Preface ..................................................... ix
1 Durability assessment of composite structures ................ 1
1.1 Introduction ............................................ 1
1.2 Historical development of damage mechanics of
composites .............................................. 3
1.3 Fatigue of composite materials .......................... 5
References ................................................... 7
2 Review of mechanics of composite materials ................... 9
2.1 Equations of elasticity ................................. 9
2.1.1 Strain-displacement relations .................... 9
2.1.2 Conservation of linear and angular momenta ...... 10
2.1.3 Constitutive relations .......................... 11
2.1.4 Equations of motion ............................. 15
2.1.5 Energy principles ............................... 15
2.2 Micromechanics ......................................... 17
2.2.1 Stiffness properties of a unidirectional
lamina .......................................... 18
2.2.2 Thermal properties of a unidirectional lamina ... 19
2.2.3 Constitutive equations for a lamina ............. 20
2.2.4 Strength of a unidirectional lamina ............. 21
2.3 Analysis of laminates .................................. 24
2.3.1 Strain-displacement relations ................... 25
2.3.2 Constitutive relationships for the laminate ..... 26
2.3.3 Stresses and strains in a lamina within a
laminate ........................................ 28
2.3.4 Effect of layup configuration ................... 28
2.4 Linear elastic fracture mechanics ...................... 29
2.4.1 Fracture criteria ............................... 30
2.4.2 Crack separation modes .......................... 31
2.4.3 Crack surface displacements ..................... 32
2.4.4 Relevance of fracture mechanics for damage
analysis ........................................ 33
References ............................................. 34
3 Damage in composite materials ............................... 36
3.1 Mechanisms of damage ................................... 37
3.1.1 Interfacial debonding ........................... 37
3.1.2 Matrix microcracking/intralaminar (ply)
cracking ........................................ 39
3.1.3 Interfacial sliding ............................. 39
3.1.4 Delamination/interlaminar cracking .............. 41
3.1.5 Fiber breakage .................................. 42
3.1.6 Fiber microbuckling ............................. 42
3.1.7 Particle cleavage ............................... 44
3.1.8 Void growth ..................................... 44
3.1.9 Damage modes .................................... 45
3.2 Development of damage in composite laminates ........... 46
3.3 Intralaminar ply cracking in laminates ................. 49
3.4 Damage mechanics ....................................... 50
References ............................................. 52
4 Micro-damage mechanics ...................................... 57
4.1 Introduction ........................................... 57
4.2 Phenomena of single and multiple fracture: ACK theory .. 58
4.2.1 Multiple matrix cracking ........................ 61
4.2.2 Perfectly bonded fiber/matrix interface: a
modified shear lag analysis ..................... 65
4.2.3 Frictional fiber/matrix interface ............... 67
4.3 Stress analysis (boundary value problem) for cracked
laminates .............................................. 68
4.3.1 Complexity and issues ........................... 68
4.3.2 Assumptions ..................................... 71
4.4 One-dimensional models: shear lag analysis ............. 73
4.4.1 Initial shear lag analysis ...................... 74
4.4.2 Interlaminar shear lag analysis ................. 77
4.4.3 Extended shear lag analysis ..................... 79
4.4.4 2-D shear lag models ............................ 80
4.4.5 Summary of shear lag models ..................... 80
4.5 Self-consistent scheme ................................. 84
4.6 2-D stress analysis: variational methods ............... 87
4.6.1 Hashin's variational analysis ................... 87
4.6.2 Effect of residual stresses ..................... 96
4.6.3 [0m/90n]s vs. [90n/0m]s laminates ............... 97
4.6.4 Improved variational analysis ................... 97
4.6.5 Related works .................................. 101
4.6.6 Comparison between 1-D and 2-D stress-based
models ......................................... 101
4.7 Generalized plain strain analysis - McCartney's
model ................................................. 104
4.8 COD-based methods ..................................... 110
4.8.1 3-D laminate theory: Gudmundson's model ........ 111
4.8.2 Lundmark-Varna model ........................... 117
4.9 Computational methods ................................. 119
4.9.1 Finite element method (FEM) .................... 120
