Preface ...................................................... xiii
About the Authors ............................................ xvii
CHAPTER 1 Introduction ......................................... 1
1.1 Failure of Solids .......................................... 1
1.2 Fracture Mechanics Concepts ................................ 2
1.3 History of Fracture Mechanics .............................. 5
1.3.1 Griffith Theory of Fracture ......................... 5
1.3.2 Fracture Mechanics as an Engineering Science ........ 6
1.3.3 Recent Developments in Fracture Mechanics
Research ........................................................ 7
References ...................................................... 8
CHAPTER 2 Griffith Theory of Fracture ......................... 11
2.1 Theoretical Strength ...................................... 11
2.1.1 An Atomistic Model ................................. 11
2.1.2 The Energy Consideration ........................... 13
2.2 The Griffith Theory of Fracture ........................... 14
2.3 A Relation among Energies ................................. 17
References ..................................................... 22
Problems ....................................................... 22
CHAPTER 3 The Elastic Stress Field around a Crack Tip ......... 25
3.1 Basic Modes of Fracture and Stress Intensity Factor ....... 25
3.2 Method of Complex Potential for Plane Elasticity
(The Kolosov-Muskhelishvili Formulas) ..................... 27
3.2.1 Basic Equations of Plane Elasticity and Airy
Stress Function .................................... 27
3.2.2 Analytic Functions and Cauchy-Riemann
Equations .......................................... 29
3.2.3 Complex Potential Representation of the Airy
Stress Function .................................... 30
3.2.4 Stress and Displacement ............................ 32
3.3 Westergaard Function Method ............................... 34
3.3.1 Symmetric Problems (Mode I) ........................ 34
3.3.2 Skew-Symmetric Problems (Mode II) .................. 36
3.4 Solutions by the Westergaard Function Method .............. 38
3.4.1 Mode I Crack ....................................... 38
3.4.2 Mode II Crack ...................................... 43
3.4.3 Mode III Crack ..................................... 46
3.4.4 Complex Representation of Stress Intensity Factor .. 48
3.5 Fundamental Solutions of Stress Intensity Factor .......... 50
3.5.1 A Finite Crack in an Infinite Plate ................ 51
3.5.2 Stress Intensity Factors for a Crack Subjected
to Arbitrary Crack Face Loads ...................... 53
3.5.3 A Semi-infinite Crack in an Infinite Medium ........ 54
3.6 Finite Specimen Size Effects .............................. 55
3.7 Williams' Crack Tip Fields ................................ 56
3.7.1 Williams' Crack Tip Stress and Displacement
Fields: Mode I and II .............................. 57
3.7.2 Williams' Crack Tip Stress and Displacement
Fields: Mode III ................................... 63
3.8 K-Dominance ............................................... 66
3.9 Irwin's K-Based Fracture Criterion ........................ 68
References ..................................................... 71
Problems ....................................................... 72
CHAPTER 4 Energy Release Rate ................................. 77
4.1 The Concept of Energy Release Rate ........................ 77
4.2 The Relations between G and K by the Crack Closure
Method .................................................... 78
4.3 The J-Integral ............................................ 82
4.3.1 J as Energy Release Rate ........................... 83
4.3.2 Path-Independence .................................. 86
4.3.3 Relation between J and K ........................... 87
4.3.4 Examples ........................................... 89
4.4 Stress Intensity Factor Calculations Using the Finite
Element Method ............................................ 92
4.4.1 Direct Method ...................................... 92
4.4.2 Modified Crack Closure Technique ................... 93
4.5 Three-Dimensional Field near Crack Front .................. 94
4.5.1 Distribution of Stress Intensity Factor over
Thickness .......................................... 95
4.5.2 Plane Strain Zone at the Crack Front ............... 99
References .................................................... 101
Problems ...................................................... 102
CHAPTER 5 Mixed Mode Fracture ................................ 105
5.1 A Simple Elliptical Model ................................ 105
5.2 Maximum Tensile Stress Criterion (MS-Criterion) .......... 108
5.3 Strain Energy Density Criterion (S-Criterion) ............ 111
5.4 Maximum Energy Release Rate Criterion (ME-Criterion) ..... 115
5.5 Experimental Verifications ............................... 117
References .................................................... 119
Problems ...................................................... 120
CHAPTER 6 Crack Tip Plasticity ............................... 123
6.1 Yield Criteria ........................................... 124
6.1.1 Tresca Yield Criterion ............................ 124
6.1.2 von Mises Yield Criterion ......................... 125
6.2 Constitutive Relationships in Plasticity ................. 125
6.2.1 Flow Theory of Plasticity ......................... 126
6.2.2 Deformation Theory of Plasticity .................. 128
6.3 Irwin's Model for Mode I Fracture ........................ 130
6.3.1 Plastic Zone Size ................................. 130
6.3.2 Effective Crack Length and Adjusted Stress
Intensity Factor .................................. 133
6.3.3 Crack Tip Opening Displacement .................... 134
6.4 The Dugdale Model ........................................ 134
6.4.1 Small-Scale Yielding .............................. 135
6.4.2 A Crack in an Infinite Plate ...................... 137
6.5 Plastic Zone Shape Estimate According to the Elastic
