Mechanical Properties of Solid Polymers PDF
Preview Mechanical Properties of Solid Polymers
244 x 168 26mm RED BOX RULES ARE FOR PROOF STAGE ONLY. DELETE BEFORE FINAL PRINTING. Ward Sweeney Mechanical Properties of Solid Polymers Third Edition I. M. Ward I. M. Ward J. Sweeney School of Physics and Astronomy, School of Engineering, Design and Technology, M J. Sweeney Leeds University, Leeds, UK University of Bradford, Bradford, UK e c h When assessing the mechanical properties of a polymer, questions of ductility, strength and a fl exibility are paramount. Understanding how a polymer behaves under stress is critical n to selecting the correct polymer for any given application. In Mechanical Properties of i c Solid Polymers, Third Edition, the approach is to provide a formal description of the a behaviour using the mathematical techniques of solid mechanics, followed by l interpretations in terms of the molecular structure and morphology. The third edition P r combines the best qualities of its highly successful predecessors and includes: o Mechanical p • Finite strain and rubber-like elasticity e • r Linear viscoelasticity and mechanical relaxation t • Anisotropic mechanical behaviour ie Properties s • Polymer composites and nanocomposites o • Non-linear viscoelasticity f • of Solid Yield, instability, and breaking phenomena S o l Drawing on more than thirty years of teaching and research experience, Ward and i d Sweeney present all aspects of mechanical behaviour in an accessible way without Polymers P compromising the in-depth treatments of foundational techniques and theories. o The result is a straightforward, rigorous and practical guide. l y m “Introduces the mechanical properties of solid polymers in a straightforward, rigorous, and practical manner… an essential volume for students and scholars of physics, e Third Edition r chemistry and chemical engineering, as well as polymer researchers, chemists, and s chemical engineers or material scientists in government and industry.” Professor F. J. Baltá-Calleja (Inst. Estructura de la Materia, CSIC, Spain) Third Edition Mechanical Properties of Solid Polymers Mechanical Properties of Solid Polymers Third Edition I. M. WARD School of Physics and Astronomy, Leeds University, Leeds, UK J. SWEENEY School of Engineering, Design and Technology, University of Bradford, Bradford, UK A John Wiley & Sons, Ltd., Publication Thiseditionfirstpublished2013 (cid:2)C 2013JohnWiley&Sons,Ltd. Registeredoffice JohnWiley&SonsLtd.,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissiontoreuse thecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,Designs andPatentsAct1988. 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LibraryofCongressCataloging-in-PublicationData Ward,I.M.(IanMacmillan),1928–author. Mechanicalpropertiesofsolidpolymers.–Thirdedition/IanM.Ward,SchoolofPhysicsandAstronomy,LeedsUniversity, Leeds,UK,JohnSweeney,SchoolofEngineering,DesignandTechnology,UniversityofBradford,Bradford,UK. pagescm Includesbibliographicalreferencesandindex. ISBN978-1-4443-1950-7(hardback) 1.Polymers–Mechanicalproperties. I.Sweeney,J.