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Mechanical Response of Polymers : An Introduction - Alan S. Wineman

Mechanical Response of Polymers

An Introduction

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

Prefacep. ix
Discussion of Response of a Viscoelastic Materialp. 1
Comparison with the Response of Classical Elastic and Classical Viscous Materialsp. 1
Response of a Classical Elastic Solidp. 1
Response of a Classical Viscous Fluidp. 3
Comments on Material Microstructurep. 6
Response of a Viscoelastic Materialp. 7
Typical Experimental Resultsp. 10
Material Propertiesp. 15
Linearity of Responsep. 17
Aging Materialsp. 21
Problemsp. 24
Constitutive Equations for One-Dimensional Response of Viscoelastic Materials: Mechanical Analogsp. 28
Maxwell Modelp. 28
Kelvin-Voigt Modelp. 35
Three-Parameter Solid or Standard Linear Solidp. 40
N Maxwell Elements in Parallelp. 45
N Kelvin-Voigt Elements in Seriesp. 50
Relaxation and Creep Spectrap. 51
Problemsp. 52
Constitutive Equations for One-Dimensional Linear Response of a Viscoelastic Materialp. 54
General Restrictions on the Constitutive Equationp. 54
Linearity of Response: Superposition of Step Incrementsp. 58
Linearity of Response: Superposition of Pulsesp. 62
Creep Forms of the Constitutive Equationp. 64
Summary of Forms of the Constitutive Equationp. 64
Problemsp. 65
Some Features of the Linear Response of Viscoelastic Materialsp. 67
Relation Between Relaxation and Creep Functionsp. 67
Characteristic Creep and Relaxation Timesp. 72
Characteristic Relaxation, Creep, and Process Timesp. 75
Some Examples Illustrating Implications of Fading Memoryp. 80
Problemsp. 83
Histories with Constant Strain or Stress Ratesp. 88
Constant Strain Rate Deformationp. 88
Constant Strain Rate Deformation and Recoveryp. 92
Influence of Rise Time T* or Strain Rate [alpha]p. 97
Work Done in a Constant Strain Rate Deformation and Recovery Testp. 98
Repeated Cyclesp. 100
Step Strain and Recoveryp. 100
Ramp Strain Approximation to a Step Strain Historyp. 103
Constant Stress Rate Loading and Unloading Historyp. 105
Problemsp. 109
Sinusoidal Oscillationsp. 115
Sinusoidal Strain Historiesp. 115
Sinusoidal Stress Historiesp. 120
Relation Between G* ([omega]) and J* ([omega])p. 123
Work per Cycle During Sinusoidal Oscillationsp. 124
Complex Viscosityp. 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 Transformp. 135
Expressions for G(t) and J(t) in Terms of G* ([omega]) and J* ([omega])p. 137
Work Done During a General Deformation Historyp. 140
Problemsp. 142
Constitutive Equation for Three-Dimensional Response of Linear Isotropic Viscoelastic Materialsp. 148
Introductionp. 148
Linearityp. 149
Uniaxial Extension, Poisson's Ratio, Isotropyp. 150
Uniaxial Extension Along the x[subscript 2] and x[subscript 3] Directionsp. 153
Shear Responsep. 153
Constitutive Equation for Three-Dimensional Responsep. 154
A Relation Between Poisson's Ratio and the Extensional and Shear Material Propertiesp. 155
Volumetric and Pure Shear Responsep. 157
Stress in Terms of Strain Historyp. 160
Sinusoidal Oscillationsp. 160
Laplace Transformation of the Constitutive Equationsp. 163
Effect of Viscoelasticity on Principal Directions of Stress and Strainp. 164
Summary of Constitutive Relationsp. 166
Relations for Special Cases of Volumetric Responsep. 168
Problemsp. 168
Axial Load, Bending, and Torsionp. 172
Introductionp. 172
Structural Components Under Axial Loadp. 172
Pure Bending of Viscoelastic Beamsp. 176
Kinematics of Deformationp. 177
Constitutive Equationp. 179
Force Analysisp. 180
Stress, Bending Moment, and Curvature Relationsp. 181
Deformation of Beams Subjected to Transverse Loadsp. 182
Beams on Hard Supports, Correspondence Principlep. 185
Delayed Contact, Direct Method of Solutionp. 190
Interaction of Polymeric Structural Components, a Viscoelastic Beam on a Viscoelastic Supportp. 195
Extrusion of a Bar, Tracking the History of a Material Elementp. 199
Traveling Concentrated Load on a Beamp. 202
Torsion of Circular Barsp. 207
Analysis of Viscoelastic Structuresp. 212
Problemsp. 212
Dynamics of Bodies with Viscoelastic Supportp. 219
Introductionp. 219
Comparison of Spring-Damper and Viscoelastic Supportsp. 219
Forced Oscillationsp. 221
Free Oscillationsp. 228
Problemp. 231
Boundary Value Problems for Linear Isotropic Viscoelastic Materialsp. 232
Introductionp. 232
Governing Equationsp. 232
Correspondence Theorem for Quasi-Static Motionp. 234
Breakdown of the Correspondence Principlep. 237
Application of the Correspondence Principle: Pressure Loading of a Viscoelastic Cylinderp. 238
Application of the Correspondence Principle: Torsion of Bars of Non-Circular Cross-Sectionp. 240
Direct Solution Methodsp. 243
Problemp. 246
Influence of Temperaturep. 247
Introductionp. 247
Thermally Induced Dimensional Changesp. 247
Mechanical Response at Different Temperaturesp. 248
Time-Temperature Superpositionp. 251
Experimental Support for Time-Temperature Superpositionp. 253
General Commentsp. 254
Effect of Temperature on Characteristic Stress Relaxation Timep. 256
Other Material Property Functionsp. 257
Implications of Time-Temperature Superposition for Processesp. 258
Rate of Workp. 259
An Experimental Studyp. 260
Extension to Time-Varying Temperature Historiesp. 262
Constitutive Equation for Time-Varying Temperature Historiesp. 268
Thermo-Viscoelastic Response of a Three Bar Structure: Formulationp. 269
Thermo-Viscoelastic Response of a Three Bar Structure: Development of Frozen-in Deformationp. 271
Thermo-Viscoelastic Response of a Three Bar Structure: Frozen-in Forcesp. 276
Thermo-Viscoelastic Response of a Three Bar Structure: Cooling Induced Warpingp. 285
Thermo-Viscoelastic Response of a Three Bar Structure: Commentsp. 292
Operator Notation for Time Derivativesp. 293
Laplace Transformp. 295
Volterra Integral Equationsp. 299
Formal Manipulation Methodsp. 305
Field Equations in Cartesian and Cylindrical Coordinatesp. 308
Referencesp. 311
Indexp. 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

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