Mechanical Properties of Solid Polymers

Providing an updated and comprehensive account of the properties
of solid polymers, the book covers all aspects of mechanical
behaviour. This includes finite elastic behavior, linear
viscoelasticity and mechanical relaxations, mechanical anisotropy,
non-linear viscoelasicity, yield behavior and fracture. New to this
edition is coverage of polymer nanocomposites, and molecular
interpretations of yield, e.g. Bowden, Young, and Argon.

The book begins by focusing on the structure of polymers,
including their chemical composition and physical structure.
It goes on to discuss the mechanical properties and behaviour of
polymers, the statistical molecular theories of the rubber-like
state and describes aspects of linear viscoelastic behaviour, its
measurement, and experimental studies.

Later chapters cover composites and experimental behaviour,
relaxation transitions, stress and yielding. The book concludes
with a discussion of breaking phenomena.

Auteur

Professor Ian M. Ward is an internationally recognized
and well respected authority on this subject. Chair in Physics at
Leeds University since 1970, he has gained a reputation as an
outstanding scientist. He is also a co-founder of the British
Polymer Physics Group and the winner of several awards, including
the Glazebrook medal of the Institute of Physics (2004) and the
Netlon award (2004) both given for his work in polymer physics.

Professor John Sweeney holds a Personal Chair in
Polymer Mechanics at the University of Bradford. He has researched
in various areas of solid polymer behaviour, including
viscoelasticity, fracture mechanics, shear banding, large
deformations and nanocomposites. He is well known for his
collaborations with Professor Ward and his association with the
internationally recognized Polymer IRC (Interdisciplinary Research
Centre).

Résumé

Providing an updated and comprehensive account of the properties of solid polymers, the book covers all aspects of mechanical behaviour. This includes finite elastic behavior, linear viscoelasticity and mechanical relaxations, mechanical anisotropy, non-linear viscoelasicity, yield behavior and fracture. New to this edition is coverage of polymer nanocomposites, and molecular interpretations of yield, e.g. Bowden, Young, and Argon.

The book begins by focusing on the structure of polymers, including their chemical composition and physical structure. It goes on to discuss the mechanical properties and behaviour of polymers, the statistical molecular theories of the rubber-like state and describes aspects of linear viscoelastic behaviour, its measurement, and experimental studies.

Later chapters cover composites and experimental behaviour, relaxation transitions, stress and yielding. The book concludes with a discussion of breaking phenomena.

Contenu

Preface xiii

1 Structure of Polymers 1

1.1 Chemical Composition 1

1.1.1 Polymerisation 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 7

1.1.6 Blends, Grafts and Copolymers 8

1.2 Physical Structure 9

1.2.1 Rotational Isomerism 9

1.2.2 Orientation and Crystallinity 10

References 16

Further Reading 17

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 23

2.5 The Generalised Hooke's Law 26

References 29

3 The Behaviour in the Rubber-Like State: Finite Strain Elasticity 31

3.1 The Generalised Definition of Strain 31

3.1.1 The CauchyGreen Strain Measure 32

3.1.2 Principal Strains 34

3.1.3 Transformation of Strain 36

3.1.4 Examples of Elementary Strain Fields 38

3.1.5 Relationship of Engineering Strains to General Strains 41

3.1.6 Logarithmic Strain 42

3.2 The Stress Tensor 43

3.3 The StressStrain Relationships 44

3.4 The Use of a Strain Energy Function 47

3.4.1 Thermodynamic Considerations 47

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 54

References 58

4 Rubber-Like Elasticity 61

4.1 General Features of Rubber-Like Behaviour 61

4.2 The Thermodynamics of Deformation 62

4.2.1 The Thermoelastic Inversion Effect 64

4.3 The Statistical Theory 65

4.3.1 Simplifying Assumptions 65

4.3.2 Average Length of a Molecule between Cross-Links 66

4.3.3 The Entropy of a Single Chain 67

4.3.4 The Elasticity of a Molecular Network 69

4.4 Modifications of Simple Molecular Theory 72

4.4.1 The Phantom Network Model 73

4.4.2 The Constrained Junction Model 73

4.4.3 The Slip Link Model 73

4.4.4 The Inverse Langevin Approximation 75

4.4.5 The Conformational Exhaustion Model 79

4.4.6 The Effect of Strain-Induced Crystallisation 80

4.5 The Internal Energy Contribution to Rubber Elasticity 80

4.6 Conclusions 83

References 83

Further Reading 85

5 Linear Viscoelastic Behaviour 87

5.1 Viscoelasticity as a Phenomenon 87

5.1.1 Linear Viscoelastic Behaviour 88

5.1.2 Creep 89

5.1.3 Stress Relaxation 91

5.2 Mathematical Representation of Linear Viscoelasticity 92

5.2.1 The Boltzmann Superposition Principle 93

5.2.2 The Stress Relaxation Modulus 96

5.2.3 The Formal Relationship between Creep and Stress Relaxation 96

5.2.4 Mechanical Models, Relaxation and Retardation Time Spectra 97

5.2.5 The Kelvin or Voigt Model 98

5.2.6 The Maxwell Model 99

5.2.7 The Standard Linear Solid 100

5.2.8 Relaxation Time Spectra and Retardation Time Spectra 101

5.3 Dynamical Mechanical Measurements: The Complex Modulus and Complex Compliance 103

5.3.1 Experimental Patterns for G 1 , G 2 and so on as a Function of Frequency 105

5.4 The Relationships between the Complex Moduli and the Stress Relaxation Modulus 109

5.4.1 Formal Representations of the Stress Relaxation Modulus and the Complex Modulus 111

5.4.2 Formal Representations of the Creep Compliance and the Complex Compliance 113

5.4.3 The Formal Structure of Linear Viscoelasticity 113 5.5 The Relaxation Strength 114</p&g...