Foreword ..................................................... xiii
Chapter 1.
Introduction to Fatigue: Fundamentals and Methodology ........... 1
André Pineau and Claude Bathias
1.1 Introduction to the fatigue of materials ................... 1
1.1.1 Brief history of fatigue: its technical and
scientific importance ............................... 1
1.1.2 Definitions ......................................... 6
1.1.3 Endurance diagrams .................................. 8
1.2 Mechanisms of fatigue damage .............................. 10
1.2.1 Introduction/background ............................ 10
1.2.2 Initiation of fatigue cracks ....................... 10
1.2.3 Propagation of fatigue cracks ...................... 12
1.3 Test systems .............................................. 13
1.4 Structural design and fatigue ............................. 15
1.5 Fatigue of polymers, elastomers and composite materials ... 16
1.6 Conclusion ................................................ 18
1.7 Bibliography .............................................. 19
Chapter 2
Modeling of Fatigue Strength and Endurance Curve ............... 23
Henri-Paul Lieurade
2.1 Introduction .............................................. 23
2.2 Nature and aspect of the scatter of fatigue test
results ................................................... 25
2.3 Determination of the endurance limit ...................... 27
2.4 Estimation methods of fatigue resistance and standard
deviation with TV cycles .................................. 27
2.4.1 Probit method ...................................... 28
2.4.2 Staircase method ................................... 33
2.4.3 Iteration method ................................... 36
2.4.4 Non-failed specimen method ......................... 41
2.4.5 Choice of test method .............................. 46
2.5 Mathematical representations and plotting methods of the
Wöhler curve .............................................. 47
2.5.1 Introduction ....................................... 47
2.5.2 Mathematical representation of the Wöhler curve .... 48
2.5.3 Adjustment methods of a Wöhler curve to test
results ............................................ 53
2.6 Estimation of the cycle number N for a given level of
stress amplitude .......................................... 55
2.6.1 Principle .......................................... 57
2.6.2 Set-up ............................................. 57
2.6.3 Application ........................................ 58
2.7 Influence of mechanical parameters on endurance ........... 59
2.7.1 Influence of the mean stress ....................... 59
2.7.2 Influence of the nature of forces .................. 60
2.8 Relationship between endurance and mechanical
characteristics (of steels) ............................... 62
2.8.1 Estimations of σD .................................. 62
2.8.2 Estimation of standard deviations .................. 65
2.8.3 Conclusion ......................................... 65
2.9 Bibliography .............................................. 66
Chapter 3
Fatigue Crack Initiation ....................................... 69
Paul Rabbe and Louis Anquez
3.1 Introduction .............................................. 69
3.2 Physical mechanisms of crack initiation ................... 70
3.2.1 Three stages of fatigue failure: a reminder ........ 70
3.2.2 Influence of stress amplitude ...................... 72
3.3 Methods of evaluating crack initiation .................... 81
3.3.1 Smooth specimens ................................... 81
3.3.2 Notch effect ....................................... 83
3.4 Practical method of structure calculation ................. 97
3.4.1 Preliminary ........................................ 97
3.4.2 The problem to be solved ........................... 99
3.4.3 Initiation parameters ............................. 100
3.4.4 The master Wöhler curve (kt = 1) .................. 101
3.4.5 Cumulative damage (kt = 1) ........................ 103
3.4.6 Specimens with kt > 1: correspondence curve ....... 104
3.4.7 Use of correspondence curves ...................... 107
3.4.8 Plotting the correspondence curves ................ 107
3.4.9 Comments and conclusion ........................... 108
3.5 Bibliography ............................................. 109
Chapter 4
Low-cycle Fatigue ............................................. 113
André Pineau
4.1 Introduction ............................................. 113
4.1.1 Application domain of low cycle plastic fatigue ... 113
4.1.2 General description of the test methods: main
issues ............................................ 116
4.2 Phenomenological description of low-cycle fatigue ........ 122
4.2.1 Background ........................................ 122
4.2.2 Cyclic work hardening ............................. 122
4.2.3 Cyclic stress-strain relationships ................ 125
4.2.4 Fatigue strength .................................. 129
4.2.5 Mathematical equations ............................ 130
4.2.6 General behavior: sequence effects and control
mode .............................................. 133
4.3 Adaptation mechanism and cracking during low-cycle
fatigue .................................................. 134
4.3.1 Introduction ...................................... 134
4.3.2 Adaptation of the material ........................ 135
4.3.3 Description and elementary interpretation of the
adaptation stage within structural alloys:
steels ............................................ 151
4.3.4 Crack initiation in LCF ........................... 164
4.3.5 Crack propagation in LCF .......................... 169
