Fracture at high temperatures

FRONT COVER ......Page 1
EDITOR'S PREFACE ......Page 5
AUTHOR'S PREFACE ......Page 6
CONTENTS ......Page 9
PART I. INTRODUCTORY CHAPTERS ON DEFORMATION AND FAILURE UNDER CREEP CONDITIONS ......Page 18
1.1 The Creep Curve ......Page 19
1.2 A Few Facts on the Micromechanisms Underlying the Creep Curve ......Page 20
1.3 Diffusion Creep ......Page 22
1.4 Inhibition of Diffusion Creep ......Page 23
1.5.1 The infinite grain boundary (an intrinsic sliding model) ......Page 24
1.5.2 Grain boundary sliding in poly crystals (extrinsic models) ......Page 26
1.6 Deformation-Mechanism Maps ......Page 27
2.1 The Nature of Creep Damage ......Page 30
2.2 Fracture-Mechanism Maps ......Page 31
2.2.1 Cleavage and brittle intergranular fracture ......Page 32
2.2.3 Necking and superplasticity ......Page 34
2.2.6 Fracture at very high temperature ......Page 37
2.3.1 The Monkman-Grant rule ......Page 38
2.3.2 The Sherby-Dorn parameter ......Page 39
2.3.4 The Kachanov equations ......Page 40
2.3.5 The 6-projection concept ......Page 42
3.1 The Equations for Equilibrium and Compatibility ......Page 43
3.2 The Material Law ......Page 44
3.3 The Equations for Antiplane Shear. Plane Stress and Plane Strain ......Page 45
3.4.2 Scaling properties for power-law materials (Ilyushin, 1946) ......Page 49
3.4.3 Path-independent integrals: J and C ......Page 50
3.4.4 The HRR crack-tip fields in power-law materials ......Page 52
3.5 Numerical Techniques in Solid Mechanics ......Page 55
4.1 The Role of Vacancy Sources in Stress-Directed Diffusion ......Page 56
4.2 Stress-Directed Diffusion Along Grain Boundaries ......Page 57
4.3 Stress-Directed Diffusion Through the Grains ......Page 59
4.4 Surface Diffusion ......Page 61
4.5 Grain-Boundary Diffusion Combined with Power-Law Creep ......Page 62
PART II. CREEP CAVITIES ......Page 64
5 INTRODUCTION TO PART II ......Page 65
5.1 Experimental Techniques ......Page 66
5.2 Materials which Exhibit Intergranular Cavitation ......Page 67
5.3 Diffusion as the General Cause for Intergranular Cavitation ......Page 69
5.4.2 The orientation of cavitating boundaries in polycrystals ......Page 70
5.5.2 Grain-boundary ledges ......Page 71
5.5.4 Grain boundary particles ......Page 73
5.6 Wedge Cracks ......Page 75
5.7.1 The observed nucleation kinetics ......Page 76
5.7.2 Is there a critical stress for cavity nucleation ......Page 79
5.8 Pre-Existing Cavities ......Page 80
6.1 Cavity Nucleation by the Rupturing of Atomic Bonds ......Page 81
6.2.1 Historical remarks and related subject areas ......Page 83
6.2.2 Cavity shapes ......Page 84
6.2.3 The free energy of a cavity ......Page 86
6.2.4 The nucleation rate according to Raj and Ashby ......Page 89
6.2.5 The Fokker-Planck equation ......Page 91
6.2.6 The steady-state nucleation rate and the nucleation stress ......Page 92
6.2.7 Transient solutions of the Fokker-Planck equation and incubation times ......Page 94
6.3 Discussion of Cavity Nucleation Theories ......Page 96
6.3.2 On possible causes for the discrepancy between theoretical and experimental nucleation stresses ......Page 97
6.3.3 The problem of continuous cavity nucleation ......Page 98
7 CAVITY NUCLEATION BY STRESS CONCENTRATIONS DURING CREEP ......Page 99
7.1 An Isolated Sliding Grain Boundary Facet (Shear-Crack Model) ......Page 100
7.1.1 Elastic analysis of a sliding facet ......Page 101
7.1.2 A sliding boundary facet (shear crack) in creeping material ......Page 103
7.1.3 Relaxation of elastic stress concentrations at a shear crack by power-law creep ......Page 104
