentration factors are available for both of the points. The real hot spot may be located somewhere between these two points and can only be found either by FEM analysis or by experimental measurements.

The actual joints are often multiplanar with several brace members. It is a quite laborious task to establish stress concentration factors for such complicated joints with numerous configurations and loading cases [12]. If such factors are not available for a particular joint, finite element analysis is then the most versatile method for establishing the hot spot stresses. Analysis of joints between square and rectangular hollow sections is even more complicated in that there are no such obvious locations of the hot spots as the crown and saddle points. These joints have been thoroughly studied in Ref. [18].

19

4 FATIGUE ANALYSIS APPROACHES 4.1 NOMINAL STRESS APPROACH In this approach fatigue strength, in the form of S-N curves, is determined by testing either small specimens or near full-scale beams. The test pieces contain various attachments giving rise to structural discontinuity effects, and various welds, but usually no macro-geometric effects. In all cases the fatigue strengths are quoted as nominal stresses ignoring the stress field discontinuity caused by the attachments. Thus, all structural discontinuity effects and all local notch effects are implicitly included in the fatigue strength so determined. Regarding fabrication tolerances, note the comments in 3.1. In some special cases, there may be other sources of stress raiser in a fatigue test, notably macro-geometric effects and concentrated load or reaction force effects, as illustrated in Figs. 9 and 10. It is important for the designer to be aware of the extent to which such effects were considered when deriving the design data. If such effects were taken into account when analysing the laboratory test data to derive a nominal stress, then the corresponding stresses must be determined by the designer. However, if the effects were ignored, their influence is already included in the fatigue design data and therefore they can also be ignored by the designer.

4.2 HOT SPOT STRESS OR STRAIN APPROACH In this approach, the fatigue strength, expressed as an S-N curve, is generally based on strains measured in the specimen near the point of crack initiation. This is in contrast to the nominal stress approach, which is based on fatigue strengths expressed as nominal stresses, calculated for example according to Eqn. (1).

One advantage of the hot spot stress approach is the possibility of predicting the fatigue lives of many types of joint configuration using a single S-N curve. Additional S-N curves would be needed if the variations in the weld type, the material thickness effect, or environmental effects had to be taken into account. Fatigue strength data based on the hot spot approach are determined from test pieces of various forms. Structural strain ranges are measured with strain gauges at several sections along the weld toe. The test result is defined either as the stress range or the strain range in the critical section, extrapolated to the weld toe from two or three strain measurement points at certain distances from the weld toe, ( see Fig. 17 and also Section 7.5.3). It is recommended that fatigue analysis is based on hot spot stress ranges instead of hot spot strain ranges. If the latter is preferred, then both the evaluation of the

20

test results and the fatigue analysis should be based on hot spot strain ranges, for consistency.

Hot spot strain (extrapolated) - Nonlinear stress peak Weld toe I-;-'-'->-r--.L'-Strain gauge A Strain gauge B

Fig. 17 Measurement of the hot spot strain range using linear extrapolation method

In the most orthodox way, the principal strains are dete11l1illed at each point using strain gauge rosettes, and the principal stresses are resolved (Section 7.4). The hot spot stress range is then the range of the principal stress obtained by extrapolation to the hot spot location (e.g. weld toe) [2].

However, it is recommended that the hot spot stresses are determined as the stresses perpendicular to the weld toe, as concluded in Ref. [4]. In general, the test pieces should be equipped with two element 90° strain gauges (see Fig. 44) in order to take the stress biaxiality into account, (see Section 7.4.2.1). Assuming that the shear strain near the weld is negligible, the structural stress perpendicular to the weld can be calculated as follows:

(6)

where

Ex is the measured strain perpendicular to the weld; lY is the measured strain parallel to the weld; E is the elastic modulus; v is Poisson's ratio.

21

First, both strain components are extrapolated to the weld toe, and then the hot spot stress is resolved from Eqn. (6). Usually, it is sufficient to apply Eqn. (6) to strain ranges for resolving the hot spot stress range, as compared with the more laborious method of resolving the actual principal stresses. In cases which always exhibit a similar degree of biaxiality (e.jeJ, it may be

preferable to simplify the approach by measuring only the strains perpendicular to the weld, and resolving a fictitious hot spot stress based on an assumed strain ratio. The definitions of hot spot stress used in North America depend on the branch of industry (as defined by API, AWS, SAE) and differ from the definitions given here. Usually the strain gauge is located differently, and no extrapolation is performed [20]. In the approach defined here, the strain gauges are placed at sufficient distances

from the weld toe to ensure that the local notch has no effect on the measured results (see Section 7.5.3). Thus, the hot spot strain range determined by extrapolation includes both macro-geometric effects and structural discontinuity effects, but not the nonlinear stress peak caused by the local Iiotc~ as denoted by the dotted curve in Fig. 17. For design, the stress and strain analysis should yield results comparable with the fatigue strength determination described above. There are three possible approaches to such an analysis: (i) (ii) (iii)

the calculated nominal stress is multiplied by the stress concentration factor, Ks, for the appropriate structural discontinuity [12-19]; strain ranges are measured during prototype or model tests at the hot spot, as described in Fig. 17; stresses and strains are analysed by FEA using shell or solid elements.

When the stresses are obtained from by FEA, the results readily include the biaxiality effects. To be consistent with the fatigue strength determination described above, the results should be expressed as normal stresses perpendicular and parallel to the weld, and shear stresses. This approach is also suitable for analysing non-proportional loading cases as discussed in Section 2.5.3. According to the definition of the structural stress, the hot spot stress is linearly distributed in the thickness direction, consisting of membrane and shell bending stress components. One of the disadvantages of the hot spot approach is that only the surface stress is considered; no distinction is made between the effects of membrane and shell bending components on crack propagation life.

22

4.3 NOTCH STRESS/STRAIN APPROACHES These approaches are based on the stress/strain state at the notch directly. Therefore, all stress raisers, including the local notch, must be taken into account in the stress/strain analysis. The stress analysis will often be divided into a global finite element analysis at the structural stress level, coupled with a local finite or boundary element analysis of the notch area. However, a notch factor, Kb if already known, is to be preferred for the resolution of the local pseudo-elastic notch stress. In a particular version of the notch stress approach, the local stress components at the notch root are calculated pseudo-elastically. In the approach described in Refs. [21-23], these components are converted into an equivalent stress amplitude. The S-N curve is determined from tests on welded joints by plotting the log equivalent stress amplitude versus log life. In principle, this approach should be valid for a wide variety of joint types and loading conditions, including biaxial non-proportional loading. Several equivalent stress definitions have been proposed.

Another novel linear-elastic approach is based on Neuber's hypothesis of microstructural support at sharp notches [24]. The fatigue-effective notch stresses are calculated for a notch root radius, which is fictitiously enlarged:

PI = p+sp*,

(7)

where

P p*

s

is the actual notch radius; is the microstructural support length of the material, and is a factor depending on the multiaxiality of the notch stress state and the applied strength hypothesis.

A worst case fatigue analysis is based on p = 0 which results into Pf = 1 mm for welded mild steels (Fig. 18). The endurance limit in terms of nominal stress, or hot spot stress at a structural discontinuity, is determined in this way. The procedure can be extended into the finite life range by taking locally elastoplastic behaviour at the notch root into account e.g. by using the macro-support formula given by Neuber. Thus, the method is used in combination with the local strain approach. An alternative method for finite life consists of using the concept of normalized S-N curves of welded joints proceeding from the endurance limit [25]. The linear-elastic approach described above has been successfully applied to standard notch cases of welded joints and to welded components including

23

comparisons with experimental data [24, 26]. Reference stress ranges for alternating and zero-to-tension load have been derived in an extensive experimental and theoretical program [27]. For an elasto-plastic notch strain analysis, as employed by e.g. SAE [28], cyclic stress/strain curves are used which are determined from tests on small smooth specimens. In order to avoid laborious non-linear stress/strain analysis, approximations such as Neuber's rule may be used, together with the stress/strain curve, to determine the local elastic-plastic stress range, .do, and strain range, .de. Cyclic stress/strain curves for different base materials and weld metals are given in [29] and for flame and plasma cut edges in structural steels in Ref. [30]. Curves for the weld metals and heat affected zones are still rather scarce.

alb-O.6

sIb-l.O

6r---------r---------r-----~

o

0.5

1.0

Silt length SIb

1.5

0

0.3

0.6

0.9

Weld ttlicknesa alb

Fig. 18 Notch stress concentration!actors at rounded notches [24J

4.4 FRACTURE MECHANICS APPROACH In this approach, stress analysis is used to determine the value of the stress intensity factor range at the various stages of crack growth. For weld toe fatigue cracks, the effect of the local notch decreases as the crack becomes deeper. There are three ways to take the local notch effect into account.

(1) The nonlinear stress distribution in the thickness direction, caused by the local notch, is calculated for example by a local FEM model with a fine mesh, or by using the boundary element method, BEM [11]. The stress intensity factor values are calculated preferably by the weight function method [31]. (2) The stress intensity factors are calculated directly by a finite element model of the cracked geometry.

24

(3) The hot spot stress is multiplied by the Mk-factor, which is computed from parametric fonnulae for different crack sizes [8,32,33]. Such parametric fonnulae have been established by curve fitting to data produced by method (1) or (2).

If the stress intensity factors are detennined e.g. by the method (3), the first step is to determine the hot spot stress at the weld toe. This should be divided into membrane and shell bending parts, because this approach distinguishes between their contributions to crack propagation. The fracture mechanics approach can then predict the number of cycles required to propagate from an initial crack depth (e.g. flaw) to a final crack size (e.g. fracture).

4.5 SUMMARY Fig. 19 summarizes how the various stress raising effects, stress categories, and fatigue analysis approaches (except fracture mechanics) are interconnected.

General stress analysis

Macrogeometric, concentrated load and misalignment efIects

Structural discontinuity effects

Local notch effects at the weld toe

Cyclic stress-strain behaviour

General nominal stress range

Nominal stress range

Structural stress range (hot spot)

Pseudo-elastic notch stress range

Elastoplastic notch strain amplitude

~~-Lo N

~:~ Lo N

LogN

Fig. 19 An overview of the definitions introduced

LogN

25

5 GUIDELINES FOR THE CHOICE OF FATIGUE ANALYSIS METHOD 5.1 NOMINAL STRESS APPROACH The nominal stress approach is widely used because most design rules for steel structures contain a standard procedure for fatigue analysis based on this approach. The nominal stress approach yields satisfactory results with minimum calculation effort if the following conditions are fulfilled: (i) there is a well defined nominal stress, not complicated by macrogeometric effects; (ii) the structural discontinuity is comparable with one of the classified details included in the design rules; (iii) the detail is free from significant imperfections *.

