Voyiadjis Advances in Damage Mechanics: Metals and Metal Matrix Composites

1. Auflage 2012
ISBN: 978-0-08-091303-2
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 541 Seiten

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.

Dr. Voyiadjis is a Member of the European Academy of Sciences, and Foreign Member of both the Polish Academy of Sciences, and the National Academy of Engineering of Korea. George Z. Voyiadjis is the Boyd Professor at the Louisiana State University, in the Department of Civil and Environmental Engineering. This is the highest professorial rank awarded by the Louisiana State University System. He is also the holder of the Freeport-MacMoRan Endowed Chair in Engineering. He joined the faculty of Louisiana State University in 1980. He is currently the Chair of the Department of Civil and Environmental Engineering. He holds this position since February of 2001. He also served from 1992 to 1994 as the Acting Associate Dean of the Graduate School. He currently also serves since 2012 as the Director of the Louisiana State University Center for GeoInformatics (LSU C4G; http://c4gnet.lsu.edu/c4g/ ).Voyiadjis' primary research interest is in plasticity and damage mechanics of metals, metal matrix composites, polymers and ceramics with emphasis on the theoretical modeling, numerical simulation of material behavior, and experimental correlation. Research activities of particular interest encompass macro-mechanical and micro-mechanical constitutive modeling, experimental procedures for quantification of crack densities, inelastic behavior, thermal effects, interfaces, damage, failure, fracture, impact, and numerical modeling. Dr. Voyiadjis' research has been performed on developing numerical models that aim at simulating the damage and dynamic failure response of advanced engineering materials and structures under high-speed impact loading conditions. This work will guide the development of design criteria and fabrication processes of high performance materials and structures under severe loading conditions. Emphasis is placed on survivability area that aims to develop and field a contingency armor that is thin and lightweight, but with a very high level of an overpressure protection system that provides low penetration depths. The formation of cracks and voids in the adiabatic shear bands, which are the precursors to fracture, are mainly investigated. He has two patents, over 332 refereed journal articles and 19 books (11 as editor) to his credit. He gave over 400 presentations as plenary, keynote and invited speaker as well as other talks. Over sixty two graduate students (37 Ph. D.) completed their degrees under his direction. He has also supervised numerous postdoctoral associates. Voyiadjis has been extremely successful in securing more than $30.0 million in research funds as a principal investigator/investigator from the National Science Foundation, the Department of Defense, the Air Force Office of Scientific Research, the Department of Transportation, National Oceanic and Atmospheric Administration (NOAA), and major companies such as IBM and Martin Marietta.

Autoren/Hrsg.

Voyiadjis, George Z.

