fatigue assessment of welded joints by local approaches second edition

Fatigue assessment of welded joints by local approaches


Related titles:
Cumulative damage of welded joints
(ISBN-13: 978-1-85573-938-3; ISBN-10: 1-85573-938-0)
Written by one of the leading experts in the field, Dr Tim Gurney, this
important book examines fatigue in welded joints, both as a result of constant loads and variable amplitude loading.
Fatigue strength of welded structures Third edition
(ISBN-13: 978-1-85573-506-4; ISBN-10: 1-85573-506-7)
Research on the fatigue behaviour of welded structures has improved our
understanding of the design methods that can reduce premature or progressive fatigue cracking. The latest edition of this standard text incorporates recent research on understanding and preventing fatigue-related
failure through good design.
Fatigue analysis of welded components: designer’s guide to the structural
hot-spot stress approach
(ISBN-13: 978-184569-124-0; ISBN-10: 1-84569-124-5)
This report from the International Institute of Welding provides practical
guidance on the use of the hot-spot stress approach to improve both the
fatigue analysis and design of welded structures.
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Fatigue assessment
of welded joints

by local approaches
Second edition
D Radaj, C M Sonsino and W Fricke

Woodhead Publishing and Maney Publishing
on behalf of
The Institute of Materials, Minerals & Mining
CRC Press
Boca Raton Boston New York Washington, DC

Cambridge England


Woodhead Publishing Limited and Maney Publishing Limited on behalf of
The Institute of Materials, Minerals & Mining
Woodhead Publishing Limited, Abington Hall, Abington, Cambridge CB1 6AH,
England
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Published in North America by CRC Press LLC, 6000 Broken Sound Parkway,
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First published 1998 by Abington Publishing, an imprint of Woodhead Publishing
Limited
Second edition 2006, Woodhead Publishing Limited and CRC Press LLC
© Woodhead Publishing Limited, 2006
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Contents

Foreword
Preface
Author contact details
1

Introduction

1

1.1

1
1

1.2

2

xv
xvii
xix

Fatigue strength assessment of welded joints
1.1.1
Present state of the art

1.1.2
Demands from industrial
product development
Basic aspects of assessment procedures
1.2.1
Multitude of parameters governing
fatigue failure
1.2.2
Global and local approaches of fatigue
strength assessment
1.2.3
Complications of local approaches for
welded joints
1.2.4
Survey of subject arrangement

2
3
3
5
8
10

Nominal stress approach for welded joints

13

2.1

13

13
13
16

2.2

Basic procedures
2.1.1
Principles of the nominal stress approach
2.1.2
Procedures for welded joints
Analysis tools
2.2.1
Books, compendia, guidelines and
design codes
2.2.2
Basic formulae
2.2.3
Permissible stresses and design S–N curves
2.2.4
Influence of mean and residual stresses
2.2.5
Influence of stress multiaxiality
2.2.6
Influence of plate thickness, weld dressing
and environment

16
16
19

23
24
27
v


vi

Contents
2.2.7
2.2.8

3

Normalised S–N curves
Fatigue strength reduction factors

28
29

Structural stress or strain approach for
seam-welded joints

33

3.1

33

3.2

3.3

Basic procedures
3.1.1
Principles of the structural stress or
strain approach
3.1.2
Structural strain approach as proposed
by Haibach
3.1.3
Hot spot structural stress approach for
tubular joints
3.1.4
Hot spot structural stress approach for
non-tubular joints
3.1.5
Alternative definitions of hot spot
structural stress
3.1.6
Structural stress approach as proposed
by Dong
3.1.7
Structural stress approach as proposed
by Xiao–Yamada
3.1.8
Structural stress approach to weld
root fatigue
Analysis tools – structural stress or
strain evaluation

3.2.1
General survey and relevant guidelines
3.2.2
Evaluation of hot spot stresses in
tubular joints
3.2.3
Evaluation of hot spot stresses in
non-tubular joints
3.2.4
Specific rules for finite element modelling
3.2.5
Further variants of structural
stress evaluation
3.2.6
Definition of structural stress
concentration factors
3.2.7
Hot spot stress concentration factors for
tubular joints
3.2.8
Hot spot stress concentration factors for
non-tubular joints
Analysis tools – endurable structural stresses
or strains
3.3.1
Endurable structural strains in
the Haibach approach