7.1.4 The time to build up elastic stress concentrations ......Page 105
7.2 The Triple Grain Junction in Polycrystals ......Page 106
7.2.1 The triple junction in elastic material ......Page 107
7.2.2 The triple junction in power-law creeping material ......Page 108
7.2.3 Stresses during Coble creep (rigid grains) ......Page 110
7.2.4 A combination of power-law creep and grain-boundary diffusion ......Page 112
7.2.6 Relaxation of elastic stress concentrations at triple points by diffusion ......Page 113
7.3.1 Elastic stress concentrations at two-dimensional particles ......Page 116
7.3.2 Elastic stress concentrations at three-dimensional particles ......Page 117
7.3.3 Stresses at two-dimensional particles during power-law creep ......Page 119
7.3.4 Stresses at three-dimensional partic!es during power-law creep ......Page 121
7.3.5 Diffusion and creep around particles during power-law creep of the grains ......Page 122
7.3.6 Stresses at particles during (free and inhibited) Coble creep ......Page 124
7.3.7 Relaxation of elastic stress concentrations at particles by creep ......Page 126
7.3.8 Relaxation of elastic stress concentrations at particles by diffusion ......Page 127
7.4 Stresses at Grain-Boundary Ledges ......Page 128
7.5 Summary of Stress Concentrations ......Page 129
8.1.1 Grain-boundary brittleness at room temperature (temper embrittlement) ......Page 130
8.1.2 Embrittlement by impurity segregation under creep conditions ......Page 131
8.1.3 Stress relief cracking or reheat cracking ......Page 133
8.2.1 Segregation equilibria ......Page 135
8.2.2 Segregation kinetics ......Page 137
8.2.3 Calculation of interface energies from adsorption data ......Page 138
8.2.4 The relevance of segregation for decohesion ......Page 141
8.2.5 The effect of segregation on cavity nucleation by vacancy condensation ......Page 143
9.1 Oxygen Attack and Related Phenomena ......Page 145
9.1.1 The equilibrium carbon-dioxide pressure in nickel ......Page 146
9.1.2 Carbon-oxides in nickel-chromium alloys ......Page 149
9.2 Hydrogen Attack ......Page 150
9.3 Helium Embrittlement ......Page 152
9.4 Kinetic Aspects ......Page 153
10.1 The Flux of Carbon to the Carbide ......Page 154
10.2 Elastic Accommodation ......Page 156
10.3 Accommodation by Power-Law Creep ......Page 158
10.4 Accommodation by Grain Boundary Diffusion ......Page 159
10.5 Decohesion of Particles by Thermal Expansion ......Page 160
10.6 Grain-Boundary Decohesion by Thermal-Expansion Anisotropy ......Page 161
11 DIFFUSIVE CAVITY GROWTH ......Page 162
11.1 Diffusional Growth of Lens-Shaped (Equilibrium) Cavities ......Page 163
11.1.1 The stress distribution between the cavities the cavity growth rate ......Page 164
11.1.2 Rupture times by diffusive cavity growth neglecting nucleation ......Page 168
11.1.3 The effect of the sintering stress on the rupture time ......Page 169
11.1.4 Removal of cavities by compressive loads or by surface tension forces ......Page 170
11.1.5 The effect of impurity segregation on diffusive cavity growth ......Page 172
11.1.6 The effect of gas pressure on the diffusive cavity growth rate ......Page 173
11.2 Diffusional Growth of Non-Equilibrium Cavities ......Page 174
11.2.2 Re-formulation of the surface diffusion problem ......Page 175
11.2.3 A steady-state solution of the surface diffusion problem in the crack-like limit ......Page 177
11.2.4 Similarity solutions for the surface diffusion problem ......Page 178
11.2.5 The relation between growth rate and stress in the crack-like limit ......Page 179