Voyiadjis, George

Inhaltsverzeichnis

1;Front Cover;1
2;Advances in Damage Mechanics: Metals and Metal Matrix Composites;4
3;Copyright Page;5
4;Table of Contents;12
5;PREFACE;8
6;CHAPTER 1. INTRODUCTION;18
6.1;1.1 Brief History of Continuum Damage Mechanics;18
6.2;1.2 Finite-strain Plasticity;20
6.3;1.3 Mechanics of Composite Materials;23
6.4;1.4 Scope of The Book;24
6.5;1.5 Notation;25
7;PART I. ISOTROPIC DAMAGE MECHANICS SCALAR FORMULATION;28
7.1;CHAPTER 2. UNIAXIAL TENSION IN METALS;30
7.1.1;2.1 Principles of Continuum Damage Mechanics;30
7.1.2;2.2 Assumptions and the Equivalence Hypothesis;32
7.1.3;2.3 Damage Evolution;34
7.1.4;2.4 Separation of Damage Due to Cracks and Voids;38
7.2;CHAPTER 3. UNIAXIAL TENSION IN ELASTIC METAL MATRIX COMPOSITES;46
7.2.1;3.1 Stresses;46
7.2.2;3.2 Strains;53
7.2.3;3.3 Constitutive Relations;59
7.2.4;3.4 Damage Evolution;65
7.3;CHAPTER 4. UNIAXIAL TENSION IN ELASTO - PLASTIC METAL MATRIX COMPOSITES: VECTOR FORMULATION OF THE OVERALL APPROACH;68
7.3.1;4.1 Preliminaries;68
7.3.2;4.2 Effective Stresses and the Yield Function;70
7.3.3;4.3 Effective Strains and the Flow Rule;71
7.3.4;4.4 Effective Constitutive Relation;73
7.3.5;4.5 Stresses in the Damaged Composite System;77
7.3.6;4.6 Damage Evolution;81
7.3.7;4.7 Elastic Constitutive Relation in the Damaged Composite System;84
7.3.8;4.8 Elasto-Plastic Constitutive Relation in the Damaged Composite System;86
7.3.9;4.9 Numerical Implementation - Example;89
8;PART II. ANISOTROPIC DAMAGE MECHANICS TENSOR FORMULATION;100
8.1;CHAPTER 5. DAMAGE AND ELASTICITY IN METALS;102
8.1.1;5.1 General States of Damage;103
8.1.2;5.2 Damage Evolution;106
8.1.3;5.3 Finite Element Formulation;108
8.1.4;5.4 Application to Ductile Fracture - Example;113
8.2;CHAPTER 6. DAMAGE AND PLASTICITY IN METALS;126
8.2.1;6.1 Stress Transformation Between Damaged and Undamaged States;126
8.2.2;6.2 Strain Rate Transformation Between Damaged and Undamaged States;131
8.2.3;6.3 The Damage Effect Tensor M;139
8.2.4;6.4 Constitutive Model;144
8.2.5;6.5 Application to Void Growth: Gurson's Model;151
8.2.6;6.6 Effective Spin Tensor;154
8.2.7;6.7 Application to Ductile Fracture - Example;155
8.3;CHAPTER 7. METAL MATRIX COMPOSITES - OVERALL APPROACH;176
8.3.1;7.1 Preliminaries;176
8.3.2;7.2 Characterization of Damage;181
8.3.3;7.3 Yield Criterion and Flow Rule;184
8.3.4;7.4 Kinematic Hardening in the Damaged Composite System;188
8.3.5;7.5 Constitutive Model;191
8.4;CHAPTER 8. METAL MATRIX COMPOSITES - LOCAL APPROACH;198
8.4.1;8.1 Assumptions;198
8.4.2;8.2 Stress and Strain Concentration Factors;200
8.4.3;8.3 Matrix and Fiber Damage Analysis;203
8.4.4;8.4 Yield Criterion and Flow Rule;207
8.4.5;8.5 Kinematic Hardening;210
8.4.6;8.6 Constitutive Model;212
8.5;CHAPTER 9. EQUIVALENCE OF THE OVERALL AND LOCAL APPROACHES;218
8.5.1;9.1 Elastic Behavior of Composites;218
8.5.2;9.2 Plastic Behavior of Composites;226
8.6;CHAPTER 10. METAL MATRIX COMPOSITES - LOCAL AND INTERFACIAL DAMAGE;236
8.6.1;10.1 Assumptions:;236
8.6.2;10.2 Theoretical Formulation of the Damage Tensor M:;239
8.6.3;10.3 Stress and Strain Concentration Factors;241
8.6.4;10.4 The Damage Effect Tensor;248
8.6.5;10.5 Effective Volume Fractions;250
8.6.6;10.6 Damage Criterion and Damage Evolution;254
8.6.7;10.7 Constitutive Model;265
