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Loading...Mechanics of Composite Materials
Second Edition
Autar K. Kaw
Contents
1 Introduction to Composite Materials . 1
Chapter Objectives 1
1.1 Introduction 1
1.2 Classification .16
1.2.1 Polymer Matrix Composites 19
1.2.2 Metal Matrix Composites 40
1.2.3 Ceramic Matrix Composites 45
1.2.4 Carbon–Carbon Composites .46
1.3 Recycling Fiber-Reinforced Composites 50
1.4 Mechanics Terminology 51
1.5 Summary .54
Key Terms 54
Exercise Set 55
References .57
General References .58
Video References .59
2 Macromechanical Analysis of a Lamina 61
Chapter Objectives 61
2.1 Introduction 61
2.2 Review of Definitions 65
2.2.1 Stress 65
2.2.2 Strain .68
2.2.3 Elastic Moduli 75
2.2.4 Strain Energy 77
2.3 Hooke’s Law for Different Types of Materials .79
2.3.1 Anisotropic Material .81
2.3.2 Monoclinic Material 82
2.3.3 Orthotropic Material (Orthogonally Anisotropic)/Specially
Orthotropic .84
2.3.4 Transversely Isotropic Material 87
2.3.5 Isotropic Material 88
2.4 Hooke’s Law for a Two-Dimensional Unidirectional Lamina .99
2.4.1 Plane Stress Assumption 99
2.4.2 Reduction of Hooke’s Law in Three Dimensions to Two
Dimensions .100
2.4.3 Relationship of Compliance and Stiffness Matrix to
Engineering Elastic Constants of a Lamina 101
2.5 Hooke’s Law for a Two-Dimensional Angle Lamina 1092.6 Engineering Constants of an Angle Lamina .121
2.7 Invariant Form of Stiffness and Compliance Matrices for an
Angle Lamina .132
2.8 Strength Failure Theories of an Angle Lamina 137
2.8.1 Maximum Stress Failure Theory 139
2.8.2 Strength Ratio 143
2.8.3 Failure Envelopes 144
2.8.4 Maximum Strain Failure Theory 146
2.8.5 Tsai–Hill Failure Theory .149
2.8.6 Tsai–Wu Failure Theory .153
2.8.7 Comparison of Experimental Results with Failure
Theories .158
2.9 Hygrothermal Stresses and Strains in a Lamina 160
2.9.1 Hygrothermal Stress–Strain Relationships for a
Unidirectional Lamina 163
2.9.2 Hygrothermal Stress–Strain Relationships for an
Angle Lamina 164
2.10 Summary .167
Key Terms 167
Exercise Set 168
References .174
Appendix A: Matrix Algebra 175
Key Terms 195
Appendix B: Transformation of Stresses and Strains .197
B.1 Transformation of Stress 197
B.2 Transformation of Strains 199
Key Terms 202
3 Micromechanical Analysis of a Lamina . 203
Chapter Objectives 203
3.1 Introduction 203
3.2 Volume and Mass Fractions, Density, and Void Content .204
3.2.1 Volume Fractions .204
3.2.2 Mass Fractions .205
3.2.3 Density 207
3.2.4 Void Content 211
3.3 Evaluation of the Four Elastic Moduli .215
3.3.1 Strength of Materials Approach .216
3.3.1.1 Longitudinal Young’s Modulus 218
3.3.1.2 Transverse Young’s Modulus 221
3.3.1.3 Major Poisson’s Ratio .227
3.3.1.4 In-Plane Shear Modulus 229
3.3.2 Semi-Empirical Models 232
3.3.2.1 Longitudinal Young’s Modulus 234
3.3.2.2 Transverse Young’s Modulus 2343.3.2.3 Major Poisson’s Ratio .236
3.3.2.4 In-Plane Shear Modulus 237
3.3.3 Elasticity Approach .239
3.3.3.1 Longitudinal Young’s Modulus 241
3.3.3.2 Major Poisson’s Ratio .249
3.3.3.3 Transverse Young’s Modulus 251
3.3.3.4 Axial Shear Modulus .256
3.3.4 Elastic Moduli of Lamina with Transversely Isotropic
Fibers .268
3.4 Ultimate Strengths of a Unidirectional Lamina .271
3.4.1 Longitudinal Tensile Strength .271
3.4.2 Longitudinal Compressive Strength 277
3.4.3 Transverse Tensile Strength .284
3.4.4 Transverse Compressive Strength 289
3.4.5 In-Plane Shear Strength 291
3.5 Coefficients of Thermal Expansion .296
3.5.1 Longitudinal Thermal Expansion Coefficient 297
3.5.2 Transverse Thermal Expansion Coefficient 298
3.6 Coefficients of Moisture Expansion 303
3.7 Summary .307
Key Terms 308
Exercise Set 308
References . 311
4 Macromechanical Analysis of Laminates . 315
Chapter Objectives 315
4.1 Introduction 315
4.2 Laminate Code .316
4.3 Stress–Strain Relations for a Laminate 318
4.3.1 One–Dimensional Isotropic Beam Stress–Strain
Relation .318
4.3.2 Strain-Displacement Equations .320
4.3.3 Strain and Stress in a Laminate 325
4.3.4 Force and Moment Resultants Related to Midplane
Strains and Curvatures .326
4.4 In-Plane and Flexural Modulus of a Laminate 340
4.4.1 In-Plane Engineering Constants of a Laminate .341
4.4.2 Flexural Engineering Constants of a Laminate 344
4.5 Hygrothermal Effects in a Laminate 350
4.5.1 Hygrothermal Stresses and Strains 350
4.5.2 Coefficients of Thermal and Moisture Expansion of
Laminates 358
4.5.3 Warpage of Laminates 362
4.6 Summary .363
Key Terms 364Exercise Set 364
References .367
5 Failure, Analysis, and Design of Laminates . 369
Chapter Objectives 369
5.1 Introduction 369
5.2 Special Cases of Laminates 370
5.2.1 Symmetric Laminates .370
5.2.2 Cross-Ply Laminates .371
5.2.3 Angle Ply Laminates 372
5.2.4 Antisymmetric Laminates 372
5.2.5 Balanced Laminate 373
5.2.6 Quasi-Isotropic Laminates .373
5.3 Failure Criterion for a Laminate .380
5.4 Design of a Laminated Composite .393
5.5 Other Mechanical Design Issues .419
5.5.1 Sandwich Composites 419
5.5.2 Long-Term Environmental Effects 420
5.5.3 Interlaminar Stresses .421
5.5.4 Impact Resistance 422
5.5.5 Fracture Resistance .423
5.5.6 Fatigue Resistance .424
5.6 Summary .425
Key Terms 426
Exercise Set 426
References .430
6 Bending of Beams . 431
Chapter Objectives 431
6.1 Introduction 431
6.2 Symmetric Beams 433
6.3 Nonsymmetric Beams .444
6.4 Summary .455
Key Terms 455
Exercise Set 456
References .457
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