5.2 HOT SPOT STRESS APPROACH The hot spot stress approach is used mainly for joints in which the weld toe orientation is transverse to the fluctuating stress component, and the crack is assumed to grow from the weld toe. The approach is not suitable for joints in which the crack would grow embedded defects or from the root of a fillet weld. Compared with the nominal stress approach, this approach is more suitable for use in the following cases: (i)

(ii) (iii) (iv) (v)

*

there is no clearly defined nominal stress due to complicated geometric effects; the structural discontinuity is not comparable with any classified details included in the design rules (nominal stress approach); for the above-mentioned reasons, the finite element method is in use with shell and/or solid element modelling; testing of prototype structures is performed using strain gauge measurements; the offset or angular misalignments exceed any fabrication tolerances specified as being consistent with the design S-N curves used in the nominal stress approach.

An imperfection is significant if, as a result of its presence, the fatigue strength of the detail is lower than specified in the design rules (e.g. welding flaws, which provide alternative sites for crack initiation, and misalignment, which introduces additional bending stress, thus increasing the stress experienced. by the detail). Guidance is given in Ref. [8].

26

5.3 NOTCH STRESS/STRAIN APPROACHES The notch stress/strain approach predicts the initiation life for a crack at the root of a notch, in contrast to the nominal and hot spot stress approaches which predict the life to complete failure in compact cross sections, or to the formation of a through-thickness macro crack in larger plate or shell structures.

5.3.1 Linear-elastic notch stress approach The effective notch stress approach described in Ref. [24] may be considered as a suitable choice for the long life (high cycle) regime, in which the crack initiation and early growth phases are dominant. fu this approach the weld reinforcement geometry is assumed to be known. This contrasts with the nominal and hot spot stress approaches, in which the local geometry is assumed to be a random variable affecting the statistical fatigue strength of the joint. The version of the linear-elastic notch stress approach described in Ref.[23] appears to be promising for cases in which multi-axial non-proportial stress states occur. fu such cases the orientation of the principal stresses varies. The use of principal stress as the equivalent stress yields non-conservative results. fu Ref. [23] the equivalent shear stress range on a critical plane, proposed originally by Findley, was found to predict the fatigue life quite satisfactorily.

5.3.2 Elastic-plastic notch strain approach The notch strain approach is best suited to uncracked parts in which an elliptical notch can be assumed, e.g. machined components, ground weld toes, or plasmacut edges. However, as-welded joints in structural steels can be expected to contain small crack-like discontinuities of depth 0.05 to 0.25 mm at the weld toe [34]. Therefore, this approach is not particularly well suited to as-welded joints. For welded joints, the notch strain approach is best suited to cases in which the crack initiation life represents a large part of the total life. As far as structural steels are concerned, this may be realised in welds which have experienced some life-improving treatments to produce smooth crack-free weld toes. Another example is plasma-cut edges. fu order to be able to predict the total life, the local notch strain approach can be used in combination with the fracture mechanics approach. The latter is used to predict the propagation life, from the size of the crack initiated in the early phase of the life to the crack causing final failure. The problem is that the initial size of the crack is not well defined. The size of the initial crack depends for example on the notch geometry.

27 The local notch strain approach requires computer calculation and a relatively large amount of data for material properties. Fortunately, comprehensive catalogues of data [29] are available in the literature. One disadvantage is that this approach is rather sensitive to the mean stress assumed in the process zone at the notch root. Failure to estimate the magnitude of welding residual stresses and their possible relaxation in the process zone may lead to considerable errors in the predicted initiation life.

5.4 FRACTURE MECHANICS APPROACH The fracture mechanics approach is a vel)' versatile method, especially whenever a damage tolerant design is required, or fitness for purpose of a structure containing flaws needs to be assessed. Fracture mechanics analysis of crack growth (see Fig. 20) yields information about: (i) (ii) (iii) (iv) (v) (vi) (vii)

the expected life of a welded joint; the remaining life of a cracked part; the tolerable crack (discontinuity) size; the required fracture toughness of the material; the frequency of in-service inspections; the required accuracy of in-service inspections; the effects of proposed improvements in design or fabrication.

25 (rr!n) 20

15 10 5

I~~::::::::=----

00

50000

100000 150000 200000 N

250000

(cycles) Fig. 20 An example of crack growth through the plate thickness at a toe ofa butt weld; a = crack depth. In contrast to the local strain approach, the fracture mechanics approach assumes

an existing initial crack. Thus, it predicts the crack propagation life from an initial size to a certain final size. As welds in structural steels are not characterised by a significant initiation life, this approach predicts the total life rather well if the input data are correct.

28

The main strength of the fracture mechanics approach is its ability to predict the effect of variations in all input parameters. It not only enables the total life to be predicted, but also the development of the crack size and shape during the life (see Fig. 20). Thus, it is an important tool for specifying material toughness requirements, fabrication tolerances, quality assurance requirements, and ill assessing the fitness for purpose of components with cracks of known size. In practice, application of the fracture mechanics approach requires computer calculation with suitable programs. It is best suited to welds in which fatigue

cracks will grow from the plate surface at the weld toe or end, from the weld root in partial penetration fillet welded joints, or from embedded flaws in butt welds [8]. With a suitable computer program such calculations are perfOlmed quite easily. Fracture mechanics can also take into account the effects of variable amplitude loading in a rational way. This feature is important in cases in which large portions of the stress range fluctuations lie below the fatigue limit determined from constant amplitude tests. Even if only a small number of stress ranges lie above the endurance limit, the crack will grow with the result that smaller and smaller stress ranges become effective as they exceed the threshold value of the stress intensity factor range. In general, successful application of the fracture mechanics approach requires a

sound knowledge of the underlying theory, and of the characteristic initial crack sizes. It is recommended that sensitivity analyses are performed, by varying all uncertain input parameters, one at a time.

6 GUIDELINES FOR FINITE ELEMENT ANALYSIS 1 GENERAL NOTES

Before a finite element program can be used for stress analysis in a reliable manner, the analyst must have a good background in conventional stress analysis, and he/she should gain experience in FE analysis preferably by making comparative analyses of different geometries, with different element types, meshes and sizes. Further important aspects are careful definition of boundary conditions, proper choice of integration schemes and proper modelling of the weld zones. A particular element type should never be used without careful study of the characteristics of the element and its suitability to the particular application. For example, in frames consisting of short beams the elements should also take shear deformations into account.

28

The main strength of the fracture mechanics approach is its ability to predict the effect of variations in all input parameters. It not only enables the total life to be predicted, but also the development of the crack size and shape during the life (see Fig. 20). Thus, it is an important tool for specifying material toughness requirements, fabrication tolerances, quality assurance requirements, and ill assessing the fitness for purpose of components with cracks of known size. In practice, application of the fracture mechanics approach requires computer calculation with suitable programs. It is best suited to welds in which fatigue

cracks will grow from the plate surface at the weld toe or end, from the weld root in partial penetration fillet welded joints, or from embedded flaws in butt welds [8]. With a suitable computer program such calculations are perfOlmed quite easily. Fracture mechanics can also take into account the effects of variable amplitude loading in a rational way. This feature is important in cases in which large portions of the stress range fluctuations lie below the fatigue limit determined from constant amplitude tests. Even if only a small number of stress ranges lie above the endurance limit, the crack will grow with the result that smaller and smaller stress ranges become effective as they exceed the threshold value of the stress intensity factor range. In general, successful application of the fracture mechanics approach requires a

sound knowledge of the underlying theory, and of the characteristic initial crack sizes. It is recommended that sensitivity analyses are performed, by varying all uncertain input parameters, one at a time.

6 GUIDELINES FOR FINITE ELEMENT ANALYSIS 1 GENERAL NOTES

Before a finite element program can be used for stress analysis in a reliable manner, the analyst must have a good background in conventional stress analysis, and he/she should gain experience in FE analysis preferably by making comparative analyses of different geometries, with different element types, meshes and sizes. Further important aspects are careful definition of boundary conditions, proper choice of integration schemes and proper modelling of the weld zones. A particular element type should never be used without careful study of the characteristics of the element and its suitability to the particular application. For example, in frames consisting of short beams the elements should also take shear deformations into account.

29 In the following sections some of the most useful element types are presented by briefly describing their application areas with reference to fatigue analysis of welded components.

6.2 ELEMENT TYPES 6.2.1 Beam elements Beam elements are mainly used for analysis of nominal stresses in frames and similar structures. A conventional beam element for analysis of three dimensional frames has 6 degrees of freedom at each end node: three displacements and three rotations. This element can describe the torsional behaviour correctly only in cases in which the cross section is not prone to warp, or warping can occur freely. Analysis of warping stresses is impossible, which is a serious drawback, when open thin-walled structures are analysed. A truck frame is an example in which warping stresses are significant and dominate the fatigue life of the joints, see Section 6.3.4.3. More advanced finite element programs contain a beam element with 7 degrees of freedom at each node, including warping. They should be used whenever torsion is present and when sections other than circular or square hollow sections are used. Usually, the beam elements are rigidly connected to each other at the nodal points. Alternatively, pinned joints can also be specified. However, in many structures the joints are semi-rigid. In addition, in tubular joints the stiffness is unevenly distributed, which causes extra bending moments. Such structural features require more sophisticated modelling than the use of rigid or pinned joints.

6.2.2

Membrane elements

Membrane elements are intended for modelling plated structures which are loaded in-plane. They cannot deal with shell bending stresses. Triangular and rectangular plate elements are suitable for solving nominal membrane stress fields in large structures such as ship hulls.

6.2.3 Thin shell elements Finite element programs contain various types of thin shell elements. These include flat elements, single curvature elements and double curvature elements. The deformation fields are usually formulated as linear (4-noded element) or parabolic (8-noded element). In general, thin shell elements are suitable for solving the elastic structural stresses according to the theory of shells. The mid-

30

plane stress is equal to the membrane stress, and the top and bottom surface stresses are superimposed membrane and shell bending stresses. Thin shell elements can only model the mid-planes of the plates. The actual material thickness is given as a property only for the element. There are also thin shells with tapered thickness, which are useful for modelling cast structures, for example. The most important drawback with thin shell elements is that they cannot model the real stiffuess and stress distribution inside, and in the vicinity of, the weld zone of intersecting shells.

