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

by Voyiadjis; Kattan

• ISBN13: 9780080446882
• ISBN10: 0080446884
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-09-20
• Publisher: Elsevier Science

Summary

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

Table of Contents

Preface to the Second Edition
Preface to the First Edition
Chapter 1: Introduction	1	(12)
1.1 Brief History of Continuum Damage Mechanics	1	(3)
1.2 Finite-Strain Plasticity	4	(2)
1.3 Mechanics of Composite Materials	6	(2)
1.4 Scope of the Book	8	(1)
1.5 Notation	9	(4)
PART I: Isotropic Damage Mechanics - Scalar Formulation
Chapter 2: Uniaxial Tension in Metals	13	(16)
2.1 Principles of Continuum Damage Mechanics	13	(2)
2.2 Assumptions and The Equivalence Hypothesis	15	(3)
2.3 Damage Evolution	18	(3)
2.4 Separation of Damage due to Cracks and Voids	21	(8)
Chapter 3: Uniaxial Tension in Elastic Metal Matrix Composites	29	(22)
3.1 Stresses	29	(8)
3.2 Strains	37	(5)
3.3 Constitutive Relations	42	(6)
3.4 Damage Evolution	48	(3)
Chapter 4: Uniaxial Tension in Elasto-Plastic Metal Matrix Composites: Vector Formulation of the Overall Approach	51	(34)
4.1 Preliminaries	51	(2)
4.2 Effective Stresses and the Yield Function	53	(1)
4.3 Effective Strains and the Flow Rule	54	(3)
4.4 Effective Constitutive Relation	57	(4)
4.5 Stresses in the Damage Composite System	61	(4)
4.6 Damage Evolution	65	(3)
4.7 Elastic Constitutive Relation in the Damaged Composite System	68	(1)
4.8 Elasto-Plastic Constitutive Relation in the Damaged Composite System	69	(3)
4.9 Numerical Implementation - Example	72	(13)
PART II: Anisotropic Damage Mechanics - Tensor Formulation
Chapter 5: Damage and Elasticity in Metals	85	(24)
5.1 General States of Damage	86	(3)
5.2 Damage Evolution	89	(2)
5.3 Finite Element Formulation	91	(5)
5.4 Application to Ductile Fracture - Example	96	(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