Metal Inelasticity in ABAQUS(ABAQUS金属非线性).ppt

DuctileMetalResponse MetalInelasticityinABAQUS 2 Overview UniaxialTestatLowTemperaturesStressandstrainmeasuresYieldStrainreversalafteryieldCyclicloadingNeckingTemperatureandstrain ratedependenceUniaxialTestatElevatedTemperatures MetalInelasticityinABAQUS 3 UniaxialTestatLowTemperatures Auniaxialtest whenperformedintensionorcompressionatarelativelylowtemperature belowtwo thirdsofthemetal smeltingtemperatureonanabsolutescale exhibitsseveralphenomenathatarebasictotheformulationoftheclassicaltheoriesofmetalplasticity Atypicalresponseisshowninthefigurebelow Typicaluniaxialstress straincurveforametal MetalInelasticityinABAQUS 4 UniaxialTestatLowTemperatures StressandstrainmeasuresTheresultsareplottedasstressversusstrain Becausenominalstrainsof20 100 arepossibleintensionfortypicalmetalsatroomtemperature aprecisedefinitionofstrainisneeded Thedominantmicromechanicalmechanismforductilityinpolycrystallinematerialsisdislocationmotion Themechanismdrivingdislocationmotionistheforce orresolvedstress associatedwiththedislocationmechanism Thus theimportantstressmeasureonthemicroscopicscaleisthetrue orCauchy stress theforceperunitofcurrentareatransmittedacrossasurfaceinthematerial MetalInelasticityinABAQUS 5 UniaxialTestatLowTemperatures Datafromtensionandcompressiontestscorrespondwhentruestressisadoptedonthemacroscaleandtheconjugatelogarithmicstrainmeasureisused Truestresssandlogarithmicstraineareconjugateinthesensethatse workperunitvolume Tensionandcompressionstress straincurvesforcopper experimentaldatafromLudwikandScheu fromHill 1950 MetalInelasticityinABAQUS 6 UniaxialTestatLowTemperatures YielddatashouldalwaysbegiveninABAQUSastruestressversuslogarithmicstrain Logarithmicstrain e isdefinedaswherelisthecurrentgaugelength l0istheoriginalgaugelength andenomistheengineeringornominalstrain Truestress s isdefinedaswheresnomistheengineeringornominalstress snom F A0 MetalInelasticityinABAQUS 7 UniaxialTestatLowTemperatures YieldYieldisthepointatwhichthedeformationisnolongerfullyrecoverable thatis itisnolongerpurelyelastic Sometimesthereisnononzerostressthatthematerialcansupportandstillrecoverelasticallywhenthestressisremoved Forexample thematerialmaycreepatverylowstresslevels particularlyathightemperatures Mostpracticaldesignsrequireamaterialtoexhibitpurelyelasticresponseuptosomenonzerostresslevel MetalInelasticityinABAQUS 8 UniaxialTestatLowTemperatures Manyimportantstructuralmaterials suchassteelatroomtemperature haveawell definedyieldpoint Withsteelthereisaverylargechangeinmodulus stiffness whenityields MetalInelasticityinABAQUS 9 UniaxialTestatLowTemperatures Inmostmetalstheyieldstressisasmallfraction typically0 1 to1 oftheelasticmodulus Thus theelasticstraininthemetalisnevermorethanthissamefraction Oneconsequenceofthisobservationisthatmodelingtheelasticresponseofthemetalaslinearisquiteaccurate InABAQUSallmetalplasticitymodelsareassociatedwithlinearelasticity Elasticityisdefinedintermsofconstant withrespecttostrain moduli suchasYoung smodulusandPoisson sratioforanisotropicmaterial Linearelasticityintroducestwosimplificationsintothematerialmodel smallelasticstrainandalinearstress elasticstrainrelationshipThesesimplificationsdonotimplythatthetotalstrainissmall however theplasticstrainsmaybearbitrarilylarge MetalInelasticityinABAQUS 10 UniaxialTestatLowTemperatures Theassumptionoflinearelasticityisnotvalidforallmaterials Voidedmaterialstypicallyexhibitanonlinearelasticresponse Whenagranularsoiliscompressedinthebulkdirection thegrainsarepushedtogethersothatthematerialstiffens Thisisanonlinearelasticresponse