Dynamic Fracture Mechanics (Cambridge Monographs on Mechanics)

COVER......Page 1
HALF-TITLE......Page 3
TITLE......Page 5
COPYRIGHT......Page 6
CONTENTS......Page 7
PREFACE......Page 13
LIST OF SYMBOLS......Page 16
1.1 Introduction......Page 21
1.1.1 Inertial effects in fracture mechanics......Page 22
1.1.2 Historical origins......Page 23
1.2.1 Notation......Page 33
1.2.2 Balance equations......Page 36
1.2.3 Linear elastodynamics......Page 42
1.2.4 Inelastic materials......Page 49
1.3.1 Analytic functions of a complex variable......Page 50
1.3.2 Laplace transforms......Page 53
1.4 Overview of dynamic fracture mechanics......Page 57
1.4.1 Basic elastodynamic solutions for a stationary crack......Page 58
1.4.2 Further results for a stationary crack......Page 60
1.4.3 Asymptotic fields near a moving crack tip......Page 62
I.4.4 Energy concepts in dynamic fracture......Page 64
1.4.5 Elastic crack growth at constant speed......Page 67
1.4.6 Elastic crack growth at nonuniform speed......Page 69
1.4.7 Plasticity and rate effects during crack growth......Page 72
2.1 Introduction......Page 75
2.2 Suddenly applied antiplane shear loading......Page 80
2.3 Green\'s method of solution......Page 85
2.4 Suddenly applied crack face pressure......Page 92
2.5 The Wiener-Hopf technique......Page 97
2.5.1 Application of integral transforms......Page 98
2.5.2 The Wiener-Hopf factorization......Page 104
2.5.3 Inversion of the transforms......Page 111
2.5.4 Higher order terms......Page 116
2.6 Suddenly applied in-plane shear traction......Page 117
2.7 Loading with arbitrary time dependence......Page 120
3.1 Introduction......Page 124
3.2 Nonuniform crack face traction......Page 126
3.2.1 Suddenly applied concentrated loads......Page 127
3.2.2 Fundamental solution for a moving dislocation......Page 130
3.2.3 The stress intensity factor history......Page 132
3.3 Sudden loading of a crack of finite length......Page 137
3.4 Three-dimensional scattering of a pulse by a crack......Page 143
3.5 Three-dimensional stress intensity factors......Page 151
3.6.1 The Irwin criterion......Page 160
3.6.2 Qualitative observations......Page 161
3.6.3 Experimental results......Page 164
4.1 Introduction......Page 172
4.2 Elastic material; antiplane shear......Page 175
4.3 Elastic material; in-plane modes of deformation......Page 180
4.3.1 Singular field for mode I......Page 181
4.3.2 Higher order terms for mode I......Page 189
4.3.3 Singular field for mode II......Page 190
4.3.4 Supersonic crack tip speed......Page 191
4.4 Elastic-ideally plastic material; antiplane shear......Page 195
4.4.1 Asymptotic fields for steady dynamic growth......Page 198
4.4.2 Comparison with equilibrium results......Page 202
4.5 Elastic-ideally plastic material; plane strain......Page 204
4.5.1 Asymptotic field in plastically deforming regions......Page 207
4.5.2 A complete solution......Page 210
4.5.3 Other possible solutions......Page 214
4.5.4 Discontinuities......Page 217
4.5.5 Elastic sectors......Page 222
4.6 Elastic-viscous material......Page 226
4.6.1 Antiplane shear crack tip field......Page 227
4.6.2 Plane strain crack tip field......Page 234
4.7 Elastic-viscoplastic material; antiplane shear......Page 235
5.1 Introduction......Page 241
5.2.1 The energy flux integral for plane deformation......Page 244
5.2.2 Some properties of F(Gamma)......Page 247
5.3.1 Dynamic energy release rate......Page 251
5.3.2 Cohesive zone models of crack tip behavior......Page 255
5.3.3 Special forms for numerical computation......Page 260
5.4.1 Strip with uniform normal edge displacement......Page 263
5.4.2 Shear crack with a cohesive zone in a strip......Page 267
5.5.1 A one-dimensional string model......Page 270
