Advances in Damage Mechanics: Metals and Metal Matrix Composites With an Introduction to Fabric Tensors

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ISBN: 9780080446882 | 0080446884
Cover: Hardcover
Copyright: 9/20/2006

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The book presents the principles of Damage Mechanics along with the latest research findings. Both isotropic and anisotropic damage mechanisms are presented. Various damage models are presented coupled with elastic and elasto-plastic behavior. The book includes two chapters that are solely dedicated to experimental investigations conducted by the authors. In its last chapter, the book presents experimental data for damage in composite materials that appear in the literature for the first time. · Systematic treatment of damage mechanics in composite materials · Includes special and advanced topics · Includes basic principles of damage mechanics · Includes new experimental data that appears in print for the first time · Covers both metals and metal matrix composite materials · Includes new chapters on fabric tensors · Second edition includes four new chapters

Preface to the Second Edition

Preface to the First Edition

Chapter 1: Introduction

(12)

1.1 Brief History of Continuum Damage Mechanics

(3)

1.2 Finite-Strain Plasticity

(2)

1.3 Mechanics of Composite Materials

(2)

1.4 Scope of the Book

(1)

1.5 Notation

(4)

PART I: Isotropic Damage Mechanics - Scalar Formulation

Chapter 2: Uniaxial Tension in Metals

(16)

2.1 Principles of Continuum Damage Mechanics

(2)

2.2 Assumptions and The Equivalence Hypothesis

(3)

2.3 Damage Evolution

(3)

2.4 Separation of Damage due to Cracks and Voids

(8)

Chapter 3: Uniaxial Tension in Elastic Metal Matrix Composites

(22)

3.1 Stresses

(8)

3.2 Strains

(5)

3.3 Constitutive Relations

(6)

3.4 Damage Evolution

(3)

Chapter 4: Uniaxial Tension in Elasto-Plastic Metal Matrix Composites: Vector Formulation of the Overall Approach

(34)

4.1 Preliminaries

(2)

4.2 Effective Stresses and the Yield Function

(1)

4.3 Effective Strains and the Flow Rule

(3)

4.4 Effective Constitutive Relation

(4)

4.5 Stresses in the Damage Composite System

(4)

4.6 Damage Evolution

(3)

4.7 Elastic Constitutive Relation in the Damaged Composite System

(1)

4.8 Elasto-Plastic Constitutive Relation in the Damaged Composite System

(3)

4.9 Numerical Implementation - Example

(13)

PART II: Anisotropic Damage Mechanics - Tensor Formulation

Chapter 5: Damage and Elasticity in Metals

(24)

5.1 General States of Damage

(3)

5.2 Damage Evolution

(2)

5.3 Finite Element Formulation

(5)

5.4 Application to Ductile Fracture - Example

(13)

Chapter 6: Damage and Plasticity in Metals

109

(50)

6.1 Stress Transformation Between Damaged and Undamaged States

109

(5)

6.1.1 Effective Stress Tensor

110

(3)

6.1.2 Effective Backstress Tensor

113

(1)

6.2 Strain Rate Transformation Between Damaged and Undamaged States

114

(8)

6.2.1 Effective Elastic Strain

115

(1)

6.2.2 Effective Plastic Strain Rate

116

(6)

6.3 The Damage Effect Tensor M

122

(6)

6.4 Constitutive Model

128

(7)

6.4.1 Damage Evolution

128

(2)

6.4.2 Plastic Deformation

130

(1)

6.4.3 Coupling of Damage and Plastic Deformation

131

(4)

6.5 Application to Void Growth - Gurson's Model

135

(3)

6.6 Effective Spin Tensor

138

(1)

6.7 Application to Ductile Fracture - Example

139

(20)

Chapter 7: Metal Matrix Composites - Overall Approach

159

(22)

7.1 Preliminaries

159

(5)

7.2 Characterization of Damage

164

(3)

7.3 Yield Criterion and Flow Rule

167

(4)

7.4 Kinematic Hardening in the Damaged Composite System

171

(2)

7.5 Constitutive Model

173

(8)

Chapter 8: Metal Matrix Composites - Local Approach

181

(20)

8.1 Assumptions

181

(2)

8.2 Stress and Strain Concentration Factors

183

(3)

8.3 Matrix and Fiber Damage Analysis

186

(4)

8.4 Yield Criterion and Flow Rule

190

(3)

8.5 Kinematic Hardening

193

(2)