33
34

37
40
40
41
43
44
45
45
46
48
51
55
57
59
61
62
62


Contents
3.3.2
3.3.3

3.4

4

Endurable hot spot stresses in tubular joints
Endurable hot spot stresses in
non-tubular joints

3.3.4
Endurable structural stresses in the Dong and
Xiao–Yamada approaches
3.3.5
Endurable multiaxial stresses or strains
3.3.6
Structural stress based assessment of weld
root fatigue
Demonstration examples
3.4.1
Welded tubular and butt joints – structural
strain approach
3.4.2
Welded tubular joints – various
design guidelines
3.4.3
Welded bridge girder with cope holes
3.4.4
Welded joints in ship structures – weld
toe fatigue
3.4.5
Welded joints in ship structures – weld
root fatigue

vii
62
65
68
70
73

81
81
82
84
84
89

Notch stress approach for seam-welded joints

91

4.1

91

4.2

Basic procedures
4.1.1
Principles and variants of the notch
stress approach
4.1.2
Critical distance approach
4.1.3
Fictitious notch rounding approach
4.1.4
Modified notch rounding approach
4.1.5
Highly stressed volume approach
Analysis tools

4.2.1
General survey and assessment procedure
4.2.2
Notch stress analysis for welded joints
4.2.3
Notch stress concentration factors of
welded joints
4.2.4
Fatigue notch factors of welded joints
4.2.5
Critical distance approach
4.2.6
Fictitious notch rounding approach –
basic procedures
4.2.7
Fictitious notch rounding approach –
refined procedures
4.2.8
Fictitious notch rounding approach –
links to structural stresses
4.2.9
Modified notch rounding approach
4.2.10 Highly stressed volume approach

91
94
96
101
105
105

105
107
108
121
125
126
131
138
143
145


viii

Contents
4.3

4.4

5

150
150
152
155
157
158
160
161
163

165
166
166
173
180
186

Notch strain approach for seam-welded joints

191

5.1

191
191
195
199
202
202
202
206
212
213
214

5.2

5.3

6

Demonstration examples
4.3.1
Welded vehicle frame corner
4.3.2
Web stiffener of welded I section girder
4.3.3
Stress relief groove in welded pressure vessel
4.3.4
End-to-shell joint of boiler
4.3.5
Stiffener-to-flange joint at ship frame corner
4.3.6
Girth butt welds of unusual manufacture
4.3.7
Tensile specimen with longitudinal
attachment
4.3.8
Gusseted shell structure
4.3.9
Laser beam welded butt and cruciform joints
Design-related notch stress evaluations
4.4.1
Comparison of basic welded joint types
4.4.2
Comparison of basic weld loading modes
4.4.3
Effect of geometrical weld parameters
4.4.4
Typical application in design

Basic procedures
5.1.1
Principles of the notch strain approach
5.1.2
Early application of the approach
5.1.3
Comprehensive exposition of the approach
5.1.4
Further refinements of the approach
Analysis tools
5.2.1
Basic formulae in early applications
5.2.2
Basic formulae for wider application
5.2.3
Special formulae for multiaxial fatigue
5.2.4
Assessment procedure
Demonstration examples
5.3.1
Fatigue life of stress-relieved
butt-welded joints
5.3.2
Fatigue life of butt-welded joints with
residual stresses
5.3.3
Fatigue life of fillet-welded cruciform joints
5.3.4
Fatigue life of welded containment detail

5.3.5
Fatigue strength of welded tubular joint

214
217
221
224
227

Crack propagation approach for seam-welded joints

233

6.1

233
233
235
237
240

Basic procedures
6.1.1
Principles of the crack propagation approach
6.1.2
Peculiarities with seam-welded joints
6.1.3
Short-crack behaviour
6.1.4
Applications of the approach

Contents
6.2

6.3

7

Analysis tools
6.2.1
General survey and relevant references
6.2.2
Methods of stress intensity factor
determination
6.2.3
Crack propagation equations
6.2.4
Crack propagation life
6.2.5
Stress intensity factors for welded joints
6.2.6
Crack shape and crack path
6.2.7
Material parameters of crack propagation
6.2.8
Initial and final crack size
6.2.9
Residual stress effects on crack propagation
6.2.10 Particular crack propagation approach

