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Applied Mechanics of Polymers Applied Mechanics of Polymers Properties, Processing, and Behavior George Youssef San DiegoStateUniversity, SanDiego,CA, USA Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2022ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans, electronicormechanical,includingphotocopying,recording,oranyinformationstorageand retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek permission,furtherinformationaboutthePublisher’spermissionspoliciesandourarrangements withorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency,can befoundatourwebsite:www.elsevier.com/permissions. Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythe Publisher(otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperience broadenourunderstanding,changesinresearchmethods,professionalpractices,ormedical treatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluating andusinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuch informationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers, includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors, assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproducts liability,negligenceorotherwise,orfromanyuseoroperationofanymethods,products, instructions,orideascontainedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-821078-9 ForinformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionsEditor:DennisMcGonagle EditorialProjectManager:VeronicaSantosIII ProductionProjectManager:DebasishGhosh CoverDesigner:VictoriaPearson TypesetbySTRAIVE,India Contents 1. Introduction and background 1 1.1 Introduction 1 1.2 Historicalperspective 6 1.3 Typeofpolymers 8 1.4 Areasofstudyinpolymerscience 12 1.4.1 Polymerchemistry 13 1.4.2 Polymerphysics 15 1.4.3 Polymermechanics 15 1.5 Industrialapplicationsofpolymers 16 1.6 Closingremarks 17 Practiceproblems 17 References 18 2. General properties of polymers 19 2.1 Introduction 19 2.2 Quasi-staticmechanicalresponse 24 2.3 Long-termproperties 33 2.3.1 Creep 33 2.3.2 Relaxation 38 2.4 Dynamicproperties 39 2.5 Otherproperties 45 Practiceproblems 45 References 47 3. Processing and manufacturing of polymers 49 3.1 Introduction 49 3.2 Extrusion 56 3.3 Sheets,films,andfilaments 60 3.4 Thermoforming 63 3.5 Injectionmolding 66 3.6 Additivemanufacturing 69 Practiceproblems 75 References 76 v vi Contents 4. Linear elastic behavior of polymers 79 4.1 Introduction 79 4.2 Stressandequilibrium 82 4.2.1 Planestress 90 4.2.2 Simpletension 91 4.2.3 Simpleshear 91 4.2.4 Hydrostaticstress 91 4.3 Strainandcompatibility 92 4.3.1 Planestrain 93 4.4 Linearelasticmaterialbehavior 94 4.4.1 Isotropicmaterials 94 4.4.2 Orthotropicmaterials 99 4.4.3 Transverseisotropicmaterials 100 4.5 Structuralcomponentdesign 101 4.6 AppliedFEAsimulationexamples 108 Practiceproblems 115 References 116 5. Hyperelastic behavior of polymers 117 5.1 Introduction 117 5.2 Theoreticalpreliminaries 118 5.2.1 Displacementfield 118 5.2.2 Deformationgradient 120 5.2.3 Polardecomposition 123 5.2.4 Straintensors 125 5.2.5 Stresstensors 126 5.3 Stress–strainrelationships 128 5.4 Hyperelasticmodels 132 5.4.1 Neo-Hookeanmodel 133 5.4.2 Mooney-Rivlinmodel 134 5.4.3 Yeohmodel 135 5.4.4 Gentmodel 136 5.4.5 Ogdenmodel 137 5.4.6 OgdenHyper-foammodel 138 5.5 Applicationsofhyperelasticmodelsincomponent design 138 Practiceproblems 143 References 143 6. Creep behavior of polymers 145 6.1 Introduction 145 6.2 Simplecreepmodels 148 6.2.1 Maxwellmodel 150 6.2.2 Kelvinmodel 152 Contents vii 6.2.3 Four-parametersmodel 154 6.2.4 Zenermodel 156 6.3 Additionalcreepmodels 158 6.3.1 Findleypowerlaw 158 6.3.2 Norton–baileylaw 159 6.3.3 Prandtl–Garofalolaw 159 6.4 Applicationsofcreepincomponentdesign 160 6.5 AppliedFEAsimulationexample 160 Practiceproblems 162 References 164 7. Viscoelastic behavior of polymers 165 7.1 Introduction 165 7.2 Theoreticalpreliminaries 167 7.2.1 Boltzmannsuperpositionprinciple 167 7.2.2 GeneralizedMaxwellmodel 168 7.2.3 GeneralizedKelvinmodel 170 7.3 Linearviscoelasticity 171 7.3.1 Small-strainlinearviscoelasticity 172 7.3.2 Large-strainlinearviscoelasticity 185 7.4 Applicationsoflinearviscoelasticityincomponent design 185 7.5 AppliedFEAsimulationexample 188 Practiceproblems 191 References 191 8. Electroactive polymers 193 8.1 Introduction 193 8.2 Theoreticalpreliminaries 195 8.3 Electrostrictivepolymers 204 8.4 Dielectricelastomers 207 8.5 Applicationsofelectroactivepolymers 214 8.6 AppliedFEAsimulationexample 215 Practiceproblems 217 References 218 9. Hydrogels 221 9.1 Introduction 221 9.2 Mechanicsofhydrogels 228 9.2.1 Hydrogeldeformationtheory 228 9.2.2 Poroelasticity 232 9.3 Applicationsofhydrogels 236 9.4 AppliedFEAsimulationexample 237 Practiceproblems 239 References 240 viii Contents 10. Failure and fracture of polymers 243 10.1 Introduction 243 10.2 Shearyielding 250 10.3 Crazing 254 10.4 Fracturemechanics 258 10.5 Fatigue 262 Practiceproblems 269 References 269 11. Characterization of polymers 273 11.1 Introduction 273 11.2 Thermalcharacterizations 278 11.2.1 Differentialscanningcalorimetry 278 11.2.2 Thermogravimetricanalyzer 281 11.3 Microscopycharacterizations 282 11.3.1 Opticalmicroscopy 284 11.3.2 