4.4 Conclusion ............................................... 172
4.5 Acknowledgements ......................................... 172
4.6 Bibliography ............................................. 173
Chapter 5
Gigacycle Fatigue ............................................. 179
Claude Bathias
5.1 Introducing the real-life fatigue life of machines ....... 179
5.2 Testing process .......................................... 181
5.2.1 Piezoelectric machines ............................ 181
5.2.2 Principle of vibratory fatigue .................... 181
5.2.3 Calculation of resonance lengths .................. 184
5.2.4 Calculation of the specimens ...................... 184
5.2.5 Calculation of the sonotrodes ..................... 186
5.3 Systems of piezoelectric fatigue machines ................ 188
5.4 SN curves above 107 cycles ............................... 190
5.4.1 General aspects of SN curves ...................... 190
5.4.2 Case of ferrous metals ............................ 193
5.4.3 Case of aluminum alloys ........................... 208
5.5 Initiation mechanism under gigacycle fatigue ............. 209
5.5.1 Non-metallic inclusions ........................... 210
5.5.2 Metallurgic defects within the matrix ............. 211
5.5.3 Microporosities ................................... 211
5.6 Assessing fatigue strength ............................... 219
5.6.1 Comparison between the staircase, Bastenaire,
Wöhler, Basquin and Stromeyer/linear methods ...... 219
5.6.2 Kitawaga diagram under gigacycle fatigue .......... 221
5.6.3 Assessment of initiation fatigue life using the
ITMA model and Paris-Hertzberg law ................ 222
5.6.4 Prediction of fatigue strength using the
Murakami model .................................... 225
5.7 Conclusion ............................................... 226
5.8 Bibliography ............................................. 226
Chapter 6
Fatigue Crack Growth Laws ..................................... 231
Jacques Masounave, Jean-Paul Baïlon and John-Ivan Dickson
6.1 Introduction ............................................. 231
6.2 Models describing crack propagation ...................... 232
6.2.1 Phenomenological models ........................... 232
6.2.2 Models based on dislocation theory ................ 237
6.2.3 Models based on the behavior of a material at
the crack-tip ..................................... 241
6.2.4 Models based on the cyclic properties of the
material .......................................... 244
6.3 Critical evaluation of the models ........................ 249
6.3.1 Influence of the parameters of cyclic behavior .... 249
6.3.2 Equations between m and С ......................... 252
6.3.3 Influences of the intrinsic parameters on
cracking .......................................... 254
6.3.4 Influence of the parameters extrinsic to
cracking .......................................... 256
6.4 Future plans ............................................. 258
6.5 Conclusion ............................................... 260
6.5.1 Metallurgic parameters ............................ 260
6.5.2 Extrinsic parameters .............................. 261
6.6 Bibliography ............................................. 261
Chapter 7
Short Crack Propagation ....................................... 269
Yves Verreman
7.1 Introduction ............................................. 269
7.2 Theoretical considerations showing the limits of LEFM .... 271
7.2.1 Propagation of cracks from a smooth edge:
Kitagawa diagram .................................. 271
7.2.2 Propagation of cracks from a macroscopic notch
root: Frost diagram ............................... 273
7.3 Experimental observations ................................ 275
7.3.1 Propagation rates of short cracks ................. 275
7.3.2 Microstructurally short cracks .................... 277
7.3.3 Mechanically short cracks ......................... 280
7.4 Role of closure in the behavior of short cracks .......... 285
7.4.1 Closure of fatigue cracks ......................... 285
7.4.2 Development of the closure of short cracks ........ 287
7.4.3 Correlation between propagation rates and
ΔKeff .............................................. 289
7.4.4 Roughness-induced crack closure ................... 290
7.5 Modeling of the behavior of short cracks ................. 291
7.5.1 Modeling of microstructurally short cracks ........ 291
7.5.2 Modeling of mechanically short cracks ............. 296
7.6 Conclusion ............................................... 302
7.7 Acknowledgements ......................................... 303
7.8 Bibliography ............................................. 303
Chapter 8
Plastic Deformation Mechanisms at the Crack Tip ............... 311
Claude Bathias
8.1 Introduction ............................................. 311
8.2 Fatigue plastic deformation at the crack tip ............. 312
8.2.1 Theoretical aspect ................................ 312
8.2.2 Experimental trials ............................... 318
8.2.3 Crystallographic aspects .......................... 320
8.3 Microfractographic aspects of the fatigue crack .......... 323
8.3.1 Fractographic observations ........................ 323
8.3.2 Mechanisms of striation formation ................. 324
8.4 Model based on displacement on crack tip opening ......... 328
8.5 Cyclic stress hardening at the crack tip ................. 331
8.6 Model based on the effective stress intensity factor ..... 334
8.6.1 Elber's model .................................... 334
8.6.2 Application of Elber's model ...................... 336
8.6.3 interpretation of the fundamental mechanisms ...... 337
