List of Figures ................................................ xi
List of Tables ............................................... xvii
Preface ....................................................... xix
1 Introduction ................................................. 1
1.1 Introduction ............................................ 1
1.2 Linear Elastic Fracture Mechanics ....................... 1
1.3 Elastic Plastic or Yielding Fracture Mechanics .......... 2
1.4 Mixed Mode Fracture ..................................... 2
1.5 Fatigue Crack Growth .................................... 3
1.6 Computational Fracture Mechanics ........................ 4
1.7 Scope of the Book ....................................... 4
References ................................................... 5
2 Linear Elastic Fracture Mechanics ............................ 6
2.1 Introduction ............................................ 6
2.2 Calculation of Theoretical Strength ..................... 6
2.3 Griffith's Explanation Based on Stress Concentration .... 8
2.4 Griffith's Theory of Brittle Fracture .................. 10
2.4.1 Irwin-Orowan Modification ........................ 12
2.5 Stress Intensity Factor (SIF) Approach ................. 13
2.5.1 Relationship between G and К ..................... 17
2.6 Concepts of Strain Energy and Potential Energy
Release Rates .......................................... 22
2.6.1 Crack Extension Under Load Control (Soft
Loading) ........................................ 22
2.6.2 Crack Extension Under Displacement Control
(Hard Loading) .................................. 23
2.7 Irwin Plastic Zone Size Correction ..................... 24
2.8 Dugdale-Barenblatt Model for Plastic Zone Size ......... 26
2.9 Crack-Tip Plastic Zone Shape ........................... 27
2.9.1 Mode I Plastic Zone ............................. 28
2.9.2 Plane Strain Constraint ......................... 30
2.9.3 Mode II and Mode III Plastic Zones .............. 30
2.10 Triaxiality at Crack Front ............................ 31
2.11 Thickness Dependence of Fracture Toughness KC ......... 33
2.12 Design Applications .................................... 34
Appendix 2.1 SIFs for Various Configurations ................ 48
Exercise .................................................... 54
References .................................................. 60
3 Determination of Crack-Tip Stress Field ..................... 65
3.1 Introduction ........................................... 65
3.2 Airy Stress Function Approach .......................... 65
3.3 Kolosoff-Muskhelishvili Potential Formulation .......... 68
3.4 Examples on Analytic and Stress Functions .............. 68
3.5 Westergaard Stress Function Approach ................... 69
3.5.1 Mode I Crack-Tip Field .......................... 71
3.5.2 Mode II Crack-Tip Field ......................... 75
3.6 Mode III Solution ...................................... 77
3.7 Williams' Eigenfunction Expansion for Mode I ........... 80
3.8 Williams' Eigenfunction Expansion for Mode II and
Mixed Mode ............................................. 83
Exercise .................................................... 84
References .................................................. 84
4 Crack Opening Displacement J Integral, and Resistance
Curve ....................................................... 86
4.1 Introduction ........................................... 86
4.2 Crack Opening Displacement ............................. 87
4.3 Special Integrals ...................................... 89
4.4 Rice's Path-Independent Integral J ..................... 91
4.5 J As Potential Energy Release Rate ..................... 92
4.6 Graphical Representation of J for Non-linear Elastic
Case ................................................... 94
4.7 Resistance Curve ....................................... 95
4.8 Stability of Crack Growth .............................. 97
Exercise ................................................... 100
References ................................................. 101
5 Determination of Stress Intensity Factors .................. 102
5.1 Introduction .......................................... 102
5.2 Analytical Methods .................................... 103
5.2.1 Boundary Collocation Method ..................... 108
5.2.2 Green's Function Approach ....................... 108
5.2.3 Method of Superposition ......................... 109
5.2.4 Weight Function Method .......................... 110
5.3 Numerical Technique: Finite Element Method ............ 113
5.3.1 Displacement and Stress-based Methods for
Extraction of SIFs ............................. 118
5.3.2 Energy-based Methods for Determination of
SIFs ........................................... 120
5.4 FEM-Based Calculation of G Associated with Kinking
of Crack .............................................. 138
5.5 Other Numerical Methods ............................... 139
5.6 Experimental Methods .................................. 140
5.6.1 Strain Gauge Technique ......................... 140
5.6.2 Photoelasticity ................................ 142
Exercise ................................................... 143
References ................................................. 146
6 Mixed Mode Brittle Fracture ................................ 152
6.1 Introduction .......................................... 152
6.2 Theory based on Potential Energy Release Rates ........ 153
6.3 Maximum Tangential Stress Criterion ................... 154
6.4 Maximum Tangential Principal Stress Criterion ......... 157
6.5 Strain Energy Density Criterion ....................... 159
Exercise ................................................... 163
References ................................................. 166
7 Fatigue Crack Growth ....................................... 168
7.1 Introduction .......................................... 168
7.2 Fatigue Crack Growth Rate under Constant Amplitude
Loading ............................................... 170
7.3 Factors Affecting Fatigue Crack Propagation ........... 174
7.4 Crack Closure ......................................... 174
7.5 Life Estimation Using Paris Law ....................... 176
7.6 Retardation of Crack Growth Due to Overloads .......... 178
7.7 Variable Amplitude Cyclic Loading ..................... 182
7.7.1 Rainflow Cycle Counting ........................ 190
7.8 Closure ............................................... 192
Appendix 7.1 Fortran Program for Crack Growth
Calculations .......................................... 192
Exercise ................................................... 196
References ................................................. 199
8 Elastic Plastic Fracture Mechanics ......................... 202
8.1 Introduction .......................................... 202
8.2 Briefs on Plasticity .................................. 202
8.2.1 Incremental Theories of Plasticity .............. 207
8.3 Crack Opening Displacement Criterion .................. 208
8.4 Mode III Crack-Tip Field for Elastic-Perfectly-
Plastic Materials ..................................... 209
8.5 Relationship between / and COD ........................ 212
8.6 Fracture Assessment Diagram and R-6 Curve ............. 213
8.7 Mode I Crack-Tip Field ................................ 216
8.7.1 Rice-Rosengren Analysis ........................ 216
8.7.2 Hutchinson's Analysis .......................... 221
8.8 Experimental Determination of ......................... 226
8.9 Alternative Methods for Measuring ..................... 227
8.10 Crack-Tip Constraints: T Stress and Q Factor .......... 230
8.11 Crack Propagation and Crack Growth Stability .......... 233
8.12 Engineering Estimates of .............................. 237
8.13 Closure ............................................... 245
Exercise ................................................... 254
References ................................................. 254
9 Experimental Measurement of Fracture Tougness Data ......... 257
9.1 Introduction .......................................... 257
9.2 Measurement of Plane Strain Fracture Toughness KIC .... 257
9.3 Measurement of JIC .................................... 263
9.4 Measurement of Critical COD δC ........................ 267
9.5 Measurement of K-Resistance Curve ..................... 269
9.5.1 Linear Elastic Material ........................ 269
9.5.2 Elastic Plastic Material ....................... 270
References .................................................... 272
Index ......................................................... 273
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