Mechanical Response of Polymers

Name: Mechanical Response of Polymers
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ISBN: 9780521644099

An Introduction

By: Alan S. Wineman, K. R. Rajagopal

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Paperback Published: 15th September 2000
ISBN: 9780521644099
Number Of Pages: 328

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Automobiles, household appliances, and electronic devices all make use of polymeric materials. As polymers are used increasingly in sophisticated industrial applications, it has become essential that mechanical engineers, who have traditionally focused on the behavior of metals, become as capable and adept with polymers. This text provides a thorough introduction to the subject of polymers from a mechanical engineering perspective, treating stresses and deformations in structural components made of polymers. Three themes are developed. First, the authors discuss the time-dependent response of polymers and its implications for mechanical response. Secondly, descriptions of mechanical response are presented for both time-dependent and frequency-dependent material properties. Finally, the stress-strain-time relation is applied to determine stresses and deformations in structures. With numerous examples and extensive illustrations, this book will help advanced undergraduate and graduate students, as well as practising mechanical engineers, make optimal and effective use of polymeric materials.

Industry Reviews

'... valuable addition to the existing literature on the subject. The strength of this book is in its carefully selected and well-arranged materials, including experimental results, extensive illustrations, and numerous examples. The authors develop the concepts systematically, in a clear and constructive manner. the ease with which this is done stimulates the reader ... this book is strongly recommended for use by the students and practicing engineers interested in effective use of polymeric materials, and should be available in university libraries.' M. S. Kuczma, Applied Mechanical Review 'This book provides a thorough introduction to the subject of polymers from a mechanical engineering perspective, treating stresses and deformations in structural components made of polymers.' Iasi Polytechnic Magazine