6.2.11 Refined crack propagation approach
Demonstration examples
6.3.1
Longitudinal and transverse
attachment joints
6.3.2
Cruciform and T-joints
6.3.3
Lap joints and cover plate joints
6.3.4
Butt-welded joints
6.3.5
Refined analysis of longitudinal
attachment joint

ix
242
242
243
245
247
250
259
263
267
268
271
275
279
279

281
286
287
292

Notch stress intensity approach for seam-welded joints 296
7.1

7.2

7.3

General considerations
7.1.1
Formal aspects of presentation
7.1.2
Principles and variants of the approach
Basic procedures and results
7.2.1
Notch stress intensity at sharp
corner notches
7.2.2
Notch stress intensity at blunt
corner notches
7.2.3
Plastic notch stress intensity at
corner notches
7.2.4
J-integral at corner notches
7.2.5

Strain energy density at corner notches
7.2.6
Fatigue limit expressed by notch stress
intensity factors
Procedures and results for fillet-welded joints
7.3.1
Notch stress intensity factors for
fillet-welded joints
7.3.2
Stress rise in front of fillet welds
7.3.3
Endurable notch stress intensity factors of
fillet-welded joints

296
296
296
297
297
301
304
307
308
310
313
313
317
319

x

Contents
7.3.4

7.4
8

Local approaches applied to a seam-welded tubular
joint
8.1
8.2

8.3
8.4

8.5

8.6
9

Endurable corner notch J-integral of
fillet-welded joints
7.3.5
Endurable corner notch strain energy
density of fillet-welded joints
7.3.6
Link to the crack propagation approach
7.3.7
Link to the hot spot structural stress approach

Weak points and potential of the approach

Subject matter of investigation
Application of the structural stress or strain
approach
8.2.1
Structural stress analysis and
strain measurement
8.2.2
Comparison of structural stress
concentration factors
8.2.3
Fatigue test results in terms of hot spot stress
Application of the elastic notch stress approach
Application of the elastic-plastic notch
strain approach
8.4.1
Notch stress and strain concentration at
weld toe
8.4.2
Fatigue strength assessment based on
notch strains
Application of the crack propagation approach
8.5.1
Basic crack propagation models
8.5.2
Crack propagation life according to
EU Report
8.5.3
Crack propagation life according to

British Standard
Method-related conclusions

321
322
323
326
332

334
334
336
336
340
343
345
348
348
351
355
355
358
362
363

Structural stress or strain approach for spot-welded
and similar lap joints

366

9.1

366

Basic procedures
9.1.1
Significance of fatigue assessment of
spot-welded and similar lap joints
9.1.2
Principles of the structural stress approach
9.1.3
Weak points of the structural
stress approach
9.1.4
Application of the structural stress approach

366
367
371
372


Contents
9.2

9.3

9.4

9.5

Analysis tools – structural stress or strain evaluation
9.2.1
General survey
9.2.2
Modelling of weld spot resultant forces
9.2.3
Computation and decomposition of weld spot
resultant forces
9.2.4
General theory of forces and stresses at
weld spots
9.2.5
Structural stress analysis at weld spots
9.2.6
Nominal structural stress in plate at weld
spot
9.2.7
Nominal structural stress in nugget at weld
spot
9.2.8
Structural strain measurement at weld spots
9.2.9
Weld spot forces by correlation of
strain patterns
Analysis tools – non-linear structural behaviour
9.3.1
Elastic-plastic deformation at weld spots
9.3.2
Large deflections at weld spots subjected to

tensile-shear loading
9.3.3
Large deflections at weld spots subjected to
cross-tension loading
9.3.4
Buckling fatigue at spot welds
Analysis tools – endurable structural stresses
or strains
9.4.1
Endurable structural stresses or strains at
weld spots compiled by Radaj
9.4.2
Endurable structural stresses at weld spots
compiled by Rupp
9.4.3
Endurable structural stresses at weld spots
compiled by Maddox
9.4.4
Endurable structural stresses at laser beam
welds in comparison
9.4.5
Endurable structural stresses at
GMA welds
9.4.6
Computer codes for fatigue assessment
at weld spots
9.4.7
Fatigue life assessment supporting car
body design
Demonstration examples

