Preface to the second edition ................................ xvii
Preface to the first edition .................................. xix
1 Introduction and overview .................................. 1
1.1 Historical background and overview ......................... 1
1.1.1 Case study: Fatigue and the Comet airplane .......... 8
1.2 Different approaches to fatigue ........................... 11
1.2.1 Total-life approaches .............................. 12
1.2.2 Defect-tolerant approach ........................... 13
1.2.3 A comparison of different approaches ............... 14
1.2.4 'Safe-life' and 'fail-safe' concepts ............... 14
1.2.5 Case study: Retirement for cause ................... 15
1.3 The need for a mechanistic basis .......................... 17
1.4 Continuum mechanics ....................................... 18
1.4.1 Elements of linear elasticity ...................... 20
1.4.2 Stress invariants .................................. 21
1.4.3 Elements of plasticity ............................. 22
1.4.4 Elements of linear viscoelasticity ................. 26
1.4.5 Viscoplasticity and viscous creep .................. 28
1.5 Deformation of ductile single crystals .................... 29
1.5.1 Resolved shear stress and shear strain .............. 30
Exercises ................................................. 33
PART ONE: CYCLIC DEFORMATION AND FATIGUE CRACK INITIATION ...... 37
2 Cyclic deformation in ductile single crystals ............. 39
2.1 CMic strain hardening in single crystals .................. 40
2.2 Cyclic saturation in single crystals ...................... 40
2.2.1 Monotonie versus cyclic plastic strains ............ 45
2.3 Instabilities in cyclic hardening ......................... 45
2.3.1 Example problem: Identification of active slip
systems ............................................ 47
2.3.2 Formation of dislocation veins ..................... 49
2.3.3 Fundamental length scales for the vein structure ... 52
2.4 Deformation along persistent slip bands ................... 52
2.5 Dislocation structure of PSBs ............................. 53
2.5.1 Composite model .................................... 57
2.5.2 Example problem: Dislocation dipoles and cyclic
deformation ........................................ 58
2.6 A constitutive model for the inelastic behavior of PSBs ... 60
2.6.1 General features ................................... 60
2.6.2 Hardening in the PSBs .............................. 61
2.6.3 Hardening at sites of PSB intersection with the
free surface ....................................... 61
2.6.4 Unloading and reloading ............................ 62
2.6.5 Vacancy generation ................................. 62
2.7 Formation of PSBs ......................................... 63
2.7.1 Electron microscopy observations ................... 63
2.7.2 Static or energetic models ......................... 65
2.7.3 Dynamic models of self-organized dislocation
structures ......................................... 68
2.8 Formation of labyrinth and cell structures ................ 69
2.8.1 Example problem: Multiple slip ..................... 71
2.9 Effects of crystal orientation and multiple slip .......... 72
2.10 Case study: A commercial FCC alloy crystal ................ 74
2.11 Monotonie versus cyclic deformation in FCC crystals ....... 78
2.12 Cyclic deformation in BCC single crystals ................. 79
2.12.1 Shape changes in fatigued BCC crystals ............. 80
2.13 Cyclic deformation in HCP single crystals ................. 82
2.13.1 Basic characteristics of Ti single crystals ........ 83
2.13.2 Cyclic deformation of Ti single crystals ........... 83
Exercises ................................................. 84
3 Cyclic deformation in noncrystalline ductile solids ....... 86
3.1 Effects of grain boundaries and multiple slip ............. 86
3.1.1 Monocrystalline versus polycrystalline FCC metals .. 87
3.1.2 Effects of texture ................................. 89
3.2 Cyclic deformation of FCC bicrystals ...................... 89
3.2.1 Example problem: Number of independent slip
systems ............................................ 91
3.3 Cyclic hardening and softening in polycrystals ............ 91
3.4 Effects of alloying, cross slip and stacking fault
energy .................................................... 95
3.5 Effects of precipitation .................................. 97
3.6 The Bauschinger effect .................................... 97
3.6.l Terminology ........................................ 98