The post processor of a finite element program should give the stresses at the integration points of the elements. If nodal point stresses are given instead, the user should take care that no average values of neighbouring elements at the intersection of shells are used as they are meaningless. The former method allows a more coarse element mesh to be used in the vicinity of such an intersection.

6.2.4 Thick shell elements

Some finite element packages also include so-called thick shell elements. These allow transverse shear deformation of the shell in the thickness direction to be taken into account. Thick shell elements work better than thin shell elements in e.g. details in which the distance between adjacent shell intersections is small, giving rise to significant shear stresses. One should, however, be aware that these elements may be prone to "lock", i.e. to be excessively stiff when used in thin shell applications. By using a reduced integration scheme, locking of thick shell elements can be avoided.

6.2.5 Solid elements

Solid elements are needed for modelling structures with three dimensional stress and deformation fields. Curved isoparametric 20-noded elements are generally the most suitable. In welded components, they are sometimes required for modelling the intersection zone of the plates or shells. A one layer mesh of solid elements can be used to model shells instead of thin shell elements. However, according to Saint Venant's principle, outside the discontinuity solid elements are no better than thin shell elements. On the contrary, a coarse mesh can greatly exaggerate the bending stiffuess of the plate. Generation of the mesh may be more laborious than with shell elements, depending on the software. At a notch such as a weld toe, use of 20-noded solid element with 3-point integration attempts to model the nonlinear stress distribution across the plate

31

thickness, usually with poor results. The correct linear shell stress distribution is achieved using one element across plate thickness and 2-point integration. The linear distribution could also be obtained using a single layer of 8-noded linear solid elements.They are not, however, well-suited to model plate bending. Experience of the use of solid elements has been reported in Ref. [35], which includes comparisons with strain gauge measurements.

6.2.6 Plane strain elements

Sometimes it is useful to study the local stress fields around notches with a local 2-D model. A cross section of unit thickness can then be modelled as a two dimensional structure using plane strain elements. The plane strain state means that either no contraction perpendicular to that plane can occur or the contraction is constant. When membrane stresses are dominant, the actual structure does contract and the plane strain assumption is no longer valid. However, in this case the plane strain assumption is required to restrict contraction at notches.

6.2.7 Axisymmetric shell and solid elements

Rotationally symmetric shells with rotationally symmetric loading can be analysed effectively by using a very simple model consisting of a 2-D cross section of the structure. Axisymmetric shell and solid elements are used according to the same principles as those in 3-D modelling. One application example would be the case shown in Fig. ge). However, axisymmetric modelling cannot deal with the effects of local nonaxisymmetric features, such as attachments, local mis~gnments etc. Nonaxisymmetric loads can be taken into account only by means of Fourier series, which may not yield sufficient accuracy, depending on the case.

6.2.8 Transition elements

When solid elements are used for modelling shell intersections, and shell elements are used· elsewhere, connection of these two element types with different numbers of nodes and degrees of freedom requires special treatment. One solution is to use a transition element. This has sufficient nodes and degrees of freedom at one side to connect to a solid element, with the opposite side connected to a shell element, and the two remaining sides to other transition elements.

32

Another solution is to use constraint equations which connect the solid element nodes to follow the deformations of the thin shell. Constraint equations can also be used to accommodate changes in mesh density. In the most up-to-date finite element programs, a pre-processing utility can

automatically take care of connecting such element types.

6.2.9 Rigid bars or links

Rigid bar elements are useful for connecting adjacent nodal points, e.g. to fulfil the continuity conditions. Kinematic constraint equations can be used to accomplish the same purpose, without undesirable side effects.

6.3 BOUNDARY ELEMENT ANALYSIS The boundary element method (BEM) complements the finite element method when analysing welded joints and structures. Its main area of application is notch stress analysis and the calculation of stress intensity factors. For analysis of a structural component, only the boundary must be discretized, i.e. twodimensional problems are reduced to boundary lines and three dimensional problems to surfaces. The number of man-hours required to solve a problem is thereby reduced significantly. On the other hand, if no inner points are defined, results are restricted to boundary line and surface values. However, this is no disadvantage in the case of notch stress or stress intensity factor analysis, because the maximum values always occur at the surface. The BEM is better suited to compact parts than to thin and oblong components. But even in the latter case, substructure techniques constitute an effective solution procedure. Typical examples from mechanical engineering are threedimensional components, such as oblique gear teeth, complex crankshafts and turbine blades. Within welding technology, the BEM is used for notch stress calculation on plane cross section models of seam and spot welds. On the other hand, stress intensity factors for welded joints can be determined based on the BEM in connection with special evaluation procedures. The best use of BEM is in combination with FEM. Thus, the global structure may be analysed with FEM, whereas the local structures of the joints may be treated by BEM, as proposed in Section 4.3 within the local notch stress concept. BEM software is available commercially, and can be used under conditions similar to FEM.

33

6.4 RESOLUTION OF NOMINAL STRESSES In simple structures the nominal stresses can be solved using elementary theories of structural mechanics based on linear-elastic behaviour. However, there are many exceptions to this rule. FEM modelling may be of great help, or even the only possible approach, in the following cases:

(i) complicated statically indeterminate structures; (ii) the macro-geometry of the structural component is of such a form that useful analytical solutions are not available. Frames, continuous beams and latticed trusses are examples of statically indeterminate (hyperstatic) structures. The nominal axial stress in a section of a member is calculated by superimposing the stresses caused by the axial force, the in-plane bending moment and the out-of-plane bending moment. For fatigue problems, the secondary bending moments must also be considered, i.e. the bending moments in the members of a trusswork caused by the deflections and the rigidity of the joints. For this reason, the use of finite element analysis is to be preferred in the fatigue analysis of simply-supported lattice girders and similar structures. As already described in Section 2.1, the effects of macro-geometry must be included in the nominal stress. Many of the cases shown in Fig. 9 may be analysed more easily or more accurately with FEM rather than using analytical methods. Thin shell elements are often the correct element types for modelling the cases shown in Fig. 9 a-d). The analyst should have a good insight into the structural behaviour of the component in order to be able to simplify the model and choose the element size such that the required accuracy is achieved.

There is a need and a possibility for extensive simplification of structural details, because the effects of structural discontinuities, as shown in Fig. 12, should be excluded from the result. These effects are implicity included in test results when fatigue analysis is based on nominal stresses. The method by which the FEM model can be simplified in the case of interacting macro-geometric and structural discontinuity effects is discussed in Section 6.7. An example of a finite element model of a very large structure is shown mFig. 21. In this case membrane elements have been used in order to keep the number of degrees of freedom manageable. It should be remembered, however, that this

model can handle neither out-of-plane loadings nor shell bending due to possible distortional behaviour caused e.g. by eccentric loadings. Moreover, stress fields at concentrated loads cannot be solved accurately.

34

L

/

1\

/

Fig. 21 Part ofa ship hull modelled with membrane elements [36].

6.5 RESOLUTION OF HOT SPOT STRESSES 6.5.1 General As described in Section 2, three of the fatigue analysis methods use hot spot stress analysis, namely the hot spot, the notch stress/strain and the fracture mechanics approaches. None of the fatigue analysis methods which use hot spot stresses implicitly includes the effects of fabrication tolerances in the fatigue strength values. Therefore, all misalignments and similar discontinuities caused by fabrication inaccuracies must be taken into account in the calculation model. If they are not modelled in the finite element mesh, the analysis results should be corrected by using analytical formulae of the type given by Eqn. (4). Since the hot spot is located at a local notch, but the nonlinear stress peak is to be excluded from the result, extrapolation of the strain gauge results from a number of points adjacent to the notch is necessary. As far the finite element method is concerned, similar extrapolation is needed. The post processor programs can give valid results at a discontinuity only in special cases. Therefore, the stresses must usually be read at the integration points of adjacent elements, or at the nodal points, some distance from the hot spot. The element mesh must be refined near the hot spot such that the stress, and the stress gradient, can be determined with sufficient accuracy at similar extrapolation points as used when the hot spot S-N curve has been established, see Section 7.5. Refinement of the mesh should be such that any further refinement does not result in significant change of the stress distribution inside the area between extrapolation points.

35

If multi-layer modelling of a plate with solid elements is used, the surface stress includes part of the nonlinear stress peak, within a distance of O.4t of local notches. Therefore, the stress results should be linearized across the thickness, or the stresses should be read outside that area and extrapolated to the weld toe. For the same reason, 20-noded solid elements should be used in one layer with reduced 2-point integration.

6.5.2 Circular hollow section joints

Circular hollow sections (CHS) are used extensively in offshore structures, in which fatigue is an important failure mode. Since extensive research has been conducted into their joints, a number of parametric formulae have been established for the calculation of stress concentration factors and hot spot stresses, see Section 3.4. Finite element analysis is necessary in more complicated cases for which valid parametric formulae cannot be foun
elements do not produce better results outside the intersection zones. However, solid or thick shell elements are sometimes necessary, particularly when small gaps in K-joints (see Fig. 26), or multiplanar joints are studied. Solid elements define the weld toe much better than shell elements. 2. The joint is modelled as the intersecting mid-planes of the tubes. 3. The dimension of the side of the element perpendicular to the intersection curve of the two tubes (denoted m or e in Fig.22) must be such that the centre point or first integration point of the element is located no further than O.4t from the imaginary weld toe projected onto the mid-planes (distance a). 4.

The dimension, b, of the element (see Fig. 22) whose side lies on the intersection curve should be less than 1124 (or 1112 for isoparametric elements) of the length of the intersection curve (assuming a Tor Y joint).

5. The maximum dimension of the sides of the element far from the intersection zone must not exceed the length of a 30° arc (or 60° for isoparametric elements). The transition from the smallest element to the largest must take place gradually. 6.

When two tubes of equal outer diameter intersect, close to the saddle point the tubes should be modelled following the line a'-b-c shown in Fig. 23. Point

36

'a' represents the intersection of the inner surface of the brace and the outer surface of the chord. 7. When ajoint is isolated from the rest of the structure, the lengths of the tubes, outside the discontinuities, should be at least 2.5 times , but preferably 3 times the diameter of the respective member, in order to avoid the effects of boundary conditions.

8. The loads at the ends of the tubes are established from prior frame analysis results. Loads producing unit nominal stresses may be applied to derive stress concentration factors.