Solution ................................................. 140
6.5.1 Principal Stresses ................................ 140
6.5.2 Plane Stress Case ................................. 141
6.5.3 Plane Strain Case ................................. 143
6.5.4 Antiplane Strain Case ............................. 145
6.6 Plastic Zone Shape According to Finite Element
Analyses ................................................. 146
6.7 A Mode III Small-Scale Yielding Solution ................. 148
6.7.1 Basic Equations ................................... 148
6.7.2 Elastic-Plastic Solution and the Crack Tip
Plastic Zone ...................................... 149
6.8 A Mode III Small-Scale Yielding Solution-Elastic
Power-Law Hardening Materials ............................ 152
6.8.1 Basic Equations ................................... 153
6.8.2 Boundary Conditions of SSY ........................ 156
6.8.3 Elastic-Plastic Solution .......................... 158
6.9 HRR Field ................................................ 162
6.10 Energy Release Rate Concept in Elastic-Plastic
Materials ................................................ 164
References .................................................... 167
Problems ...................................................... 168
CHAPTER 7 Elastic-Plastic Fracture Criteria ................. 171
7.1 Irwin's Adjusted Stress Intensity Factor Approach ........ 171
7.2 K Resistance Curve Approach .............................. 173
7.3 J-Integral as a Fracture Parameter ....................... 177
7.4 Crack Tip Opening Displacement Criterion ................. 178
7.5 Crack Tip Opening Angle Criterion ........................ 181
References .................................................... 185
Problems ...................................................... 186
CHAPTER 8 Interfacial Cracks between Two Dissimilar Solids ... 189
8.1 Crack Tip Fields ......................................... 189
8.1.1 Asymptotic Stress and Displacement Fields ......... 189
8.1.2 Mode III Case ..................................... 194
8.1.3 Dundurs' Parameters ............................... 197
8.2 Complex Function Method and Stress Intensity Factors ..... 197
8.2.1 Stress Intensity Factor Solutions for Two Typical
Crack Problems .................................... 198
8.2.2 Further Comments on the Stress Intensity Factor
Definitions ....................................... 200
8.3 Crack Surface Contact Zone and Stress Oscillation Zone ... 203
8.3.1 Crack Surface Contact Zone ........................ 203
8.3.2 Stress Oscillation Zone ........................... 205
8.4 Energy Release Rate ...................................... 207
8.4.1 Energy Release Rate ............................... 207
8.4.2 Stress Intensity Factor Calculations .............. 209
8.5 Fracture Criterion ....................................... 212
8.6 Crack Kinking Out of the Interface ....................... 213
8.7 Contact and Friction in Interfacial Cracks ............... 215
8.7.1 Crack Tip Fields .................................. 215
8.7.2 Finite Element Procedure for Energy Calculation ... 218
8.7.3 Fracture Criterion ................................ 220
8.7.4 Effect of Compressive Loading ..................... 223
References .................................................... 223
Problems ...................................................... 224
CHAPTER 9 Cohesive Zone Model ................................ 227
9.1 The Barenblatt Model ..................................... 227
9.2 Cohesive Zone Concept in Continuum Mechanics and
Cohesive Laws ............................................ 230
9.2.1 The Dugdale Model ................................. 233
9.2.2 A Linear Softening Model .......................... 233
9.2.3 A Trapezoidal Model ............................... 234
9.2.4 An Exponential Model .............................. 234
9.2.5 A Cohesive Zone Model Based on Necking ............ 235
9.3 A Discussion on the Linear Hardening Law ................. 235
9.4 Cohesive Zone Modeling and LEFM .......................... 238
9.5 Cohesive Zone Modeling of Interfacial Fracture ........... 240
9.5.1 Mixed Mode Cohesive Law ........................... 240
9.5.2 Cohesive Energy Density ........................... 241
9.5.3 Cohesive Zone Length .............................. 243
References .................................................... 246
Problems ...................................................... 246
CHAPTER 10 Special Topics ..................................... 247
10.1 Fracture Mechanics of Anisotropic Solids ................. 247
10.1.1 Basic Plane Elasticity Equations of Anisotropic
Solids ............................................ 248
10.1.2 A Mode I Crack in an Infinite Anisotropic Plate
under Uniform Crack Surface Pressure .............. 250
10.1.3 A Mode II Crack in an Infinite Anisotropic Plate
under Uniform Crack Surface Shear ................. 251
10.1.4 Energy Release Rate ............................... 252
10.2 Fracture Mechanics of Nonhomogeneous Materials ........... 253
10.2.1 Basic Plane Elasticity Equations of Nonhomogenous
Materials ......................................... 254
10.2.2 Crack Tip Stress and Displacement Fields .......... 256
10.2.3 Energy Release Rate ............................... 260
10.2.4 Stress Intensity Factors for a Crack in a Graded
Interlayer between Two Dissimilar Materials ....... 264
10.3 Dynamic Fracture Mechanics ............................... 266
10.3.1 Basic Equations of Plane Elastodynamics ........... 266
10.3.2 Stationary Cracks under Dynamic Loading ........... 268
10.3.3 Dynamic Crack Propagation ......................... 271
10.3.4 Yoffe Crack ....................................... 281
References .................................................... 284
APPENDIX: Stress Intensity Factors ............................ 287
Index ......................................................... 295
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