3.6.2 Mechanisms ......................................... 99
3.7 Shakedown ................................................ 101
3.8 Continuum models for uniaxial and multiaxial fatigue ..... 102
3.8.1 Parallel sub-element model ........................ 104
3.8.2 Field of work hardening moduli .................... 106
3.8.3 Two-surface models for cyclic plasticity .......... 110
3.8.4 Other approaches .................................. 112
3.9 Cyclic creep or ratchetting .............................. 113
3.10 Metal-matrix composites subjected to thermal cycling ..... 115
3.10.1 Thermoelastic deformation ......................... 115
3.10.2 Characteristic temperatures for thermal fatigue ... 117
3.10.3 Plastic strain accumulation during thermal
cycling ........................................... 119
3.10.4 Effects of matrix strain hardening ................ 120
3.10.5 Example problem: Critical temperatures for
thermal fatigue in a metal-matrix composite ....... 122
3.11 Layered composites subjected to thermal cycling .......... 123
3.11.1 Thermoelastic deformation of a bilayer ............ 124
3.11.2 Thin-film limit: the Stoney formula ............... 127
3.11.3 Characteristic temperatures for thermal fatigue ... 128
Exercises ................................................ 129
4 Fatigue crack initiation in ductile solids ............... 132
4.1 Surface roughness and fatigue crack initiation ........... 132
4.1.1 Earlier observations and viewpoints ............... 133
4.1.2 Electron microscopy observations .................. 134
4.2 Vacancy-dipole models .................................... 137
4.3 Crack initiation along PSBs .............................. 141
4.4 Role of surfaces in crack initiation ..................... 143
4.5 Computational models for crack initiation ................ 143
4.5.1 Vacancy diffusion ................................. 143
4.5.2 Numerical simulations ............................. 145
4.5.3 Example problem: Effects of vacancies ............. 146
4.6 Environmental effects on crack initiation ................ 147
4.7 Kinematic irreversibility of cyclic slip ................. 148
4.8 Crack initiation along grain and twin boundaries ......... 149
4.9 Crack initiation in commercial alloys .................... 152
4.9.1 Crack initiation near inclusions and pores ........ 152
4.9.2 Micromechanical models ............................ 155
4.10 Environmental effects in commercial alloys ............... 156
4.11 Crack initiation at stress concentrations ................ 157
4.11.1 Crack initiation under far-field cyclic
compression ....................................... 158
Exercises ................................................ 162
5 Cyclic deformation and crack initiation in brittle
solids ................................................... 165
5.1 Degrees of brittleness ................................... 166
5.2 Modes of cyclic deformation in brittle solids ............ 167
5.3 Highly brittle solids .................................... 169
5.3.1 Mechanisms ........................................ 169
5.3.2 Constitutive models ............................... 170
5.3.3 On possible effects of cyclic loading ............. 175
5.3.4 Elevated temperature behavior ..................... 176
5.4 Semi-brittle solids ...................................... 179
5.4.1 Crack nucleation by dislocation pile-up ........... 179
5.4.2 Example problem: Cottrell mechanism for sessile
dislocation formation ............................. 180
5.4.3 Cyclic deformation ................................ 182
5.5 Transformation-toughened ceramics ........................ 184
5.5.1 Phenomenology ..................................... 185
5.5.2 Constitutive models ............................... 187
5.6 Fatigue crack initiation under far-field cyclic
compression .............................................. 191
5.6.1 Example problem: Crack initiation under
far-field cyclic compression ...................... 196
Exercises ................................................ 197
6 Cyclic deformation and crack initiation in
noncrystalline solids .................................... 200
6.1 Deformation features of semi-/noncrystalline solids ...... 200
6.1.1 Basic deformation characteristics ................. 200
6.1.2 Crazing and shear banding ......................... 201
6.1.3 Cyclic deformation: crystalline versus
noncrystalline materials .......................... 203
6.2 Cyclic stress-strain response ............................ 205
6.2.1 Cyclic softening .................................. 205
