Polymer engineering science and viscoelasticity : an introduction

A mechanics perspective on the mathematics of viscoelasticity and a materials view of the physical mechanisms behind the polymer deformation processes, are provided by this book. The book fills a critical niche. Clearly written and well-organized, the volume includes an introduction to and mathematical description of the basic materials science of polymers, time-temperature-frequency dependence, and unique deformation mechanisms of polymers.

1 Introduction	p. 1
1.1 Historical Background	p. 1
1.1.1 Relation between Polymer Science and Mechanics	p. 6
1.1.2 Perspective and Scope of this Text	p. 10
1.2 Review Questions	p. 14
2 Stress and Strain Analysis and Measurement	p. 15
2.1 Some Important and Useful Definitions	p. 15
2.2 Elementary Definitions of Stress, Strain and Material Properties	p. 17
2.3 Typical Stress-Strain Properties	p. 23
2.4 Idealized Stress-Strain Diagrams	p. 27
2.5 Mathematical Definitions of Stress, Strain and Material Characteristics	p. 28
2.6 Principal Stresses	p. 40
2.7 Deviatoric and Dilatational Components of Stress and Strain	p. 42
2.8 Failure (Rupture or Yield) Theories	p. 46
2.9 Atomic Bonding Model for Theoretical Mechanical Properties	p. 49
2.10 Review Questions	p. 52
2.11 Problems	p. 53
3 Characteristics, Applications and Properties of Polymers	p. 55
3.1 General Classification and Types of Polymers	p. 55
3.2 Typical Applications	p. 61
3.3 Mechanical Properties of Polymers	p. 66
3.3.1 Examples of Stress-Strain Behavior of Various Polymers	p. 68
3.4 An Introduction to Polymer Viscoelastic Properties and Characterization	p. 75
3.4.1 Relaxation and Creep Tests	p. 75
3.4.2 Isochronous Modulus vs. Temperature Behavior	p. 79
3.4.3 Isochronous Stress-Strain Behavior-Linearity	p. 82
3.5 Phenomenological Mechanical Models	p. 84
3.5.1 Differential Stress-Strain Relations and Solutions for a Maxwell Fluid	p. 86
3.5.2 Differential Stress-Strain Relations and Solutions for a Kelvin Solid	p. 91
3.5.3 Creep of a Three Parameter Solid and a Four Parameter Fluid	p. 93
3.6 Review Questions	p. 95
3.7 Problems	p. 96
4 Polymerization and Classification	p. 99
4.1 Polymer Bonding	p. 99
4.2 Polymerization	p. 103
4.3 Classification by Bonding Structure Between Chains and Morphology of Chains	p. 108
4.4 Molecular Configurations	p. 111
4.4.1 Isomers	p. 111
4.4.2 Copolymers	p. 114
4.4.3 Molecular Conformations	p. 115
4.5 Random Walk Analysis of Chain End-to-End Distance	p. 118
4.6 Morphology	p. 122
4.7 Molecular Weight	p. 131
4.8 Methods for the Measurement of Molecular Weight	p. 139
4.9 Polymer Synthesis Methods	p. 146
4.10 Spectrography	p. 153
4.11 Review Questions	p. 155
4.12 Problems	p. 157
5 Differential Constitutive Equations	p. 159
5.1 Methods for the Development of Differential Equations for Mechanical Models	p. 160
5.2 A Note on Realistic Creep and Relaxation Testing	p. 165
5.3 Generalized Maxwell and Kelvin Models	p. 168
5.3.1 A Caution on the Use of Generalized Differential Equations	p. 176
5.3.2 Description of Parameters for Various Elementary Mechanical Models	p. 177
5.4 Alfrey's Correspondence Principle	p. 180
5.5 Dynamic Properties - Steady State Oscillation Testing	p. 181
5.5.1 Examples of Storage and Loss Moduli and Damping Ratios	p. 191
5.5.2 Molecular Mechanisms Associated with Dynamic Properties	p. 196
5.5.3 Other Instruments to Determine Dynamic Properties	p. 198
5.6 Review Questions	p. 199
5.7 Problems	p. 199
6 Hereditary Integral Representations of Stress and Strain	p. 201
6.1 Boltzman Superposition Principle	p. 201
6.2 Linearity	p. 208
6.3 Spectral Representation of Viscoelastic Materials	p. 208
6.4 Interrelations Among Various Viscoelastic Properties	p. 211
6.5 Review Questions	p. 217
6.6 Problems	p. 217
