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Mechanics of Fibrous Composites

by: Herakovich, Carl T.

Mechanics of Fibrous Composites

by: Herakovich, Carl T.

ISBN 13:
9780471106364
ISBN 10:
0471106364
Edition: 1st
Format: Paperback
Copyright: 12/16/1997
Publisher: Wiley

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Summary

Comprehensive coverage of micro and macro mechanics of composite materials. * Case studies on designing composite materials and laminates. * Uses both SI and U.S. Customary units throughout. * This is the only book that covers laminated tubes and damage mechanics and the only one that presents an extensive array of actual experimental results for the nonlinear, inelastic response of polymeric and metallic matrix composites.

CHAPTER 1 THE WHAT AND THE WHY OF FIBROUS COMPOSITES

(28)

1.1 Introduction

(1)

1.2 Definition of a Composite

(3)

1.3 Fibers

(4)

1.3.1 Fiber Types

(2)

1.3.2 Fiber Properties

(2)

1.4 Matrix Materials

(2)

1.5 Composite Forms

(3)

1.5.1 Unidirectional Lamina

(1)

1.5.2 Woven Fabrics

(1)

1.5.3 Laminates

(1)

1.5.4 Hybrid Composites

(2)

1.5.5 Chopped Fiber

(1)

1.6 Composite Properties

(2)

1.7 Advantages of Composites

(3)

1.7.1 Specific Stiffness and Specific Strength

(1)

1.7.2 Tailored Design

(1)

1.7.3 Fatigue Life

(1)

1.7.4 Dimensional Stability

(1)

1.7.5 Corrosion Resistance

(1)

1.7.6 Cost-Effective Fabrication

(1)

1.7.7 Conductivity

(1)

1.7.8 Overall Cost Considerations

(1)

1.8 Applications

(5)

1.8.1 Aerospace

(1)

1.8.2 Composite Railway Carrier

(2)

1.8.3 Athletic and Recreational Equipment

(1)

1.8.4 Automotive

(1)

1.8.5 Infrastructure Structures

(1)

1.8.6 Industrial

(1)

1.8.7 Medical Applications

(1)

1.8.8 Electronic

(1)

1.8.9 Military

(1)

1.9 Fabrication Methods

(4)

1.9.1 Autoclave Curing

(1)

1.9.2 Filament Winding

(1)

1.9.3 Pultrusion

(1)

1.9.4 Braiding

(2)

1.9.5 Resin Transfer Molding

(1)

1.9.6 Metal Matrix Composites

(1)

1.10 Summary

(1)

References

(1)

Additional Reading Selections

(1)

Exercises

(1)

CHAPTER 2 CONCEPTS OF SOLID MECHANICS

(18)

2.1 Introduction

(1)

2.2 Tensors

(3)

2.3 Deformation

(1)

2.4 Strain

(1)

2.5 Stress

(1)

2.6 Equilibrium

(1)

2.7 Boundary Conditions

(1)

2.7.1 Tractions

(1)

2.7.2 Free Surface Boundary Conditions

(1)

2.8 Continuity Conditions

(1)

2.8.1 Displacement Continuity

(1)

2.8.2 Traction Continuity

(1)

2.9 Compatibility

(1)

2.10 Constitutive Equations

(1)

2.11 Plane Stress

(1)

2.12 Plane Strain

(1)

2.13 Generalized Plane Problems

(1)

2.14 Strain Energy Density

(1)

2.15 Minimum Principles

(3)

2.15.1 Minimum Potential Energy

(1)

2.15.2 Minimum Complementary Energy

(1)

2.15.3 Bounds and Uniqueness

(1)

References

(1)

Exercises

(1)

CHAPTER 3 3-D CONSTITUTIVE EQUATIONS

(31)

3.1 Effective Property Concept

(1)

3.2 Generalized Hooke's Law

(1)

3.3 Material Symmetry

(5)

3.3.1 Monoclinic Material

(2)

3.3.2 Orthotropic Material

(1)

3.3.3 Transversely Isotropic Material

(2)

3.3.4 Isotropic Material

(1)

3.4 Engineering Constants

(4)

3.5 Coordinate Transformations

(7)

3.5.1 Stress and Strain Transformation about an Axis

(1)

3.5.2 Stiffness Transformation

(2)

3.5.3 Compliance Transformation

(1)

3.5.4 Transversely Isotropic Material

(1)

3.5.5 0 Dependence of Transformed Stiffness

(2)