6.2.2 Thermal effects ................................... 207
6.2.3 Example problem: Hysteretic heating ............... 207
6.2.4 Experimental observations of temperature rise ..... 209
6.2.5 Effects of failure modes .......................... 210
6.3 Fatigue crack initiation at stress concentrations ........ 211
6.4 Case study: Compression fatigue in total knee
replacements ............................................. 213
Exercises ................................................ 217
PART TWO: TOTAL-LIFE APPROACHES ............................... 219
7 Stress-life approach ..................................... 221
7.1 The fatigue limit ........................................ 222
7.2 Mean stress effects on fatigue life ...................... 224
7.3 Cumulative damage ........................................ 227
7.4 Effects of surface treatments ............................ 228
7.5 Statistical considerations ............................... 231
7.6 Practical applications ................................... 235
7.6 Example-problem: Effects of surface treatments ........... 235
7.6.2 Case study: HCF in aircraft turbine engines ...... 236
7.7 Stress-life response of polymers ......................... 237
7.7.1 General characterization .......................... 237
7.7.2 Mechanisms ........................................ 238
7.8 Fatigue of organic composites ............................ 239
7.8.1 Discontinuously reinforced composites ............. 240
7.8.2 Continuous-fiber composites ....................... 240
7.9 Effects of stress concentrations ......................... 242
7.9.1 Fully reversed cyclic loading ................... 242
7.9.2 Combined effects of notches and mean stresses ..... 243
7.9.3 Nonpropagating tensile fatigue cracks ............. 244
7.9.4 Example problem: Effects of notches ............... 244
7.10 Multiaxial cyclic stresses ............................... 246
7.10.1 Proportional and nonproportional loading .......... 246
7.10.2 Effective stresses in multiaxial fatigue loading .. 247
7.10.3 Stress-life approach for tension and torsion ...... 248
7.10.4 The critical plane approach ....................... 250
Exercises ................................................ 254
8 Strain-life approach ..................................... 256
8.1 Strain-based approach to total life ...................... 256
8.1.1 Separation of low-cycle and high-cycle fatigue
lives ............................................. 256
8.1.2 Transition life ................................... 257
8.1.3 Example problem: Thermal fatigue life of
a metal-matrix composite .......................... 260
8.2 Local strain approach for notched members ................ 262
8.2.1 Neuber analysis ................................... 263
8.3 Variable amplitude cyclic strains and cycle counting ..... 265
8.3.1 Example problem: Cycle counting ................... 265
8.4 Multiaxial fatigue ....................................... 268
8.4.1 Measures of effective strain ...................... 268
8.4.2 Case study: Critical planes of failure ............ 269
8.4.3 Different cracking patterns in multiaxial
fatigue ........................................... 271
8.4.4 Example problem: Critical planes of failure in
multiaxial loading ................................ 273
8.5 Out-of-phase loading ..................................... 276
Exercises ................................................ 278
PART THREE: DAMAGE-TOLERANT APPROACH .......................... 281
9 Fracture mechanics and its implications for fatigue ...... 283
9.1 Griffith fracture theory ................................. 283
9.2 Energy release rate and crack driving force .............. 285
9.3 Linear elastic fracture mechanics ........................ 288
9.3.1 Macroscopic modes of fracture ..................... 288
9.3.2 The plane problem ................................. 289
9.3.3 Conditions of K-dominance ......................... 295
9.3.4 Fracture toughness ................................ 296
9.3.5 Characterization of fatigue crack growth .......... 296
9.4 Equivalence of Q and К ................................... 297
9.4.1 Example problem: Q and К for the DCB specimen ..... 298
9.4.2 Example problem: Stress intensity factor for
a blister test .................................... 300
9.5 Plastic zone size in monotonic loading ................... 302
9.5.1 The Irwin approximation ........................... 302
9.5.2 The Dugdale model ................................. 303
