Advances in Damage Mechanics: Metals and Metal Matrix Composites

by Voyiadjis

• ISBN13: 9780080436012
• ISBN10: 0080436013
• Format: Hardcover
• Copyright: 1999-11-09
• Publisher: Elsevier Science

Summary

This book provides in a single and unified volume a clear and thorough presentation of the recent advances in continuum damage mechanics for metals and metal matrix composites. Emphasis is placed on the theoretical formulation of the different constitutive models in this area, but sections are added to demonstrate the applications of the theory. In addition, some sections contain new material that has not appeared before in the literature. The book is divided into three major parts: Part I deals with the scalar formulation and is limited to the analysis of isotropic damage in materials; Parts II and III deal with the tensor formulation and is applied to general states of deformation and damage. The material appearing in this text is limited to plastic deformation and damage in ductile materials (e.g. metals and metal matrix composites) but excludes many of the recent advances made in creep, brittle fracture, and temperature effects since the authors feel that these topics require a separate volume for this presentation. Furthermore, the applications presented in this book are the simplest possible ones and are mainly based on the uniaxial tension test.

Table of Contents

Preface	vii
Introduction	1	(12)
Brief History of Continuum Damage Mechanics	1	(2)
Finite-Strain Plasticity	3	(3)
Mechanics of Composite Materials	6	(1)
Scope of the Book	7	(1)
Notation	8	(5)
PART I: ISOTROPIC DAMAGE MECHANICS-SCALAR FORMULATION
Uniaxial Tension in Metals	13	(16)
Principles of Continuum Damage Mechanics	13	(2)
Assumptions and The Equivalence Hypothesis	15	(2)
Damage Evolution	17	(4)
Separation of Damage due to Cracks and Voids	21	(8)
Uniaxial Tension in Elastic-Metal Matrix Composites	29	(22)
Stresses	29	(7)
Strains	36	(6)
Constitutive Relations	42	(6)
Damage Evolution	48	(3)
Uniaxial Tension in Elasto-Plastic Metal Matrix Composites: Vector Formulation of Overall Approach	51	(34)
Preliminaries	51	(2)
Effective Stresses and the Yield Function	53	(1)
Effective Strains and the Flow Rule	54	(2)
Effective Constitutive Relation	56	(4)
Stresses in the Damage Composite System	60	(4)
Damage Evolution	64	(3)
Elastic Constitutive Relation in Damaged Composite System	67	(2)
Elasto-Plastic Constitutive Relation in the Damaged Composite System	69	(3)
Numerical Implementation-Example	72	(13)
PART II: ANISOTROPIC DAMAGE MECHANICS-TENSOR FORMULATION
Damage and Elasticity in Metals	85	(24)
General States of Damage	86	(3)
Damage Evolution	89	(2)
Finite Element Formulation	91	(5)
Application to Ductile Fracture-Example	96	(13)
Damage and Plasticity in Metals	109	(50)
Stress Transformation Between Damaged and Undamaged States	109	(5)
Effective stress tensor	110	(3)
Effective backstress tensor	113	(1)
Stress Rate Transformation Between Damaged and Undamaged States	114	(8)
Effective elastic strain	115	(1)
Effective plastic strain rate	116	(6)
The Damage Effect Tenson M	122	(5)
Constitutive Model	127	(7)
Damage evolution	127	(2)
Plastic deformation	129	(1)
Coupling of damage and plastic deformation	130	(4)
Application to Void Growth-Gurson's Model	134	(3)
Effective Spin Tensor	137	(1)
Application to Ductile Fracture-Example	138	(21)
Metal Matrix Composites-Overall Approach	159	(22)
Preliminaries	159	(5)
Characterization of Damage	164	(3)
Yield Criterion and Flow Rule	167	(4)
Kinematic Hardening in the Damaged Composite System	171	(3)
Constitutive Model	174	(7)
Metal Matrix Composites-Local Approach	181	(20)
Assumptions	181	(2)
Stress and Strain Concentration Factors	183	(3)
Matrix and Fiber Damage Analysis	186	(4)
Yield Criterion and Flow Rule	190	(3)
Kinematic Hardening	193	(2)
Constitutive Model	195	(6)
Equivalence of the Overall And Local Approaches	201	(18)
Elastic Behavior of Composites	201	(8)
Overall approach	202	(2)
Local approach	204	(3)
Equivalence of the two approaches	207	(3)
Plastic Behavior of Composites	209	(1)
Overall approach	210	(4)
Local approach	214	(3)
Equivalence of the two approaches	217	(2)
Metal Matrix Composites-Local and Interfacial Damage	219	(54)
Assumptions	219	(3)
Theoretical Formulation of the Damage Tensor M	222	(2)
Stress and Strain Concentration Factors	224	(7)
