Mechanical Properties of Solid Polymers

Preface xiii 1 Structure of Polymers 1 1.1 Chemical Composition 1 1.2 Physical Structure 9 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 Generalised Hooke's Law 26 3 The Behaviour in the Rubber-Like State: Finite Strain Elasticity 31 3.1 The Generalised 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 47 4 Rubber-Like Elasticity 61 4.1 General Features of Rubber-Like Behaviour 61 4.2 The Thermodynamics of Deformation 62 4.3 The Statistical Theory 65 4.4 Modifications of Simple Molecular Theory 72 4.5 The Internal Energy Contribution to Rubber Elasticity 80 4.6 Conclusions 83 5 Linear Viscoelastic Behaviour 87 5.1 Viscoelasticity as a Phenomenon 87 5.2 Mathematical Representation of Linear Viscoelasticity 92 5.3 Dynamical Mechanical Measurements: The Complex Modulus and Complex Compliance 103 5.4 The Relationships between the Complex Moduli and the Stress Relaxation Modulus 109 5.5 The Relaxation Strength 114 6 The Measurement of Viscoelastic Behaviour 119 6.1 Creep and Stress Relaxation 119 6.2 Dynamic Mechanical Measurements 123 6.3 Wave-Propagation Methods 127 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 140 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 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 Experimental Studies of Mechanical Anisotropy in Oriented Polymers 185 8.5 Interpretation of Mechanical Anisotropy: General Considerations 192 8.6 Experimental Studies of Anisotropic Mechanical Behaviour and Their Interpretation 198 8.7 The Aggregate Model for Chain-Extended Polyethylene and Liquid Crystalline Polymers 212 8.8 Auxetic Materials: Negative Poisson's Ratio 216 9 Polymer Composites: Macroscale and Microscale 227 9.1 Composites: A General Introduction 227 9.2 Mechanical Anisotropy of Polymer Composites 228 9.3 Short Fibre Composites 233 9.4 Nanocomposites 238 9.5 Takayanagi Models for Semi-Crystalline Polymers 241 9.6 Ultra-High-Modulus Polyethylene 250 9.7 Conclusions 255 10 Relaxation Transitions: Experimental Behaviour and Molecular Interpretation 261 10.1 Amorphous Polymers: An Introduction 261 10.2 Factors Affecting the Glass Transition in Amorphous Polymers 263 10.3 Relaxation Transitions in Crystalline Polymers 269 10.4 Conclusions 282 11 Non-linear Viscoelastic Behaviour 285 11.1 The Engineering Approach 286 11.2 The Rheological Approach 289 11.3 Creep and Stress Relaxation as Thermally Activated Processes 306 11.4 Multi-axial Deformation: Three-Dimensional Non-linear Viscoelasticity 313 12 Yielding and Instability in Polymers 319 12.1 Discussion of the Load-Elongation Curves in Tensile Testing 320 12.2 Ideal Plastic Behaviour 327 12.3 Historical Development of Understanding of the Yield Process 335 12.4 Experimental Evidence for Yield Criteria in Polymers 338 12.5 The Molecular Interpretations of Yield 342 12.6 Cold-Drawing, Strain Hardening and the True Stress-Strain Curve 359 12.7 Shear Bands 366 12.8 Physical Considerations Behind Viscoplastic Modelling 369 12.9 Shape Memory Polymers 371 13 Breaking Phenomena 379 13.1 Definition of Tough and Brittle Behaviour in Polymers 379 13.2 Principles of Brittle Fracture of Polymers 380 13.3 Controlled Fracture in Brittle Polymers 385 13.4 Crazing in Glassy Polymers 386 13.5 The Structure and Formation of Crazes 391 13.6 Controlled Fracture in Tough Polymers 400 13.7 The Molecular Approach 413 13.8 Factors Influencing Brittle-Ductile Behaviour: Brittle-Ductile Transitions 414 13.9 The Impact Strength of Polymers 422 13.10 The Tensile Strength and Tearing of Polymers in the Rubbery State 430 13.11 Effect of Strain Rate and Temperature 432 References 439 Further Reading 447 Index 449