9.5.3 The Barenblatt model ............................. 304
9.6 Plastic zone size in cyclic loading ...................... 304
9.7 Elastic-plastic fracture mechanics ....................... 307
9.7.1 The J-integral .................................... 307
9.7.2 Hutchinson-Rice-Rosengren (HRR) singular fields ... 308
9.7.3 Crack tip opening displacement .................... 309
9.7.4 Conditions of J-dominance ......................... 310
9.7.5 Example problem: Specimen size requirements ....... 312
9.7.6 Characterization of fatigue crack growth .......... 313
9.8 Two-parameter representation of crack-tip fields ......... 316
9.8.1 Small-scale yielding .............................. 318
9.8.2 Large-scale yielding .............................. 318
9.9 Mixed-mode fracture mechanics ............................ 319
9.10 Combined mode I-mode II fracture in ductile solids ....... 320
9.11 Crack deflection ......................................... 322
9.11.1 Branched elastic cracks ........................... 324
9.11.2 Multiaxial fracture due to crack deflection ....... 326
9.12 Case study: Damage-tolerant design of aircraft fuselage .. 327
Exercises ................................................ 328
10 Fatigue crack growth in ductile solids ................... 331
10.1 Characterization of crack growth ......................... 331
10.1.1 Fracture mechanics approach ....................... 332
10.1.2 Fatigue life calculations ......................... 334
10.2 Microscopic stages of fatigue crack growth ............... 335
10.2.1 Stage I fatigue crack growth ...................... 335
10.2.2 Stage II crack growth and fatigue striations ...... 335
10.2.3 Models for striation formation .................... 337
10.2.4 Environmental effects on stage II fatigue ......... 340
10.3 Different regimes of fatigue crack growth ................ 341
10.4 Near-threshold fatigue crack growth ...................... 343
10.4.1 Models for fatigue thresholds ..................... 345
10.4.2 Effects of microstructural size scale ............. 346
10.4.3 Effects of slip characteristics ................... 347
10.4.4 Example problem: Issues of length scales .......... 351
10.|,5 On the determination of fatigue thresholds ........ 352
10.5 Intermediate region of crack growth ...................... 354
10.6 High growth rate regime .................................. 357
10.7 Case study: Fatigue failure of aircraft structures ....... 358
10.8 Case study: Fatigue failure of total hip components ...... 364
10.9 Combined mode I-mode II fatigue crack growth ............. 368
10.9.1 Mixed-mode fatigue fracture envelopes ............. 369
10.9.2 Path of the mixed-mode crack ...................... 370
10.9.3 Some general observations ......................... 372
10.10 Combined mode I-mode III fatigue crack growth ........... 373
10.10.1 Crack growth characteristics ..................... 374
10.10.2 Estimation of intrinsic growth resistance ........ 378
Exercises ................................................ 379
11 Fatigue crack growth in brittle solids ................... 383
11.1 Some general effects of cyclic loading on crack growth ... 384
11.2 Characterization of crack growth in brittle solids ....... 385
11.2.1 Crack growth under static loads ................... 385
11.2.2 Crack growth under cyclic loads ................... 386
11.3 Crack growth resistance and toughening of brittle
solids ................................................... 388
11.3.1 Example problem: Fracture resistance and
stability of crack growth ......................... 389
11.4 Cyclic damage zone ahead of tensile fatigue crack ........ 392
11.5 Fatigue crack growth at low temperatures ................. 393
11.6 Case study: Fatigue cracking in heart valve prostheses ... 396
11.7 Fatigue crack growth at elevated temperatures ............ 399
11.7.1 Micromechanisms of deformation and damage due to
intergranular/interfacial glassy films ............ 399
11.7.2 Crack growth characteristics at high
temperatures ...................................... 402
11.7.3 Role of viscous films and ligaments ............... 403
Exercises ................................................ 406
12 Fatigue crack growth in noncrystalline solids ............ 408
12.1 Fatigue crack growth characteristics ..................... 408
12.2 Mechanisms of fatigue crack growth ....................... 411
12.2.1 Fatigue striations ................................ 411
12.2.2 Discontinuous growth bands ........................ 413