11.2.6 Rupture times for non-equilibrium growth ......Page 181
11.2.7 Experiments on copper and silver containing water vapor bubbles ......Page 183
11.2.8 Void-shape instability/finger-like cavity growth ......Page 184
12 CONSTRAINED DIFFUSIVE CAVITATION OF GRAIN BOUNDARIES ......Page 186
12.1.1 A tensile-crack model for the calculation of constrained growth rates ......Page 187
12.1.2 Comparison with measured cavity growth rates ......Page 189
12.1.3 Additional remarks on constrained cavity growth rates ......Page 193
12.3 On the Irrelevance of Constrained Cavity Growth for Rupture Lifetimes ......Page 195
12.4.1 Rupture lifetime of prestrained Nimonic 80A ......Page 196
12.4.2 Rupture lifetime of prestrained Inconel alloy X-750 ......Page 197
12.4.3 Rupture time of a-brass with implanted water vapor bubbles ......Page 198
12.5.1 The constrained limit (Hutchinson's model) ......Page 199
12.5.2 The unconstrained limit ......Page 200
12.5.3 The effect of cavitation on diffusion creep ......Page 201
12.6.1 Self-consistent models for constrained cavitation ......Page 202
12.6.2 The penny-shaped crack in a finite cylinder ......Page 204
12.6.3 Interactions between closely spaced facets in the presence of grain boundary sliding ......Page 205
12.7.1 Failure by large strains ......Page 207
12.7.2 Rupture lifetimes for continuous nucleation of cavitating facets ......Page 208
12.7.3 The combined effect of necking and continuous nucleation ......Page 210
12.8 Conclusions on Constrained Cavitation ......Page 211
13.1 Inhibited Cavity Growth Rates ......Page 212
13.2 Time to Cavity Coalescence and Time to Rupture for Inhibited Growth ......Page 214
14.1 Hole Growth by Creep Flow of the Grains ......Page 215
14.1.1 The growth of isolated holes in linearly viscous materials ......Page 216
14.1.2 An isolated circular-cylindrical void in nonlinear viscous material ......Page 218
14.1.3 Spherical voids in nonlinear material under axi-symmetric loading. Comparison with penny-shaped cracks ......Page 220
14.1.4 Strain to failure neglecting void interaction effects ......Page 223
14.1.5 Void interaction effects ......Page 224
14.2 Cavity Growth by Grain Boundary Sliding ......Page 226
15.1.1 Models for the interactive growth mechanism ......Page 229
15.1.2 Comparison with experiments ......Page 232
15.2.1 Elasticity effects in the growth of equilibrium-shaped cavities ......Page 234
15.2.2 Crack-like cavity growth with elastic accommodation ......Page 235
16.1 The Cavity Size Distribution Function ......Page 239
16.2 The Cavitated Area Fraction and the Rupture Lifetime ......Page 241
16.2.1 Lifetimes for diffusive cavity growth and continuous nucleation ......Page 242
16.2.3 Constrained diffusive growth and continuous nucleation ......Page 245
16.2.5 Plastic hole growth and continuous nucleation ......Page 247
16.3.1 Rupture lifetimes of ferritic steels ......Page 248
16.3.2 Lifetimes of austenitic steels ......Page 251
16.3.3 Rupture lifetimes of astroloy ......Page 253
16.4 Density Changes During Cavitation ......Page 254
17.1 Nucleation ......Page 256
17.2 Cavity Growth Rates and Rupture Lifetimes for Instantaneous Nucleation ......Page 257
17.3 Rupture Lifetimes for Continuous Nucleation ......Page 260
18.1 Micromechanisms of Creep-Fatigue Failure ......Page 261
18.2 Theories of Cavitational Failure for Slow-Fast Fatigue Loading ......Page 262
18.2.1 Cycles to failure for unconstrained diffusive cavity growth ......Page 263