8.7 Conclusion ............................................... 342
8.8 Bibliography ............................................. 343
Chapter 9
Local Approach to Fatigue Crack Growth ........................ 347
Sylvie Pommier
9.1 Introduction ............................................. 347
9.2 Plasticity at the crack tip .............................. 348
9.2.1 Irwin's plastic zones ............................. 348
9.2.2 T-Stress effect ................................... 351
9.2.3 Role of strain hardening of the material .......... 352
9.3 Cyclic plasticity at the crack tip ....................... 355
9.3.1 Cyclic elastic-plastic behavior of the
material .......................................... 355
9.3.2 Plasticity induced history effect in fatigue
crack growth ...................................... 357
9.4 Local approach to fatigue crack growth ................... 366
9.4.1 Approach .......................................... 366
9.4.2 Scale-up method ................................... 367
9.4.3 Application ....................................... 370
9.4.4 Extensions ........................................ 372
9.5 Conclusion ............................................... 372
9.6 Bibliography ............................................. 373
Chapter 10
Corrosion Fatigue ............................................. 377
Regis Pelloux and Jean-Marc Genkin
10.1 Introduction ............................................. 377
10.2 Crack initiation .................................... 378
10.2.1 Aqueous medium ............................... 378
10.2.2 Gaseous environment .......................... 383
10.3 Short cracks ........................................ 384
10.4 Long crack propagation .............................. 385
10.4.1 Experimental observations .................... 385
10.4.2 Corrosion fatigue models ..................... 393
10.5 Conclusions ......................................... 397
10.6 Bibliography ........................................ 397
Chapter 11
Effect of Environment ......................................... 401
Jean Petit and Christine Sarrazin-Baudoux
11.1 Introduction ............................................. 401
11.2 Effect of environment on lifetime under high-cycle
fatigue conditions ....................................... 403
11.2.1 Initial work ...................................... 403
11.2.2 Mechanisms ........................................ 404
11.2.3 Influence of atmospheric pressure and frequency ... 407
11.2.4 Combined effects of microstructure and
environment ....................................... 408
11.2.5 Effects of combining temperature and
environment ....................................... 409
11.2.6 Effect of the environment under ultra high-cycle
fatigue conditions ................................ 410
11.3 Influence of the environment on fatigue crack
propagation .............................................. 411
11.3.1 Initial work ...................................... 411
11.3.2 Propagation of fatigue cracks under a vacuum
(inert reference environment) ..................... 415
11.3.3 Environmentally-assisted propagation .............. 421
11.3.4 Cracking path ..................................... 427
11.3.5 Influence of different factors .................... 431
11.4 Conclusion ............................................... 443
11.5 Bibliography ............................................. 444
Chapter 12
Fatigue under Variable Amplitude Loadings ..................... 457
Thierry Palin-Luc
12.1 Introduction ............................................. 457
12.2 Variable amplitude loadings .............................. 460
12.2.1 Why should we carry out fatigue tests under
variable amplitude loadings? ...................... 460
12.2.2 Characterization of loading signals and
terminology ....................................... 464
12.2.3 From in service recordings to test spectra ........ 467
12.3 Fatigue tests under variable amplitude loadings .......... 478
12.3.1 General methodology of the simulation tests ....... 478
12.3.2 Test benches ...................................... 478
12.3.3 Block-program tests ............................... 478
12.3.4 Variable amplitude fatigue tests and spectra ...... 480
12.3.5 Tests under random loading ........................ 482
12.3.6 Representation of the test results ................ 483
12.4 Factors influencing the test results under variable
amplitude loading ........................................ 486
12.4.1 Counting method used to build the sequence ........ 486
12.4.2 Number of loading levels .......................... 486
12.4.3 Application order of the loading levels ........... 487
12.4.4 Loading frequency ................................. 488
12.4.5 Limitation of the signals under high stresses ..... 488
12.4.6 Irregularity factor ............................... 488
12.4.7 Type of spectrum .................................. 489
12.4.8 "Small cycles" or cycles with low amplitude ....... 490
12.4.9 Accelerated fatigue tests ......................... 490
12.5 Fatigue lifetime assessment under variable amplitude
loading .................................................. 493
12.5.1 Main methodology .................................. 493
12.5.2 Characteristics of multiaxial loading ............. 495
12.5.3 Towards no cycle counting ......................... 496
12.6 Conclusion ............................................... 497
12.7 Bibliography ............................................. 498
List of Authors ............................................... 503
Index ......................................................... 505
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