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

by I. M. Ward (IRC in Polymer Science and Technology, School of Physics and Astronomy, University of Leeds, UK); J. Sweeney (IRC in Polymer Science and Technology, School of Engineering, Design and Technology, University of Bradford, UK)

• ISBN13: 9780471496250
• ISBN10: 0471496251
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-05-01
• Publisher: WILEY

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