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1.Introduction1

1.1 Basic Concepts1

1.2 Constituent Materials for Composites5

1.2.1 Reinforcement Materials including Nanoreinforcements10

1.2.2 Matrix and Filler Materials12

1.3 Structural Applications of Composites18

1.4 Multifunctional Applications of Composites28

1.5 Fabrication Processes31

1.6 Elements of Mechanical Behavior of Composites42

1.7 Review of Basic Mechanics of Materials Equations44

References55

2.Lamina Stress-Strain Relationships57

2.1 Introduction57

2.2 Effective Moduli in Stress-Strain Relationships58

2.3 Symmetry in Stress-Strain Relationships62

2.4 Orthotropic and Isotropic Engineering Constants69

2.5 Specially Orthotropic Lamina73

2.6 Generally Orthotropic Lamina78

References94

3.Effective Moduli of a Continuous Fiber-Reinforced Lamina95

3.1 Introduction95

3.2 Elementary Mechanics of Materials Models104

3.2.1 Longitudinal Modulus106

3.2.2 Transverse Modulus110

3.2.3 Shear Modulus and Poisson’s Ratio112

3.3 Improved Mechanics of Materials Models120

3.4 Elasticity Models124

3.4.1 Finite Difference Models126

3.4.2 Finite Element Models129

3.4.3 Closed-Form and Variational Models133

3.5 Semiempirical Models134

References140

4.Strength of a Continuous Fiber-Reinforced Lamina143

4.1 Introduction143

4.2 Multiaxial Strength Criteria146

4.2.1 Maximum Stress Criterion147

4.2.2 Maximum Strain Criterion151

4.2.3 Quadratic Interaction Criteria153

4.3 Micromechanics Models for Lamina Strength167

4.3.1 Longitudinal Strength168

4.3.2 Transverse Strength176

4.3.3 In-Plane Shear Strength180

4.3.4 Multiaxial Strength181

References186

5.Analysis of Lamina Hygrothermal Behavior191

5.1 Introduction191

5.2 Hygrothermal Degradation of Properties193

5.3 Lamina Stress-Strain Relationships including Hygrothermal Effects208

5.4 Micromechanics Models for Hygrothermal Properties217

References228

6.Analysis of a Discontinuously Reinforced Lamina231

6.1 Introduction231

6.2 Aligned Discontinuous Fibers232

6.2.1 Stress and Strength Analysis233

6.2.2 Modulus Analysis239

6.3 Off-Axis-Aligned Discontinuous Fibers249

6.3.1 Stress and Strength Analysis249

6.3.2 Modulus Analysis251

6.4 Randomly Oriented Discontinuous Fibers260

6.4.1 Stress and Strength Analysis261

6.4.2 Modulus Analysis262

6.5 Nanofibers and Nanotubes271

6.5.1 Stress and Strength Analysis274

6.5.2 Modulus Analysis275

6.6 Particulates279

6.6.1 Stress and Strength Analysis280

6.6.2 Modulus Analysis282

6.7 Hybrid Multiscale Reinforcements284

References294

7.Analysis of Laminates299

7.1 Introduction299

7.2 Theory of Laminated Beams300

7.2.1 Flexural Stresses and Deflections300

7.2.2 Shear Stresses and Deflections305

7.3 Theory of Laminated Plates with Coupling317

7.4 Stiffness Characteristics of Selected Laminate Configurations324

7.4.1 Specially Orthotropic Laminates325

7.4.2 Generally Orthotropic Laminates325

7.4.3 Symmetric Laminates326

7.4.4 Antisymmetric Laminates327

7.4.5 Quasi-Isotropic Laminates327

7.5 Derivation and Use of Laminate Compliances335

7.5.1 Inversion of Laminate Force-Deformation Equations335

7.5.2 Determination of Lamina Stresses and Strains337

7.5.3 Determination of Laminate Engineering Constants338

7.5.4 Comparison of Measured and Predicted Compliances341

7.6 Hygrothermal Effects in Laminates350

7.6.1 Hygrothermal Degradation of Laminates350

7.6.2 Hygrothermal Stresses in Laminates350

7.6.3 Laminate Hygrothermal Expansion Coefficients353

7.7 Interlaminar Stresses354

7.8 Laminate Strength Analysis360

7.8.1 First Ply Failure and Subsequent Ply Failures Due to In-Plane Stresses360

7.8.2 Delamination Due to Interlaminar Stresses363

7.9 Deflection and Buckling of Laminates383

7.9.1 Analysis of Small Transverse Deflections384

7.9.2 Buckling Analysis390

7.10 Selection of Laminate Designs394

7.11 Application of Laminate Analysis to Composite Structures401

7.11.1 Composite Sandwich Structures401

7.11.2 Composite Grid Structures404

References417

8.Analysis of Viscoelastic and Dynamic Behavior421

8.1 Introduction421

8.2 Linear Viscoelastic Behavior of Composites425

8.2.1 Boltzmann Superposition Integrals for Creep and Relaxation428

8.2.2 Differential Equations and Spring-Dashpot Models432

8.2.3 Quasielastic Analysis442

8.2.4 Sinusoidal Oscillations and Complex Modulus Notation445

8.2.5 Elastic-Viscoelastic Correspondence Principle449

8.2.6 Temperature and Aging Effects455

8.3 Dynamic Behavior of Composites474

8.3.1 Longitudinal Wave Propagation and Vibrations in Specially Orthotropic Composite Bars475

8.3.2 Flexural Vibration of Composite Beams481

8.3.3 Transverse Vibration of Laminated Plates485

8.3.4 Analysis of Damping in Composites492

8.4 Nanoenhancement of Viscoelastic and Dynamic Properties502

References514

9.Analysis of Fracture519

9.1 Introduction519

9.2 Fracture Mechanics Analyses of Through-Thickness Cracks519

9.2.1 Stress Intensity Factor Approach522

9.2.2 Strain Energy Release Rate Approach526

9.2.3 Virtual Crack Closure Technique530

9.3 Stress Fracture Criteria for Through-Thickness Notches536

9.4 Interlaminar Fracture543

9.5 Nanoenhancement of Fracture Toughness555

References562

10.Mechanical Testing of Composites and Their Constituents569

10.1 Introduction569

10.2 Measurement of Constituent Material Properties570

10.2.1 Fiber Tests570

10.2.2 Neat Resin Matrix Tests573

10.2.3 Constituent Volume Fraction Measurement576

10.3 Measurement of Basic Composite Properties578

10.3.1 Tensile Tests578

10.3.2 Compressive Tests582

10.3.3 Shear Tests585

10.3.4 Flexure Tests594

10.3.5 Interlaminar Fracture Tests595

10.3.6 Fiber/Matrix Interface Tests599

10.3.7 Open-Hole and Filled-Hole Tests601

10.3.8 Bearing Tests602

10.3.9 Pull-Through Tests604

10.4 Measurement of Viscoelastic and Dynamic Properties613

10.4.1 Creep Tests613

10.4.2 Vibration Tests617

10.5 Measurement of Hygrothermal Properties624

10.5.1 Glass Transition Temperature Tests625

10.5.2 Thermal Expansion Tests625

10.5.3 Moisture Absorption Tests626

References630

11.Answers to Selected Problems639

Appendix A：Matrix Concepts and Operations641

Appendix B：Stress Equilibrium Equations651

Appendix C：Strain-Displacement Equations655

Index657