3.6 Summary of 3-D Constitutive Equations

(3)

3.7 Material Dependence of Transformed Stiffness

(2)

3.8 Thermal Effects

(5)

3.8.1 Thermal Strains and Coefficient of Thermal Expansion

(2)

3.8.2 Constitutive Equation

(3)

3.9 Moisture Effects

(1)

3.9.1 Hygroscopic Expansion

(1)

3.9.2 Hygro-Thermo-Elastic Constitutive Equation

(1)

3.10 Summary

(1)

References

(1)

Exercises

(2)

CHAPTER 4 PLANE STRESS CONSTITUTIVE EQUATIONS

(34)

4.1 Plane Stress Stiffness and Compliance

(4)

4.1.1 Reduced Stiffness Matrix

(1)

4.1.2 Reduced Stiffness and Compliance for Orthotropic Material

(1)

4.1.3 Compliance and Stiffness in Terms of Engineering Constants

(1)

4.2 Constitutive Equations in Material Coordinates

(1)

4.3 2-D Transformations about an Axis

(5)

4.3.1 Lamina Stress-Strain Relations in Global Coordinates

(3)

4.4 Stiffness and Compliance 0 Dependence

(3)

4.5 Lamina Engineering Constants

(10)

4.5.1 Axial Modulus

(1)

4.5.2 Poisson's Ratio

(2)

4.5.3 Transverse Modulus

(1)

4.5.4 Shear Modulus

(2)

4.5.5 Coefficients of Mutual Influence

(1)

4.5.6 Additional Lamina Engineering Constants

(2)

4.5.7 Comparison of Theory and Experiment

(2)

4.6 Measurement of Material Engineering Constants

100

(2)

4.6.1 Axial and Shear Moduli

102

(1)

4.7 Invariant Properties of Reduced Stiffness

102

(1)

4.8 Thermal Effects

103

(5)

4.8.1 Coefficient of Thermal Expansion

103

(2)

4.8.2 Thermo-Elastic Constitutive Equation

105

(3)

4.9 Moisture Effects

108

(1)

4.9.1 Hygroscopic Expansion

108

(1)

4.9.2 Hygrothermal Constitutive Equations

108

(1)

4.10 Summary

109

(1)

References

109

(1)

Exercises

109

(3)

CHAPTER 5 LAMINATION THEORY

112

(73)

5.1 Introduction

112

(1)

5.2 Notation

112

(2)

5.3 Assumptions of Lamination Theory

114

(1)

5.4 Strain-Displacement Relationships

114

(2)

5.5 Stresses

116

(1)

5.6 In-Plane Forces per Unit Length

116

(2)

5.7 Moments per Unit Length

118

(1)

5.8 Laminate Constitutive Relations

119

(3)

5.9 Symmetric Laminates

122

(2)

5.10 Special Laminates

124

(6)

5.10.1 Specially Orthotropic Laminates

125

(1)

5.10.2 Balanced Laminates

126

(1)

5.10.3 Quasi-Isotropic Laminates

127

(3)

5.11 Examples for Laminate [A], [B], and [D] Values

130

(6)

5.12 Laminate Engineering Constants

136

(2)

5.12.1 Angle-Ply Laminates

138

(5)

5.12.2 General Laminates

143

(1)

5.12.3 Comparison of Angle-Ply Engineering Constants

143

(2)

5.13 Stress Distributions

145

(7)

5.13.1 Stresses Due to N(x) Loading

146

(5)

5.13.2 Stresses Due to Moment Loading

151

(1)

5.13.3 Comment on Stress Distributions

152

(1)

5.14 Stresses and Strains in Angle-Ply Laminates

152

(7)

5.14.1 Stresses in Principal Material Coordinates

152

(6)

5.14.2 Strains in Principal Material Coordinates

158

(1)

5.15 Unsymmetric Laminates

159

(4)

5.16 Thermo-Elastic Lamination Theory

163

(8)

5.16.1 Thermal Forces and Moments

163

(2)

5.16.2 Laminate Coefficient of Thermal Expansion

165

(1)

5.16.3 Angle-Ply CTE Comparisons

166

(2)

5.16.4 Thermal Stresses

168

(1)

5.16.5 Application to Unsymmetric Laminates

169

(2)

5.17 Hygrothermal Laminate Analysis

171

(1)

5.18 Laminate Through-Thickness Properties

172

(7)

5.18.1 Through-Thickness Poisson's Ratios

173

(4)