(John)author II.Title. TA455.P58W372012 620.1(cid:3)9204292–dc23 2012020163 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ClothISBN:9781444319507 Setin10/12ptTimesbyAptaraInc.,NewDelhi,India. Contents Preface xiii 1 StructureofPolymers 1 1.1 ChemicalComposition 1 1.1.1 Polymerisation 1 1.1.2 Cross-LinkingandChain-Branching 3 1.1.3 AverageMolecularMassandMolecularMassDistribution 4 1.1.4 ChemicalandStericIsomerismandStereoregularity 5 1.1.5 LiquidCrystallinePolymers 7 1.1.6 Blends,GraftsandCopolymers 8 1.2 PhysicalStructure 9 1.2.1 RotationalIsomerism 9 1.2.2 OrientationandCrystallinity 10 References 16 FurtherReading 17 2 TheMechanicalPropertiesofPolymers:GeneralConsiderations 19 2.1 Objectives 19 2.2 TheDifferentTypesofMechanicalBehaviour 19 2.3 TheElasticSolidandtheBehaviourofPolymers 21 2.4 StressandStrain 22 2.4.1 TheStateofStress 22 2.4.2 TheStateofStrain 23 2.5 TheGeneralisedHooke’sLaw 26 References 29 3 TheBehaviourintheRubber-LikeState:FiniteStrainElasticity 31 3.1 TheGeneralisedDefinitionofStrain 31 3.1.1 TheCauchy–GreenStrainMeasure 32 3.1.2 PrincipalStrains 34 3.1.3 TransformationofStrain 36 3.1.4 ExamplesofElementaryStrainFields 38 3.1.5 RelationshipofEngineeringStrainstoGeneralStrains 41 3.1.6 LogarithmicStrain 42 3.2 TheStressTensor 43 3.3 TheStress–StrainRelationships 44 vi Contents 3.4 TheUseofaStrainEnergyFunction 47 3.4.1 ThermodynamicConsiderations 47 3.4.2 TheFormoftheStrainEnergyFunction 51 3.4.3 TheStrainInvariants 51 3.4.4 ApplicationoftheInvariantApproach 52 3.4.5 ApplicationofthePrincipalStretchApproach 54 References 58 4 Rubber-LikeElasticity 61 4.1 GeneralFeaturesofRubber-LikeBehaviour 61 4.2 TheThermodynamicsofDeformation 62 4.2.1 TheThermoelasticInversionEffect 64 4.3 TheStatisticalTheory 65 4.3.1 SimplifyingAssumptions 65 4.3.2 AverageLengthofaMoleculebetweenCross-Links 66 4.3.3 TheEntropyofaSingleChain 67 4.3.4 TheElasticityofaMolecularNetwork 69 4.4 ModificationsofSimpleMolecularTheory 72 4.4.1 ThePhantomNetworkModel 73 4.4.2 TheConstrainedJunctionModel 73 4.4.3 TheSlipLinkModel 73 4.4.4 TheInverseLangevinApproximation 75 4.4.5 TheConformationalExhaustionModel 79 4.4.6 TheEffectofStrain-InducedCrystallisation 80 4.5 TheInternalEnergyContributiontoRubberElasticity 80 4.6 Conclusions 83 References 83 FurtherReading 85 5 LinearViscoelasticBehaviour 87 5.1 ViscoelasticityasaPhenomenon 87 5.1.1 LinearViscoelasticBehaviour 88 5.1.2 Creep 89 5.1.3 StressRelaxation 91 5.2 MathematicalRepresentationofLinearViscoelasticity 92 5.2.1 TheBoltzmannSuperpositionPrinciple 93 5.2.2 TheStressRelaxationModulus 96 5.2.3 TheFormalRelationshipbetweenCreepandStressRelaxation 96 5.2.4 MechanicalModels,RelaxationandRetardationTimeSpectra 97 5.2.5 TheKelvinorVoigtModel 98 5.2.6 TheMaxwellModel 99 5.2.7 TheStandardLinearSolid 100 5.2.8 RelaxationTimeSpectraandRetardationTimeSpectra 101 5.3 DynamicalMechanicalMeasurements:TheComplexModulus andComplexCompliance 103 5.3.1 ExperimentalPatternsforG ,G andsoonasaFunction 1 2 ofFrequency 105 Contents vii 5.4 TheRelationshipsbetweentheComplexModuliandtheStress RelaxationModulus 109 5.4.1 FormalRepresentationsoftheStressRelaxationModulus andtheComplexModulus 111 5.4.2 FormalRepresentationsoftheCreepComplianceandthe ComplexCompliance 113 5.4.3 TheFormalStructureofLinearViscoelasticity 113 5.5 TheRelaxationStrength 114 References 116 FurtherReading 117 6 TheMeasurementofViscoelasticBehaviour 119 6.1 CreepandStressRelaxation 119 6.1.1 