Fundamentals of fracture mechanics

Cover......Page 1
Title Page......Page 3
Copyright......Page 4
Contents......Page 6
1.2.1 Deformation and Strain Tensor......Page 16
1.2.2 Traction and Stress Tensor......Page 21
1.2.3 Traction–Stress Relation......Page 23
1.2.4 Equilibrium Equations......Page 24
1.2.5 Stress Transformation......Page 27
1.2.7 Principal Stresses and Principal Planes......Page 30
1.2.8 Transformation of Displacement and Other Vectors......Page 34
1.2.10 Definition of Elastic Material and Stress–Strain Relation......Page 35
1.2.11 Number of Independent Material Constants......Page 39
1.2.12 Material Planes of Symmetry......Page 40
1.2.13 Stress–Strain Relation for Isotropic Materials—Green’s Approach......Page 45
1.2.14 Navier’s Equation of Equilibrium......Page 48
1.3 Some Classical Problems in Elasticity......Page 51
1.3.1 In-Plane and Out-of-Plane Problems......Page 53
1.3.2 Plane Stress and Plane Strain Problems......Page 54
1.3.3 Airy Stress Function......Page 57
1.3.4 Some Classical Elasticity Problems in Two Dimensions......Page 60
1.3.5 Thick Wall Spherical Pressure Vessel......Page 87
Exercise Problems......Page 90
2.2 Williams’ Method to Compute the Stress Field near a Crack Tip......Page 100
2.2.1 Satisfaction of Boundary Conditions......Page 103
2.2.2 Acceptable Values of n and ג......Page 105
2.2.3 Dominant Term......Page 107
2.2.4 Strain and Displacement Fields......Page 111
2.3 Stress Intensity Factor and Fracture Toughness......Page 115
2.4 Stress and Displacement Fields for Antiplane Problems......Page 116
2.6 Direction of Crack Propagation......Page 117
2.7 Mixed Mode Failure Curve for In-Plane Loading......Page 120
2.9 Concluding Remarks......Page 122
Exercise Problems......Page 123
3.2 Griffith’s Energy Balance......Page 128
3.3 Energy Criterion of Crack Propagation for Fixed Force and Fixed Grip Conditions......Page 130
3.3.1 Soft Spring Case......Page 133
3.3.2 Hard Spring Case......Page 134
3.4 Experimental Determination of G[sub(c)]......Page 135
3.4.2 Fixed Grip Experiment......Page 137
3.5 Relation between Strain Energy Release Rate (G) and Stress Intensity Factor (K)......Page 138
3.6.1 Griffith Crack......Page 141
3.6.2 Circular or Penny-Shaped Crack......Page 144
3.6.3 Semi-infinite Crack in a Strip......Page 145
3.6.4 Stack of Parallel Cracks in an Infinite Plate......Page 146
3.6.5 Star-Shaped Cracks......Page 148
3.6.6 Pressurized Star Cracks......Page 150
3.6.7 Longitudinal Cracks in Cylindrical Rods......Page 153
3.7 Concluding Remarks......Page 156
References......Page 157
Exercise Problems......Page 158
4.2 First Approximation on the Plastic Zone Size Estimation......Page 162
4.2.1 Evaluation of r[sub(p)]......Page 163
4.2.2 Evaluation of α;r[sub(p)]......Page 164
4.3 Determination of the Plastic Zone Shape in Front of the Crack Tip......Page 165
4.4 Plasticity Correction Factor......Page 170
4.5.1 Plane Stress Case......Page 172
4.5.2 Plane Strain Case......Page 173
4.6 Dugdale Model......Page 174
4.7 Crack Tip Opening Displacement......Page 176
4.8.1 Compact Tension Specimen......Page 179
4.8.2 Three-PointB end Specimen......Page 183
4.8.3 Practical Examples......Page 185
4.9 Concluding Remarks......Page 186
Exercise Problems......Page 187
5.2 Derivation of J-Integral......Page 190
5.3 J-Integral over a Closed Loop......Page 193
5.4 Path Independence of J-Integral......Page 195
5.5 J-Integral for Dugdale Model......Page 197
5.6 Experimental Evaluation of Critical J-Integral Value, J[sub(c)]......Page 198
5.7 Concluding Remarks......Page 202
Exercise Problems......Page 203
6.3 Fatigue Analysis—Fracture Mechanics Approach......Page 204
6.4 Fatigue Analysis for Materials Containing Microcracks......Page 208
Exercise Problems......Page 210
7.2 Slit Crack in a Strip......Page 212
7.3 Crack Intersecting a Free Surface......Page 214
7.4 Strip with a Crack on Its One Boundary......Page 215
7.5 Strip with Two Collinear Identical Cracks on Its Two Boundaries......Page 216
7.6 Two Half Planes Connected over a Finite Region Forming Two Semi-infinite Cracks in a Full Space......Page 217
7.7 Two Cracks Radiating Out from a Circular Hole......Page 218
7.8 Two Collinear Finite Cracks in an Infinite Plate......Page 219
7.10 Pressurized Crack......Page 221
7.11 Crack in a Wide Strip with a Concentrated Force at Its Midpoint and a Far Field Stress Balancing the Concentrated Force......Page 222
7.12 Circular or Penny-Shaped Crack in a Full Space......Page 224
7.13 Elliptical Crack in a Full Space......Page 227
7.13.1 Special Case 1—Circular Crack......Page 228
7.14 Part-through Surface Crack......Page 229
7.14.3 Plasticity Correction......Page 230
7.15 Corner Cracks......Page 231
7.15.1 Corner Cracks with Almost Equal Dimensions......Page 232
7.15.3 Corner Crack at One Edge of a Circular Hole......Page 233
References......Page 234
Exercise Problems......Page 235
8.2 Boundary Collocation Technique......Page 236
8.2.2 Rectangular Cracked Plate......Page 238
8.3.1 Stress and Displacement Matching......Page 239
8.3.2 Local Strain Energy Matching......Page 243
8.3.3 Strain Energy Release Rate......Page 244
8.3.4 J-Integral Method......Page 247
8.4 Special Crack Tip Finite Elements......Page 248
8.5 Quarter Point Quadrilateral Finite Element......Page 251
References......Page 254
9.2 Background Knowledge......Page 256
9.3 Griffith Crack in Biaxial State of Stress......Page 257
9.3.1 Stress and Displacement Fields in Terms of Westergaard Stress Function......Page 258
9.3.2 Westergaard Stress Function for the Griffith Crack under Biaxial Stress Field......Page 259
9.3.3 Stress Field Close to a Crack Tip......Page 265
9.4 Concentrated Load on a Half Space......Page 267
9.5 Griffith Crack Subjected to Concentrated Crack Opening Loads P......Page 270
9.5.1 Stress Intensity Factor......Page 271
9.6 Griffith Crack Subjected to Nonuniform Internal Pressure......Page 272
9.7 Infinite Number of Equal Length, Equally Spaced Coplanar Cracks......Page 273
References......Page 274
Exercise Problems......Page 275
10.2 Stress Singularities at Crack Corners......Page 276
10.3 Fracture Toughness and Strength of Brittle Matrix Composites......Page 278
10.3.1 Experimental Observation of Strength Variations of FRBMCs with Various Fiber Parameters......Page 280
10.3.2 Analysis for Predicting Strength Variations of FRBMCs with Various Fiber Parameters......Page 282
10.3.4 Experimental Observation of Fracture Toughness Increase in FRBMCs with Fiber Addition......Page 291
10.4 Dynamic Effect......Page 292
References......Page 293
Exercise Problems......Page 295
Index......Page 298