Somematerialsexhibitlargeelasticstrainsbeforeyield Thisseminarwillnotconsiderthesematerialsandwillfocusentirelyonmetals wheretheassumptionoflinearelasticityisappropriate MetalInelasticityinABAQUS 11 However themodulusatpointAistheelasticmodulusifthestrainreversesdirection Suchbehaviorhasacomputationalconsequence thematerialstiffness d d atpointAisnotdependentonthestressorstrainalone Thedirectionofstraining thesignof relativetothepreviousincrement mustalsobeknown UniaxialTestatLowTemperatures StrainreversalafteryieldIfthematerialisstrainedbeyondyieldandthestrainisthenreversed thematerialimmediatelyrecoversitselasticstiffness Inthefigure themodulusatpointAistheverylowwork hardeningmodulusifthestraincontinuesintheoriginaldirection MetalInelasticityinABAQUS 12 UniaxialTestatLowTemperatures Iftheunloadingdoesnotcontinuebeyondtheelasticrangeandthestrainisagainreversed thematerialyieldsagainat orverycloseto pointA Thisobservationisgeneralized theelasticdeformationdoesnotaffectyielding Thematerialisalsoseentoundergoworkhardening theyieldstressofthepreviouslystrainedmaterialishigherthanthatoftheoriginalspecimen MetalInelasticityinABAQUS 13 UniaxialTestatLowTemperatures Workhardeningisoneoftheeffectsofcoldworking Coldworkingisplasticdeformationthattakesplaceatlowtemperatures Othereffectsinclude inducedanisotropy andthe Bauschingereffect Inducedanisotropyimpliestheworkhardeningisnotisotropic Thehardeningisnotisotropicinthesensethatthestrengthofthematerialisnotenhancedequallyforalldirectionsofsubsequentloading Followingcoldworkinginagivendirection differenceswillappearbetweenthevaluesofthetensileyieldstrengthinthatdirectionandinadirectionnormaltoit MetalInelasticityinABAQUS 14 UniaxialTestatLowTemperatures Iftheunloadingiscontinuedsothatyieldoccursintheoppositedirection asshownbelow theyieldstressinthisdirection pointC hasbeenreducedcomparedtothatoftheoriginalspecimen pointY ThisistheBauschingereffect MetalInelasticityinABAQUS 15 UniaxialTestatLowTemperatures Theeffectsofcoldworking workhardening inducedanisotropy andtheBauschingereffect canberemovedbyheatingtoarelativelyhightemperature followedbyslowcooling Thisprocessiscalledannealing MetalInelasticityinABAQUS 16 UniaxialTestatLowTemperatures CyclicloadingHavingconsideredstrainreversal thenaturalextensionistoexaminecyclicloading Thisisrelevantforthedesignofjetengines forexample wherelowcyclefatigue LCF isaconcern Atypicalresponseofmetalwhenuniaxialloadsarecontinuallyreversedtoprovideacyclictestisshowninthefigureatright Thisisknownasa pull push test Cyclichardeningunderconstantsymmetricstraincycles Pull Push MetalInelasticityinABAQUS 17 UniaxialTestatLowTemperatures Variouscyclictestsarepossible Inthiscasethespecimeniscycledbetweenfixedstrainlimitsthatareequalintensionandcompression push pull Overseveralcyclestherangeofstressduringwhichthematerialprovidespurelyelasticresponsechangessize Insomematerialsthisinvolvesa30 40 changefromthevirgintothehighlycycledcondition Plottingtheelasticstressrangeateachcycle Dsn asafunctionofthecyclenumber n resultsinthebehaviorsshowninthefiguresonthenextpage Mostmaterialsexhibitcyclichardening wherebytheelasticstressrangeincreaseswitheachcycle someexhibitcyclicsoftening wheretheelasticrangedecreaseswitheachcycle andstillothermetalsshowtransienthardeningafterafewcycles followedbysoftening MetalInelasticityinABAQUS 18 UniaxialTestatLowTemperatures MetalInelasticityinABAQUS 19 UniaxialTestatLowTemperatures Cyclichardeningmostcommonlyoccursinwell annealedspecimens Cyclicsofteningoftenisassociatedwithpreviouslycoldworkedmaterials Plasticstrain Stress cyclic cyclic Tensile annealed Tensile