8.6.8;10.8 Physical Characterization of Damage;269
8.6.9;10.9 Numerical Solution of Uniaxially Loaded Symmetric Laminated Composites;272
8.6.10;10.10 Finite Element Analysis;275
8.7;CHAPTER 11. SYMMETRIZATION OF THE EFFECTIVE STRESS TENSOR;290
8.7.1;11.1 Preliminaries:;290
8.7.2;11.2 Explicit Symmetrization Method:;292
8.7.3;11.3 Square Root Symmetrization Method:;299
8.7.4;11.4 Implicit Symmetrization Method:;307
8.8;CHAPTER 12. EXPERIMENTAL DAMAGE INVESTIGATION;314
8.8.1;12.1 Specimen Design and Preparation:;315
8.8.2;12.2 Mechanical Testing of Specimens:;320
8.8.3;12.3 SEM and Image Analysis:;322
8.8.4;12.4 Damage Characterization:;328
8.8.5;12.5 Application to Uniaxial Tension -Example:;329
8.8.6;12.6 Theory vs. Experiment for Uniaxial Tension:;332
8.8.7;12.7 Evaluation of Damage Parameters:;341
8.9;CHAPTER 13. HIGH CYCLIC FATIGUE DAMAGE FOR UNI-DIRECTIONAL METAL MATRIX COMPOSITES;352
8.9.1;13.1 Cyclic/Fatigue Damage Models in the Literature;352
8.9.2;13.2 Damage Mechanics Applied to Composite Materials;354
8.9.3;13.3 Stress and Strain Concentration Tensors;355
8.9.4;13.4 Effective Volume Fractions;357
8.9.5;13.5 Proposed Micro-Mechanical Fatigue Damage Model;358
8.9.6;13.6 Return to the Damage Surface;362
8.9.7;13.7 Numerical Analysis - Application;363
8.10;CHAPTER 14. ANISOTROPIC CYCLIC DAMAGE-PLASTICITY MODELS FOR METAL MATRIX COMPOSITES;372
8.10.1;14.1 Anisotropic Yield Surface Model for Directionally Reinforced Metal Matrix Composites;372
8.10.2;14.2 Comparison with Other Anisotropic Yield Surfaces;383
8.10.3;14.3 Numerical Simulation of the Initial Anisotropie Yield Surface;387
8.10.4;14.4. Cyclic Damage Models : Constitutive Modeling and Micromechanical Damage;391
8.10.5;14.5 Overall Effective Elasto-Plastic Stiffness Tensor : Micromechanical Model;398
8.10.6;14.6 Overall Effective Elasto-Plastic Stiffness Tensor : Continuum-Damage Model;403
8.10.7;14.7 Damage;403
8.10.8;14.8 Numerical Simulation and Discussions;407
9;PART III. ADVANCED TOPICS IN DAMAGE MECHANICS;418
9.1;CHAPTER 15. DAMAGE IN METAL MATRIX COMPOSITES USING THE GENARALIZED CELLS MODEL;420
9.1.1;15.1 Theoretical Preliminaries;420
9.1.2;15.2 Theoretical Formulation;428
9.1.3;15.3 Numerical Simulation of the Model;436
9.2;CHAPTER 16. THE KINEMATICS OF DAMAGE FOR FINITE-STRAIN ELASTO-PLASTIC SOLIDS;448
9.2.1;16.1 Theoretical Preliminaries;449
9.2.2;16.2 Description of Damage State;449
9.2.3;16.3 Fourth-Order Anisotropic Damage Effect Tensor;451
9.2.4;16.4 The Kinematics of Damage for Elasto-Plastic Behavior with Finite Strains;452
9.2.5;16.5 Irreversible Thermodynamics;465
9.2.6;16.6 Constitutive Equation for Finite Elasto-Plastic Deformation with Damage Behavior;469
9.2.7;16.7 Application to Metals;470
9.3;CHAPTER 17. A COUPLED ANISOTROPIC DAMAGE MODEL FOR THE INELASTIC RESPONSE OF COMPOSITE MATERIALS;472
9.3.1;17.1 Theoretical Formulation;473
9.3.2;17.2 Constitutive Equations;495
9.3.3;17.3 Computational Aspects of the Model;499
9.3.4;17.4 Implementation of the Viscoplastic Damage Model;511
10;References;524
11;Appendices: Listing of Damage Formulas;542
11.1;Appendix 1. Formulas for Chapter 7;543
11.2;Appendix 2. Formulas for Chapter 8;544
11.3;Appendix 3. Formulas for Chapter 11;546
11.4;Appendix 4. Formulas for Chapter 12;550
12;SUBJECT INDEX;554

