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9780471496250

An Introduction to the Mechanical Properties of Solid Polymers, 2nd Edition

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  • ISBN13:

    9780471496250

  • ISBN10:

    0471496251

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2004-05-01
  • Publisher: WILEY

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Summary

Provides a comprehensive introduction to the mechanical behaviour of solid polymers. Extensively revised and updated throughout, the second edition now includes new material on mechanical relaxations and anisotropy, composites modelling, non-linear viscoelasticity, yield behaviour and fracture of tough polymers.The accessible approach of the book has been retained with each chapter designed to be self contained and the theory and applications of the subject carefully introduced where appropriate. The latest developments in the field are included alongside worked examples, mathematical appendices and an extensive reference. Fully revised and updated throughout to include all the latest developments in the field Worked examples at the end of the chapter An invaluable resource for students of materials science, chemistry, physics or engineering studying polymer science

Table of Contents

Preface xi
1 Structure of Polymers
1(18)
1.1 Chemical composition
1(8)
1.1.1 Polymerization
1(2)
1.1.2 Cross-linking and chain-branching
3(1)
1.1.3 Average molecular mass and molecular mass distribution
4(1)
1.1.4 Chemical and steric isomerism and stereoregularity
5(2)
1.1.5 Liquid crystalline polymers
7(2)
1.1.6 Blends, grafts and copolymers
9(1)
1.2 Physical structure
9(10)
1.2.1 Rotational isomerism
9(2)
1.2.2 Orientation and crystallinity
11(5)
References
16(1)
Further reading
16(3)
2 The Deformation of an Elastic Solid
19(12)
2.1 The state of stress
19(1)
2.2 The state of strain
20(4)
2.2.1 The engineering components of strain
21(3)
2.3 The generalized Hooke's law
24(1)
2.4 Finite strain elasticity: the behaviour of polymers in the rubber-like state
25(6)
2.4.1 The definition of components of stress
25(1)
2.4.2 The generalized definition of strain
26(2)
2.4.3 The strain energy function
28(2)
References
30(1)
Further reading
30(1)
3 Rubber-Like Elasticity
31(22)
3.1 General features of rubber-like behaviour
31(2)
3.2 The thermodynamics of deformation
33(2)
3.3 The statistical theory
35(8)
3.3.1 Simplifying assumptions
35(1)
3.3.2 The average length of a molecule between cross-links
36(1)
3.3.3 The entropy of a single chain
37(2)
3.3.4 The elasticity of a molecular network
39(4)
3.4 Modifications of the simple molecular network
43(3)
3.5 Recent developments in the molecular theory of rubber elasticity
46(7)
References
51(1)
Problems for Chapters 2 and 3
51(2)
4 Principles of Linear Viscoelasticity
53(26)
4.1 Viscoelasticity as a phenomenon
53(6)
4.1.1 Linear viscoelastic behaviour
54(1)
4.1.2 Creep
55(3)
4.1.3 Stress relaxation
58(1)
4.2 Mathematical representation of linear viscoelasticity
59(11)
4.2.1 The Boltzmann superposition principle
59(4)
4.2.2 The stress relaxation modulus
63(1)
4.2.3 Mechanical models, retardation and relaxation time spectra
63(7)
4.3 Dynamic mechanical measurements: the complex modulus and complex compliance
70(9)
4.3.1 Experimental patterns for G1, G2, etc. as a function of frequency
73(1)
4.3.2 The Alfrey approximation
73(3)
References
76(1)
Problems for Chapter 4
76(3)
5 The Measurement of Viscoelastic Behaviour
79(16)
5.1 Creep and stress relaxation
80(3)
5.1.1 Creep conditioning
80(1)
5.1.2 Specimen characterization
80(1)
5.1.3 Experimental precautions
80(3)
5.2 Dynamic mechanical measurements
83(5)
5.2.1 The torsion pendulum
83(3)
5.2.2 Forced vibration methods
86(1)
5.2.3 Dynamic mechanical thermal analysis (DMTA)
87(1)
5.3 Wave-propagation methods
88(7)
5.3.1 The kilohertz frequency range
88(1)
5.3.2 The megahertz frequency range: ultrasonic methods
89(3)
5.3.3 The hypersonic frequency range: Brillouin spectroscopy
92(1)
References
92(3)