9.5.1
Spot-welded axle suspension arm
9.5.2
Spot-welded engine support member
9.5.3
Laser beam welded pillar-to-rocker
connection

xi
373
373
373
376
380
382
383
388
389
392
393
393
395
398
400
405
405
411
417
417
420

426
427
429
429
430
432


xii

Contents

10

Stress intensity approach for spot-welded and similar
lap joints
10.1 Basic procedures
10.1.1 Principles of the stress intensity
approach
10.1.2 Weak points of the stress intensity
approach
10.1.3 Links to other approaches and
application relevance
10.2 Analysis tools – evaluation of stress intensity
factors
10.2.1 General survey and basic definitions
10.2.2 Stress intensity factors of lap joints based on
structural stresses
10.2.3 Stress intensity factors of lap joints with
unequal plate thickness

10.2.4 Stress intensity factors of lap joints in
dissimilar materials
10.2.5 Stress intensity factors of lap joints under
large deflections
10.2.6 Early stress intensity factor solutions for
lap joints
10.2.7 Stress intensity factor formulae based on
nominal structural stresses
10.2.8 Links to the notch stress approach
10.3 Analysis tools – fatigue assessment based on stress
intensity factors
10.3.1 Endurable stress intensity factors
10.3.2 Equivalent stress intensity factors under
mixed mode conditions
10.3.3 J-integral and nugget rotation variants
10.4 Comparative evaluation of spot-welded and
similar specimens
10.4.1 General survey
10.4.2 Spot-welded tensile-shear specimens
10.4.3 Spot-welded cross-tension and
peel-tension specimens
10.4.4 Spot-welded hat section specimens
10.4.5 Spot-welded H-shaped specimens
10.4.6 Spot-welded double-cup specimens
10.4.7 Laser beam-welded tensile-shear and
peel-tension specimens

433
433
433

436
442
443
443
447
453
457
459
461
465
467
471
471
476
482
483
483
486
490
493
501
507
510


Contents
11

12

Notch- and crack-based approaches for spot-welded
and similar lap joints

xiii

513

11.1 Basic procedures
11.1.1 Principles of the notch stress, notch strain
and crack propagation approaches
11.1.2 Weak points and potential of the notch
stress approach
11.1.3 Weak points and potential of the notch
strain approach
11.1.4 Weak points and potential of the crack
propagation approach
11.2 Analysis tools
11.2.1 Fatigue assessment through conventional
notch stress approach
11.2.2 Fatigue assessment through improved
notch stress approach
11.2.3 Fatigue assessment through notch
strain approach
11.2.4 Fatigue assessment through simplified
small-size notch approach
11.2.5 Fatigue assessment through crack
propagation approach
11.2.6 Residual stress distribution in
spot-welded joints
11.2.7 Hardness distribution in spot-welded joints

11.3 Comprehensive modelling examples
11.3.1 General survey
11.3.2 Modelling examples presented by Lawrence
11.3.3 Modelling examples presented by Sheppard
11.3.4 Modelling examples presented by Henrysson
11.3.5 Modelling example presented by Nykänen

513

542
547
550
550
551
556
559
566

Significance, limitations and potential of local
approaches

568

12.1 Significance of local approaches
12.2 Limitations of local approaches
12.3 Potential of local approaches

568
570
576

Bibliography
Index

579
635

513
517
518
522
524
524
527
531
535
538



Foreword

Fatigue design of welded components and structures is normally based on
S–N curves, often contained in official codes or standards. Such S–N curves
are usually derived from published test data obtained from fatigue tests on
representative welded specimens and expressed in terms of nominal stress.
However, there are important limitations to this approach that can be
addressed using local approaches.
Perhaps the most important limitation arises from the rapidly increasing
use, by a wide range of industries, of detailed stress analysis (e.g. finite

