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Cyclic Plasticity of Metals Modeling Fundamentals and Applications Elsevier Series on Plasticity of Materials ThePlasticityofMaterialsbookseriessummarizesfoundationalknowledgeandoutlinesrecentdevel- opmentsinthefieldofmaterialsplasticity.Featuringinvestigationsatallscales,includingexperimental, constitutivemodeling,andnumericalapproachesforgoverningequations,eachvolumeintheseriesaimsto providevision,insight,andsolutionstofundamentalandappliedproblems,aswellasunifyingmulti-scale approaches.Itcoversabroadrangeofcontentinmechanics,materialsciences,manufacturing,mechanical, automotive,civil,environmental,mining,andpetroleumengineeringforanarrayofaudiencesincluding students,researchers,andprofessionalengineers. SeriesEditor-in-Chief:FrédéricBarlat ProfessorFrédéricBarlatisoneoftheleadingresearchersinthefieldofmechanicsofmaterialsandhas publishedover250articlesinpeer-reviewedscientificjournals.FollowinghisPhD,hejoinedAlcoaTech- nicalCenteroutsidePittsburgh,PAwhereheworkedforover20yearsbeforemovingtoSouthKoreawhere hebecameafullprofessoratPohangUniversityofScienceandTechnology.Heisanhonorarymemberof theRomanianAcademyandreceivedthe2013KhanInternationalAwardforoutstandinglife-longcontri- butionstothefieldofplasticity.Hisresearchfocusesonthedevelopmentofinnovativeplasticitytheories formetalsaswellasmanufacturingtechnologiesforsheetproducts. SeriesDeputyEditor:OanaCazacu Dr.CazacuisaProfessorofMechanicsatUniversityofFlorida’sGraduateResearchEngineeringandEdu- cationCenter(UF/REEF).ShehasHabilitationandDoctoraldegreesfromtheUniversityofLille(France) andhasbeentherecipientofvisitingchairprofessorshipsinEuropeandAustralia.SheisanAssociateEdi- torofMechanicsResearchCommunicationandtheInternationalJournalofMaterialFormingandalsothe authorofamonograph,12bookchapters,over150peer-reviewedpapers,andhaseditedanother5books. Sheiswidelyrecognizedforhercontributionstomodelingplasticanisotropyanddamageinmetallicand geologicalmaterials. SeriesDeputyEditor:RenéDeBorst Dr.DeBorstistheCentenaryProfessorofCivilEngineeringattheUniversityofSheffield.Hewasprevi- ouslyDistinguishedProfessoratDelftUniversityofTechnologyandEindhovenUniversityofTechnology, andtheRegiusProfessorofCivilEngineeringandMechanicsattheUniversityofGlasgow.Hisworkcov- ersseveraltopicsinengineeringmechanicsandmaterials,suchasplasticityandfractureofconcrete,soils, composites,andrubbers,aswellasthedevelopmentofnumericalmodelsfordeformationandfailure.He istheauthorof2books,haseditedanother14booksandconferenceproceedings,andhaswrittenover230 peer-reviewedpapersand30bookchapters.HeisamemberoftheRoyalNetherlandsAcademyofArtsand Sciences,afellowoftheRoyalSocietyofEdinburgh,andtheRoyalAcademyofEngineeringinLondon. HealsoholdsanhonorarydoctoratefromINSALyon. SeriesDeputyEditor:A.ErmanTekkaya Dr. A. Erman Tekkaya is currently a professor and the director of the Institute for Metal Forming and LightweightComponents(IUL)attheTechnischeUniversitätDortmund.Hisresearchinterestscoverfun- damentalsandtechnologyofnovelmetalformingprocesses,materialcharacterizationformodelingthe materialbehaviorduringplasticdeformations,anddamage-controlledmetalformingprocessesimproving theusabilityoftheformedcomponents.HewasawardedtheInternationalPrizeforResearch&Develop- mentinPrecisionForgingbytheJapaneseSocietyforTechnologyofPlasticityin2014.Heisafellowof