The Damage Effect Tensor	231	(2)
Effective Volume Fractions	233	(4)
Damage Criterion And Damage Evolution	237	(1)
Damage Criterion	237	(9)
Damage evolution of the matrix	242	(4)
Damage evolution of the fibers	246	(1)
Interfacial damage evolution	247	(1)
Constitutive Model	248	(4)
Physical Characterization of Damage	252	(3)
Numerical Solution of Uniaxially-Loaded Symmetric Laminated Composites	255	(3)
Finite Element Analysis	258	(15)
Symmetrization of Effective Stress Tensor	273	(24)
Preliminaries	273	(2)
Explicit Symmetrization Method	275	(7)
Square-Root Symmetrization Method	282	(8)
Implicit Symmetrization Method	290	(7)
Experimental Damage Investigation	297	(38)
Specimen Design and Preparation	298	(5)
Mechanical Testing of Specimens	303	(2)
SEM and Image Analysis	305	(6)
Damage Characterization	311	(1)
Application to Uniaxial Tension-Example	312	(3)
Laminate layup (0/90)s	312	(2)
Laminate layup (±45)s	314	(1)
Theory vs. Experiment for Uniaxial Tension	315	(9)
Evaluation of Damage Parameters	324	(11)
Overall quantification of damage	327	(5)
Local quantification of damage	332	(3)
High Cyclic Fatigue Damage for Uni-Directional Metal Matrix Composites	335	(20)
Cyclic/Fatigue Damage Models in the Literature	335	(2)
Damage Mechanics Applied to Composite Materials	337	(1)
Stress and Strain Concentration Tensors	338	(2)
Effective Volume Fractions	340	(1)
Proposed Micro-Mechanical Fatigue Damage Model	341	(4)
Return to the Damage Surface	345	(1)
Numerical Analysis Applications	346	(9)
Anisotropic Cyclic Damage-Plasticity Models for Metal Matrix Composites	355	(48)
Anisotropic Yield Surface Model For Directionally Reinforced Metal Matrix Composites	355	(11)
Comparison with other Anisotropic Yield Surfaces	366	(4)
Numerical Simulation of Initial Anisotropic Yield Surface	370	(4)
Cyclic Damage Models: Constitutive Modeling and Micromechanical Damage	374	(7)
Overall Effective Elasto-Plastic Stiffness Tensor: Micromechanical Model	381	(5)
Overall Effective Elasto-Plastic Stiffness Tensor: Continuum-Damage Model	386	(1)
Damage	386	(4)
Numerical Simulation and Discussions	390	(13)
PART III: ADVANCED TOPICS IN DAMAGE MECHANICS
Damage in Metal Matrix Composites Using the Generalized Cells Model	403	(28)
Theoretical Preliminaries	403	(8)
The generalized cells model	403	(6)
Incremental damage model	409	(2)
Theoretical Formulation	411	(8)
Basic assumptions	411	(1)
Local-overall relations of the damage tensors	411	(1)
Damaged strain and stress concentration tensors	412	(2)
Damage criterion	414	(4)
Overall damaged stiffness tensor for the model	418	(1)
Numerical Simulation of the Model	419	(12)
The Kinematics of Damage for Finite-Strain Elasto-Plastic Solids	431	(24)
Theoretical Preliminaries	432	(1)
Description of Damage State	432	(2)
Fourth-Order Anisotropic Damage Effect Tensor	434	(1)
The Kinematics of Damage for Elasto-Plastic Behavior with Finite Strains	435	(13)
A multiplicative decomposition	437	(7)
Fictitious damage deformation gradients	444	(2)
An Additive decomposition	446	(2)
Irreversible Thermodynamics	448	(4)
Constitutive Equation for Finite Elasto-Plastic Deformation with Damage Behavior	452	(1)
Application to Metals	453	(2)
A Coupled Anisotropic Damage Model for the Inelastic Response of Composite Materials	455	(52)
Theoretical Formulation	456	(22)
Plastic potential and yield criterion	461	(1)
Rate independent damage	462	(3)
Rate dependent damage coupled with rate dependent plasticity	465	(3)
Characterizing internal state variables of the rate dependent models	468	(1)
A physical interpretation of the damage tensor&phis;	469	(7)
Incremental expression for the damage tensor	476	(2)
Constitutive Equations	478	(4)
Constitutive equations for the composite material	478	(3)
Laminate analysis	481	(1)
Computational Aspects of the Models	482	(12)
Program flow for elasto-plastic and damage model	483	(1)
Plastic corrector algorithm	484	(1)
Damage corrector algorithm	485	(2)
Discussion of the results for the elaso-plastic damage analysis	487	(7)
Implementation of the Viscoplastic Damage Model	494	(13)
Flow of the program	494	(1)
Viscoplastic corrector algorithm	495	(2)
Damage corrector algorithm	497	(1)
Discussion for the results of viscoplastic damage analysis	497	(10)
References	507	(18)
Appendices: Listing of Damage Formulas	525	(12)
Subject Index	537