5.18.2 Through-Thickness Coefficient of Thermal Expansion

177

(1)

5.18.3 Through-Thickness Coefficient of Hygroscopic Expansion

178

(1)

5.19 Designing with Laminates

179

(3)

5.20 Summary

182

(1)

References

182

(1)

Exercises

183

(2)

CHAPTER 6 TEST METHODS

185

(37)

6.1 Introduction

185

(1)

6.2 Quality Assessment

186

(3)

6.2.1 Microscopy

186

(1)

6.2.2 Ultrasonic Inspection

186

(1)

6.2.3 X-Ray

187

(2)

6.3 Physical Properties

189

(3)

6.3.1 Density

189

(1)

6.3.2 Fiber Volume Fraction

190

(1)

6.3.3 Void Content

190

(1)

6.3.4 Moisture Content

191

(1)

6.4 Mechanical Property Characterization

192

(26)

6.4.1 General Considerations

192

(1)

6.4.2 Strain Measurement

192

(1)

6.4.3 Tensile Testing

193

(11)

6.4.4 Shear Testing

204

(9)

6.4.5 Compression Testing

213

(3)

6.4.6 Four-Point Bending

216

(1)

6.4.7 Thermal Expansion

217

(1)

References

218

(1)

ASTM Standards

219

(2)

Exercises

221

(1)

CHAPTER 7 MATERIAL RESPONSE

222

(25)

7.1 Introduction

222

(1)

7.2 Polymer Matrix Composites

223

(11)

7.2.1 Unidirectional Aramid/Epoxy

223

(4)

7.2.2 Carbon/Epoxy

227

(5)

7.2.3 Carbon/Polyimide

232

(2)

7.3 Metal Matrix Composites

234

(11)

7.3.1 Unidirectional Boron/Aluminum

236

(4)

7.3.2 Silicon-Carbide Titanium

240

(5)

7.4 Summary

245

(1)

References

245

(2)

CHAPTER 8 INTERLAMINAR STRESSES

247

(56)

8.1 Introduction

247

(2)

8.1.1 Historical Review

248

(1)

8.2 Finite-Width Coupon

249

(16)

8.2.1 Equilibrium Considerations

250

(10)

8.2.2 Mismatch Considerations

260

(3)

8.2.3 Displacement Fields

263

(1)

8.2.4 Design Considerations

263

(2)

8.3 Finite-Element Analysis

265

(10)

8.3.1 Displacement Formulation

265

(3)

8.3.2 Free Edge Deformations

268

(7)

8.4 Complementary Energy Formulation

275

(9)

8.4.1 Global Equilibrium Formulation (KL Solution)

276

(3)

8.4.2 Complementary Energy Minimization

279

(1)

8.4.3 Extension/Bending Formulation with Mismatch Terms

280

(4)

8.5 Interlaminar Stress Distributions

284

(15)

8.5.1 Cross-Ply Laminates

285

(1)

8.5.2 Angle-Ply Laminates

285

(9)

8.5.3 Quasi-Isotropic Laminates

294

(5)

8.6 Summary

299

(1)

References

299

(2)

Exercises

301

(2)

CHAPTER 9 FAILURE AND DAMAGE

303

(59)

9.1 Introduction

303

(1)

9.2 Failure Mechanisms

303

(4)

9.2.1 Axial Tensile Strength

304

(2)

9.2.2 Axial Compressive Strength

306

(1)

9.3 Macroscopic Failure Theories

307

(18)

9.3.1 Maximum Stress Theory

309

(4)

9.3.2 Maximum Strain Theory

313

(1)

9.3.3 Tsai-Hill Theory

314

(2)

9.3.4 Tensor Polynomial Failure Criterion

316

(3)

9.3.5 Comparison of Failure Criteria

319

(1)

9.3.6 Comparisons for Off-Axis Laminae

320

(5)

9.4 Laminate Failures

325

(7)

9.4.1 Free Edge-Initiated Failure in Angle-Ply Laminates

325

(4)

9.4.2 Stacking Sequence-Dependent Angle-Ply Laminate Failure

329

(3)

9.4.3 Quasi-Isotropic Laminate Failures

332

(1)

9.5 Damage Mechanics

332

(27)

9.5.1 Mesoscale Composite Damage Theory

333

(9)

9.5.2 Mesoscale Damage Parameter Determination

342

(7)

9.5.3 Failure Prediction

349

(1)