theInternationalAcademyforProductionEngineering(CIRP)andmemberoftheBoardofTrusteesofthe GermanResearchAssociationforSteelApplication(FOSTA).Hehaspublishedover210peer-reviewed papersandhasover30patentsgrantedorfiled. Availableandforthcomingvolumes • Gradient-EnhancedContinuumPlasticitybyGeorgeVoyiadjis(2020) • PlasticityofMetallicMaterialsbyOanaCazacuandBenoitRevil-Baudard(2020) • Material Modeling with the Visco-Plastic Self-Consistent Approach by Carlos Tome and Ricardo Lebensohn(2021) • ThermomechanicsofSolidsandStructuresbyMarkoCanadija(2022) Elsevier Series on Plasticity of Materials Cyclic Plasticity of Metals Modeling Fundamentals and Applications Series Editors Frédéric Barlat Oana Cazacu René De Borst A. Erman Tekkaya Edited by Hamid Jahed Ali A. Roostaei Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2022ElsevierInc.Allrightsreserved. MATLAB®isatrademarkofTheMathWorks,Inc.andisusedwithpermission. TheMathWorksdoesnotwarranttheaccuracyofthetextorexercisesinthisbook. Thisbook’suseordiscussionofMATLAB®softwareorrelatedproductsdoesnotconstituteendorsement orsponsorshipbyTheMathWorksofaparticularpedagogicalapproachorparticularuseofthe MATLAB®software. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationabout thePublisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyright ClearanceCenterandtheCopyrightLicensingAgency,canbefoundatourwebsite: www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher (otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperience broadenourunderstanding,changesinresearchmethods,professionalpractices,ormedicaltreatment maybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingand usinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuch informationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,including partiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assume anyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability, negligenceorotherwise,orfromanyuseoroperationofanymethods,products,instructions,orideas containedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-819293-1 ForinformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionsEditor:DennisMcGonagle EditorialProjectManager:RafaelG.Trombaco ProductionProjectManager:SuryaNarayananJayachandran Designer:MatthewLimbert TypesetbyVTeX Contents Listofcontributors xi Foreword xv Preface xix PartOne Introduction 1 1 Experimentalobservationsincyclicloadingofmetals 3 AliA.RoostaeiandHamidJahed 1.1 Introduction 3 1.2 Bauschingerphenomenon 3 1.2.1 Earlyreverseyielding 3 1.2.2 Transienthardeningandpermanentsoftening 4 1.2.3 Hardeningstagnation 4 1.2.4 Microstructurelink 5 1.3 Cyclichardening/softening 6 1.3.1 Fully-reversedloading 6 1.3.2 Additionalnonproportionalhardening 8 1.3.3 Microstructurelink 8 1.4 Meanstress/strainresponseevolution 9 1.4.1 Meanstressrelaxation 9 1.4.2 Ratcheting 9 1.4.3 Microstructurelink 11 1.5 Direction-dependentbehavior 11 1.5.1 Tension–compressionasymmetry 13 1.5.2 Directionalanisotropy 14 1.5.3 Microstructurelink 15 1.6 Masingbehavior 17 1.7 Closingremarks 19 References 19 2 Fundamentalsofcyclicplasticitymodels 23 AliA.RoostaeiandHamidJahed 2.1 Statesofstressandstrain 23 2.1.1 Stresstensors 