coldworked Comparisonofcyclicresponsesforacoldworkedspecimen MetalInelasticityinABAQUS 20 UniaxialTestatLowTemperatures Unsymmetriccyclesofstressbetweenprescribedlimitswillcauseprogressive creep or ratchetting inthedirectionofthemeanstress Typically transientratchettingisfollowedbystabilization zeroratchetstrain forlowmagnitudesofmeanstress whileaconstantincreaseintheaccumulatedratchettingstrainisobservedathighermagnitudesofmeanstress Ratchetting asthefigureimplies isaprogressiveincreaseinstrainateachcycle MetalInelasticityinABAQUS 21 UniaxialTestatLowTemperatures Cyclicloadingbetweenunsymmetricstrainvaluesresultsinprogressiverelaxationofthemeanstresstowardzeroastheasymptoticresponse Inotherwords theBauschingereffectiseliminated MetalInelasticityinABAQUS 22 UniaxialTestatLowTemperatures Acomplextheoryisrequiredtomodeltheseeffects whichareimportantincaseswherecyclic inelasticdeformationofthemetalisexpectedtooccur typicallyinlow cyclefatigueproblems Inaddition hightemperatureeffectsmayalsobeimportant addingfurthercomplexitytothetheory Forexample jetenginesrunathightemperatures thus creepbecomesimportant creepfatigue MetalInelasticityinABAQUS 23 UniaxialTestatLowTemperatures NeckingTheforce ornominalstress forceperoriginalarea reachesapeakinauniaxialtensiontest afterwhichitdropsoffuntilthespecimenfractures Nominalstress strainresponse MetalInelasticityinABAQUS 24 UniaxialTestatLowTemperatures Theresponseafterthisinstabilityisnolongeruniform Themajorityofdeformationoccursinalocalregioninthematerial localization Complexdeformationpatternsthatoftenexhibitshearbandingandotherevidenceoftexturedevelopmentforminthelocal neck regions Shearbandsareimportantinsheetformingapplications Formingprocessesareoftenlimitedbythedevelopmentofthesebands Necking fromAsaro 1982 MetalInelasticityinABAQUS 25 UniaxialTestatLowTemperatures Anestimateofwhenneckingwilloccurcanbemadewithaveryelementaryanalysisbyassumingthatthematerialisapproximatelyincompressible whichistruefortheplasticpartofthedeformation Considerauniformbarwithauniaxialload Aslongasthestressisuniformanduniaxial thetotalforceonthespecimen F isdefinedbywhereAisthecurrentareaofthespecimenandsisthetruestress DifferentiatinggivestherateofchangeofF MetalInelasticityinABAQUS 26 UniaxialTestatLowTemperatures Assumethemetalisincompressible Metalsareelasticallycompressible However theelasticstrainsaresmall 0 1 1 andthestrainatneckingislarge 30 40 Thus itisreasonabletoneglectelasticstrainsinthiscalculation Incompressibledeformationthenprovidestherelationshipwherelisthecurrentgaugelength l0istheoriginalgaugelength andA0istheoriginalcross sectionalarea MetalInelasticityinABAQUS 27 UniaxialTestatLowTemperatures DifferentiatinggivessothatThelogarithmicstrain e isdefinedas MetalInelasticityinABAQUS 28 UniaxialTestatLowTemperatures CombiningtheexpressionfordAwiththerelationshipfordFanddividingbydlgivesSubstitutingfordlinthefirsttermontheright handsideandcombiningtermsgivesTheslopeofthetruestress logarithmicstraincurveisds de Thus instabilitybeginsapproximately whendF dl 0 atthatis whenthestressisequaltotheworkhardeningslopeofthetruestress logarithmicstraincurve MetalInelasticityinABAQUS 29 UniaxialTestatLowTemperatures Theslopeofthetruestress s versuslogstrain e curveisstillpositiveattheonsetofnecking Logstrain Nominalstrain Truestress Nominalstress Failure MetalInelasticityinABAQUS 30 UniaxialTestatLowTemperatures Thisargumentispurelystructural Itsaysnothingaboutthematerialexceptthatthespecimenisapproximatelyincompressible Forexample thesameresultwouldapplytoanelasticmaterial suchasrubber ifthestressinthematerialwereeveraslargeasitsstiffness