CreepConditioning 119 6.1.2 SpecimenCharacterisation 120 6.1.3 ExperimentalPrecautions 120 6.2 DynamicMechanicalMeasurements 123 6.2.1 TheTorsionPendulum 124 6.2.2 ForcedVibrationMethods 126 6.2.3 DynamicMechanicalThermalAnalysis(DMTA) 126 6.3 Wave-PropagationMethods 127 6.3.1 TheKilohertzFrequencyRange 128 6.3.2 TheMegahertzFrequencyRange:UltrasonicMethods 129 6.3.3 TheHypersonicFrequencyRange:BrillouinSpectroscopy 131 References 131 FurtherReading 133 7 ExperimentalStudiesofLinearViscoelasticBehaviourasaFunction ofFrequencyandTemperature:Time–TemperatureEquivalence 135 7.1 GeneralIntroduction 135 7.1.1 AmorphousPolymers 135 7.1.2 TemperatureDependenceofViscoelasticBehaviour 138 7.1.3 CrystallinityandInclusions 138 7.2 Time–TemperatureEquivalenceandSuperposition 140 7.3 TransitionStateTheories 143 7.3.1 TheSiteModelTheory 145 7.4 TheTime–TemperatureEquivalenceoftheGlassTransition ViscoelasticBehaviourinAmorphousPolymersandtheWilliams, LandelandFerry(WLF)Equation 147 7.4.1 TheWilliams,LandelandFerryEquation,theFreeVolume TheoryandOtherRelatedTheories 153 7.4.2 TheFreeVolumeTheoryofCohenandTurnbull 154 7.4.3 TheStatisticalThermodynamicTheoryofAdamandGibbs 154 7.4.4 AnObjectiontoFreeVolumeTheories 155 7.5 NormalModeTheoriesBasedonMotionofIsolatedFlexibleChains 156 7.6 TheDynamicsofHighlyEntangledPolymers 160 References 163 viii Contents 8 AnisotropicMechanicalBehaviour 167 8.1 TheDescriptionofAnisotropicMechanicalBehaviour 167 8.2 MechanicalAnisotropyinPolymers 168 8.2.1 TheElasticConstantsforSpecimensPossessing FibreSymmetry 168 8.2.2 TheElasticConstantsforSpecimensPossessing OrthorhombicSymmetry 170 8.3 MeasurementofElasticConstants 171 8.3.1 MeasurementsonFilmsorSheets 171 8.3.2 MeasurementsonFibresandMonofilaments 181 8.4 ExperimentalStudiesofMechanicalAnisotropyinOrientedPolymers 185 8.4.1 SheetsofLow-DensityPolyethylene 186 8.4.2 FilamentsTestedatRoomTemperature 186 8.5 InterpretationofMechanicalAnisotropy:GeneralConsiderations 192 8.5.1 TheoreticalCalculationofElasticConstants 192 8.5.2 OrientationandMorphology 197 8.6 ExperimentalStudiesofAnisotropicMechanicalBehaviour andTheirInterpretation 198 8.6.1 TheAggregateModelandMechanicalAnisotropy 198 8.6.2 CorrelationoftheElasticConstantsofanOrientedPolymer withThoseofanIsotropicPolymer:TheAggregateModel 198 8.6.3 TheDevelopmentofMechanicalAnisotropywithMolecular Orientation 201 8.6.4 TheSonicVelocity 206 8.6.5 AmorphousPolymers 208 8.6.6 OrientedPolyethyleneTerephthalateSheetwith OrthorhombicSymmetry 209 8.7 TheAggregateModelforChain-ExtendedPolyethyleneandLiquid CrystallinePolymers 212 8.8 AuxeticMaterials:NegativePoisson’sRatio 216 References 220 9 PolymerComposites:MacroscaleandMicroscale 227 9.1 Composites:AGeneralIntroduction 227 9.2 MechanicalAnisotropyofPolymerComposites 228 9.2.1 MechanicalAnisotropyofLamellarStructures 228 9.2.2 ElasticConstantsofHighlyAlignedFibreComposites 230 9.2.3 MechanicalAnisotropyandStrengthofUniaxiallyAligned FibreComposites 233 9.3 ShortFibreComposites 233 9.3.1 TheInfluenceofFibreLength:ShearLagTheory 234 9.3.2 DebondingandPull-Out 236 9.3.3 PartiallyOrientedFibreComposites 236 9.4 Nanocomposites 238 9.5 TakayanagiModelsforSemi-CrystallinePolymers 241 9.5.1 TheSimpleTakayanagiModel 242
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