23 2.1.2 Straintensors 32 2.2 Stress–strainrelations 35 2.2.1 Elasticity 35 2.2.2 Yieldcriteria 37 vi Contents 2.2.3 Plasticity 41 2.3 Hardeningrules 45 2.3.1 Isotropichardening 45 2.3.2 Kinematichardening 46 2.3.3 Combinedhardening 50 2.4 Closingremarks 50 References 50 PartTwo Cyclicplasticitymodels 53 3 Multisurfacecyclicplasticity 55 MeijuanZhang,MiguelÁngelSánz,KhanhNguyen,and FranciscoJ.Montáns 3.1 Introduction 55 3.2 Generalframeworkforsmallstrainsbasedonstoredenergiesand elasticcorrectorrates 57 3.3 Overlayandnestedsurfacemodels.TheMrózmodel 60 3.4 AtranslationruleforanimplicitimplementationoftheMróz model 65 3.5 MultisurfacemodelusingPragertranslationrule 68 3.6 Connectionwithsubloadingandboundingsurfacemodels 78 3.7 Rheology-basedmodelswithoutexplicitbackstress 81 3.8 Comparisonofmultisurfacemodelsformultiaxialcyclicbehavior 83 3.9 LargestrainsformulationofBesselingmodels 86 3.10 Concludingremarks 96 References 97 4 Two-surfacecyclicplasticity 101 SeyedBehzadBehraveshandYannisF.Dafalias 4.1 Introduction 101 4.2 Fundamentalsoftwo-surfaceplasticity 102 4.2.1 Modelingofuniaxialloading 102 4.2.2 Generalizationtomultiaxialloading 111 4.2.3 Overshootingphenomenon 114 4.2.4 Solvedproblems 116 4.3 Furtherdevelopmentofthetwo-surfaceplasticity 127 4.3.1 McDowellmodel 127 4.3.2 Yoshida–Uemorimodel 129 4.3.3 Hassan–Kyriakidesmodel 131 4.4 Generalassessmentandcurrenttrends 133 4.4.1 Generalassessment 133 4.4.2 Currenttrends 135 4.5 Conclusion 136 Acknowledgments 137 References 137 Contents vii 5 Nonlinearkinematichardeningcyclicplasticity 139 A.Varvani-Farahani 5.1 Introduction 139 5.2 Kinematichardeningmodels 140 5.2.1 Uncoupledmultisurfacehardeningmodels 140 5.2.2 Coupledkinematichardeningmodels 142 5.2.3 Evaluationofvariousmodelsbasedonstrain-controlled cyclicresults 151 5.3 Kinematichardeningrulescoupledwithinfluentialdescriptions 152 5.3.1 Kinematichardeningrulescoupledwithviscoplasticflow description 152 5.3.2 KinematichardeningrulescoupledwiththeNeuber hypothesisinthepresenceofstressraisers 160 5.3.3 Kinematichardeningrulescoupledwithyieldsurface distortion 164 5.3.4 Kinematichardeningrulescoupledwithcontinuumdamage mechanics 165 5.3.5 Kinematichardeningrulescoupledwithcrystalplasticity 165 5.4 Closingremarks 166 Acknowledgments 168 References 168 6 Distortionalhardeningcyclicplasticity 175 RenéMarek,SlavomírParma,andHeidiP.Feigenbaum 6.1 Introduction 175 6.1.1 Observingphenomenainstressspace 177 6.2 Experimentalmeasurementofyieldsurfacedistortion 178 6.2.1 Developmentofexperimentalresearch 179 6.2.2 Experimentalmethodstodetectyieldsurfacesdistortion 182 6.2.3 Yielddefinition 186 6.2.4 Elasticmoduliinfluence 189 6.2.5 Observedyieldsurfacedistortion 192 6.2.6 Synthesisofexperimentalresults 194 6.3 Modelingofyieldsurfacedistortion 197 6.3.1 Notablemodelsfeaturinguniaxialdistortion 197 6.3.2 Modelingmultiaxialdistortion 202 6.3.3 Yieldsurfaceconvexity 202 6.3.4 Showcasemodelofuniaxialdistortion 203 6.3.5 Evolutionrulesfordistortion 206 6.3.6 Modelingtheeffectofdistortionbyothermethods 208 6.4 Numericalsimulationsanddemonstrations 210 6.4.1 Calibrationfromexperimentaldata 210 6.4.2 Fewremarksonnumericalimplementation 212 6.4.3 Preservationoftheeffectofdistortion 213 6.4.4 Effectofdistortiononbiaxialratchetingpredictions 214 viii