8.6 Constitutive Model

195

(6)

Chapter 9: Equivalence of the Overall and Local Approaches

201

(18)

9.1 Elastic Behavior of Composites

201

(8)

9.1.1 Overall Approach

202

(2)

9.1.2 Local Approach

204

(3)

9.1.3 Equivalence of the Two Approaches

207

(2)

9.2 Plastic Behavior of Composites

209

(10)

9.2.1 Overall Approach

210

(4)

9.2.2 Local Approach

214

(3)

9.2.3 Equivalence of the Two Approaches

217

(2)

Chapter 10: Metal Matrix Composites - Local and Interfacial Damage

219

(54)

10.1 Assumptions

219

(3)

10.2 Theoretical Formulation of the Damage Tensor M

222

(2)

10.3 Stress and Strain Concentration Factors

224

(7)

10.4 The Damage Effect Tensor

231

(2)

10.5 Effective Volume Fractions

233

(4)

10.6 Damage Criterion and Damage Evolution

237

(11)

10.6.1 Damage Criterion

237

(5)

10.6.2 Damage Evolution of the Matrix

242

(4)

10.6.3 Damage Evolution of the Fibers

246

(1)

10.6.4 Interfacial Damage Evolution

247

(1)

10.7 Constitutive Model

248

(4)

10.8 Physical Characterization of Damage

252

(3)

10.9 Numerical Solution of Uniaxially Loaded Symmetric Laminated Composites

255

(3)

10.10 Finite Element Analysis

258

(15)

Chapter 11: Symmetrization of the Effective Stress Tensor

273

(24)

11.1 Preliminaries

273

(2)

11.2 Explicit Symmetrization Method

275

(7)

11.3 Square Root Symmetrization Method

282

(8)

11.4 Implicit Symmetrization Method

290

(7)

Chapter 12: Experimental Damage Investigation

297

(38)

12.1 Specimen Design and Preparation

298

(5)

12.2 Mechanical Testing of Specimens

303

(2)

12.3 SEM and Image Analysis

305

(6)

12.4 Damage Characterization

311

(1)

12.5 Application to Uniaxial Tension - Example

312

(3)

12.5.1 Laminate Layup (0/90),

312

(2)

12.5.2 Laminate Layup (±45)s

314

(1)

12.6 Theory vs. Experiment for Uniaxial Tension

315

(9)

12.7 Evaluation of Damage Parameters

324

(11)

12.7.1 Overall Quantification of Damage

327

(5)

12.7.2 Local Quantification of Damage

332

(3)

Chapter 13: High Cyclic Fatigue Damage for Uni-Directional Metal Matrix Composites

335

(20)

13.1 Cyclic/Fatigue Damage Models in the Literature

335

(2)

13.2 Damage Mechanics Applied to Composite Materials

337

(1)

13.3 Stress and Strain Concentration Tensors

338

(2)

13.4 Effective Volume Fractions

340

(1)

13.5 Proposed Micro-Mechanical Fatigue Damage Model

341

(4)

13.6 Return to the Damage Surface

345

(1)

13.7 Numerical Analysis-Applications

346

(9)

Chapter 14: Anisotropic Cyclic Damage-Plasticity Models for Metal Matrix Composites

355

(54)

14.1 Anisotropic Yield Surface Model for Directionally Reinforced Metal Matrix Composites

355

(12)

14.2 Comparison with other Anisotropic Yield Surfaces

367

(5)

14.3 Numerical Simulation of the Initial Anisotropic Yield Surface

372

(4)

14.4 Cyclic Damage Models: Constitutive Modeling and Micromechanical Damage

376

(7)

14.5 Overall Effective Elasto-Plastic Stiffness Tensor: Micromechanical Model

383

(6)

14.6 Overall Effective Elasto-Plastic Stiffness Tensor: Continuum-Damage Model

389

(1)

14.7 Damage

389

(6)

14.8 Numerical Simulation and Discussions

395

(14)

Part III: Advanced Topics in Damage Mechanics

Chapter 15: Damage in Metal Matrix Composites Using the Generalized Cells Model

409

(32)

15.1 Theoretical Preliminaries

409

(10)

15.1.1 The Generalized Cells Model

409

(9)

15.1.2 Incremental Damage Model

418

(1)

15.2 Theoretical Formulation

419

(11)

15.2.1 Basic Assumptions

419

(1)

