Engineering Plasticity - S J Yuan

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Résumé :

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 Classical Theory 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 Exponent n 59

2.5.3.2 Lankford Parameter R 62

2.5.3.3 Plane Anisotropic Exponent ?R 62

2.5.3.4 Yield-to-Tensile Ratio ? s ?? 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 Non-Uniaxial Loading Condition 73

3.1 P-p Experimental Results of Thin-Walled Tubes 73

3.1.1 Lode Experiment 73

3.1.2 P-p Experiments on Thin-Walled Tubes M...

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