Preface xiii 1 Fundamentals of Classical Plasticity 1 1.1 Stress 1 1.1.1 The Concept of Stress Components 1 1.1.2 Description of the Stress State 2 1.1.2.

1 Stresses on an Arbitrary Inclined Plane 2 1.1.2.2 Stress Components on an Oblique Plane 4 1.1.2.3 Special Stresses 6 1.1.

2.4 Common Stress States 7 1.1.3 Stress Tensors and Deviatoric Stress Tensors 7 1.1.4 Mohr Stress Circles 9 1.1.4.

1 Mohr Circles for a Two-Dimensional Stress System 9 1.1.4.2 Mohr Circles for a Three-Dimensional Stress System 12 1.1.5 Equations of Force Equilibrium 13 1.2 Strain 15 1.2.

1 Nominal Strain and True Strain 15 1.2.2 Strain Components as Functions of Infinitesimal Displacements 17 1.2.3 The Maximum Shear Strains and the Octahedral Strains 20 1.2.4 Strain Rates and Strain Rate Tensors 21 1.2.

5 Incompressibility and Chief Deformation Types 23 1.3 Yield Criteria 25 1.3.1 The Concept of Yield Criterion 25 1.3.2 Tresca Yield Criterion 26 1.3.3 Mises Yield Criterion 26 1.

3.4 Twin Shear Stress Yield Criterion 27 1.3.5 Yield Locus and Physical Concepts of Tresca, Mises, and Twin Shear Stress Yield Criteria 27 1.3.5.1 Interpretation of Tresca Yield Criterion 29 1.3.

5.2 Interpretation of Twin Shear Stress Yield Criterion 30 1.3.5.3 Interpretation of Mises Yield Criterion 31 1.4 A General Yield Criterion 33 1.4.1 Representation of General Yield Criterion 33 1.

4.2 Yield Surface and Physical Interpretation 34 1.4.3 Simplified Yield Criterion 34 1.5 ClassicalTheory about Plastic Stress Strain Relation 35 1.5.1 Early Perception of Plastic Stress Strain Relations 36 1.5.

2 Concept of the Gradient-Based Plasticity and Its Relation with Mises Yield Criterion 37 1.5.2.1 Concept of the Plastic Potential 37 1.5.2.2 Physical Interpretation of the Plastic Potential 38 1.5.

2.3 Physical Interpretation of Mises Yield Function (Plastic Potential) 39 1.6 Effective Stress, Effective Strain, and Stress Type 42 1.6.1 Effective Stress 42 1.6.2 Effective Strain 42 1.6.

3 Stress Type 44 References 44 2 Experimental Research on Material Mechanical Properties under Uniaxial Tension 47 2.1 Stress Strain Relationship of Strain-Strengthened Materials under Uniaxial Tensile Stress State 47 2.2 The Stress Strain Relationship of the Strain-Rate-Hardened Materials in Uniaxial Tensile Tests 48 2.3 Stress Strain Relationship in Uniaxial Tension during Coexistence of Strain Strengthening and Strain Rate Hardening 50 2.4 Bauschinger Effect 56 2.5 Tensile Tests for Automotive Deep-Drawing Steels and High-Strength Steels 57 2.5.1 Test Material and Experiment Scheme 57 2.

5.2 True Stress Strain Curves in Uniaxial Tension 58 2.5.3 Mechanical Property Parameters of Sheets 58 2.5.3.1 Strain-Hardening Exponentn 59 2.5.

3.2 Lankford ParameterR 62 2.5.3.3 Plane Anisotropic Exponent R 62 2.5.3.4 Yield-to-Tensile Ratio s¨M b 62 2.

5.3.5 Uniform Elongation m 62 2.6 Tensile Tests on Mg-Alloys 63 2.7 Tension Tests on Ti-Alloys 63 2.7.1 Mechanical Properties of Ti-3Al-2.5V Ti-Alloy Tubes at High Temperatures 65 2.

7.2 Strain Hardening of Ti-3Al-2.5V Ti-Alloy in Deformation at High Temperatures 69 References 71 3 Experimental Research on Mechanical Properties of Materials under a Non-Uniaxial Loading Condition 73 3.1 P-p Experimental Results ofThin-Walled Tubes 73 3.1.1 Lode Experiment 73 3.1.2 P-p Experiments onThin-Walled Tubes Made of Superplastic Materials 78 3.

1.2.1 Experiment Materials and Specimens 78 3.1.2.2 Loading Methods 80 3.1.2.

3 Experimental Results and Analysis 80 3.1.3 Experiments on Tubes Subjected to Internal Pressure and Axial Compressive Forces 86 3.1.3.1 Experimental Device 86 3.1.3.

2 Material Properties 88 3.1.3.3 Experimental Results 89 3.2 Results from P-M Experiments onThin-Walled Tubes 91 3.2.1 Taylor-Quinney Experiments 91 3.2.

2 P-M Experiments on Superplastic Material 94 3.3 Biaxial Tension Experiments on Sheets 95 3.3.1 Equipment for Biaxial Tension of Cruciform Specimens 96 3.3.2 Design of Cruciform Tensile Specimens 96 3.3.3 Application of Cruciform Biaxial Tensile Test 97 3.