6 Experimental Studies of Linear Viscoelastic Behaviour as a Function of Frequency and Temperature: Time-Temperature Equivalence
95(26)
6.1 General introduction
95(6)
6.1.1 Amorphous polymers
95(3)
6.1.2 Temperature dependence of viscoelastic behaviour
98(3)
6.1.3 Crystallinity and inclusions
101(1)
6.2 Time-temperature equivalence and superposition
101(3)
6.3 Molecular interpretations of time-temperature equivalence
104(9)
6.3.1 Molecular rate processes with a constant activation energy: the site model theory
104(4)
6.3.2 The Williams-Landel-Ferry (WLF) equation
108(5)
6.4 Flexible molecular chain models
113(8)
6.4.1 Normal mode theories
113(3)
6.4.2 The dynamics of highly entangled polymers
116(3)
References
119(2)
7 Anisotropic Mechanical Behaviour
121(42)
7.1 Elastic constants and polymer symmetry
121(4)
7.1.1 Specimens possessing orthorhombic symmetry
122(1)
7.1.2 Specimens possessing uniaxial symmetry, often termed transverse isotropy
123(2)
7.2 Measuring elastic constants
125(6)
7.2.1 Measurements on films or sheets
125(4)
7.2.2 Measurements on filaments
129(2)
7.3 Experimental studies of mechanical anisotropy in oriented polymers
131(8)
7.3.1 Sheets of low-density polyethylene
132(2)
7.3.2 Filaments tested at room temperature
134(5)
7.4 Interpretation of mechanical anisotropy: general considerations
139(3)
7.4.1 Theoretical calculations of elastic constants
139(2)
7.4.2 Orientation and morphology
141(1)
7.5 Experimental studies of anisotropic mechanical behaviour and their interpretation
142(10)
7.5.1 The aggregate model and mechanical anisotropy
143(1)
7.5.2 Correlation between the elastic constants of a highly oriented and an isotropic polymer
143(3)
7.5.3 The development of mechanical anisotropy with molecular orientation
146(3)
7.5.4 The anisotropy of amorphous polymers
149(1)
7.5.5 Later applications of the aggregate model
150(2)
7.6 The aggregate model for chain-extended polyethylene and liquid crystalline polymers
152(5)
7.7 Auxetic materials: negative Poisson's ratio
157(6)
References
160(3)
8 Polymer Composites: Macroscale and Microscale
163(30)
8.1 Composites: a general introduction
163(1)
8.2 Mechanical anisotropy of polymer composites
164(6)
8.2.1 Mechanical anisotropy of lamellar structures
164(2)
8.2.2 Elastic constants of highly aligned fibre composites
166(3)
8.2.3 Mechanical anisotropy and strength of uniaxially aligned fibre composites
169(1)
8.3 Short fibre composites
170(4)
8.3.1 The influence of fibre length: shear lag theory
171(2)
8.3.2 Debonding and pull-out
173(1)
8.3.3 Partially oriented fibre composites
174(1)
8.4 Takayanagi models for semicrystalline polymers
174(10)
8.4.1 The simple Takayanagi model
175(2)
8.4.2 Takayanagi models for dispersed phases
177(2)
8.4.3 Modelling polymers with a single-crystal texture
179(5)
8.5 Ultrahigh-modulus polyethylene
184(6)
8.5.1 The crystalline fibril model
184(3)
8.5.2 The crystalline bridge model
187(3)
8.6 Conclusions
190(3)
References
190(1)
Problems for Chapters 7 and 8
191(2)
9 Relaxation Transitions: Experimental Behaviour and Molecular Interpretation
193(26)
9.1 Amorphous polymers: an introduction
193(1)
9.2 Factors affecting the glass transition in amorphous polymers
194(8)
9.2.1 Effect of chemical structure
195(2)
9.2.2 Effect of molecular mass and cross-linking
197(1)
9.2.3 Blends, grafts and copolymers
198(2)
9.2.4 Effect of plasticizers
200(2)
9.3 Relaxation transitions in crystalline polymers
202(14)
9.3.1 General introduction
202(1)
9.3.2 Relaxation in low crystallinity polymers
203(2)
9.3.3 Relaxation processes in polyethylene
205(7)
9.3.4 Relaxation processes in liquid crystalline polymers
212(4)
9.4 Conclusions
216(4)
References
216(3)
10 Creep, Stress Relaxation and Non-linear Viscoelasticity 219(22)
10.1 The engineering approach
220(1)
10.1.1 Isochronous stress-strain curves
220(1)
10.2 The rheological approach
220(11)
10.2.1 Adaptations of linear theory - differential models
221(3)
10.2.2 Adaptations of linear theory - integral models
224(4)
10.2.3 More complicated single-integral representations
228(3)