Brace

Chord

C=min(e, m)

• Node * Integration point

Fig. 22 Determination o/the maximum element size [2}. The shaded zone in Fig. 24 exhibits three-dimensional behaviour, which cannot be modelled with thin shell elements. Therefore, the hot spot stress must be determined by extrapolation from the integration points of adjacent elements, as shown in Fig. 25. The ARSEM recommendations [2] presuppose that the design S-N curve has been constructed using maximum principal stresses, calculated from principal strains measured by strain gauge rosettes from laboratory test pieces, and extrapolated to the weld toe. Exact extrapolation rules are available for strain measurements. In principle, the same rules should apply also for FEM analysis, although this is not explicitly stated.

37

Brace _.-.-- ----

Chord

s s

~-t---l- ~ ~~ ~~

_________________

~

i

;

l

__~~~L-----L-

C

Fig. 23 Modification of the brace at the saddle point ofa joint with tubes of equal diameter [2].

Zone whose behaviour is strongly three-dimensional Theoretical intersection on the shells

Fig. 24 Intersection zone exhibiting 3-D behaviour [2}.

38

Chord Brace Real ,tress distribution

Extrapolation

¥

Real stress dIstribution

Fig. 25 Extrapolation ofstructural stress to weld toe (hot spot) [2).

6.5.3 Square and rectangular hollow section joints Rectangular hollow section (RHS) joints differ from CHS joints in that: 1.

The stiffness distribution in the flat sidewalls is quite different from that of cylindrical shells. 2. There are chord comers near the brace side walls, see Fig. 26. Often the actual gap between adjacent cross weld toes is much smaller than the distance between mid-plane intersections, Fig. 26. Therefore thin shell elements cannot model the stiffness distribution correctly in the details shown in Fig. 26. Experience gained from RHS joint analysis has been reported in Refs. [18,37]. It is recommended that the weld and adjacent parts of members are modelled using solid elements, Fig. 27, in order to obtain correct stiffness properties. The remainder of the joint may be modelled with thin shell elements. To connect the shell elements to the solid elements, suitable transition elements have been used. Another possibility is to write constraint equations which make the solid element nodes follow the rotations of the shell elements.

39

g

Fig. 26 Details in which thin shell elements are not appropriate.

Fig. 27 Weld zone modelled with solid elements [37]. If thin shell elements alone are used for easy mesh generatio~ methods for satisfactory stiffness modelling are shown in Figs. 28 and 29. The first method uses thin shell elements with increased thicknesses in the intersection regio~ according to Fig. 28. This method has not been thoroughly verified in the

40

literature. However, there should be no objection to the use of this solution. The second method is to model the weld fIllet with inclined shell elements as shown in Fig. 29.

Fig. 28 Use ofthin shell elements with increased thickness in the weld zone.

t +

Fig. 29 Use of inclined shell elements for modelling the intersection region.

6.5.4 Miscellaneous details 6.5.4.1 Gusset or stiffener on plate Fig. 30 shows an example of FEM results gained from a study using a test piece with double gusset plates. Because of symmetry, no bending stresses develop. The locally increased area concentrates the membrane stress on the line of the gussets. The test piece was modelled using a fIne multi-layer solid element mesh

41

for demonstrating the actual stress distribution. In the vicinity of the end of the gusset plate, the local stress increases rapidly at a distance of 2 mm, or 20 % of the plate thickness, ahead of the weld toe. A linear extrapolation line has also been drawn. When such a test piece is modelled with thin shell elements, the entire gusset is connected to one nodal line only. In the vicinity of the gusset, the membrane stress concentration is highly exaggerated, see Fig. 31. The principal stress appears to increase in a non-linear manner along the longitudinal line. However, the distribution along a transverse line shows that the stress peak is very narrow when compared with the actual thickness of the gusset. The actual stress on a transverse line can be estimated by finding the average stress within the width of the gusset. Linear extrapolation of the average stress from two transverse lines to the end of the gusset yields the hot spot stress at the weld toe of the actual structure. Suitable distances of those lines from the gusset end are 0.4 t and 1. 0 t, where t is the thickness of the main plate. Correspondingly, a suitable maximum size range for the first 8-noded element is 0.4 t to 0.8 1, depending on where the stresses are given by the program, at the nodal points or at the centre points of the elements.

Longitudinal top and middle stress distribution

2,0 f t - - - - - + - - - - I - - - - I - - - - I

l,Sr---

l,OI------=:::::::j:===--+---l-----1 0,5 1 - - - - - + - - - - - 1 - - - - - - - 1 1 - - - - 1

Distance from the weld toe 1 1 1 1 1 1

~,

.

Lx

Fig. 30 Stress distribution along the centre line of a double-gusset test piece established using a fine solid element mesh.

1 1 1 1 1 1 I

42

If 4-noded elements of the size recommended above are used, the stress gradients appear to be more exaggerated. However, use of the same averaging and extrapolation technique still yields acceptable results. In this example the postprocessor plotted the stresses at nodal points, which gives

the stresses along the gusset line. If the stresses were expressed as element centre point values, the gradients would be somewhat different. Gussets welded on the top side of a plate also introduce shell bending stresses. For example, if a hydraulic actuator is connected through such gussets to a boom with a box-type cross-section, several stress-raising phenomena can be identified [38]. By using FEM, and modelling the detail in various ways, it is possible to differentiate between the following effects which cause stress concentration in the flange at the end of the gusset: (a)

concentration of the membrane stress due to the cross-sectional area of the gussets; (b) plate bending stresses due to the eccentricity of the gussets; (c) plate bending stresses due to the bending stiffness of the gussets which prevent the flange from following the curvature of the beam as a whole; (d) plate bending stresses due to the loads acting on the. gussets. It should be noted that a plate .containing a one-sided gusset, as well as a transverse butt weld with an angular misalignment, behaves in a geometrically nonlinear manner. At high loads the out-of-plane displacements change the distribution of the bending moment along the structure. Tension stress usually decreases shell bending in the more flexible part. This phenomenon should be taken into account in cases in which there are no webs or longitudinal stiffeners in the vicinity. Reference [39] deals with the intersection zone between the deck and superstructure of a ship. Tests were conducted with specimens quite. similar to the cases discussed above. The specimens were modelled with thin shell elements, but no averaging was perfonned although the gusset was 20 mm thick. Extrapolation from the point 0.4 t from the gusset, following the steep tangent of the apparent stress curve, resulted in very conservative life predictions. The authors recommended that the extrapolation be made from points LOt and 2.0 t from the hot spot. However, these results are valid for the specific thickness ratio between the main plate and the gusset. Therefore, correction of the apparent stress curve by averaging the thin shell results over the gusset width, and extrapolating from points 0.4 t and LOt, as recommended in this document, is to be preferred.

43 1.5,-----------------,

z

J-.y -50

-40

-30

-20

-10

0

10

20

30

.co

50

3r------------------~

2.5

0.6 o~~~~~~~~~~~~~~

-10 -5

0

6

10 15

20

25

30

35

.co

45

50

55

60

Fig. 31 Comparison ofstress distributions in double-gusset test pieces established using solid and thin shell elements.

6.5.4.2 Gusset at plate edge

One detail which causes trouble in the analysis of structural stresses and fatigue perfonnance is an abrupt change in plate width, e.g. a gusset plate attached to an edge, or a crossing of two beams, as shown in Fig. 32, and cases (a) and (b) in Fig. 12. The stress distribution exhibits a steep increase in the vicinity of the comer. Both the structural stress distribution, caused by the gusset geometry, and the effect of the local notch are nonlinear and these two effects interact. Therefore, it is not easy to distinguish between the local effect of weld toe geometry and the effect of the structural discontinuity in the details in question. A similar problem has been studied in Ref. [10] in order to separate the effect of weld toe geometry from the effect of the weld fillet. There are significant differences in the fatigue behaviour of gusset details, depending on whether the weld ends are as-welded, as shown in Fig. 33 a, or if the comer is rounded by grinding, as shown in Fig. 33 b. Various fatigue analysis methods could be applied but, unfortunately, experimental data for these particular details is scarce.

44

c)

Fig. 32. Various details including edge gussets, and other details with sharp corners. In the case shown in Fig. 33 (a), with an as-welded end weld at the plate edge, the fonnation of an edge crack is encouraged. Such a crack grows across the plate width. Small micro-crack-like discontinuities with a depth of about 0.3 mm may be assumed to exist at the weld toe. In such a case the fatigue life is dominated by the crack propagation phase. The nonlinear stress peak has a strong effect on the early stages of crack growth, but the effect fades as the crack propagates several rnilljrnetres. In addition, the structural stress distribution along the crack growth path decreases, and the nominal stress level is attained at a distance which depends on the breadth of the plate strip or the size of the gusset. The fracture mechanics approach would be the only analysis method which takes the effects of the actual stress distributions into account. However, a simpler engineering approach would often be preferable. Then a method of determination for the hot spot stress in such joints should be defined, such that the general S-N curve used in the hot spot approach would conservatively predict the fatigue life. In the case shown in Fig. 33b, the comers are rounded by grinding. Weld reinforcements are present on the surfaces of the plate only, causing a non-linear stress distribution across the plate thickness. Thus, quarter-elliptical comer cracks are expected to grow from the weld toes as shown. The hot spot stress is equal to the local structural stress at the edge at the location of the weld toe, determined using an element mesh fine enough to take into account the effect of the comer radius. A fracture mechanics simulation of the crack growth may be quite complicated in this case. On the other hand, the hot spot approach may sometimes be quite conservative due to the fact that very short lengths of weld toe are exposed to the highest stresses.

As comer grinding will be perfonned anyway, it would be advantageous to perfonn toe grinding over short lengths at the same time. In such cases, the local stress/strain method would predict the crack initiation life.

45

If the detail shown in Fig. 33a has similarly finished comers as the case in Fig. 33b, there are no weld toes exposed to high transverse stresses. Assuming that the ground area is defect-free, the crack initiation life will dominate the fatigue life. The initiation life can be predicted using local stress or strain methods, based on the maximum notch stress or strain. The depth of the initiated crack after the predicted number of initiation cycles is proportional to the notch radius. If the radius is small, the initial crack will be shallow, and a significant crack propagation life may remain. In this case it may be sufficient to combine the local stress/strain methods and the crack growth simulation using fracture mechanics. Unfortunately, the depth of the crack after the initiation phase is not well defined.