5.5.2 Double cantilever beam configuration......Page 274
5.5.3 Splitting of a beam with a wedge......Page 277
5.5.4 Steady crack growth in a plate under bending......Page 281
5.5.5 Crack growth in a pressurized cylindrical shell......Page 282
5.6.1 The path-independent integral......Page 284
5.6.2 Relationship to stress intensity factor......Page 289
5.6.3 An application......Page 291
5.7.1 The weight function based on a particular solution......Page 294
5.7.2 A boundary value problem for the weight function......Page 300
5.8 Energy radiation from an expanding crack......Page 309
6.1 Introduction......Page 316
6.2 Steady dynamic crack growth......Page 318
6.2.1 General solution procedure......Page 319
6.2.2 The Yoffe problem......Page 320
6.2.3 Concentrated shear traction on the crack faces......Page 325
6.2.4 Superposition and cohesive zone models......Page 326
6.2.5 Approach to the steady state......Page 330
6.3 Self-similar dynamic crack growth......Page 333
6.3.1 General solution procedure......Page 334
6.3.2 The Broberg problem......Page 338
6.3.3 Symmetric expansion of a shear crack......Page 350
6.3.4 Nonsymmetric crack expansion......Page 354
6.3.5 Expansion of circular and elliptical cracks......Page 356
6.4 Crack growth due to general time-independent loading......Page 360
6.4.1 The fundamental solution......Page 362
6.4.2 Arbitrary initial equilibrium field......Page 370
6.4.3 Some illustrative cases......Page 373
6.4.4 The in-plane shear mode of crack growth......Page 375
6.5 Crack growth due to time-dependent loading......Page 376
6.5.1 The fundamental solution......Page 378
6.5.2 Arbitrary delay time with crack face pressure......Page 382
6.5.3 Incident plane stress pulse......Page 385
7.1 Introduction......Page 387
7.2 Antiplane shear crack growth......Page 389
7.3 Plane strain crack growth......Page 398
7.3.1 Suddenly stopping crack......Page 399
7.3.2 Arbitrary crack tip motion......Page 407
7.3.3 In-plane shear crack growth......Page 412
7.4 Crack tip equation of motion......Page 413
7.4.1 Tensile crack growth......Page 415
7.4.2 Fine-scale periodic fracture resistance......Page 421
7.4.3 Propagation and arrest of a mode II crack......Page 427
7.4.4 A one-dimensional string model......Page 430
7.4.5 Double cantilever beam: approximate equation of motion......Page 441
7.5.1 Incident plane stress pulse......Page 446
7.5.2 An influence function for general loading......Page 451
7.6 Rapid expansion of a strip yield zone......Page 452
7.7 Uniqueness of elastodynamic crack growth solutions......Page 457
8.2 Viscoelastic crack growth......Page 462
8.3 Steady crack growth in an elastic-plastic material......Page 468
8.3.1 Plastic strain on the crack line......Page 471
8.3.2 A growth criterion......Page 479
8.3.3 A formulation for the complete field......Page 481
8.3.4 The toughness-speed relationship......Page 485
8.3.5 The steady state assumption......Page 487
8.4 High strain rate crack growth in a plastic solid......Page 489
8.4.1 High strain rate plasticity......Page 490
8.4.2 Steady crack growth with small-scale yielding......Page 494
8.4.3 An approximate analysis......Page 497
8.4.4 Rate effects and crack arrest......Page 501
8.5 Fracture mode transition due to rate effects......Page 505
8.5.1 Formulation......Page 506
8.5.2 A rate-dependent cohesive zone......Page 508
8.5.3 The crack growth criteria......Page 514
8.6 Ductile void growth......Page 518
8.6.1 Spherical expansion of a void......Page 520
8.6.2 A more general model......Page 526
8.7 Microcracking and fragmentation......Page 528
8.7.1 Overall energy considerations......Page 529
8.7.2 Time-dependent strength under pulse loading......Page 532
BIBLIOGRAPHY......Page 541
INDEX......Page 579