element analysis) in design. The distinction between nominal and local
stresses is not always clear, but an alternative design approach based on
structural stress allows better utilisation of modern stress analysis methods.
Other limitations prompt the need for ways of modelling the fatigue
process, rather than simply relating applied stress and fatigue life as in the
S–N curve. In particular, there is little scope for allowing for differences
(e.g. geometry, welding process, material, defects) between the weld detail
under consideration and those tested to generate the S–N curve. Furthermore, no information is provided by the S–N curve about the progress of
fatigue damage, only the total fatigue life is presented. Local approaches
based on the notch stress (or local strain) method and/or fracture mechanics attempt to model the whole fatigue process by considering the influence
of all significant parameters.
The first edition of this book presented a systematic survey of the various
local approaches to the fatigue assessment of weld details, including the
basis of each method, background research, development and practical
applications. That survey has been updated and built on in this second
edition, with particular attention to the important new research done to
develop the structural hot spot stress, notch stress and crack propagation
approaches. Of special value is the increased coverage of the application of
local approaches in the assessment of joints in thin-sheet structural components. The addition of Wolfgang Fricke as author, with his extensive experience of the fatigue design and performance of ships and other large
xv


xvi

Foreword

welded structures, complements the already wide experience Dieter Radaj
and Morris Sonsino bring from the automotive, offshore, aircraft and
mechanical engineering industries. The resulting authoritative new book
provides a valuable aid to designers of fatigue-loaded welded structures

from any industry, to broaden their design capabilities beyond the use of
basic S–N curves, but also to prepare them for the inevitable changes to
come in current fatigue design standards. It will also help teachers and those
concerned with fatigue R&D who need a broad overview of modern fatigue
assessment methods and significant published work.
Stephen Maddox
Chairman, Commission XIII, International Institute of Welding


Preface

In the interval of nearly one decade since publication of the first edition
of Fatigue assessment of welded joints by local approaches substantial
progress has been achieved in methods development and application of
local approaches. Structural strength and durability assessment based on
these approaches have become a vital part of design verification and optimisation, especially in combination with finite element analysis. Welded
joints are of primary concern within these assessments because fatigue
failures originate mostly from these areas of geometric and material
discontinuity.
The task of the first edition was to review the available knowledge on
local approaches to the fatigue assessment of welded joints, to gather the
data necessary for their practical application and to demonstrate the power
of the local concept by way of demonstration examples from research and
industry. It covered the hot spot structural stress approach, the elastic notch
stress and elastic-plastic notch strain approaches describing crack initiation,
and the fracture mechanics approach covering crack propagation. Seamwelded and spot-welded joints in structural steels and aluminium alloys
were mainly considered.
The task of the second edition is to add new developments and applications while tightening up the older material. Progress has been tremendous
during the last decade, the number of references considered in the book
jumping up to nearly one thousand. These developments were set off by

increasing demands in automobile design, ocean engineering and shipbuilding among other fields of application. Major method extensions refer
to the hot spot structural stress approach, to the notch stress or strain
concept with very small notch radius applicable to thin-sheet structural
components and to the crack propagation methods. The notch stress intensity factor approach with application to seam-welded joints is now discussed
as a new assessment method. The chapters of the book are rearranged, the
first part of the book comprising seam-welded joints, the second part spotwelded and similar lap joints. The second edition is completely reworked.
xvii


xviii

Preface

The cooperation of three authors in doing this guarantees a versatile and
balanced presentation.
The book is intended for designers, structural analysts and testing engineers who are responsible for the fatigue-resistant in-service behaviour of
welded structures. It should become a reference work for researchers in the
field, and it should support activities directed to standardisation of local
approaches. Last but not least, it should give guidance to those students and
experts who want to know more about the theoretical background and
experimental confirmation of these methods. This book on fatigue assessment of welded joints supplements the first author’s German work Ermüdungsfestigkeit covering the fundamentals of fatigue of non-welded
materials and structural components.
The authors wish to express their sincere thanks to Steve Maddox, Chairman of Commission XIII ‘Fatigue behaviour of welded components and
structures’ in the International Institute of Welding (IIW), for his appreciative foreword. They gratefully acknowledge the support given by the following colleagues in the correct presentation of some data in the second
edition: Pingsha Dong, Hans-Fredrik Henrysson, Adolf Hobbacher and
Paolo Lazzarin. The last-mentioned scientist has comprehensively supported the expositions on the notch stress intensity approach for seamwelded joints.
The many insertions into the manuscript of the second edition were put
into a well-executed typescript by Claudia Raschke whose effective service
facilitated the authors’ tasks substantially. The graphical artwork added to
the second edition was prepared with great skill by Herbert Jäger. The

authors are greatly indebted to these two persons.
It has been a pleasure working with Woodhead Publishing and the copyeditor, Marilyn Grant, who converted the complex reworked manuscript
into a handbook of high quality.
Dieter Radaj, Cetin Morris Sonsino and Wolfgang Fricke