Contents 6.5 Conclusions 217 Acknowledgments 218 References 219 7 Computationalmethodsforcyclicplasticity 227 KaterinaD.PapouliaandM.RezaHirmand 7.1 Introduction 227 7.2 Thermomechanicalframework 228 7.2.1 Example:NonassociativeinviscidvonMisesplasticitywith isotropicandnonlinearkinematichardening 235 7.2.2 Example:MultisurfaceinviscidvonMisesplasticitywith Mrózkinematichardening 239 7.2.3 Example:Initiallyanisotropicviscoplasticitywithnonlinear isotropichardening,linearkinematichardening,and dynamicrecovery 242 7.3 Variationalprinciples 244 7.3.1 Displacementmethod 245 7.3.2 Assumedpressureanddilatationmethod 248 7.4 Constitutiveupdatealgorithms 250 7.4.1 Elastic–plasticoperatorsplit 252 7.4.2 Closestpointprojectionalgorithm 253 7.4.3 Algorithmictangentmoduli 255 7.4.4 Example:J plasticitywithnonlinearkinematichardening 256 2 7.4.5 Geometricalinterpretation 260 7.4.6 Returnmappingalgorithmforviscoplasticity 262 7.4.7 Cuttingplanealgorithm 263 7.4.8 Yieldsurfaceswithnondifferentiablepoints 265 7.5 Minimumprincipleforthedissipationpotential 269 7.6 Generalizedandendochronicplasticity 273 7.7 Closure 276 References 277 PartThree Applicationsofcyclicplasticity 281 8 Cyclicplasticityappliedtothenotchanalysisofmetals 283 GrzegorzGlinka,AliA.Roostaei,andHamidJahed 8.1 Introduction 283 8.2 Stressstatesatanotchtip 283 8.3 TheNeuberrule 285 8.3.1 TheoriginalNeuberrule(MethodA) 287 8.3.2 TheNeuberrulebasedontheequivalenceofthestrain energydensity(MethodB) 288 8.3.3 TheNeuberrulebasedonthelinearpseudoelasticnotchtip stress(MethodC) 290 Contents ix 8.3.4 TheNeuberrulebasedonthepseudoelasticstressfield aheadofanotchtip(MethodD) 292 8.4 EquivalentStrainEnergyDensity(ESED)rule 293 8.4.1 TheoriginalESEDrule(MethodE) 293 8.4.2 ThecorrectedESEDrule(MethodF) 295 8.4.3 TheESEDrulebasedonthelinearpseudoelasticstressat thenotchtip(MethodG) 298 8.4.4 TheESEDrulebasedonthedistributionofthe pseudoelasticstressaheadofthenotchtip(MethodH) 298 8.5 Notchesunderuniaxialcyclicloadings 300 8.5.1 Constantamplitudecyclicloading 301 8.5.2 Variableamplitudecyclicloading 303 8.5.3 Biaxialtransformationofconstitutiverelationship 304 8.6 Notchesundermultiaxialcyclicloading 304 8.6.1 Proportionalmultiaxialloading 305 8.6.2 Nonproportionalmultiaxialloading 312 8.7 Extensionofthenotchanalysistoasymmetric/anisotropicmetals 317 8.7.1 Analysisprocedure 318 8.7.2 Experimentalvalidation 318 8.8 Summary 320 References 322 9 Applicationofcyclicplasticityformodelingratchetinginmetals 325 GuozhengKangandQianhuaKan 9.1 Introduction 325 9.2 Evolutionfeaturesofratcheting 326 9.2.1 Effectofcyclicsoftening/hardeningbehavior 326 9.2.2 Effectofstresslevel 328 9.2.3 Effectofstressrate 329 9.2.4 Effectofambienttemperature 329 9.2.5 Effectofloadingpath 331 9.3 Cyclicplasticitymodelsofratcheting 332 9.3.1 Outlineofcyclicplasticitymodels 333 9.3.2 Simulationofratchetinginmetals 337 9.4 Ratchetingofstructurecomponentsanditseffectonfatiguefailure 343 9.4.1 Finiteelementmodel 345 9.4.2 Validatingratchetingstrainpredictions 346 9.4.3 Simulatedequivalentplasticstrainfieldanditsevolution 346 9.4.4 Predictionofrollingcontactfatiguecrackinitiationlife 347 9.5 Closingremarks 351 References 351 10 Applicationofcyclicplasticitytofatiguemodeling 357 JafarAlbinmousaandTimothyTopper 10.1 Introduction 357