12.2.3 Combined effects of crazing and shear flow ........ 417
12.2.4 Shear bands ....................................... 419
12.2.5 Some general observations ......................... 420
12.2.6 Example problem: Fatigue crack growth in epoxy
adhesive .......................................... 422
12.3 Fatigue of metallic glasses .............................. 424
12.4 Case study: Fatigue fracture in rubber-toughened epoxy ... 426
Exercises ................................................ 430
PART FOUR: ADVANCED TOPICS .................................... 433
13 Contact fatigue: sliding, rolling and fretting ........... 435
13.1 Basic terminology and definitions ........................ 435
13.2 Mechanics of stationary contact under normal loading ..... 439
13.2.1 Elastic indentation of a planar surface ........... 440
13.2.2 Plastic deformation ............................... 442
13.2.3 Residual stresses during unloading ................ 443
13.2.4 Example problem: Beneficial effects of surface
compressive stresses .............................. 444
13.3 Mechanics of sliding contact fatigue ..................... 445
13.3.1 Sliding of a sphere on a planar surface ........... 446
13.3.2 Partial slip and complete sliding of a cylinder
on a planar surface ............................... 447
13.3.3 Partial slip of a sphere on a planar surface ...... 448
13.3.4 Cyclic variations in tangential force ............. 449
13.4 Rolling contact fatigue .................................. 451
13.4.1 Hysteretic energy dissipation in rolling contact
fatigue ........................................... 452
13.4.2 Shakedown limits for rolling and sliding contact
fatigue ........................................... 453
13.5 Mechanisms of contact fatigue damage ..................... 457
13.5.1 Types of microscopic damage ....................... 457
13.5.2 Case study: Contact fatigue cracking in gears ..... 457
13.6 Fretting fatigue ......................................... 462
13.6.1 Definition and conditions of occurrence ........... 462
13.6.2 Fretting fatigue damage ........................... 463
13.6.3 Palliatives to inhibit fretting fatigue ........... 466
13.6.4 Example problem: Fracture mechanics methodology
for fretting fatigue fracture ..................... 469
13.7 Case study: Fretting fatigue in a turbogenerator rotor ... 474
13.7.1 Design details and geometry ....................... 474
13.7.2 Service loads and damage occurrence ............... 474
Exercises ................................................ 481
14 Retardation and transients in fatigue crack growth ....... 483
14.1 Fatigue crack closure .................................... 484
14.2 Plasticity-induced crack closure ......................... 486
14.2.1 Mechanisms ........................................ 486
14.2.2 Analytical models ................................. 490
14.2.3 Numerical models .................................. 493
14.2.4 Effects of load ratio on fatigue thresholds ....... 494
14.3 Oxide-induced crack closure .............................. 496
14.3.1 Mechanism ......................................... 496
14.3.2 Implications for environmental effects ............ 497
14.4 Roughness-induced crack closure .......................... 500
14.4.1 Mechanism ........................................ 500
14.4.2 Implications for tnicrostructural effects on
threshold fatigue ................................ 501
14.5 Viscous fluid-induced crack closure ...................... 503
14.5.1 Mechanism ........................................ 503
14.6 Phase transformation-induced crack closure ............... 504
14.7 Some basic features of fatigue crack closure ............. 505
14.8 Issues and difficulties in the quantification of crack
closure .................................................. 506
14.9 Fatigue crack deflection ................................. 507
14.9.1 Linear elastic analyses ........................... 508
14.9.2 Experimental observations ......................... 511
14.9.3 Example problem: Possible benefits of
deflection ....................................... 512
14.10 Additional retardation mechanisms ....................... 515
14.10.1 Crack-bridging and trapping in composite
materials ........................................ 515
14.10.2 On crack retardation in advanced metallic
systems .......................................... 518
14.11 Case study: Variable amplitude spectrum loads ........... 519
14.12 Retardation following tensile overloads ................. 520
14.12.1 Plasticity-induced crack closure ................. 521