Author contact details

Prof Dr-Ing Dieter Radaj, fax: +49 (0)711 440 3163
Prof Dr-Ing Cetin Morris Sonsino, email:
Prof Dr-Ing Wolfgang Fricke, email:

xix



1
Introduction

1.1

Fatigue strength assessment of welded joints

1.1.1 Present state of the art
Fatigue failure of structural members, comprising crack initiation, crack
propagation and final fracture is an extremely localised process in respect
of its origin. Therefore, the local parameters of geometry, loading and
material have a major influence on the fatigue strength and service life of
structural members. They must be taken into account as close to reality as
possible when performing fatigue strength assessments and especially so

when optimising the design in respect of fatigue resistance.
Design rules for fatigue-resistant structures, on the other hand, take local
effects only roughly into account. They are based mainly on the nominal
stress approach, which is a global concept in principle. The permissible
nominal stresses depend on the ‘notch class’, ‘detail class’ or ‘fatigue class’
(FAT) of the welded joint being considered. They are supplemented by
general design recommendations.
The code-related state of the art is unsatisfactory in those fields of engineering where structural members are subjected to fatigue-relevant variable load amplitudes with appreciable numbers of cycles or where nominal
stresses cannot be meaningfully defined. Local concepts are applied in these
areas based on local strain measurements, mainly by strain gauges, and by
local stress calculations mainly based on the finite element method. Both
the testing engineer and the structural analyst urgently need well-founded
methods for evaluating these local stresses and strains in respect of fatigue
strength and service life.
These needs can be met only insufficiently if at all. The multitude of proposals on how to assess the fatigue resistance of structural members based
on local parameters is difficult to overview and evaluate.1 Different fields
of engineering, ‘schools’ of researchers and national communities prefer
different approaches. All proposals are more or less incomplete in respect
of user demands, and the local parameter data, for the most part, lack
1


2

Fatigue assessment of welded joints by local approaches

statistical proof. As a result, the application of local approaches lags behind
the possibilities provided by computerised structural analysis.

1.1.2 Demands from industrial product development

The demands originating from industrial product development concerning
local approaches are twofold:
–
–

An overview covering methods and data available for application is
needed.
Standardisation of the procedures and their incorporation into design
codes are required.

This book is intended mainly to satisfy the first demand. Industrial users
should obtain all the available information so that they can decide on the
best way to treat their individual fatigue problems on the basis of local
approaches. They must then supplement the information available from the
book and the quoted literature by their own empirical and experimental
data.
The second demand can only partly be satisfied. There is no generally
acknowledged theory of local fatigue strength available on which a uniform
analytical scheme could be based. On the one hand there are manifold procedural variants and data sets and on the other hand there are innumerable fatigue problems in industry. Any general standardisation of the local
approaches would interfere with the development of further methods,
which must always be adapted to the application being considered. Only
carefully selected parts of the procedure are suited to standardisation or at
least to defining a guideline. Substantial progress with regard to the standardisation of analytical strength assessments based on local stresses (structural or notch stresses) has been achieved by the IIW recommendations3
and by the FKM guideline.1
The subjects in this book are restricted to welded joints, which are of
paramount economic relevance. Additionally, welded joints show peculiarities in respect of fatigue behaviour which make a separate treatment of the
fatigue assessment methods desirable. Finally, part of the local approaches
has been developed for welded joints independently of the methods developed for non-welded members. Restriction to welded joints is therefore
well justified.
The following books give additional guidance on fatigue assessment of

welded joints by local approaches: Haibach2 (in-service fatigue strength,
highly related to design, emphasis on analysis and statistics) and Radaj4
(also related to design, covers early stage of development of local
approaches). The contribution by Seeger8 in a more general handbook lays
emphasis on assessment methods with inclusion of variable-amplitude and