Howtheinstabilitywouldmanifestitself intheformofaneck texturedevelopment etc dependsonotherthings thematerial rateandtemperatureeffects etc MetalInelasticityinABAQUS 31 UniaxialTestatLowTemperatures Temperatureandstrain ratedependenceTheinelasticbehaviorofmetalsconsideredsofarhasbeenatonetemperatureandatonestrainrate Rateandtemperatureeffectsarecrucialtothedetailedunderstandingofinelasticlocalizationproblems Varyingthetemperatureandthestrainrateprovidesresultslikethoseshowninthefiguresbelow Stress straindataatdifferenttemperaturesandstrainrates MetalInelasticityinABAQUS 32 UniaxialTestatLowTemperatures Betweenroomtemperatureandabouttwo thirdsofthemetal smeltingtemperature thenormalrangeofapplicationofmetals thereisanapproximatelylinearreductionofyieldstresswithincreasingtemperature Strain ratedependencegenerallyprovidesanincreaseinyieldstresswithstrainrate Theeffectisimportantonlywhenthestrainratechangesbyordersofmagnitude Atstrainratescommonlyencounteredinmanufacturingprocessesordynamicevents 101 103persecond theyieldstressofcommonstructuralmetalsincreasesby20 50 comparedtothevaluesforquasi staticloads MetalInelasticityinABAQUS 33 UniaxialTestatLowTemperatures Inarapidprocessinvolvinglargeamountsofplasticdeformation suchasamanufacturingprocess adynamiceventlikeacarcrash orfastfracture twocompetingeffectsareseen Theinelasticdeformationgivesrisetoheatingofthematerial whichraisesthetemperatureand thus reducesthematerial syieldstrength Atthesametimetheraisedstrainratecausesviscoplasticeffects enhancingthematerial sstrength Theneteffectdependsstronglyonthestrainrate theamountofstraining andtherelativeimportanceofrateeffects strainhardening andtemperaturesofteninginthematerial sresponse MetalInelasticityinABAQUS 34 UniaxialTestatLowTemperatures TheheatingofthematerialbyplasticdeformationcanbemodeledinABAQUSaseitherafullycoupledtemperature deformationanalysisor insomecases asanadiabaticprocess theassumptioninanadiabaticanalysisisthattheeventissofastthereisnotenoughtimefortheheattodiffusefromthepointwhereitiscreatedbyplasticworking Insuchmodelsthematerialproperties liketheyieldstress arealsousuallydefinedtobetemperaturedependent Asthetemperaturecontinuestoincrease inelasticstrainingoccursmoreandmorereadilybelowtheyieldstress aspecimenheldatconstantstress belowyield willcreep Formostmetalsofpracticalengineeringinterest creepisimportantonlyinhigh temperatureapplications Examples jetengine nuclearreactor etc UniaxialTestatElevatedTemperatures MetalInelasticityinABAQUS 36 UniaxialTestatElevatedTemperatures Twouniaxialexperimentsarecommonlyperformedtomeasurethehigh temperaturecreepresponseofmetals Thecreeptest wheretheloadisheldconstantandthestrainismeasured Therelaxationtest wherethestrainisheldconstantandthestressismeasuredasafunctionoftime MetalInelasticityinABAQUS 37 UniaxialTestatElevatedTemperatures Creeptest Relaxationtest Suddenlyapplysandholdit Suddenlyapplyeandholdit Longperiodoftimecomparedtotimeofprimarycreep MetalInelasticityinABAQUS 38 UniaxialTestatElevatedTemperatures Inthecreeptestmostmetalsexhibitthreedistinctregimesofresponse Assoonastheloadisapplied thespecimenrespondsintheprimarycreepregime wherestrainratechangesrapidlywithtime Example militaryjetThepilotopens closesthethrottle itisneveropenedlongenoughtoaccumulatesecondarycreep Next theresponseunderconstantstresssettlesintothesecondarycreepregime wherethestrainrateisconstant Usuallythisregimeextendsforalongperiodoftime Example burstingpressurevesselApplypressureandatemperatureincreasetothevesselandletitsitthereforsometime theburstingisduetotheaccumulationofsecondarycreep