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1 | (14) |
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1.1 Historical Background |
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1 | (13) |
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1.1.1 Relation Between Polymer Science and Mechanics |
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6 | (4) |
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1.1.2 Perspective and Scope of This Text |
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10 | (4) |
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14 | (1) |
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2 Stress and Strain Analysis and Measurement |
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15 | (42) |
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2.1 Some Important and Useful Definitions |
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15 | (2) |
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2.2 Elementary Definitions of Stress, Strain and Material Properties |
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17 | (6) |
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2.3 Typical Stress-Strain Properties |
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23 | (4) |
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2.4 Idealized Stress-Strain Diagrams |
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27 | (1) |
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2.5 Mathematical Definitions of Stress, Strain and Material Characteristics |
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28 | (12) |
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40 | (2) |
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2.7 Deviatoric and Dilatational Components of Stress and Strain |
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42 | (5) |
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2.8 Failure (Rupture or Yield) Theories |
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47 | (3) |
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2.9 Atomic Bonding Model for Theoretical Mechanical Properties |
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50 | (3) |
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53 | (1) |
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54 | (3) |
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3 Characteristics, Applications and Properties of Polymers |
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57 | (44) |
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3.1 General Classification and Types of Polymers |
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57 | (6) |
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63 | (5) |
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3.3 Mechanical Properties of Polymers |
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68 | (10) |
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3.3.1 Examples of Stress-Strain Behavior of Various Polymers |
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70 | (8) |
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3.4 An Introduction to Polymer Viscoelastic Properties and Characterization |
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78 | (9) |
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3.4.1 Relaxation and Creep Tests |
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78 | (4) |
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3.4.2 Isochronous Modulus Versus Temperature Behavior |
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82 | (3) |
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3.4.3 Isochronous Stress-Strain Behavior: Linearity |
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85 | (2) |
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3.5 Phenomenological Mechanical Models |
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87 | (11) |
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3.5.1 Differential Stress-Strain Relations and Solutions for a Maxwell Fluid |
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90 | (5) |
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3.5.2 Differential Stress-Strain Relations and Solutions for a Kelvin Solid |
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95 | (2) |
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3.5.3 Creep of a Three Parameter Solid and a Four Parameter Fluid |
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97 | (1) |
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98 | (1) |
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99 | (2) |
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4 Polymerization and Classification |
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101 | (68) |
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101 | (4) |
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105 | (4) |
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4.3 Classification by Bonding Structure Between Chains and Morphology of Chains |
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109 | (3) |
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4.4 Molecular Configurations |
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112 | (8) |
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112 | (3) |
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115 | (2) |
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4.4.3 Molecular Conformations |
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117 | (3) |
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4.5 Random Walk Analysis of Chain End-to-End Distance |
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120 | (4) |
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124 | (9) |
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133 | (8) |
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4.8 Methods for the Measurement of Molecular Weight |
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141 | (7) |
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4.9 Polymer Synthesis Methods |
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148 | (6) |
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154 | (3) |
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4.11 Microscopes/Microscopy |
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157 | (8) |
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165 | (1) |
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166 | (3) |
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5 Differential Constitutive Equations |
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169 | (42) |
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5.1 Methods for the Development of Differential Equations for Mechanical Models |
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170 | (5) |
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5.2 A Note on Realistic Creep and Relaxation Testing |
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175 | (3) |
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5.3 Generalized Maxwell and Kelvin Models |
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178 | (12) |
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5.3.1 A Caution on the Use of Generalized Differential Equations |
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186 | (1) |
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5.3.2 Description of Parameters for Various Elementary Mechanical Models |
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187 | (3) |
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5.4 Alfrey's Correspondence Principle |
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190 | (1) |
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5.5 Dynamic Properties: Steady State Oscillation Testing |
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191 | (17) |
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5.5.1 Examples of Storage and Loss Moduli and Damping Ratios |
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201 | (4) |
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5.5.2 Molecular Mechanisms Associated with Dynamic Properties |
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205 | (2) |
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5.5.3 Other Instruments to Determine Dynamic Properties |
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207 | (1) |
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208 | (1) |
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209 | (2) |
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6 Hereditary Integral Representations of Stress and Strain |
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211 | (20) |
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6.1 Boltzmann Superposition Principle |
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211 | (7) |
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218 | (1) |
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6.3 Spectral Representation of Viscoelastic Materials |
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219 | (3) |
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6.4 Interrelations Among Various Viscoelastic Properties |
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222 | (7) |
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229 | (1) |
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229 | (2) |
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7 Time and Temperature Behavior of Polymers |
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231 | (56) |
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7.1 Effect of Temperature on Viscoelastic Properties of Amorphous Polymers |
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232 | (3) |