Introduction

3

multiaxial loading conditions. The fundamentals of the analysis of fatigue
strength and its application to non-welded members are presented in books
by Haibach,2 Dowling951 and Radaj.6 The analysis of welding residual
stresses and distortion is found in Radaj’s book.7

1.2

Basic aspects of assessment procedures

1.2.1 Multitude of parameters governing fatigue failure
The local approaches to fatigue assessment reviewed in this book aim to
cover the dominating parameters of extremely complex physical processes
in order to make them controllable by the engineer. These processes
comprise primarily microstructural phenomena (moving dislocations,
micro-crack initiation on slip bands and further crack growth by local slip
mechanisms at the crack tip) but can be approximately described by a
macroscopic elastic or elastic-plastic stress and strain analysis according
to continuum mechanics which refers to the cyclic deformation causing
initiation and propagation of the ‘technical crack’ with inclusion of the

final fracture, Fig. 1.1. A technical crack is considered to have been
initiated (usually at the surface) if its surface length reaches values which
can be detected by common technical means, e.g. 1 mm, and its depth
0.5 mm.
The initiation of the technical crack by cyclic loading under definite local
material conditions is primarily governed by the amplitudes of the cyclic
stress and strain components at the notch root, with the volume of the
highly stressed material, the multiaxiality of the cyclic stress state and its
static mean value (possibly fluctuating) also being of importance. The total
number of parameters influencing the critical values of the cyclic stress and
strain components which describe crack initiation are summarised in Table
1.1 which refers to the local approach insofar as local stresses and strains
are introduced to characterise the loading type. The number of influencing
parameters is large, but can be handled within the procedure of strength
assessment. However, a problem arises from the restricted possibilities of
decoupling the effects of these influencing parameters in the case of engineering tasks.

Dislocation
movement

Crack
nucleation

Crack initiation (physical)
Crack initiation (technical)

Microcrack
propagation

Macrocrack

propagation

Crack propagation (stable)

Final
fracture
C. p. (unstable)

Crack propagation (technical)

Fig. 1.1. Micro- and macrophenomena of material fatigue.


4

Fatigue assessment of welded joints by local approaches

Table 1.1. Parameters governing fatigue crack initiation; after Radaj5
Structural member

Surface

Material

Shape
Size
Dimensions

Roughness
Hardness

Residual stress

Type
Alloy
Microstructure

Loading type

Loading course

Environment

Stress amplitude
Mean stress including residual stress
Multiaxiality including phase angle

Amplitude spectrum
Amplitude sequence
Rest periods

Temperature
Corrosion

Crack propagation by cyclic loading is primarily governed by the amplitudes of the cyclic stress intensity factor or of the cyclic J-integral at the
crack tip. Most of the parameters which determine the critical value of
stress, strain or energy at the crack tip causing crack propagation are identical to those which cause crack initiation. Only the influence of the surface diminishes whereas crack shape, crack size and crack path gain in
importance.
The multitude of parameter constellations governing fatigue are advantageously structured according to Haibach,2 based on the main testing and
analysis procedures used to obtain the above-mentioned critical values for
fatigue strength or service life assessments, Fig. 1.2.

The description of fatigue strength proceeds from the S–N curve
(nominal stress amplitude versus number of cycles) of the unnotched specimen (a). The S–N curve of the notched specimen (b) is gained therefrom
by considering the stress concentration factor and the notch radius. Finally,
the S–N curve of the structural component (c) results from additionally
considering size and surface effects (including residual stresses). This path
a–b–c or e–f–g is connected with the problem of strength dependent on
shape and size (German idiom ‘Gestaltfestigkeit’). On the other hand, the
fatigue life curve resulting from variable-amplitude loading can be derived
from the S–N curve resulting from constant-amplitude loading by introducing a damage accumulation hypothesis. This is the path a–e, b–f or c–g
from conventional fatigue strength to service fatigue strength. The problem
of damage accumulation can be partly solved by determining the fatigue
life curve of the notched specimen under standard load sequences, path
d–f–g instead of c–g.
The structuring of the parameter field and procedures mentioned above
does not mean that every fatigue strength assessment starts with the S–N
curve of the unnotched specimen and ends with the life curve of the struc-