9.5.4 Mesoscale Composite Damage Theory Predictions

350

(9)

9.6 Summary

359

(1)

References

359

(2)

Exercises

361

(1)

CHAPTER 10 LAMINATED TUBES

362

(40)

10.1 Introduction

362

(1)

10.2 Single-Layer Elasticity Solution

363

(12)

10.2.1 Strains in Cylindrical Coordinates

363

(1)

10.2.2 Compatibility

364

(1)

10.2.3 Constitutive Equations

365

(1)

10.2.4 Equilibrium

366

(1)

10.2.5 Displacements

366

(4)

10.2.6 Stress Boundary Conditions

370

(1)

10.2.7 Simplified Displacements

370

(1)

10.2.8 Strains

370

(1)

10.2.9 Stresses

371

(1)

10.2.10 Normal Stress Boundary Conditions

372

(1)

10.2.11 Axial Force

372

(1)

10.2.12 Torque

373

(1)

10.2.13 Thermomechanical Loading

373

(1)

10.2.14 Pure Thermal Loading

373

(1)

10.2.15 Special Fiber Orientations

374

(1)

10.3 Laminated Tube

375

(5)

10.3.1 Layer Displacements

375

(1)

10.3.2 Traction Continuity Conditions

375

(1)

10.3.3 Displacement Continuity Conditions

375

(1)

10.3.4 Reduced Displacements

376

(1)

10.3.5 Layer Strains

376

(1)

10.3.6 Layer Stresses

377

(1)

10.3.7 Axial Force

377

(1)

10.3.8 Torque

377

(1)

10.3.9 Boundary Conditions

378

(1)

10.3.10 Traction and Displacement Continuity Requirements

378

(1)

10.3.11 Simultaneous Equations for a Laminated Tube

378

(2)

10.4 Tube Response

380

(9)

10.4.1 Effective Axial Modulus

380

(1)

10.4.2 Effective Poisson's Ratio

380

(1)

10.4.3 Effective Axial Shear Modulus

381

(1)

10.4.4 Effective Coefficients of Thermal Expansion

382

(2)

10.4.5 Axial-Rotational Coupling

384

(5)

10.5 Stress Distributions

389

(10)

10.5.1 Axial Stresses XXX(x)

390

(3)

10.5.2 Hoop Stresses XXX(0)

393

(1)

10.5.3 Radial Stresses XXX(r)

393

(1)

10.5.4 Shear Stresses XXX(x0)

393

(6)

10.6 Nonlinear Response and Dynamic Loading

399

(1)

10.7 Solid Cylinders

399

(1)

10.8 Summary

399

(1)

References

400

(1)

Exercises

401

CHAPTER 11 MICROMECHANICS

402

(47)

11.1 Introduction

402

(1)

11.2 Effective Properties

402

(2)

11.3 Strength of Materials Approximations

404

(8)

11.3.1 Effective Axial Modulus

404

(1)

11.3.2 Effective Axial Poisson's Ratio

405

(2)

11.3.3 Effective Transverse Modulus

407

(1)

11.3.4 Effective Axial Shear Modulus

408

(3)

11.3.5 Degree of Orthotropy

411

(1)

11.3.6 Summary for Strength of Materials Approaches

411

(1)

11.4 Continuum Approaches

412

(34)

11.4.1 Equivalent Homogeneity

412

(1)

11.4.2 Volumetric Averaging

412

(1)

11.4.3 Hill's Concentration Factors

413

(1)

11.4.4 Voigt Approximation

414

(2)

11.4.5 Reuss Approximation

416

(1)

11.4.6 Concentric Cylinder Assemblage Model

417

(7)

11.4.7 The Method of Cells

424

(12)

11.4.8 The Generalized Method of Cells

436

(1)

11.4.9 Self-Consistent Method

436

(2)

11.4.10 Mori-Tanaka Method

438

(1)

11.4.11 Micromechanics Using Finite Elements

438

(1)

11.4.12 Model Comparisons

439

(7)

11.5 Summary

446

(1)

References

446

(2)

Exercises

448

(1)

Appendix A MATRIX INVERSION

449

(1)

Appendix B BOOKS ON COMPOSITES

450

(3)

Author Index

453

(3)

Subject Index

456

Amazon no longer offers textbook rentals. We do!

Mechanics of Fibrous Composites

Mechanics of Fibrous Composites

9780471106364

0471106364

Summary

Author Biography

Table of Contents

Supplemental Materials

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