If the radius is fairly large, e.g. 10 mm, the propagation life may be neglected.

a)

b)

Crack surface

Crack surface

····Crack ""Crack

"" IT

nom

........ IT hs

Effect of weld fillet Fig. 33 (a) Non-load-carrying and (b) load carrying gusset at a plate edge.

Hot spot stress approaches for simple engineering analyses Development of fatigue analysis methods for the particular joint types in question is still in progress. In this section, two alternative methods are proposed for

46

detennination of the hot spot stress [40]. Both methods appear to yield acceptable results. The fIrst method is well suited for strain measurements with gauges placed at the edge of the plate. The second method is more suitable for fInite element analyses. Method 1 Three extrapolation points at fIxed distances of 4,8 and 12 mm from the weld toe at the plate edge are defmed, and quadratic extrapolation to the weld toe is perfonned, giving a local structural stress. Due to the fIxed locations, different amounts of the non-linear peak stress are included in the local structural stress, depending on the size of the detail. This automatically accounts for the size effect, but makes FE analysis quite laborious. The following equation yields the local hot spot stress according to quadratic extrapolation: ~1s

= 3~(4)-3~(8)+0'-C12),

(8)

where o(x) is the stress x mm from the weld toe. In this method, the local hot spot stress is compared with the basic hot spot

fatigue strength valid for 25 mm thick plates.

L

Fig. 34 Edge gusset studied in Ref [40}.

Method 2 Two extrapolation points at the plate edge are defIned relative to the apparent size: 0.151app and O.31app ' The hot spot stress is determined by linear extrapolation. The size effect must be accounted for by multiplying the hot spot fatigue strength by a conventional size effect factor, f(t), depending on the apparent thickness.

47

The apparent size is detennined as [41]: tapp=min{B, 1.5L, I5H},

(9)

where B, L, andH are defmed in Fig. 34. In this method, the basic hot spot fatigue strength valid for 25 mm thick plate

must be reduced by multiplying by the size effect factor, f(t): 0.25 (

ref )

J(t)= t tapp

(10)

,

where

Method 2 can be used in cases in which at least one of the dimensions B, L, or H is small enough. The accuracy of the size effect may not be sufficient when tapp exceeds 300 mm.

6.5.4.3 Cover plate ends

Cover plate endings are the most serious stress raisers in beams with welded cover plates on the flanges [42], as shown in Fig. 35. Many attempts have been made to increase the fatigue strength of a beam by redesigning the cover plate endings, but without any great success [32]. In spite of this, some improvement could be anticipated· by using finite element analysis. In excavator or crane booms, many details resemble cover plates and constitute potential fatigue crack sites.

)

Cant. longitudinal fillets

~ ~

~;..:;:..=.:~-

Fig. 35 Cover plate endings [32].

48

Fig. 36 shows several ways to model cover plate ends. Thin shell elements may be used to model the separate mid-planes of the flange and the cover plate, or they can be substituted by one plate with a thickness equal to the total thickness of the two plates. Some experiments have shown that this simplified model yields acceptable hot spot stresses in the single plate, although the displacement results are not accurate. The welds could be modelled by connecting the offset plate to the flange by vertical thin shell elements. Adding inclined shell elements (Fig. 36b) is useful if other discontinuities are in the vicinity. Such intersecting shell elements have, however, the disadvantage of false averaging at the common node by the post-processing program.

! (a)

~ Shell element

=:=:==+-1-.-.-,---'1

1';= : =1

(b)

!______ Rigid bar (c)

: : I, .

t/;.

,

Rigid bar

(d)

.

(e)

Fig. 36 Various modelling approaches for cover plate endings a) double shells connected by a vertical shell; b) double shells connected by vertical and inclined shell elements; c) double shells connected by rigid bars; d) single shell with offset, connected by rigid bars; e) solid element modelling. Solid elements can also be used, allowing the weld to be realistically modelled and thus avoiding the aforementioned problems [35]. Such a modelling of the welds is especially important when there are other discontinuities in the vicinity. The axial stiffness is unevenly distributed across the flange width, Fig. 37. At a web plate, the rotations caused by eccentricity are restrained, which increases the

49

stiffness and results in a concentration of membrane stress. Some of the membrane stress is shifted from the web to the flange, which further increases the flange stresses. Far from webs the membrane stress is decreased, whereas the bending stress is increased. In the case of a straight cover plate end, it is recommended that the surface stress distributions are plotted along longitudinal lines at the web -and far from the web and along two transverse lines, one 0.4 t and the other 1.0 t from the cover plate end. Linear extrapolation to the cover plate end yields the estimated structural stresses at various points along the weld toe as well as the hot spot stress. The element size must be chosen such that valid results can be plotted at the abovementioned lines. A full-width straight cover plate on a box section appears to result in an essentially singular stress state at the edges, which requires careful modelling.

Fig. 37 I-beam with cover plate (1/4 model with solid elements). A more complicated design of cover plate end may be useful if a beam is subjected to biaxial bending. In this case, the maximum nominal stresses occur at the flange edges. The cover plate end could be extended, like a blunt arrow-head, into the middle part of the flange. Depending on the loading, the hot spot may be located at the end of the cover plate or at the edge of the flange. In the latter case the maximum principal stresses are not perpendicular to the weld, depending on the design. Some extra care is needed in planning the mesh and interpreting the results.

50

6.5.4.3 Chassis frames of trucks Chassis frames of trucks are rarely welded designs, but trailer frames usually are. Such a ladder-like frame experiences severe torsional defonnation, especially in off-road use. Problems arise in the joints between the cross-beams and the webs of the main beams. Torsion generates warping stresses in the beams and shell bending stresses in the webs at the joints. Some manufacturers have established the stresses by modelling the whole frame (or one half of it, because of symmetry) using thin shell elements. Satisfactory results can be achieved with such a model, provided the joints to be studied can be modelled with meshes fine enough to yield accurate hot spot stresses. However, the large number of degrees of freedom demands very heavy computing techniques. A better solution might be to solve the nominal stresses and defonnations first with a coarse thin shell model, and then to use these results as input for studying isolated joints modelled with a fine mesh. The use of beam element modelling is not recommended for the following reasons: (a) (b) (c) (d)

The beam elements should be able to deal with warping torsion [43]. The joints should be modelled as semi-rigid joints with reference to various degrees of freedom. Thirdly, the eccentricities of the shear centres of the open cross sections etc. should be taken into account. There are certain couplings between the degrees of freedom, which should also be modelled [43]. For example, the bimoment in an eccentrically joined cross-beam is transmitted to the main girder not only as a bimoment, but partly as a bending moment also.

Use of the above-mentioned analysis method requires that isolated thin shell models of joints are studied first, yielding all the stiffness values as well as the stress concentration factors, Ks, for all potential hot spots and basic load cases. After using such a FE program for solving the forces and moments, the hot spot stresses can be calculated using Ks factors and superposition.

6.6 RESOLUTION OF NONLINEAR STRESS PEAKS Nonlinear stress peaks must also be included in the calculated load effects when either the notch stress/strain approaches or the fracture mechanics approach is to be used. Analysis of nonlinear stress peaks is required in such cases only when no valid analytical solution in the fonn of a theoretical notch factor, ~, or a function, Mia) [32], is available.

51

The solution of nonlinear stress peak distributions at a local notch using FEM requires a very fme element mesh. Fortunately, a two dimensional model is able to yield a satisfactory solution if the notch is fairly long. In such a detail, plane strain elements are used. Fig. 38 shows an example of an FEM model for solving the Kt-factor at a weld toe with a relatively small radius. Comparison with a parametric formula obtained from the literature [31] has shown that this model, when used with parabolic elements, yields satisfactory results. In many cases, only the maximum nonlinear stress peak at the surface needs to be established. Then the boundary element method, BEM, is sufficient (see Section 6.3).

~

- -.----.--.----_...

Fig. 38 Element mesh for establishing the stress concentration factor at a weld toe.

6.7 SuPERPOSITION OF THE EFFECTS OF MACRO-GEOMETRY AND STRUCTURAL DISCONTINUITY When a large structure contains macro-geometric effects, such as those shown in Fig. 9, it is desirable to simplify the thin shell model by omitting smaller scale structural discontinuities and attachments, as shown in Fig. 12. This model then

52

gives nominal stresses. The effects of structural discontinuities can then be superimposed on the nominal stresses in the following ways: (i) isolated parts of the structure are modelled with a fine enough mesh, loading them with the displacements given by the large scale model; (ii) as above, but loaded with stresses given by the large scale model; (iii) a stress concentration factor is used, established from a separate model which includes the structural discontinuity. N one of the above-mentioned methods gives exact results, because the attachments affect the stiffness distribution. The analyst should tIy at least two alternative ways in order to establish the magnitude of the error. The accuracy of the method described above improves as the difference between the areas of influence of the macro-geometIy and the structural discontinuity increases. If, for example, a hole in a plate interacts with a butt weld containing an offset

misalignment, the effects of each discontinuity can be established separately using stress concentration factors, ~ and Kxn. By multiplying these two factors, somewhat conservative results are produced when compared with FEM results when both discontinuities are included in the same model, Fig. 39. One experiment gave a difference of 10%. Another feature of this case is that the hot spot stress only exists over very short lengths of the weld toe. The probability of the characteristic initial crack size being located at the point of maximum stress is lower than in the specimens from which the S-N curves are derived. The fatigue analysis tends to give conservative predictions. However, this depends again on the manufacturing procedure; whether welding is performed before or after the hole is cut.

Fig. 39 Thin shell model for calculation of the interaction between a hole and an offiet misalignment.

53

7 EXPERIMENTAL DETERMINATION OF STRESSES 7.1 GENERAL Experimental stress analysis is an established, popular and proven method that is routinely used to design or to assess engineering structures. Of the numerous methods available, the 'electrical resistance strain (ERS) gauge is widely recognized as being the most versatile and practical. The main drawback of strain gauge technology is that it only yields strain values point by point. A method yielding a picture of the whole strain field would be desirable. Even a rough picture would help in choosing the locations and orientations of the strain gauges. Such a technique is the brittle lacquer method. Prior application of the method can often save a large number of strain gauges whilst the accuracy of the strain gauge measurements is maintained. Brittle lacquer is sprayed on the regions to be examined. After a drying period, the structure is loaded. Cracks appear in the highly strained regions. The orientation of the cracks is perpendicular to the direction of the major principal tensile strain. The density of the cracks indicates the magnitude of the strain. However, the accuracy of the method is not high enough for it to be used alone. The other drawback is a high threshold strain, after which cracking begins to occur. Therefore, the use of the method involves high loading or high stress concentrations. Another method for studying the strain field is the so-called SPATE method. A very sensitive camera measures the temperature changes of the specimen during cyclic loading. A monitor shows the stress field in similar way as the colourful postprocessed results of FE analysis. This method requires expensive equipment and extensive laboratory testing.