15.2.2 Local-Overall Relations of the Damage Tensors

420

(2)

15.2.3 Damaged Strain and Stress Concentration Tensors

422

(1)

15.2.4 Damage Criterion

423

(6)

15.2.5 Overall Damaged Stiffness Tensor for the Model

429

(1)

15.3 Numerical Simulation of the Model

430

(11)

Chapter 16: The Kinematics of Damage for Finite-Strain Elasto-Plastic Solids

441

(38)

16.1 Theoretical Preliminaries

442

(1)

16.2 Description of Damage State

443

(2)

16.3 Fourth-Order Anisotropic Damage Effect Tensor

445

(3)

16.4 The Kinematics of Damage for Elasto-Plastic Behavior with Finite Strains

448

(20)

16.4.1 A Multiplicative Decomposition

451

(11)

16.4.2 Fictitious Damage Deformation Gradients

462

(2)

16.4.3 An Additive Decomposition

464

(4)

16.5 Irreversible Thermodynamics

468

(6)

16.6 Constitutive Equation for Finite Elasto-Plastic Deformation with Damage Behavior

474

(2)

16.7 Application to Metals

476

(3)

Chapter 17: A Coupled Anisotropic Damage Model for the Inelastic Response of Composite Materials

479

(66)

17.1 Theoretical Formulation

481

(30)

17.1.1 Plastic Potential and Yield Criterion

488

(1)

17.1.2 Rate Independent Damage

489

(5)

17.1.3 Rate Dependent Damage Coupled with Rate Dependent Plasticity

494

(4)

17.1.4 Characterizing Internal State Variables of the Rate Dependent Models

498

(2)

17.1.5 A Physical Interpretation of the Damage Tensor

500

(9)

17.1.6 Incremental Expression for the Damage Tensor

509

(2)

17.2 Constitutive Equations

511

(6)

17.2.1 Constitutive Equations for the Composite Material

512

(3)

17.2.2 Laminate Analysis

515

(2)

17.3 Computational Aspects of the Model

517

(14)

17.3.1 Program Flow for Elasto-Plastic and Damage Model

518

(2)

17.3.2 Plastic Corrector Algorithm

520

(1)

17.3.3 Damage Corrector Algorithm

521

(2)

17.3.4 Discussion of the Results for the Elasto-Plastic Damage Analysis

523

(8)

17.4 Implementation of the Viscoplastic Damage Model

531

(14)

17.4.1 Flow of the Program

531

(1)

17.4.2 Viscoplastic Corrector Algorithm

532

(2)

17.4.3 Damage Corrector Algorithm

534

(1)

17.4.4 Discussion for the Results of Viscoplastic Damage Analysis

534

Part IV: Damage Mechanics with Fabric Tensors

Chapter 18: Damage Mechanics and Fabric Tensors

545

(44)

18.1 Introduction

545

(4)

18.2 Fabric Tensors

549

(5)

18.3 General Hypothesis and New Formulation of Damage Mechanics

554

(3)

18.4 The Damage Tensor and Fabric Tensors

557

(6)

18.5 Case of Plane Stress

563

(4)

18.6 Application to Micro-Crack Distributions

567

(9)

18.7 Application to Parallel Micro-Cracks

576

(4)

18.8 Thermodynamics and Damage Evolution

580

(9)

Chapter 19: Continuum Approach to Damage Mechanics of Composite Materials with Fabric Tensors

589

(30)

19.1 Introduction

589

(3)

19.2 Continuum Approach

592

(8)

19.3 Damage Evolution

600

(6)

19.4 Example

606

(13)

Chapter 20: Micromechanical Approach to Damage Mechanics of Composite Materials with Fabric Tensors

619

(42)

20.1 Introduction

619

(3)

20.2 Elastic Constitutive Equations

622

(8)

20.3 Damage Evolution

630

(18)

20.4 Numerical Examples

648

(13)

Chapter 21: Experimental Study and Fabric Tensor Quantification of Micro-Crack Distributions in Composite Materials

661

(26)

21.1 Introduction

661

(1)

21.2 Composite Material Specimens

662

(2)

21.3 SEM Images

664

(4)

21.4 Fabric Tensors

668

(4)

21.5 Results

672

(15)

References

687

(22)

Appendix A: Listing of Damage Formulas

709

(12)

Subject Index

721

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Advances in Damage Mechanics: Metals and Metal Matrix Composites With an Introduction to Fabric Tensors

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