10.2.4 Comparison of single-integral models
231(1)
10.3 Creep and stress relaxations as thermally activated processes
231(11)
10.3.1 The Eyring equation
231(2)
10.3.2 Applications of the Eyring equation to creep
233(3)
10.3.3 Applications of the Eyring equation to stress relaxation
236(2)
10.3.4 Applications of the Eyring equation to yield
238(1)
References
239(2)
11 Yielding and Instability in Polymers 241(32)
11.1 Discussion of load-elongation curves in tensile testing
242(8)
11.1.1 Necking and the ultimate stress
243(3)
11.1.2 Necking and cold-drawing: a phenomenological discussion
246(1)
11.1.3 Use of the Considère construction
247(2)
11.1.4 Definition of yield stress
249(1)
11.2 Ideal plastic behaviour
250(8)
11.2.1 The yield criterion: general considerations
250(1)
11.2.2 The Tresca yield criterion
251(1)
11.2.3 The Coulomb yield criterion
251(2)
11.2.4 The von Mises yield criterion
253(2)
11.2.5 Geometrical representations of the Tresca, von Mises and Coulomb yield criteria
255(1)
11.2.6 Combined stress states
256(2)
11.3 Historical development of understanding of the yield process
258(3)
11.3.1 Adiabatic heating
258(2)
11.3.2 The isothermal yield process: the nature of the load drop
260(1)
11.4 Experimental evidence for yield criteria in polymers
261(5)
11.4.1 Application of Coulomb yield criterion to yield behaviour
261(1)
11.4.2 Direct evidence of the influence of hydrostatic pressure on yield behaviour
262(4)
11.5 The molecular interpretations of yield and cold-drawing
266(2)
11.5.1 Yield as an activated rate process: the Eyring equation
266(1)
11.5.2 Alternative models: nucleation-controlled mechanisms
266(1)
11.5.3 Pressure dependence and general states of stress
267(1)
11.6 Cold-drawing
268(5)
11.6.1 General considerations
268(1)
11.6.2 The natural draw ratio, maximum draw ratios and molecular networks
269(1)
11.6.3 Crystalline polymers
270(1)
References
270(3)
12 Breaking Phenomena 273(68)
12.1 Definition of tough and brittle behaviour in polymers
273(1)
12.2 Principles of brittle fracture of polymers
274(6)
12.2.1 Griffith fracture theory
274(1)
12.2.2 The Irwin model
275(2)
12.2.3 The strain energy release rate
277(3)
12.3 Controlled fracture in brittle polymers
280(1)
12.4 Crazing in glassy polymers
281(5)
12.5 The structure and formation of crazes
286(10)
12.5.1 The structure of crazes
288(3)
12.5.2 Craze initiation and growth
291(4)
12.5.3 Crazing in the presence of fluids and gases: environmental crazing
295(1)
12.6 Controlled fracture in tough polymers
296(11)
12.6.1 The J-integral
298(4)
12.6.2 Essential work of fracture
302(3)
12.6.3 Crack opening displacement
305(2)
12.7 The molecular approach
307(3)
12.8 Factors influencing brittle-ductile behaviour: brittle-ductile transitions
310(5)
12.8.1 The Ludwig-Davidenkov-Orowan hypothesis
310(1)
12.8.2 Notch sensitivity and Vincent's aB-o diagram
311(4)
12.9 The impact strength of polymers
315(10)
12.9.1 Flexed-beam impact
315(4)
12.9.2 Falling-weight impact
319(2)
12.9.3 Toughened polymers: high-impact polyblends
321(1)
12.9.4 Crazing and stress whitening
322(2)
12.9.5 Dilatation bands
324(1)
12.10 The tensile strength and tearing of polymers in the rubbery state
325(3)
12.10.1 The tearing of rubbers: extension of Griffith theory
325(1)
12.10.2 Molecular theories of the tensile strength of rubbers
326(2)
12.11 Effect of strain rate and temperature
328(3)
12.12 Fatigue in polymers
331(10)
References
335(4)
Problems for Chapters 11 and 12
339(2)
Appendix 1 341(12)
A1.1 Scalars, vectors and tensors
341(1)
A1.2 Tensor components of stress
341(1)
A1.3 Tensor components of strain
342(1)
A1.4 Generalized Hooke's law
342(1)
A1.5 Engineering strains and matrix notation
343(2)
A1.6 The elastic moduli of isotropic materials
345(2)
A1.7 Transformation of tensors from one set of coordinate axes to another
347(3)
A1.8 The Mohr circle construction
350(1)
References
351(2)
Appendix 2 353(4)
A2.1 Rivlin, Mooney, Ogden
353(3)
References
356(1)
Answers to Problems 357(20)
Index 377

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