7.2

INTRODUCTION TO STRAIN GAUGE TECHNOLOGY

The fundamental relationships between resistance change and strain are shown in Fig. 40. When a conductor of length, L, and cross-sectional area, A, is elongated, the length increases and the area decreases according to Poisson's ratio to produce an increase in resistance. The resistance change, L1RIR, is related to the length change, giL (engineering strain, c), by the strain sensitivity factor, S: (11)

54

Note that both the numerator and denominator are dimensionless. The engmeenng strain is usually expressed in microstrain (i.e. micrometres per metre). ~M

r'I/It--""'@---i ~(oE------_--_m-----W I:--m------:m------~M - ~ j _

1

--

Legend:

R 2 P AL - Resistance. ohms

S 2 ALIL !;'RIR = S train - Sensltlvlty -- -

L "Conductor Length

(gage factor when applied to a specific gage)

A • Cross SectIOn Area p • Resistivity Constant

ARIR = Resistance Change ALIL 2 St~in

Fig. 40 Fundamental relationships between resistance change and strain. If the strain sensitivity were dependent only upon dimensional change resulting from the usual Poisson ratio of 0.3, then all metallic conductors would have a theoretical value of 1.6 in the elastic range and 2.0 in the plastic range. However, the resistivity constant varies with strain, and gauge-factors can range from 2.0 to 4.5 for materials used in metallic strain gauges.

Thus, for the overall resistance change to be a linear function of applied strain, the resistivity change must be proportional to the internal stress level, at least within the elastic limit. Therefore, only gauge alloys that display a strain sensitivity of approximately 2.0 in the elastic region can exhibit essentially linear behaviour over very large ranges. Such an alloy is Constantan, a commercial copper-nickel product: it is the oldest and most widely used. However, there are numerous other strain-sensitive alloys, each suited to specific tasks. Because strain gauges, when properly compensated for temperature effects, can achieve overall accuracies of ±0.10% or better, and because of their relatively low cost, great flexibility, and wide variety of configurations, they are used in a broad range of applications. Resistance gauges are made in a variety of shapes, sizes, and types; most are smaller than a postage stamp. Gauge lengths as short as 0.38 mm are available, and strains as small as 0.000001, or 1 microstrain, can be detected. The selection of the appropriate strain gauge for a given application and environment is not a simple procedure: the gauge manufacturer should be consulted with respect to such aspects as sensitivity, size, location, grid, backing, adhesive, etc.

55

The selection of alloy and backing should take into account the following criteria: type of strain measurement (static, dynamic); operating temperature; test duration; accuracy required; cyclic endurance required. The output of metallic strain gauges is a resistance change as a function of applied strain level. At strain sensitivities of the order of 2.0, these resistance changes will be of the order of hundreds to a few thousand parts per million. Such values are generally much too low for direct measurement in a typical ohmmeter circuit. Therefore, bridge circuits such as the Wheatstone (Fig. 41) are usually employed.

Excitation voltage

Fig. 41 Basic strain gauge bridge circuit (Wheatstone bridge).

More information about strain gauge technology is given in Refs. [44-46].

703

APPLICATIONS OF STRAIN GAUGES

The application of strain gauges for fatigue analysis purposes of welded components can be divided into the following main areas.

56

(1) Measurement of nominal strains in a structure, at points located remote from structural discontinuities, i.e. outside the area of structural stress concentrations. With suitably placed gauges the strains can be divided into parts resulting from axial force, bending moments, shear force, torsion etc, if required. . (2) Measurement of structural strains near hot spots in order to determine the hot spot stresses at local discontinuities in a component. (3) Measurement of structural strains as above, but from fatigue test pieces in order to establish hot spot S-N curves. (4) Study of the dynamic response of a structure, in order to evaluate realistic dynamic load factors to be used in stress calculations. (5) Verification of the results obtained by the finite element method. Such comparisons are very useful in developing skills in structural analysis. In particular, realistic assumptions concerning loads and load combinations, and secondary actions such as side thrust forces on crane runways, can be elucidated effectively. (6) Experimental determination of structural stress concentration factors, K, using methods (1) and (2) simultaneously. (7) Recording of strain histories, using either method (1) or method (2), under different operational conditions in order to collect stress range occurrence data for structural components subjected to variable amplitude loading. Besides recording strain histories, a direct on-line strain range counting process may also be chosen.

7.4

CONFIGURATIONS FOR VARIOUS CRITERIA

In order to obtain the complete state of strain at the surface of a structure, it is

necessary to define the magnitude and direction of the principal strains. 7.4.1 Uniaxial Stress

When the stress state at the point of measurement is known to be uniaxial and the directions of the principal axes are also known with reasonable accuracy (± 5%), then a "single grid" gauge, as shown in Fig. 42, would be used. A typical application would be the determination of the in-plane bending stress at the centreline of the bottom flange of a girder. Single grid strain gauges may be used in groups to determine axial and bending parts of a uniaxial combined stress, such as that found in a simple beam-column.

57

By placing the gauges on opposite flange surfaces, the individual components of axial and bending stresses can be calculated. Moreover, by using more gauges and connecting them to separate Wheatstone bridges in suitable ways, axial and bending strains can be determined directly without any calculations. ~---------------------------------------------------------

a)

b) Matrix length

Fig. 42 Bonded electrical strain gauges: (aj a single gauge; (bj a multiple-grid strip gauge.

7.4.2 Biaxial Stresses In many structures it may be necessary to investigate the effect of biaxial

stresses; the determination of the uniaxial strain alone may sometimes lead to grossly unconservative conclusions. This is particularly true for crane runway girders (Fig. 43), or any structure that may be subject to complex and/or general, unaccountable, stresses, especially those resulting from out-of-plane forces, secondary bending, and eccentric loading. The type of strain gauge grid to be used for determining biaxial stress depends on whether the orientation of the principal axes is known.

Fig. 43 A travelling crane creates non-proportional hi-axial stresses.

58

7.4.2.1 Axes known

When the orientation of the principal axes is known in advance, a two element 90° gauge (Fig. 44) can be used. The gauge axes are aligned with the principal axes.

...

-1

,

-2

"--1

Fig. 44 Two-element gauge (t-rosette).

7.4.2.2 Axes not known

In the most general case of surface stresses, when the orientation of the principal axes is not known, a three element rosette must be used to determine the principal stresses. The rosette can be positioned in any orientation, although it is usually aligned with a significant axis of the structure under investigation. Three element rosettes are available in both 45° rectangular and 60° delta configurations (Fig. 45). The most common choice is the rectangular configuration, as the equations for deriving the principal stresses are simplified considerably.

I

,

II

m

Fig. 45 Two different rosettes with three elements. An easier method for determining the direction of the principal axes would in many cases involve prior use of brittle lacquer [44-46].

59

7.4.3 Stress Gradient In cases involving a steep stress gradient, e.g. when studying hot spot stresses at a

structural discontinuity, the application of a single gauge may give an inaccurate answer. The problem can be avoided by using multiple-grid strip strain gauges. The hot spot stress can determined by extrapolating in a similar way to FEM analysis, see Sections 6.4 and 7.5.3. Since the strain gauge tends to integrate, or average, the strain over the area covered by the gauge, and since the average of any non-uniform strain distribution is always less than the maximum, strain gauges with short grids should be used at stress gradients. Typically, a gauge length of 2 or 3 mm is used in multiple-grid strip strain gauges.

7.5

APPLICATION EXAMPLES

7.5.1 General

The goal in strain gauge applications is normally to determine the state of stress at the surface. Thus, the strain readings must be converted to stress evaluations. The procedure is essentially straightforward, using well established relationships between the variables, although the manipulation of formulae and numbers can be cumbersome if the stress state is bi-axial with unknown axis orientations. The formulae can be found in Refs. [44,46]. In a general case, the first step is to transform the measured strain gauge readings

into principal strains, that is, to determine the maximum strain in the body and the plane on which it acts. This is essentially the same procedure used to transfOlm stresses. Having solved for the principal strains, the associated principal stresses can be readily calculated using the elastic modulus, E, and Poisson's ratio, v.

7.5.2

Measurement of nominal stresses

The S-N curves of conventional design codes are based on the nominal stress range remote from all discontinuities present in the test pieces. Therefore, the stress range determined from the component must exclude the strain concentration caused by the corresponding discontinuity. According to Saint Venant's principle, the effect of the discontinuity disappears a certain distance remote from the discontinuity. The user is assumed to have sufficient experience in stress analysis to be able to place the strain gauges appropriately. Therefore, only a few problematic points are discussed in the following.

60

It can be concluded that the use of the nominal stress method may be ambiguous

in such cases. The application of the hot spot method would often be a better choice.

7.5.2.1 Transverse butt weld

Studies have shown that the local notch stress at a transverse butt weld decays to the value of the structural stress at a distance from the toe of approximately O.3t, where t is the plate thickness. Thus, if the strain gauge is placed such that the whole gauge lies outside that borderline, the structural stress range thus determined should be the valid nominal stress range. In practice, this is not exactly the case. In test pieces, the presence of a small amount of unintentional misalignment must be expected, which causes secondary bending stresses. Correspondingly, the conventional S-N curve for a butt weld allows for a small unknown amount of secondary bending stress in addition to the nominal stress. Real structural components may include larger misalignments than those in the test pieces. The strain gauge should then be placed on the concave side in order to include the extra bending stress in the value of the nominal stress, Fig. 46. Nominal stress may be measured at a distance of 1.0 t from the weld toe. In Fig. 46, two gauges are shown which allow the hot spot stress to be determined also.

t

Fig. 46 Measurement ofstrains at a misaligned butt joint. Maximum structural stress is found in the lower plate on the concave side.

