9780080446882

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

by ;
  • ISBN13:

    9780080446882

  • ISBN10:

    0080446884

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2006-09-20
  • Publisher: Elsevier Science
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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

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