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