7.5.2.2 Eccentric attachments

Design codes do not usually make any distinction between an attachment welded on one side of a plate, or symmetric attachments welded on both sides, Fig. 47. In the former case, secondary shell bending occurs due to the eccentricity. Moreover, the angular distortion due to welding tends to be larger than in the symmetric case. In the latter symmetric case, no significant shell bending stresses occur. Membrane stress concentration due to the locally-increased crosssectional area is then the main"effect. The magnitude of secondary bending due to

61

one-sided attachment depends on whether there is a web or stiffener on the other side.

b) ~

Fig. 47 Single (a) and double (b) cover plates have different effects. In case the S-N curve of the design code is based on test pieces with no

secondary bending, the shell bending stress due to the eccentricity should be included in the measured nominal stress. However, the membrane stress concentration should be excluded. These requirements cannot easily be met. Accurate evaluation of the nominal stress requires strain gauge pairs attached on both sides of the plate, and placed at different distances from the attachment.

7.5.2.3 Secondary bending stresses in crane runways Fig. 48 shows an example of how strain gauges can be used to quantify the localized compression membrane stresses, as well as the secondary bending stresses, in the web under an eccentric wheel load. The membrane and bending stresses can be separated by means of two gauges, as shown in Fig. 48.

Eccentric Crane / Wheel Loading

Strain Gauges Placed on Opposite Sides of Girder Web

Fig. 48 An example ofstrain gauges attached on both sides ofa web in order to measure vertical membrane and bending stresses.

62

7.5.2.4 Regions near macro-geometric effects When a weld is located in a region with macro-geometric effects (Fig. 9), the gauges must be located such that this effect can be measured and included in the nominal stress. The case of a weld located within the stress concentration of a large circular hole illustrates this principle quite clearly, (see Fig. 39). The stress to be used in conjunction with the nominal S-N curve must include the stress raising effect of the hole at the location of the weld. If the hole is quite small, e.g. a drilled hole for a bolt, then the area of the maximum stress is very small. It is questionable whether the maximum peak should be included in the nominal stress. Some design codes do not assume it to be included. Instead, they may alter the fatigue classification of such a weld.

7.5.2.5 Regions with a stress gradient Bending stresses in a beam usually change along its length. If an attachment is welded to the beam, and in order to avoid the local stress concentration being included the gauge is placed somewhat remote from the discontinuity, the correct value of the beam bending stress cannot be measured. If the bending moment distribution is known, the result may be corrected by calculation. Otherwise, another gauge should be placed behind the first one in order to determine the stress gradient.

7.5.3 Measurement of hot spot stresses The most important factors to influence the choice of strain gauge positions are the hot spot location and the orientation of the principal axes. Sometimes these are obvious due to symmetry; in more general cases, one of the following means maybe used: (i) several candidate spots are instrumented with strain gauges or rosettes; (ii) prior investigation using brittle lacquer is made; (iii) the results of a prior FEM analysis are taken into account. Usually, there is a stress gradient at the hot spot. Therefore, two or three gauges should be placed in sequence, as shown in Fig. 49, in order to be able to extrapolate the results to the weld toe, see also Section 4.2. The centre point of the first gauge should be placed at a distance 0.4 t from the weld toe. The gauge length should not exceed 0.2 t. If this is not possible due to a small plate

63

thickness, the leading edge of the gauge should be placed at a distance 0.3t from the weld toe.

O.3t

Fig. 49 Recommended locations ofstrain gauges for determination of hot spot stresses in plate structures. a) low bending stresses; b) high bending stresses, stiff elastic foundation (quadratic extrapolation); c) thin plate, gauge grid length >0.2 t.

Two gauges and linear extrapolation to the weld toe yield satisfactory results in cases in which the stress increases roughly linearly when approaching the leading gauge. This is often the case when the stress concentration consists mainly of membrane stresses. However, shell bending stresses caused by e.g. an eccentric attachment often show a nonlinear increase. Thus, there may not be a clear region of linear stress increase. In such a case, utilization of three gauges and quadratic extrapolation are recommended. The distribution of shell bending stresses depends on the beam-on-elasticfoundation effect, [9,47]. In a curved shell, as in a tubular joint, the curvature of the shell introduces a rather stiff elastic foundation. Other examples of stiff foundations are a web or a longitudinal stiffener under a flange plate. In such regions with stiff foundation the stress distribution tends to be non-linear. Therefore, quadratic extrapolation is recommended. For more details, see Ref. [18]. Usually it is practical to use multiple-grid strip gauges with at least three gauge grids instead of two or three single gauges. The first gauge grid should then be placed as shown in Fig. 49. However, the other grids do not usually fit exactly to the points shown in Figs. 49 (a) or (b). In order to get consistent results, a curve should be fitted to the plotted results. Then linear extrapolation should be made

64

using the curve values at the points shown in Fig. 49 (a). In cases when strong nonlinearity is present, quadratic extrapolation should be made using the fitted curve. Then, more than three gauge grids are to be recommended. Using two extrapolation points, as shown in Fig. 49 (a), the hot spot stress is calculated according to equation (12).

a hs = 1.67 a(O.4t) -

0.67 a(1.0t) ,

(12)

where o(x) is the stress x mm from the weld toe. Using three extrapolation points, as shown in Fig. 49(b), the quadratic extrapolation can be performed according to equation (13).

a hs = 2.52a(0.4t) - 224a(0.9t) + 0.72a(1.4t) .

(13)

For tubular joints some recommendations exist, which allow the use of linear extrapolation. See for example Refs. [18,36]. The requirement that bi-axial stress states should be evaluated introduces an extra complication into the determination of the hot spot stress. The use of gauge rosettes and establishing principal stresses at each measuring point makes the approach too expensive for many applications. Often the stress state can be concluded to differ only slightly from uniaxial. Thus, a simple fictitious uniaxial stress may be used as the equivalent stress. Decisions have to be made case by case.

7.5.4 Strain gauges and fatigue test specimens If a fatigue test specimen is instrumented with strain gauges to establish the hot spot stress, the recommendations given in Section 7.5.3 apply. To achieve valid results it is important that the measured results represent accurately the conditions at the crack initiation site. If the initiation site is not obvious and the magnitude of the stresses changes along the weld, several strain gauge sets must be attached. In complicated joints a large number of strain gauges are needed, unless brittle lacquer or some other full-field method can be used fos initial guidance on gauge locations.

65

7.6

STRESS SPECTRUM AND CUMULATIVE FATIGUE DAMAGE

The accuracy of fatigue calculations depends not only on appropriate design criteria, correct analysis methods, and accurate maximum load data, but also on the stress spectrum. All too often a design is based on arbitrary load conditions, all taken at their maxima. Strain gauges allow the determination of actual stress ranges. For example, if the movements of cranes working under normal operating conditions are monitored, then the problem is described completely. Having a well defined spectrum allows the designer to apply the principle of cumulative fatigue damage, as expressed by Miner's rule. Even a crude evaluation of crane movements will substantially alter the design assessment in a positive fashion. Although electrical resistance strain gauges have been in existence for some fifty years, some of the most exciting advances have occurred in instrumentation to monitor and collect strain data. The old manual method of reducing strain gauge data for fatigue analysis from traces on a chart has progressed to the use of a multichannel unit known as an on-board real time analyzer. The development of the microprocessor has of course made this possible. Strain readings can be continuously collected, stored, digitized, and analyzed. Computer software is now available to determine stress ranges and spectra from the digitized data. Such programs can also be tailored to correlate test results to the appropriate design code.

8.

CONCLUDING REMARKS

This document gives guidelines for determination of stresses, both for research and design use. The material properties to be used in the fatigue analysis are not given. The reason is that usually design calculations are performed according to some design code as agreed between vendor and customer. The whole safety concept, including the safety factors and design S-N curves or other strength data, should conform to a harmonised design code system. Unfortunately, at present, there is no unified international standard applicable to all application fields of fatigue loaded welded structures. Instead, separate design codes for ship structures, offshore structures, cranes, pressure vessels etc. are in use. An ideal way to use these recommendations would be with a system, in which

(i) the design loads and their combinations and occurrences used in the fatigue calculations are defined in the design code for the particular product type; (ii) the stresses and stress ranges are determined according to this document;

65

7.6

STRESS SPECTRUM AND CUMULATIVE FATIGUE DAMAGE

The accuracy of fatigue calculations depends not only on appropriate design criteria, correct analysis methods, and accurate maximum load data, but also on the stress spectrum. All too often a design is based on arbitrary load conditions, all taken at their maxima. Strain gauges allow the determination of actual stress ranges. For example, if the movements of cranes working under normal operating conditions are monitored, then the problem is described completely. Having a well defined spectrum allows the designer to apply the principle of cumulative fatigue damage, as expressed by Miner's rule. Even a crude evaluation of crane movements will substantially alter the design assessment in a positive fashion. Although electrical resistance strain gauges have been in existence for some fifty years, some of the most exciting advances have occurred in instrumentation to monitor and collect strain data. The old manual method of reducing strain gauge data for fatigue analysis from traces on a chart has progressed to the use of a multichannel unit known as an on-board real time analyzer. The development of the microprocessor has of course made this possible. Strain readings can be continuously collected, stored, digitized, and analyzed. Computer software is now available to determine stress ranges and spectra from the digitized data. Such programs can also be tailored to correlate test results to the appropriate design code.

8.

CONCLUDING REMARKS

This document gives guidelines for determination of stresses, both for research and design use. The material properties to be used in the fatigue analysis are not given. The reason is that usually design calculations are performed according to some design code as agreed between vendor and customer. The whole safety concept, including the safety factors and design S-N curves or other strength data, should conform to a harmonised design code system. Unfortunately, at present, there is no unified international standard applicable to all application fields of fatigue loaded welded structures. Instead, separate design codes for ship structures, offshore structures, cranes, pressure vessels etc. are in use. An ideal way to use these recommendations would be with a system, in which

(i) the design loads and their combinations and occurrences used in the fatigue calculations are defined in the design code for the particular product type; (ii) the stresses and stress ranges are determined according to this document;

66

(iii) the design fatigue strengths in the form of S-N curves, crack growth rates etc. are given in a fatigue analysis standard which is common for all product types. An important aspect is that the design fatigue strength data used should be derived from test data in a way which is consistent with this document. Meanwhile, before such a common fatigue analysis standard is available, the user of this document should ensure that the fatigue strength data to be used are expressed in terms of stress values which are consistent with the calculated stresses. It is the intention of the International Institute of Welding to prepare an

international ISO standard as described in paragraph (iii) above.