Preface	p. ix
Discussion of Response of a Viscoelastic Material	p. 1
Comparison with the Response of Classical Elastic and Classical Viscous Materials	p. 1
Response of a Classical Elastic Solid	p. 1
Response of a Classical Viscous Fluid	p. 3
Comments on Material Microstructure	p. 6
Response of a Viscoelastic Material	p. 7
Typical Experimental Results	p. 10
Material Properties	p. 15
Linearity of Response	p. 17
Aging Materials	p. 21
Problems	p. 24
Constitutive Equations for One-Dimensional Response of Viscoelastic Materials: Mechanical Analogs	p. 28
Maxwell Model	p. 28
Kelvin-Voigt Model	p. 35
Three-Parameter Solid or Standard Linear Solid	p. 40
N Maxwell Elements in Parallel	p. 45
N Kelvin-Voigt Elements in Series	p. 50
Relaxation and Creep Spectra	p. 51
Problems	p. 52
Constitutive Equations for One-Dimensional Linear Response of a Viscoelastic Material	p. 54
General Restrictions on the Constitutive Equation	p. 54
Linearity of Response: Superposition of Step Increments	p. 58
Linearity of Response: Superposition of Pulses	p. 62
Creep Forms of the Constitutive Equation	p. 64
Summary of Forms of the Constitutive Equation	p. 64
Problems	p. 65
Some Features of the Linear Response of Viscoelastic Materials	p. 67
Relation Between Relaxation and Creep Functions	p. 67
Characteristic Creep and Relaxation Times	p. 72
Characteristic Relaxation, Creep, and Process Times	p. 75
Some Examples Illustrating Implications of Fading Memory	p. 80
Problems	p. 83
Histories with Constant Strain or Stress Rates	p. 88
Constant Strain Rate Deformation	p. 88
Constant Strain Rate Deformation and Recovery	p. 92
Influence of Rise Time T* or Strain Rate [alpha]	p. 97
Work Done in a Constant Strain Rate Deformation and Recovery Test	p. 98
Repeated Cycles	p. 100
Step Strain and Recovery	p. 100
Ramp Strain Approximation to a Step Strain History	p. 103
Constant Stress Rate Loading and Unloading History	p. 105
Problems	p. 109
Sinusoidal Oscillations	p. 115
Sinusoidal Strain Histories	p. 115
Sinusoidal Stress Histories	p. 120
Relation Between G* ([omega]) and J* ([omega])	p. 123
Work per Cycle During Sinusoidal Oscillations	p. 124
Complex Viscosity	p. 125
Examples of Calculation of G* ([omega]) and J* ([omega])	p. 125
Low and High Frequency Limits of G* ([omega]) and J* ([omega])	p. 130
Fourier Integral Theorem, Fourier Transform	p. 135
Expressions for G(t) and J(t) in Terms of G* ([omega]) and J* ([omega])	p. 137
Work Done During a General Deformation History	p. 140
Problems	p. 142
Constitutive Equation for Three-Dimensional Response of Linear Isotropic Viscoelastic Materials	p. 148
Introduction	p. 148
Linearity	p. 149
Uniaxial Extension, Poisson's Ratio, Isotropy	p. 150
Uniaxial Extension Along the x[subscript 2] and x[subscript 3] Directions	p. 153
Shear Response	p. 153
Constitutive Equation for Three-Dimensional Response	p. 154
A Relation Between Poisson's Ratio and the Extensional and Shear Material Properties	p. 155
Volumetric and Pure Shear Response	p. 157
Stress in Terms of Strain History	p. 160
Sinusoidal Oscillations	p. 160
Laplace Transformation of the Constitutive Equations	p. 163
Effect of Viscoelasticity on Principal Directions of Stress and Strain	p. 164
Summary of Constitutive Relations	p. 166
Relations for Special Cases of Volumetric Response	p. 168
Problems	p. 168
Axial Load, Bending, and Torsion	p. 172
Introduction	p. 172
Structural Components Under Axial Load	p. 172
Pure Bending of Viscoelastic Beams	p. 176
Kinematics of Deformation	p. 177
Constitutive Equation	p. 179
Force Analysis	p. 180
Stress, Bending Moment, and Curvature Relations	p. 181
Deformation of Beams Subjected to Transverse Loads	p. 182
Beams on Hard Supports, Correspondence Principle	p. 185
Delayed Contact, Direct Method of Solution	p. 190
Interaction of Polymeric Structural Components, a Viscoelastic Beam on a Viscoelastic Support	p. 195
Extrusion of a Bar, Tracking the History of a Material Element	p. 199
Traveling Concentrated Load on a Beam	p. 202
Torsion of Circular Bars	p. 207
Analysis of Viscoelastic Structures	p. 212
Problems	p. 212
Dynamics of Bodies with Viscoelastic Support	p. 219
Introduction	p. 219
Comparison of Spring-Damper and Viscoelastic Supports	p. 219
Forced Oscillations	p. 221
Free Oscillations	p. 228
Problem	p. 231
Boundary Value Problems for Linear Isotropic Viscoelastic Materials	p. 232
Introduction	p. 232
Governing Equations	p. 232
Correspondence Theorem for Quasi-Static Motion	p. 234
Breakdown of the Correspondence Principle	p. 237
Application of the Correspondence Principle: Pressure Loading of a Viscoelastic Cylinder	p. 238
Application of the Correspondence Principle: Torsion of Bars of Non-Circular Cross-Section	p. 240
Direct Solution Methods	p. 243
Problem	p. 246
Influence of Temperature	p. 247
Introduction	p. 247
Thermally Induced Dimensional Changes	p. 247
Mechanical Response at Different Temperatures	p. 248
Time-Temperature Superposition	p. 251
Experimental Support for Time-Temperature Superposition	p. 253
General Comments	p. 254
Effect of Temperature on Characteristic Stress Relaxation Time	p. 256
Other Material Property Functions	p. 257
Implications of Time-Temperature Superposition for Processes	p. 258
Rate of Work	p. 259
An Experimental Study	p. 260
Extension to Time-Varying Temperature Histories	p. 262
Constitutive Equation for Time-Varying Temperature Histories	p. 268
Thermo-Viscoelastic Response of a Three Bar Structure: Formulation	p. 269
Thermo-Viscoelastic Response of a Three Bar Structure: Development of Frozen-in Deformation	p. 271
Thermo-Viscoelastic Response of a Three Bar Structure: Frozen-in Forces	p. 276
Thermo-Viscoelastic Response of a Three Bar Structure: Cooling Induced Warping	p. 285
Thermo-Viscoelastic Response of a Three Bar Structure: Comments	p. 292
Operator Notation for Time Derivatives	p. 293
Laplace Transform	p. 295
Volterra Integral Equations	p. 299
Formal Manipulation Methods	p. 305
Field Equations in Cartesian and Cylindrical Coordinates	p. 308
References	p. 311
Index	p. 313
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521644099
ISBN-10: 0521644097
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 328
Published: 15th September 2000
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 25.5 x 17.93 x 2.16
Weight (kg): 0.69