18.2.2 Cycles to failure for plastic hole growth ......Page 265
18.2.3 Cycles to failure for unconstrained growth ......Page 266
18.2.4 Summary of fatigue lifetimes for different cavity growth mechanisms ......Page 267
18.3.1 Low-cycle fatigue tests on Al-5%Mg ......Page 268
18.3.2 Low-cycle fatigue tests on nickel ......Page 269
18.3.3 Low-cycle fatigue tests on copper ......Page 270
18.3.4 Low-cycle fatigue tests on austenitic steel ......Page 271
18.4 Why Do Cavities Grow under Balanced Cyclic Loading ......Page 272
18.5 Discussion ......Page 273
PART III. CREEP CRACK GROWTH AND CREEP-FATIGUE CRACK GROWTH ......Page 275
19.1 The Relevance of Cracks ......Page 276
19.2 The First Aspect: Deformation Fields in Cracked Bodies ......Page 277
19.3.1 Grain boundary cavitation ahead of the crack tip ......Page 278
19.3.2 Corrosive processes at the crack tip ......Page 279
20.1 Definition of the C*-Integral ......Page 280
20.2 Stress Fields and the C*-Integral in Power-Law Viscous Materials ......Page 281
20.2.1 The C*-integral in power-law viscous materials ......Page 282
20.2.2 Crack-tip fields in power-law viscous materials ......Page 284
21 C*-CONTROLLED CREEP CRACK GROWTH BY GRAIN-BOUNDARY CAVITATION ......Page 285
21.1 Creep Crack Growth Based on a Local Critical-Strain Criterion ......Page 286
21.2 Strain-Controlled Cavity Growth and Stress-Controlled Nucleation ......Page 290
21.3 Diffusive Growth of a Constant Number of Cavities ......Page 292
21.4 Diffusive Cavity Growth and Stress-Controlled Nucleation ......Page 293
21.5.1 Tests on a 1Cr-1/2Mo steel ......Page 294
21.5.2 Comparison of the data with models ......Page 296
21.5.3 Conclusions ......Page 298
22.1 Limitations to C* Set by Blunting ......Page 299
22.2 The Third Dimension in Fracture Mechanics and its Practical Consequences ......Page 301
22.2.1 The C*-integral in three dimensions ......Page 302
22.2.3 The singularity at the intersection of the crack front with the surface ......Page 303
22.2.4 Ranges of validity of singular fields in parallel-sided specimens with straight crack fronts ......Page 305
22.2.5 Conditions for plane strain near the crack tip ......Page 306
22.2.6 Thumbnail-shaped crack fronts ......Page 308
22.2.7 Shear lips ......Page 309
22.2.8 Crack-tip fields in side-grooved specimens ......Page 310
22.2.9 The compliance and C* in parallel-sided and side-grooved specimens ......Page 311
23.1 Stationary Crack under Step Loading ......Page 314
23.1.1 Similarity solutions in the small-scale creep, or short-time, limit ......Page 315
23.1.2 The crack-tip field in the short-time limit ......Page 317
23.1.3 The complete stress field in the short-time limit ......Page 318
23.1.4 The creep zone ......Page 319
23.1.5 A characterisitc transition time ......Page 321
23.1.6 Interpolation formulas for the transient regime ......Page 322
23.1.7 Possible generalizations and related work ......Page 324
23.2.1 Derivation of the singularity at growing cracks for Mode III ......Page 325
23.2.2 The growing crack singularity: results for Mode I ......Page 327
23.2.3 Fields for steady-state crack growth under small-scale creep conditions ......Page 328
23.2.4 Steady-state crack growth during extensive creep of the whole specimen ......Page 329
23.2.5 The evolution of the asymptotic field under non-steady-state conditions ......Page 330
23.3.1 Analysis of the case r_HR < x_c and a-a0 < r_cr ......Page 332
23.3.2 Crack growth subject to a critical-strain criterion for small-scale creep ......Page 334
23.4.2 A 1Cr-1/2Mo steel ......Page 337