REFERENCES 1. IIDA K., Application of hot spot strain concept to fatigue life prediction. Welding in the World Vol. 22 (1984), No 9110, pp. 222-246. 2. Design Guides for Offshore Structures. Welded Tubular Joints. ARSEM, Association de Recherche sur les Structures Metalliques Marines, 1987. (English translation). 3. ASTM Designation E 1049, 1985. Standard Practices for Cycle Counting in Fatigue Analysis. Annual Book of ASTM Standards, Vol 03.01.,9 p. 4. WYLDE J.G., Application on Fatigue Design Rules for Welded Steel Joints. Report 29811986, The Welding Institute, Abington, Cambridge 1986. IIW-Doc. XIII-1342-89. 5. ASME Boiler and Pressure Vessel Code. Section ill, Rules for Construction of Nuclear Vessels. 6. ENV 1993 (1992) Eurocode 3: Design of Steel Structures. 7. MADDOX S.J., Fitness-for-purpose assessment of misalignment in transverse butt welds subject to fatigue loading. The Welding Institute Report No. 279/1985. Abington Cambridge 1985. IIW-Doc. XID-1180-85. 8. IIW Guidance on Assessment of the Fitness for Purpose of Welded Structures. Draft for Development. IIWIIIS-SST-1157-90. 322 p. 9. PARTANEN T., Factors Affecting the Fatigue Behaviour of Misaligned Transverse Butt Joints in Plate Structures. In: M.Bramat (Ed.), Engineering

66

(iii) the design fatigue strengths in the form of S-N curves, crack growth rates etc. are given in a fatigue analysis standard which is common for all product types. An important aspect is that the design fatigue strength data used should be derived from test data in a way which is consistent with this document. Meanwhile, before such a common fatigue analysis standard is available, the user of this document should ensure that the fatigue strength data to be used are expressed in terms of stress values which are consistent with the calculated stresses. It is the intention of the International Institute of Welding to prepare an

international ISO standard as described in paragraph (iii) above.

REFERENCES 1. IIDA K., Application of hot spot strain concept to fatigue life prediction. Welding in the World Vol. 22 (1984), No 9110, pp. 222-246. 2. Design Guides for Offshore Structures. Welded Tubular Joints. ARSEM, Association de Recherche sur les Structures Metalliques Marines, 1987. (English translation). 3. ASTM Designation E 1049, 1985. Standard Practices for Cycle Counting in Fatigue Analysis. Annual Book of ASTM Standards, Vol 03.01.,9 p. 4. WYLDE J.G., Application on Fatigue Design Rules for Welded Steel Joints. Report 29811986, The Welding Institute, Abington, Cambridge 1986. IIW-Doc. XIII-1342-89. 5. ASME Boiler and Pressure Vessel Code. Section ill, Rules for Construction of Nuclear Vessels. 6. ENV 1993 (1992) Eurocode 3: Design of Steel Structures. 7. MADDOX S.J., Fitness-for-purpose assessment of misalignment in transverse butt welds subject to fatigue loading. The Welding Institute Report No. 279/1985. Abington Cambridge 1985. IIW-Doc. XID-1180-85. 8. IIW Guidance on Assessment of the Fitness for Purpose of Welded Structures. Draft for Development. IIWIIIS-SST-1157-90. 322 p. 9. PARTANEN T., Factors Affecting the Fatigue Behaviour of Misaligned Transverse Butt Joints in Plate Structures. In: M.Bramat (Ed.), Engineering

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Design in Welded Connections. Proc. IIW Conf. Madrid 1992. Pergamon Press, 1992. 10. Van DELFT D.R.V., A two Dimensional Analysis of the Stresses at the Vicinity of the Weldtoes of Welded Tubular Joints. Delft University of Technology, Department of Civil Engineering. Stevin Laboratory Report 6-81-8. Delft 1981. 58 p. 11. RADAJ D., Schwingfestigkeit von Biegetragern mit Quersteife nach dem Kerbgrundkonzept. Der Stahlbau 8/1985, S. 243-249. 12. ROMEYN A., PUTHLI RS., de KONING C.H.M. & WARDENIER J., Stress and Strain Concentration Factors of Multiplanar Joints Made of Circular Hollow Sections. Proc. ISOPE '91. 13. POTVIN A.B., KUANG J.G., LEICK RD. & KAHLICH J.L., Stress Concentrations in Tubular Joints. SPE Journal, August 1977. 14. WORDSWORTH A.C., Stress Concentrations at K, KT Tubular Joints. ICE Conference, Fatigue m Offshore Structural Steel. Paper No. 27. London, February 1981. 15. TEYLER R., GIBSTEIN M.B., BJORNSTAD H. & HAUGEN G., Parametric Stress Analysis ofT-Joints. DnV Report No. 77-523. November 1977. 16. Recommended Fatigue Design Procedure for Hollow Section Joints.Part I: Hot sot stress method for nodal joints. IIW Doc. XllI-1158-85 (XV-582-85). 17. EFTHYMIOU M., Development ofSCF Formulae and Generalized Influence Functions for Use in Fatigue Analysis. Shell International Petroleum, Maastschappij B. V. 18. Van WINGERDE A.M., The Fatigue Design of Welded Joints Made of Square Hollow Sections. Delft University of Tecbnology, Delft, 1992. 182 p. 19. Van WINGERDEA.M., PUTHLIR.S., WARDENIERJ. & DUTTAD., The Fatigue Design of Welded Joints Made of Square Hollow Sections. Proc. Int. Symp. Fatigue and Fracture in Steel and Concrete Structures. Madras, Dec. 1991. nw Doc. XIII-1455-92. 20. MARSHALL P.W., Design of Welded Tubular Connections. Basis and Use of AWS Code Provisions. Developments in Civil Engineering, 37. Elsevier, 1992.412 p. 21. LAWRENCE F.V.,Jr. et al., Predicting the fatigue resistance of welds. FCP Report No. 36. College of Engineering, University of Illinois. Urbana IL, 1980.

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22. YUNG J.-Y. & LAWRENCE F.V.,Jr., Predicting the Fatigue Life of Welds under Combined Bending and Torsion. Report No. 125, College of Engineering, University of Illinois. Urbana IL, 1986,27 p. 23. SILJANDER O.A., Non-proportional Biaxial Fatigue of Welded Joints. Thesis. Graduate College of the University of Illinois. Urbana IL, 1991. 24. RADAJ D., Design and Analysis of Fatigue Resistant Welded Structures. Abington Publishing, 1990. 25. OLIVIER R, & RITTER W., Catalogue of S-N Curves of Welded Joints in Structural Steels. DVS Report No. 56. 26. PETERS HAGEN H., Erfahrungen mit dem Kerbspannungskonzept nach Radaj. DVM-Arbeitskreis Betriebsfestigkeit. Ingolstadt, October 1989. 27. KOTTGEN V.B., OLIVIER R. & SEEGER T., Fatigue Analysis of Welded Connections Based on Local Stresses. IIW-Doc. XIII-1408-91, July 1992. 28. Fatigue Design Handbook. Society of Automotive Engineers, Inc., Warrendale 1968. 129 p. 29. BOLLER Chr. & SEEGER T., Materials data for cyclic loading. Materials Science Monographs, 42 A-E. Elsevier 1987. 30. PAETZ OLD H., Schadigungsparameter-Wohlerlinien fuer normal- und hoherfesten Schiffsbaustahl. Institut fuer Schiftbau der Universitat Hamburg. Report No. 507, 1990. 31. NIU X. & GLINKA G., The weld profile effect on stress intensity factors in weldments. Int J of Fracture, Vol. 35, No.1, pp. 3-20. 32. GURNEY T.R., Fatigue of welded structures. 2nd edition. Cambridge University Press. Cambridge 1979. 33. HOB BACHER A., Recommendations for assessment of weld imperfections in respect to fatigue. IIW-Doc. XIII-1266-88. 34. YAMADA K. & HIRT M.A., Fatigue Crack Propagation from Fillet Weld . Toes. Journal of the Structural Division, ASCE, Vol. 108, No. ST7, July 1982, pp. 1526-1540.

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35. PETERSHAGEN H., FRICKE W. & MASSEL T., Application of the Local Approach to the Fatigue Strength Assessment of Welded Structures in Ships. IIW-Doc. XIII-1409-91 36. RUTHER M. & HENRY J., Recommendation for Hot-Spot Stress Definition in Welded Joints. Bureau Veritas - Research and Development Centre. IIW-Doc. XIII-1416-91. 37. PUTHLI RS., WARDENIER J., de KONlNG C.H.M., WINGERDE A.M. & van DOOREN F .J., Numerical and Experimental Determination of Strain (Stress) Concentration Factors of Welded Joints between Square Hollow Sections. Heron, Vo1.33 (1988) no.2. 50 p. 38. NIEMI E., Aspects of Good Design Practice. In: Fatigue Design, ESIS 16 (Edited by J. Solin, G. Marquis, A. Siljander, and S. Sipila) 1993, Mechanical Engineering Publications, London, pp. 333-351. 39. HUGILL P.N. & SUMPTER J.D.G., Fatigue Life Prediction at a Ship Deck/Superstructure Intersection. Strain, August 1990. pp. 107-112. 40. NIEMI E., On the Determination of Hot Spot Stresses in the Vicinity of Edge Gussets. Doc. IIW XIII-1555-94. Lappeemanta University of Technology, Lappeemanta 1994. 18 p. 41. PARTANEN T., TORVI T. & NIEMI E., On Size Effects in Fatigue of Welded Joints. IIW Doc. XIII-1535-1994. Lappeemanta University of Technology, Lappeemanta 1994. 19 p. 42. HOBBACHER A., Design Recommendations for Cyclic Loaded Welded Steel Structures. IIW-Doc. XIII-998-81. 43. BJORK T., AGIFAP, Advanced Graphical Interactive Frame Analysis Program. Users Manual. Lappeemanfu University of Technology, Dept of Mechanical Engineering. Lappeemanta, Finland, 1990. 44. DALLY J.W. & RILEY W.F., Experimental Stress Analysis. 2nd ed., McGraw-Hill, 1978. 571 p. 45. Manual on Experimental Stress Analysis. 3rd ed., edited by W.H. Tuppeny, Jr. & A.S. Kobayashi. Society for Experimental Mechanics, 1978. &7 p. 46. WINDOW A.L. & HOLISTER G.S., Strain Gauge Technology. Applied Science Publishers, 1982.356 p. 47. YAGI J. et aI., Definition of Hot Spot Stress in Welded Plate Type Structure for Fatigue Assessment. IIW-Doc. XIII-1414-91.