7 Time and Temperature Behavior of Polymers	p. 221
7.1 Effect of Temperature on Viscoelastic Properties of Amorphous Polymers	p. 222
7.2 Development of Time Temperature-Superposition-Principle (TTSP) Master Curves	p. 225
7.2.1 Kinetic Theory of Polymers	p. 228
7.2.2 WLF Equation for the Shift Factor	p. 230
7.2.3 Mathematical Development of the TTSP	p. 235
7.2.4 Potential Error for Lack of Vertical Shift	p. 241
7.3 Exponential Series Representation of Master Curves	p. 242
7.3.1 Numerical Approach to Prony Series Representation	p. 245
7.3.2 Determination of the Relaxation Modulus from a Relaxation Spectrum	p. 251
7.4 Constitutive Law with Effective Time	p. 254
7.5 Molecular Mechanisms Associated with Viscoelastic Response	p. 256
7.6 Entropy Effects and Rubber Elasticity	p. 257
7.7 Physical and Chemical Aging	p. 264
7.8 Review Questions	p. 271
7.9 Problems	p. 271
8 Elementary Viscoelastic Stress Analysis for Bars and Beams	p. 275
8.1 Fundamental Concepts	p. 275
8.2 Analysis of Axially Loaded Bars	p. 278
8.3 Analysis of Circular Cylinder Bars in Torsion	p. 282
8.4 Analysis of Prismatic Beams in Pure Bending	p. 284
8.4.1 Stress Analysis of Beams in Bending	p. 284
8.4.2 Deformation Analysis of Beams in Bending	p. 285
8.5 Stresses and Deformation in Beams for Conditions other than Pure Bending	p. 288
8.6 Shear Stresses and Deflections in Beams	p. 296
8.7 Review Questions	p. 297
8.8 Problems	p. 297
9 Viscoelastic Stress Analysis in Two and Three Dimensions	p. 299
9.1 Elastic Stress-Strain Equations	p. 299
9.2 Viscoelastic Stress-Strain Relations	p. 301
9.3 Relationship Between Viscoelastic Moduli (Compliances)	p. 303
9.4 Frequently Encountered Assumptions in Viscoelastic Stress Analysis	p. 304
9.5 General Viscoelastic Correspondence Principle	p. 306
9.5.1 Governing Equations and Solutions for Linear Elasticity	p. 306
9.5.2 Governing Equations and Solutions for Linear Viscoelasticity	p. 308
9.6 Thick Wall Cylinder and Other Problems	p. 311
9.6.1 Elasticity Solution of a Thick Wall Cylinder	p. 311
9.6.2 Elasticity Solution for a Reinforced Thick Wall Cylinder (Solid Propellant Rocket Problem)	p. 314
9.6.3 Viscoelasticity Solution for a Reinforced Thick Wall Cylinder (Solid Propellant Rocket Problem)	p. 316
9.7 Solutions Using Broadband Bulk, Shear and Poisson's Ratio Measured Functions	p. 322
9.8 Review Questions	p. 324
9.9 Problems	p. 325
10 Nonlinear Viscoelasticity	p. 327
10.1 Types of Nonlinearities	p. 327
10.2 Approaches to Nonlinear Viscoelastic Behavior	p. 332
10.3 The Schapery Single-Integral Nonlinear Model	p. 338
10.3.1 Preliminary Considerations	p. 338
10.3.2 The Schapery Equation	p. 340
10.3.3 Determining Material Parameters from a Creep and Creep Recovery Test	p. 348
10.4 Empirical Approach To Time-Stress-Superposition (TSSP)	p. 357
10.5 Review Questions	p. 362
10.6 Problems	p. 363
11 Rate and Time-Dependent Failure: Mechanisms and Predictive Models	p. 365
11.1 Failure Mechanisms in Polymers	p. 366
11.1.1 Atomic Bond Separation Mechanisms	p. 367
11.1.2 Shear Bands	p. 370
11.1.3 Crazing	p. 373
11.2 Rate Dependent Yielding	p. 375
11.3 Delayed or Time Dependent Failure of Polymers	p. 381
11.3.1 A Mathematical Model for Viscoelastic-Plastic Behavior	p. 383
The Nagdi-Murch Model	p. 384
The Crochet Model Time Dependent Yielding Model	p. 386
Long Term Delayed Yielding and Three-Dimensional Problems	p. 392
11.3.2 Analytical Approaches to Creep Rupture	p. 394
Activation Energy Approach to Creep Rupture	p. 394
The Zhurkov Method	p. 397
Cumulative Creep Damage of Polymers	p. 398
Reiner-Weissenberg Criteria for Failure	p. 403
11.4 Review Questions	p. 413
11.5 Problems	p. 413
Appendix A	p. 415
Appendix B	p. 419
References	p. 423
Author Index	p. 437
Index	p. 443

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