Scanningelectronmicroscopy 285 11.3.3 Transmissionelectronmicroscopy 287 11.3.4 Atomicforcemicroscopy 287 11.4 Spectroscopycharacterizations 291 11.4.1 UV–visiblespectroscopy 292 11.4.2 Fouriertransforminfraredspectroscopy 293 11.4.3 Ramanspectroscopy 294 11.4.4 Terahertztime-domainspectroscopy 295 Practiceproblems 296 References 297 Index 301 Chapter 1 Introduction and background 1.1 Introduction Polymers are one of the primary classes of materials rivaling metals and ceramics while being an integral part of the remarkable and transformative hybrid materials of polymer matrix composites. Polymers are commonly referred to as plastics, but we ought to formalize this nomenclature since the classification of polymers is important for the fundamental understanding of their physicalpropertiesandmechanicalbehaviors,aswillbediscussedlater. Polymersareubiquitousinmanyapplicationsrangingfromaerospacetoauto- motive,fromconsumergoodstohouseholdgoods,andfromsportsgeartobio- medical devices. In fact, we daily encounter polymers, intentionally or unintentionally, in even some of the most mundane activities. For example, anobservanteyewouldnoticepolymerseverywhereintheinteriorofanaircraft assoonasyoustepinsidethefuselagecabin,wherethestructuralcabinwindow systemandtheaccompanyingdustcoverthatweoftenareaskedtolowerdown duringtakeoffandlanding,aremadeofdifferentpolymers.Anothercommon transportation vehicle that encompasses a large percentage of polymers is the passengerautomobile,whichhasnearly30%ofallitspartsmadeofdifferent typesofpolymersdependingonthedesignrequirements.Thedashboard,instru- mentpanel,interiortrim,seating,interlayerinthe frontandrear windshields, andcarpetfibersarejustafewexamplesofinteriorpartsinthecarthataremade ofpolymers.Manyautomotiveexteriorpartsarealsomadeofpolymerswhere theyaresubjectedtoaggressiveloadingandenvironmentalconditionssuchas the tires (being the most obvious), the bumpers, the undercarriage, the wheel housing,theradiatorsupport,andthemanypartsinthefuelsystem,againjust to list afew examples. Evidentfromthediversityoftheapplicationsmentionedaboveisthebroad rangeofoperatingandenvironmentalconditions.Polymersthatareusedunder thehoodofacararerequiredtoendurecombinedthermalandmechanicalload- ingforalongduration,whilethosethatareusedinthefuelsystemarerequired toresistaggressivechemicals,e.g.,thefuel,whilesupportingaworkingpres- sure of (cid:1)345kPa (mechanical loads). Moreover, some polymers have to bear substantial mechanical loads while being abrasive resistant, e.g., tires help AppliedMechanicsofPolymers.https://doi.org/10.1016/B978-0-12-821078-9.00011-9 Copyright©2022ElsevierInc.Allrightsreserved. 1 2 Appliedmechanicsofpolymers supportasizableportionofthecarweight((cid:1)25%)whileenduringabrasiondur- ing contact with the road. In all, the class of polymeric materials itself is as diverseastheapplicationstheyareintegratedinto.Therefore, thegoalofthis textbook is to provide the fundamental background to assist engineers in per- forming meaningful stress analyses based on material constitutive models derived fromthe theory ofcontinuummechanics.These materialmodelsrep- resentanddescribethemechanicalbehaviorofthepolymerusedinthedesign. With this background in mind, it is now fitting to briefly define polymers notingthatthetermpolymeriscommonlyusedinterchangeablywiththeword macromolecule,withinthepolymersciencecommunity.Thebasicdefinitionof polymerscomesfromtheGreekrootsoftheword,wheretheoriginof‘poly’in Greekiseither“polus’meaning“much’or‘polloi”meaning“many.”Polymers are then materials of many repeating parts, units, or “mers” (from the Greek word “meros”). Polymers are compounds consisting of repeating long-chain unitsthatareconnected,whereeachsinglechainmayhavethousandsoreven millionsoftherepeatingmers.Moreover,polymersarematerialswithinterdig- itated molecules with different length scales. Generally, polymers are either hydrocarbons (covalently-bonded carbon-hydrogen backbone) or silicones (silicon-oxygenbackbone).Thismolecularstructureisresponsiblefortheover- all properties of polymers. Polymers can either be natural (e.g., human DNA and hair) or engineered (such as nylon and polyvinyl chloride). Some of the overarchingadvantagesandlimitationsofpolymersaresuccinctlysummarized inTable1.1,whichisnotintendedtobecomprehensiveorapplicablyinclusive to all types of polymers. While time-dependent properties are included in the tableasanexampleofgeneraldisadvantage,thismightbeadesirableattributes for polymers used indynamic or impact situations. Before delvingintomoredetails, therearethree questionsthatweneedto ask and answer to not only motivate the whole field of study of polymer mechanicsbutalsotogainaninsightfulperspectiveaboutthisinterestingclass TABLE1.1 Generaladvantagesandlimitationsofengineeringpolymers. Generaladvantages Generallimitations Lowdensityrelativetometals LowYoung’smodulus(stiffness) Goodstrength-to-weightratio Lowstrengthrelativetometals Highcorrosionresistance Limited-servicetemperature Lowelectricalandthermalconductivity Susceptibilitytoultravioletandother radiation Moisture,abrasion,andimpact Time-dependentproperties resistance

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