Leseproben

Chapter 1 Introduction
In this introductory chapter, several issues concerning history, problems and approaches to various topics are discussed. The three topics of continuum damage mechanics, finite-strain plasticity and mechanics of composite materials are introduced. First, a brief history of continuum damage mechanics is given. This is followed by outlining some recent problems in finite-strain plasticity. Then the different approaches in the mechanics of composite materials are described. The chapter is concluded with an outline of the scope of the book and the notation used. 1.1 Brief History of Continuum Damage Mechanics
Continuum damage mechanics was introduced by Kachanov [1] in 1958 and has now reached a stage which allows practical engineering applications. In contrast to fracture mechanics which considers the process of initiation and growth of micro-cracks as a discontinuous phenomenon, continuum damage mechanics uses a continuous variable, f, which is related to the density of these defects as shown in Figures 1.1 - 1.3 (Wang et al. [2], Bettge et al. [3], Voyiadjis and Venson [4]) in order to describe the deterioration of the material before the initiation of macro-cracks. Fig 1.1 Cavities and Micro-cracks in Grain Boundaries (Wang et al., [2]) Fig 1.2 Cracks at Inclusion Surface (Bettge et al., [3]) Fig 1.3 Damage in Metal Matrix Composites (Voyiadjis and Venson [4]) Based on the damage variable f, constitutive equations of evolution are developed to predict the initiation of macro-cracks for different types of phenomena. Lemaitre [5] and Chaboche [6] used it to solve different types of fatigue problems. Leckie and Hayhurst [7], Hult [8], and Lemaitre and Chaboche [9] used it to solve creep and creep-fatigue interaction problems. Also, it was used by Lemaitre for ductile plastic fracture [10, 11] and for a number of other applications [12]. The damage variable, based on the effective stress concept, represents average material degradation which reflects the various types of damage at the micro-scale level like nucleation and growth of voids, cavities, micro-cracks, and other microscopic defects as shown in Figures 1.1, - 1.2. For the case of isotropic damage, the damage variable is scalar and the evolution equations are easy to handle. It has been argued [12] that the assumption of isotropic damage is sufficient to give good predictions of the load carrying capacity, the number of cycles or the time to local failure in structural components. However, development of anisotropic damage and plasticity has been confirmed experimentally [13-15] even if the virgin material is isotropic. This has prompted several researchers to investigate the general case of anisotropic damage. The theory of anisotropic damage mechanics was developed by Sidoroff and Cordebois [16-18], and later used by Lee, et al [15], and Chow and Wang [19, 20] to solve simple ductile fracture problems. Prior to this latest development, Krajcinovic and Foneska [21], Murakami and Ohno [22], Murakami [23], and Krajcinovic [24] investigated brittle and creep fracture using appropriate anisotropic damage models. Although these models are based on a sound physical background, they lack vigorous mathematical justification and mechanical consistency. Consequently, more work needs to be done to develop a more involved theory capable of producing results that can be used for practical applications [21, 25]. In the general case of anisotropic damage, the damage variable has been shown to be tensorial in nature [22, 26]. This damage tensor was shown to be an irreducible even-rank tensor [27, 28]. Several other basic properties of the damage tensor have been outlined by Betten [29, 30] in a rigorous mathematical treatment using the theory of tensor functions. Lemaitre [31] summarized the work done in the last fifteen years to describe crack behavior using the theory of continuum damage mechanics. Also Lemaitre and Dufailly [32] described eight different experimental methods (direct and indirect) to measure damage according to the effective stress concept [33]. Chaboche [34-36] described different definitions of the damage variable based on indirect measurement procedures. Examples of these are damage variables based on the remaining life, the micro-structure and several physical parameters like density change, resistivity change, acoustic emissions, the change in fatigue limit, and the change in mechanical behavior through the concept of effective stress. 1.2 Finite-strain Plasticity
The widely used tools of classical fracture mechanics employ global concepts in analyzing ductile rupture. These include strain energy release rate, contour integrals, and even stress intensity factors which are based on an overall global analysis of the cracked structure using energy considerations. These concepts have been very successful in predicting crack behavior in two-dimensional elasticity or small strain plasticity that involves only proportional loading paths. However, these concepts suffer from the following disadvantages: 1 The hypotheses involved are too restrictive thus leading to large safety factors for their implementation. 2 It is difficult to use the concepts of classical fracture mechanics for more sophisticated problems involving finite strain plasticity, ductile fracture due to large deformation, time-dependent behavior, three-dimensional effects (nonproportional loading paths), and delamination of composites. In order to develop a model for a coupled theory of continuum damage mechanics and finite strain plasticity, a suitable stress corotational rate is needed. The Jaumann stress rate has been studied extensively in the past, but this rate will limit the theory to plasticity models which do not exhibit kinematic hardening (Lee, et al [37] and Dafalias [38]). According to these investigators, a monotonie simple shear loading causes oscillating shear stress response when use is made of the Jaumann stress rate for a kinematic hardening plasticity model. A number of plausible explanations of the phenomenon have been presented. Lee, et al. [37] proposed a modified corotational rate using the spin of the principal direction of a with the largest absolute eigenvalue, where a is the deviatoric component of the shift stress tensor. An alternate approach by Onat [39, 40] defines the spatial spin equal to the anti-symmetric part of d ij ? a jk multiplied by a constant, where d? is the plastic part of the spatial strain rate d . The non-oscillatory solution for simple shear is obtained by the proper choice of the constant. Dafalias [38, 41] and Loret [42] obtained similar relations by associating the corotational rate with the material substructure as defined by Mandel [43, 44]. Mandel [43] used the triad of director vectors attached to the material substructure and developed the theory of plasticity such that the substructure corotational rate is defined in terms of the spin of the director vectors. He postulated that the constitutive relations require not only the plastic component of the spatial strain rate tensor but also the plastic component of the spatial spin tensor. However, Onat and Leckie [28] have shown that it is advantageous to consider the internal structure and its orientations as a single entity and to use tensorial state variables for the representation of this entity [22, 26, 45-47]. Dafalias [41] and Loret [42] discussed the macroscopic constitutive relations for the plastic spin using the representation theorem for isotropic, second-rank, anti-symmetric, tensor-valued functions. The importance of the material substructure in defining objective corotational rates is also argued by Pecherski [48]. In inelastic finite deformations of polycrystalline metals, the material moves with respect to the underlying crystal lattice. The lattice itself undergoes elastic deformation and relative rigid-body rotations due to the lattice mis-orientation [48]. The work outlined above [37-42] imposes a retardation of the material spin W in order to obtain a non-oscillatory solution for the simple shear problem. The analysis of the solution of the simple shear test problem in [39-42] results in an unbounded non-oscillatory solution for the shear stress that increases montonically with increased deformation. Concurrently, the normal stress approaches an asymptotic upper bound. In the case of reference [37], both the shear and the normal stresses are unbounded and increase monotonically with increased deformation. We also note that in [39-42], the principal directions of a tend toward the bisector direction of the plane coordinate axes while in [37] the maximum principal direction of a inclines towards the horizontal axis. The above proposed solutions fail in the...