3.3.1 Forming Limit 97 3.3.3.2 Prediction of Yielding Locus 97 3.3.3.

3 Analysis of Composite Materials 99 3.4 Influences of Hydrostatic Stress on Mechanical Properties of Materials 100 3.4.1 Testing Technique in High-Pressure Experiments 101 3.4.2 Influences of Hydrostatic Stresses on Flow Behavior of Materials 103 3.4.3 Influences of Hydrostatic Pressure on Fracture Behavior of Materials 106 3.

5 Experimental Researches Other Than Non-Uniaxial Tension 114 3.5.1 Plane Compression Experiments 114 3.5.2 Loading Experiments along Normal and Tangential Directions 118 3.5.3 Other Combined LoadingMethods 119 References 119 4 Yield Criteria of Different Materials 123 4.1 Predicting Capability of a Yield Criterion Affected by Multiple Factors 123 4.

2 Construction of a Proper Yield Criterion in Consideration of Multifactor-Caused Effects 129 4.2.1 A Proper Frame of Yield Criterion 130 4.2.2 Practical Yield Criterion with Multifactor-Caused Effects 133 4.2.3 Material Yielding Behavior Affected by Different Factors 136 4.2.

3.1 Convexity of Yield Locus at Plane Stress State 137 4.2.3.2 Stress-Type-Caused Effects 143 4.2.3.3 Hydrostatic-Stress-Caused Effects 145 4.

2.4 Simplified Forms of the Yield Criterion 148 4.2.5 Verification of the Yield CriterionThrough Experiments 151 4.3 Anisotropic Materials 156 4.3.1 Experimental Description of Anisotropic Behavior of Rolled Sheet Metals 156 4.3.

1.1 Uniaxial Tension 157 4.3.1.2 Biaxial Tension 159 4.3.2 Brief Review of the Anisotropic Yield and Plastic Potential Functions 160 4.3.

3 Nonassociated-Flow-Rule-Based Yield Function and Plastic Potential 165 4.3.3.1 Anisotropic Yield Criterion 165 4.3.3.2 Anisotropic Plastic Potential 172 4.3.

4 Associated-Flow-Rule-Based Anisotropic Yield Criterion 174 4.3.5 Experimental Verification of Two Kinds of Anisotropic Yield Criteria 178 References 184 5 Plastic Constitutive Relations of Materials 187 5.1 Basic Concepts about Plastic Deformation of Materials and Relevant Plastic Constitutive Relations 187 5.1.1 Effects of Material, Strength, and Property Transformation on Material Plastic Deformation 187 5.1.2 General Description of Subsequent Hardening Increments and Convexity of Yield Function 189 5.

1.3 Effects of Flow Rules on Judgment of Condition of Stable Plastic Deformation of Materials 196 5.2 Equivalent Hardening Condition in Material Plastic Deformation 197 5.2.1 Universal Forms of Plastic Potential and Yield Criterion in Constructing Plastic Constitutive Relations 198 5.2.2 Relationship between Yield Function and Plastic Potential in Describing Equivalent Hardening Increments 199 5.2.

3 Equivalent Hardening Condition Corresponding to Associated Flow Rule 201 5.2.4 Equivalent Hardening Condition Related to Nonassociated Flow Rule 206 5.3 Softening and Strength Property Changes in Plastic Deformation of Materials 209 5.3.1 Mechanical Models Mimicking Plastic Deformation of Sensitive-to-Pressure Materials 210 5.3.2 Dynamic Models to Imitate the Stress Strain Relation of Anisotropic Material 215 5.

3.3 Softening and Material Strength Property Changes in a Stable Plastic Deformation 219 5.4 Influences of Loading Path on Computational Accuracy of Incremental Theory 227 5.4.1 Discontinuous Stress Path 227 5.4.2 Unrealistic Strain Path 229 References 231 6 Description of Material Hardenability with Different Models 233 6.1 Plastic Constitutive Relations of Sensitive-to-Pressure Materials 233 6.

1.1 Experimental Characterizations of Yield Function and Corresponding Plastic Potential 234 6.1.2 Predictions-Based Constitutive Relations and in Comparison with Experimental Results 237 6.1.2.1 Influences of Hardening Models upon Description of Plastic Deformation of Materials 238 6.1.

2.2 Yieldability and Plastic Flowability of Sensitive-to-Pressure Materials 239 6.1.2.3 Prediction of the Volumetric Plastic Strain 240 6.1.2.4 Predictions of Stress Strain Relations in Uniaxial Tension and Compression 243 6.

1.2.5 Stress Strain Relations in Compression Affected by Superimposed Pressures 247 6.2 Anisotropic Hardening Model of Rolled Sheet Metals Characterized by Multiple Experimental Stress Strain Relations and Changeable Anisotropic Parameters 248 6.2.1 A Constitutive Model to Describe Anisotropic Hardening and Anisotropic Plastic Flow of Rolled Sheet Metals 249 6.2.2 Transformation from Special 3D Stress State into 2D Stress States 252 6.

2.3 Predictions of Anisotropic Hardening and Plastic Flow Behavior 254 6.2.3.1 Subsequent Yield Locus of Anisotropic Materials 254 6.2.3.2 Predictions of All Experimental Stress Strain Relations in Yield Function 260 6.

2.4 Experimental Verification 262 6.2.4.1 Predictions of Stress Strain Relations in Uniaxial Tensions in Different Directions 262 6.2.4.2 Predictions of Changeable Anisotropic Parameters 267 6.

3 Plastic Constitutive Relation with the Bauschinger Effects 271 6.3.1 Basic Concepts of the Bauschinger Effect.