Mechanical Properties of Solid Polymers - Hine, Peter

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Résumé :
Mechanical Properties of Solid Polymers Fourth Edition is a fully revised and updated version of the 2012 edition. It covers all aspects of mechanical behavior, including finite elastic behavior, linear viscoelasticity and mechanical relaxations, mechanical anisotropy, non linear viscoelasticity, yield behavior and fracture.--...

Biographie:

Preface xiii

1 Structure of Polymers 1

1.1 Chemical Composition 1

1.1.1 Polymerization 1

1.1.2 Cross-Linking and Chain-Branching 3

1.1.3 Average Molecular Mass and Molecular Mass Distribution 4

1.1.4 Chemical and Steric Isomerism and Stereoregularity 5

1.1.5 Liquid Crystalline Polymers 6

1.1.6 Naturally Occurring Polymers 7

1.1.7 Polymers from Renewable Sources 8

1.1.8 Blends, Grafts and Copolymers 9

1.2 Physical Structure 9

1.2.1 Rotational Isomerism 10

1.2.2 Orientation and Crystallinity 10

References 17

Further Reading 18

2 The Mechanical Properties of Polymers: General Considerations 19

2.1 Objectives 19

2.2 The Different Types of Mechanical Behaviour 19

2.3 The Elastic Solid and the Behaviour of Polymers 21

2.4 Stress and Strain 22

2.4.1 The State of Stress 22

2.4.2 The State of Strain - Engineering Components 23

2.5 The Generalized Hooke's Law 26

References 29

3 Finite Strain Elasticity 31

3.1 The Generalized Definition of Strain 31

3.1.1 The Cauchy-Green Strain Measure 32

3.1.2 Principal Strains 34

3.1.3 Transformation of Strain 37

3.1.4 Examples of Elementary Strain Fields 38

3.1.5 Relationship of Engineering Strains to General Strains 40

3.1.6 Logarithmic Strain 42

3.2 The Stress Tensor 43

3.3 The Stress-Strain Relationships 44

3.4 The Use of a Strain-Energy Function 48

3.4.1 Thermodynamic Considerations 48

3.4.1.1 Development of Strain-Energy Functions 48

3.4.1.2 Finite Strains 50

3.4.2 The Form of the Strain-Energy Function 51

3.4.3 The Strain Invariants 51

3.4.4 Application of the Invariant Approach 52

3.4.5 Application of the Principal Stretch Approach 55

3.4.6 Compressible Material 59

References 62

Further Reading 63

4 Rubber-Like Elasticity 65

4.1 General Features of Rubber-Like Behaviour 65

4.2 The Thermodynamics of Deformation 66

4.2.1 The Thermoelastic Inversion Effect 68

4.3 The Statistical Theory 69

4.3.1 Simplifying Assumptions 69

4.3.2 Average Length of a Molecule between Cross-Links 70

4.3.3 The Entropy of a Single Chain 71

4.3.4 The Elasticity of a Molecular Network 73

4.4 Modifications of Simple Molecular Theory 76

4.4.1 The Phantom Network Model 76

4.4.2 The Constrained Junction Model 77

4.4.3 The Slip-Link Model 77

4.4.4 The Inverse Langevin Approximation 79

4.4.5 The Conformational Exhaustion Model 82

4.4.6 The Effect of Strain-Induced Crystallization 84

4.5 The Internal Energy Contribution to Rubber Elasticity 85

4.6 Applications Using Finite Element Modelling 87

4.7 Conclusions 88

References 88

Further Reading 91

5 Linear Viscoelastic Behaviour 93

5.1 Viscoelasticity as a Phenomenon 93

5.1.1 Linear Viscoelastic Behaviour 94

5.1.2 Creep 95

5.1.3 Stress Relaxation 97

5.2 Mathematical Representation of Linear Viscoelasticity 98

5.2.1 The Boltzmann Superposition Principle 98

5.2.2 The Stress Relaxation Modulus 102

5.2.3 The Formal Relationship Between Creep and Stress Relaxation 102

5.2.4 Mechanical Models, Relaxation and Retardation Time Spectra 103

5.2.5 The Kelvin or Voigt Model 104

5.2.6 The Maxwell Model 105

5.2.7 The Standard Linear Solid 106

5.2.8 Relaxation Time Spectra and Retardation Time Spectra 107

5.3 Dynamical Mechanical Measurements: The Complex Modulus and Complex Compliance 109

5.3.1 Expe...

Sommaire:

Preface xiii

1 Structure of Polymers 1

1.1 Chemical Composition 1

1.2 Physical Structure 9

References 17

Further Reading 18

2 The Mechanical Properties of Polymers: General Considerations 19

2.1 Objectives 19

2.2 The Different Types of Mechanical Behaviour 19

2.3 The Elastic Solid and the Behaviour of Polymers 21

2.4 Stress and Strain 22

2.5 The Generalized Hooke's Law 26

References 29

3 Finite Strain Elasticity 31

3.1 The Generalized Definition of Strain 31

3.2 The Stress Tensor 43

3.3 The Stress-Strain Relationships 44

3.4 The Use of a Strain-Energy Function 48

References 62

Further Reading 63

4 Rubber-Like Elasticity 65

4.1 General Features of Rubber-Like Behaviour 65

4.2 The Thermodynamics of Deformation 66

4.3 The Statistical Theory 69

4.4 Modifications of Simple Molecular Theory 76

4.5 The Internal Energy Contribution to Rubber Elasticity 85

4.6 Applications Using Finite Element Modelling 87

4.7 Conclusions 88

References 88

Further Reading 91

5 Linear Viscoelastic Behaviour 93

5.1 Viscoelasticity as a Phenomenon 93

5.2 Mathematical Representation of Linear Viscoelasticity 98

5.3 Dynamical Mechanical Measurements: The Complex Modulus and Complex Compliance 109

5.4 The Relationships Between the Complex Moduli and the Stress Relaxation Modulus 114

5.5 The Relaxation Strength 120

References 122

Further Reading 122

6 The Measurement of Viscoelastic Behaviour 125

6.1 Creep and Stress Relaxation 125

6.2 Dynamic Mechanical Thermal Analysis (DMTA) 128

6.3 Wave-Propagation Methods 128

References 132

7 Experimental Studies of Linear Viscoelastic Behaviour as a Function of Frequency and Temperature: Time-Temperature Equivalence 135

7.1 General Introduction 135

7.2 Time-Temperature Equivalence and Superposition 141

7.3 Transition-State Theories 143

7.4 The Time-Temperature Equivalence of the Glass Transition Viscoelastic Behaviour in Amorphous Polymers and the Williams, Landel and Ferry (WLF) Equation 147

7.5 Normal-Mode Theories Based on Motion of Isolated Flexible Chains 156

7.6 The Dynamics of Highly Entangled Polymers 160

References 163

8 Anisotropic Mechanical Behaviour 167

8.1 The Description of Anisotropic Mechanical Behaviour 167

8.2 Mechanical Anisotropy in Polymers 168

8.3 Measurement of Elastic Constants 171

8.4 Development of Mechanical Anisotropy in Oriented Polymers 181

8.5 Interpretation of Mechanical Anisotropy: General Considerations 188

8.6 Experimental Studies of Anisotropic Mechanical Behaviour and Their Interpretation 193

8.7 The Aggregate Model for Chain-Extended Polyethylene and Liquid Crystalline Polymers 208

8.8 Auxetic Materials: Negative Poisson's Ratio 212

References 215

9 Morphology and Structural Effects 223

9.1 Evolution of Structures Under Tension: Cavitation 223

9.2 Effects of Stress Field 225

9.3 One-Dimensional Modelling 229

9.4 Three-Dimensional Models 235

References 241

10 Relaxation Transitions: Experimental Behaviour and Molecular Interpretation 245

10.1 Amorphous Polymers: An Introduction 245

10.2 Factors Affecting the Glass Transition in Amorphous and Low Crystallinity Polymers 247

10.3 Relaxation Transitions in Crystalline Polymers 252

10.4 Conclusions 265

References 265

11 Non-linear Viscoelastic Behaviour 269