14.12.2 Crack tip blunting ............................... 522
14.12.3 Residual compressive stresses .................... 523
14.12.4 Deflection or bifurcation of the crack ........... 523
14.12.5 Near-threshold mechanisms ........................ 524
14.13 Transient effects following compressive overloads ....... 526
14.13.1 Compressive overloads applied to notched
materials ........................................ 529
14.14 Load sequence effects ................................... 529
14.14.1 Block tensile load sequences ..................... 530
14.14.2 Tension-compression load sequences ............... 533
14.15 Life prediction models .................................. 534
14.15.1 Yield zone models ................................ 534
14.15.2 Numerical models of crack closure ................ 535
14.15.3 Engineering approaches ........................... 536
14.15.4 The characteristic approach ...................... 536
Exercises ................................................ 537
15 Small fatigue cracks ..................................... 541
15.1 Definitions of small cracks .............................. 543
15.2 Similitude ............................................... 543
15.3 Microstructural aspects of small flaw growth ............. 544
15.4 Threshold conditions for small flaws ..................... 545
15.4.1 Transition crack size ............................. 545
15.4.2 Critical size of cyclic plastic zone .............. 547
15.4.3 Slip band models .................................. 548
15.5 Fracture mechanics for small cracks at notches ........... 550
15.5.1 Threshold for crack nucleation .................... 551
15.5.2 Example problem: Crack growth from notches ........ 552
15.6 Continuum aspects of small flaw growth ................... 554
15.6.1 Two-parameter characterization of short fatigue
cracks ............................................ 554
15.6.2 Near-tip plasticity ............................... 556
15.6.3 Notch-tip plasticity .............................. 556
15.7 Effects of physical smallness of fatigue flaws ........... 559
15.7.1 Mechanical effects ................................ 559
15.7.2 Environmental effects ............................. 561
15.8 On the origins of 'short crack problem' .................. 562
15.9 Case study: Small fatigue cracks in surface coatings ..... 564
15.9.1 Theoretical background for cracks approaching
interfaces perpendicularly ........................ 564
15.9.2 Application to fatigue at surface coatings ........ 566
Exercises ................................................ 568
16 Environmental interactions: corrosion-fatigue and
creep-fatigue ............................................ 570
16.1 Mechanisms of corrosion-fatigue .......................... 570
16.1.1 Hydrogenous gases ................................. 571
16.1.2 Aqueous media ..................................... 572
16.1.3 Metal embrittlement ............................... 574
16.2 Nucleation of corrosion-fatigue cracks ................... 574
16.2.1 Gaseous environments .............................. 575
16.2.2 Aqueous environments .............................. 575
16.3 Growth of corrosion-fatigue cracks ....................... 577
16.3.1 Types of corrosion-fatigue crack growth ........... 579
16.3.2 Formation of brittle striations ................... 581
16.3.3 Effects of mechanical variables ................... 583
16.3.4 Models of corrosion-fatigue ....................... 585
16.4 Case study: Fatigue design of exhaust valves for cars .... 586
16.5 Fatigue at low temperatures .............................. 588
16.6 Damage and crack initiation at high temperatures ......... 589
16.6.1 Micromechanisms of damage ......................... 590
16.6.2 Life prediction models ............................ 594
16.7 Fatigue crack growth at high temperatures ................ 598
16.7.1 Fracture mechanics characterization .............. 598
16.7.2 Characterization of creep-fatigue crack growth ... 601
16.7.3 Summary and some general observations ............ 603
16.8 Case study: Creep-fatigue in steam-power generators ...... 604
Exercises ................................................ 608
Appendix ...................................................... 609
References .................................................... 614
Author index .................................................. 659
Subject index ................................................. 669
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