23.4.3 Nimonic 80A ......Page 338
24 INSTANTANEOUS PLASTICITY ......Page 340
24.1 Deformation Fields in Elastic/Plastic Material ......Page 341
24.2 Growth of a Creep Zone in an Initially Fully-Plastic Body ......Page 342
24.3 The Special Case N = l/n ......Page 343
24.4 An Experimental Example for J-Controlled Creep Crack Growth ......Page 344
25.1 Strain-Hardening Model for Primary Creep ......Page 345
25.1.1 Primary creep of the whole specimen ......Page 346
25.1.2 Growth of a primary-creep zone in an elastic field ......Page 347
25.1.3 Growth of a secondary-creep zone in a primary-creep field ......Page 348
25.1.4 Summary and introduction of a load parameter map ......Page 350
25.2.1 The constitutive equations ......Page 351
25.2.2 Solutions for crack geometries ......Page 352
25.2.3 Elasticity effects and load parameter map ......Page 354
25.3 Analysis of an Experiment in the Transition Range Between J, C*_h and C ......Page 355
26.2 The Effect of Diffusion Creep on the Deformation Fields in Cracked Bodies ......Page 359
26.3 Crack Growth Rates Assuming a Critical-Strain Criterion ......Page 361
27.1.1 The constitutive model ......Page 362
27.1.2 The relation between fracture mechanics and damage mechanics ......Page 363
27.2.2 Crack growth rates ......Page 365
27.2.3 Approximate and numerical methods in small-scale damage ......Page 366
27.2.4 The process zone ......Page 367
27.3 The Range of Validity of the Small-Scale Damage Approximation in Extensively Creeping Specimens ......Page 368
27.4 The Evolution of Damage and Crack Growth for Small-Scale Creep ......Page 369
27.4.1 Crack grows faster than creep zone ......Page 370
27.4.2 Creep zone grows faster than process zone ......Page 371
27.6 The Evolution of the Crack Length and the Lifetime ......Page 372
27.7 Discussion ......Page 375
28 CREEP-FATIGUE CRACK GROWTH ......Page 377
28.1.1 The alternating slip model (also called the crack-tip blunting model) ......Page 378
28.1.2 Fatigue crack growth by grain boundary cavitation ......Page 380
28.1.3 Corrosive effects in creep-fatigue crack growth ......Page 381
28.2.2 Growth by cavitation in viscous materials ......Page 383
28.3.1 Elastic-plastic deformation fields ......Page 384
28.3.3 Z-controlled crack growth rates by alternating slip ......Page 385
28.4.1 Stress fields in elastic/nonlinear viscous material after a load step ......Page 386
28.4.2 Gradual load variations in elastic/nonlinear viscous material ......Page 387
28.4.3 Stress fields for rapid cyclic loading ......Page 389
28.4.4 Crack growth rates by the alternating slip mechanism ......Page 390
28.4.5 Fatigue crack growth by cavitation ahead of the crack ......Page 391
28.5.1 An approximate general expression for the crack growth rate by alternating slip ......Page 392
28.5.2 Creep-fatigue crack growth rates in fracture mechanics specimens ......Page 393
28.5.3 Fatigue lifetimes of initially smooth specimens by microcrack growth ......Page 394
28.6 Discussion ......Page 397
28.7 Summary ......Page 398
APPENDICES ......Page 400
APPENDIX A: MATERIAL PARAMETERS ......Page 401
APPENDIX B: ELASTIC STRESS FIELDS AT NOTCHES, CRACKS AND GRAIN BOUNDARY TRIPLE POINTS ......Page 403
B.l.l The eigenvalue equation for sharp notches ......Page 404
B.l.2 Crack-tip fields ......Page 405
B.2 The Stress Singularity at a Triple Junction of Sliding Grain Boundaries ......Page 407
APPENDIX C: CALCULATION OF C* FOR TEST SPECIMEN CONFIGURATIONS ......Page 408
REFERENCES ......Page 413
INDEX ......Page 429
BACK COVER ......Page 431