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7.2 Development of Time Temperature-Superposition-Principle (TTSP) Master Curves |
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235 | (17) |
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7.2.1 Kinetic Theory of Polymers |
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238 | (3) |
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7.2.2 WLF Equation for the Shift Factor |
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241 | (4) |
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7.2.3 Mathematical Development of the TTSP |
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245 | (7) |
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7.2.4 Potential Error for Lack of Vertical Shift |
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252 | (1) |
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7.3 Exponential Series Representation of Master Curves |
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252 | (13) |
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7.3.1 Numerical Approach to Prony Series Representation |
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256 | (5) |
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7.3.2 Determination of the Relaxation Modulus from a Relaxation Spectrum |
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261 | (4) |
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7.4 Constitutive Law with Effective Time |
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265 | (2) |
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7.5 Molecular Mechanisms Associated with Viscoelastic Response |
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267 | (1) |
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7.6 Entropy Effects and Rubber Elasticity |
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268 | (7) |
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7.7 Physical and Chemical Aging |
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275 | (7) |
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282 | (1) |
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282 | (5) |
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8 Elementary Viscoelastic Stress Analysis for Bars and Beams |
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287 | (24) |
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287 | (2) |
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8.2 Analysis of Axially Loaded Bars |
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289 | (5) |
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8.3 Analysis of Circular Cylinder Bars in Torsion |
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294 | (2) |
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8.4 Analysis of Prismatic Beams in Pure Bending |
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296 | (5) |
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8.4.1 Stress Analysis of Beams in Bending |
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296 | (1) |
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8.4.2 Deformation Analysis of Beams in Bending |
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297 | (4) |
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8.5 Stresses and Deformation in Beams for Conditions Other Than Pure Bending |
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301 | (8) |
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8.6 Shear Stresses and Deflections in Beams |
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309 | (1) |
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309 | (1) |
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310 | (1) |
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9 Viscoelastic Stress Analysis in Two and Three Dimensions |
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311 | (28) |
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9.1 Elastic Stress-Strain Equations |
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311 | (2) |
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9.2 Viscoelastic Stress-Strain Relations |
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313 | (2) |
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9.3 Relationship Between Viscoelastic Moduli (Compliances) |
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315 | (1) |
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9.4 Frequently Encountered Assumptions in Viscoelastic Stress Analysis |
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316 | (2) |
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9.5 General Viscoelastic Correspondence Principle |
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318 | (5) |
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9.5.1 Governing Equations and Solutions for Linear Elasticity |
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318 | (2) |
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9.5.2 Governing Equations and Solutions for Linear Viscoelasticity |
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320 | (3) |
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9.6 Thick Wall Cylinder and Other Problems |
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323 | (11) |
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9.6.1 Elasticity Solution of a Thick Wall Cylinder |
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323 | (3) |
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9.6.2 Elasticity Solution for a Reinforced Thick Wall Cylinder (Solid Propellant Rocket Problem) |
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326 | (2) |
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9.6.3 Viscoelasticity Solution for a Reinforced Thick Wall Cylinder (Solid Propellant Rocket Problem) |
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328 | (6) |
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9.7 Solutions Using Broadband Bulk, Shear and Poisson's Ratio Measured Functions |
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334 | (2) |
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336 | (1) |
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336 | (3) |
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10 Nonlinear Viscoelasticity |
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339 | (40) |
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10.1 Types of Nonlinearities |
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339 | (5) |
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10.2 Approaches to Nonlinear Viscoelastic Behavior |
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344 | (6) |
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10.3 The Schapery Single-Integral Nonlinear Model |
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350 | (20) |
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10.3.1 Preliminary Considerations |
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350 | (3) |
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10.3.2 The Schapery Equation |
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353 | (8) |
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10.3.3 Determining Material Parameters from a Creep and Creep Recovery Test |
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361 | (9) |
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10.4 Empirical Approach To Time-Stress-Superposition (TSSP) |
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370 | (5) |
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375 | (1) |
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376 | (3) |
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11 Rate and Time-Dependent Failure: Mechanisms and Predictive Models |
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379 | (50) |
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11.1 Failure Mechanisms in Polymers |
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380 | (9) |
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11.1.1 Atomic Bond Separation Mechanisms |
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381 | (3) |
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384 | (3) |
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387 | (2) |
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11.2 Rate Dependent Yielding |
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389 | (6) |
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11.3 Delayed or Time Dependent Failure of Polymers |
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395 | (32) |
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11.3.1 A Mathematical Model for Viscoelastic-Plastic Behavior |
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398 | (9) |
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11.3.2 Analytical Approaches to Creep Rupture |
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407 | (20) |
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427 | (1) |
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427 | (2) |
Appendix A Step and Singularity Functions |
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429 | (4) |
Appendix B Transforms |
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433 | (4) |
Appendix C Durability and Accelerated Life Predictions of Structural Polymers |
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437 | (12) |
Appendix D Herbert Leaderman: A Master of Polymer Physics and Mechanics |
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449 | (6) |
References |
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455 | (18) |
Author Index |
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473 | (6) |
Subject Index |
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479 | |