MetalInelasticityinABAQUS 39 UniaxialTestatElevatedTemperatures Finally inthetertiarycreepregimethematerialbeginstofail causingthestrainratetoincreasewithtime Neckingandcrackingoccur micromechanicaleffectsmayalsocontributetofailure Someofthetertiaryeffectsareassociatedwithgeometrychanges particularlyiftheexperimentisaconstantloadtestratherthanaconstanttruestresstest MetalInelasticityinABAQUS 40 UniaxialTestatElevatedTemperatures Relaxationdataareoftenunavailableorunreliable mainlybecausetherelativelylargethermalexpansioncoefficientofmostmetalsmakesitnecessarytomaintainextremelytightcontroloftemperaturetoachieveaconstantstraintest Thus mostmetalsarecalibratedbycreeptests ThecreepmodelsinABAQUSmodelthesecondarycreepregimeonly theyprovideaconstantcreepstrainrateforagivenstresslevel ModelingofprimarycreeprequirestheuseofusersubroutineCREEPinABAQUStodefinethebehavior MetalInelasticityinABAQUS 41 UniaxialTestatElevatedTemperatures Typicallysecondarycreepmodelshaveapowerlawform whereA q andn q aretemperature dependentmaterialparameters Forimportantstructuralmetalsnistypicallyintherangeof3 8 thusprovidingaveryrapidgrowthofcreepstrainratewithincreasingstress MetalInelasticityinABAQUS 42 UniaxialTestatElevatedTemperatures CyclicloadingofaspecimenrevealssubstantialBauschingereffectsandcyclicsofteningundercreepconditions secondary CreepandSwelling Lecture6 MetalInelasticityinABAQUS 44 Overview BasicAssumptionsElasticityStressPotentialsDeviatoricCreepModelsVolumetricSwellingInelasticFlowinCreep SwellingModelsTemperatureandFieldVariableDependenceAnalysisProceduresCreepIntegrationandTimeIncrementation BasicAssumptions MetalInelasticityinABAQUS 46 BasicAssumptions Thecreepandswellingmodelsassumethatsomeinelasticdeformationwilloccurwheneverthestressinthematerialisnonzero Thisassumptionisusuallyvalidwhenthematerialisatahightemperature whereqmisthematerial smeltingtemperature Theinelasticcreepdeformationispurelydeviatoric Theelasticdeformationofthematerialusingacreepmodelislinear Volumetricswellingmodelsalsoassumethattheelasticdeformationislinear CreepandvolumetricswellingmodelsareavailableonlyinABAQUS Standard Nonzerodeviatoricstressrequiredforcreep nonzerohydrostaticstressrequiredforswelling Elasticity MetalInelasticityinABAQUS 48 Elasticity Definetheelasticconstantsofthematerialwiththelinearelasticmaterialmodel Elasticpropertiescanbespecifiedasisotropicoranisotropic Elasticpropertiesmaydependontemperature q and orpredefinedfieldvariables fi Asnotedearlier linearelasticityshouldnotbeusediftheelasticstrainsinthematerialarelarge Material name Material 1 Elastic2 e11 0 3 StressPotentials MetalInelasticityinABAQUS 50 StressPotentials Creepmodelsuseanequivalentuniaxialdeviatoricstresspotential todefinetheinelasticdeformationthatoccursinthematerial ABAQUScanuseeithertheMisesstresspotentialorHill sanisotropicstresspotential MisesStressPotentialTheMisesstresspotentialisdefinedaswhereSisthedeviatoricstresstensorCreepbehaviordefinedwiththisstresspotentialisisotropic TheMisesstresspotentialisthedefaultforallcreepmodels MetalInelasticityinABAQUS 51 StressPotentials Hill sanisotropicstresspotentialHill sanisotropicstresspotentialisdefinedasABAQUScalculatesthevaluesoftheconstantsF G H L M andNfromcreepstressratios Thecreepstressratioscanbedependentonqand orfi DeviatoricCreepModels MetalInelasticityinABAQUS 53 DeviatoricCreepModels TwosimplecreeplawsarebuiltintoABAQUS Standard thepowerlawandthehyperbolic sinelaw Thesetwocreepmodelsaresimpleandareintendedformodelingsecondaryorsteady statecreep TheymodeldeviatoriccreepbehavioronlySeeLecture2fordetailsaboutobservedcree