4.9.2 Finite strip method ............................ 121
4.9.3 Layerwise theory ............................... 123
4.10 Other methods ......................................... 124
4.11 Changes in thermal expansion coefficients ............. 125
4.12 Summary ............................................... 126
References ............................................ 126
5 Macro-damage mechanics ..................................... 134
5.1 Introduction .......................................... 134
5.2 Continuum damage mechanics (CDM) of composite
materials ............................................. 138
5.2.1 RVE for damage characterization ................ 139
5.2.2 Characterization of damage ..................... 141
5.2.3 A thermodynamics framework for materials
response ....................................... 144
5.2.4 Stiffness-damage relationships ................. 148
Case 1: Cracking in one off-axis orientation ... 152
Case 2: Cross-ply laminates .................... 152
Evaluation of material constants ...................... 153
5.3 Synergistic damage mechanics (SDM) .................... 155
5.3.1 Two damage modes ............................... 156
5.3.2 Three damage modes ............................. 165
5.4 Viscoelastic composites with ply cracking ............. 170
5.5 Summary ............................................... 176
References ............................................ 177
6 Damage progression ......................................... 179
6.1 Introduction .......................................... 179
6.2 Experimental techniques ............................... 180
6.3 Experimental observations ............................. 185
6.3.1 Initiation of ply cracking ..................... 185
6.3.2 Crack growth and multiplication ................ 187
6.3.3 Crack shapes ................................... 189
6.3.4 Effect of cracking ............................. 189
6.3.5 Loading and environmental effects .............. 191
6.3.6 Cracking in multidirectional laminates ......... 193
6.4 Modeling approaches ................................... 194
6.4.1 Strength-based approaches ...................... 194
6.4.2 Energy-based approaches ........................ 198
6.4.3 Strength vs. energy criteria for multiple
cracking ....................................... 210
6.5 Randomness in ply cracking ............................ 211
6.6 Damage evolution in multidirectional laminates ........ 217
6.7 Damage evolution under cyclic loading ................. 223
6.8 Summary ............................................... 229
References ............................................ 230
7 Damage mechanisms and fatigue-life diagrams ................ 237
7.1 Introduction .......................................... 237
7.2 Fatigue-life diagrams ................................. 237
7.3 On-axis fatigue of unidirectional composites .......... 238
7.4 Effects of constituent properties ..................... 241
7.5 Unidirectional composites loaded parallel to the
fibers ................................................ 242
7.5.1 Polymer matrix composites (PMCs) ............... 242
7.5.1.1 Experimental studies of mechanisms ..... 247
7.5.2 Metal matrix composites (MMCs) ................. 250
7.5.3 Ceramic matrix composites (CMCs) ............... 252
7.6 Unidirectional composites loaded inclined to the
fibers ................................................ 257
7.7 Fatigue of laminates .................................. 259
7.7.1 Angle-ply laminates ............................ 260
7.7.2 Cross-ply laminates ............................ 261
7.7.3 General multidirectional laminates ............. 263
7.8 Fatigue-life prediction ............................... 265
7.8.1 Cross-ply laminates ............................ 266
7.8.2 General laminates .............................. 273
7.9 Summary ............................................... 273
References ............................................ 274
8 Future directions .......................................... 276
8.1 Computational structural analysis ..................... 276
8.2 Multiscale modeling of damage ......................... 278
8.2.1 Length scales of damage ........................ 280
8.2.2 Hierarchical multiscale modeling ............... 282
8.2.3 Implication on multiscale modeling:
Synergistic damage mechanics ................... 286
8.3 Cost-effective manufacturing and defect damage
mechanics ............................................. 287
8.3.1 Cost-effective manufacturing ................... 288
8.3.2 Defect damage mechanics ........................ 291
8.4 Final remarks .................................... 296
References ............................................ 298
Author index ............................................... 301
Subject index .............................................. 303
| 
