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DYNAMICRECRYSTALLIZATIONKINETICSOFCU036CR003ZRALLOYDURINGHOTCOMPRESSIONGUOLIANGJI,FANGLIQIN,LIYUANZHU,QIANGLI,ANDLEILISUBMITTEDJUNE21,2016INREVISEDFORMDECEMBER24,2016PUBLISHEDONLINEMAY1,2017BASEDONCOMPRESSIONTESTSINTHETEMPERATURERANGEOF800950C176CANDTHESTRAINRATERANGEOF000120S21ONAGLEEBLE3500THERMOMECHANICALSIMULATOR,THEDYNAMICRECRYSTALLIZATIONDRXKINETICSOFCU036CR003ZRALLOYISDEVELOPEDBYFURTHERANALYSISOFTRUESTRESSSTRAINCURVESANDBYINVESTIGATINGMICROSTRUCTURESUNDERDIFFERENTDEFORMATIONCONDITIONSTHEKINETICSOFDYNAMICRECRYSTALLIZATIONISEXPRESSEDASTHEMODIFIEDJMAKMODEL,ANDEFFECTSOFVARYINGSTRAINRATEANDTEMPERATUREONTHEMODELPARAMETERS,INCLUDINGTHECRITICALSTRAIN,PEAKSTRAINANDMATERIALSCONSTANTKD,AREINVESTIGATEDTHECOMPLETEDRXGRAINSIZEISDESCRIBEDASAPOWERLAWFUNCTIONOFZENERHOLLOMONPARAMETERZ,ANDITAGREESWELLWITHTHEEXPERIMENTALDATAKEYWORDSCOMPRESSIONTESTS,CUCRZRALLOYS,DYNAMICRECRYSTALLIZATION,MICROSTRUCTURE1INTRODUCTIONWORKHARDENINGWH,DYNAMICRECOVERYDRVANDDYNAMICRECRYSTALLIZATIONDRXAREIMPORTANTPHYSICALMETALLURGYPHENOMENAINHOTWORKINGOFMETALMATERIALS,ANDDYNAMICRECRYSTALLIZATIONEASILYOCCURSFORMETALSANDALLOYSWITHLOWTOMEDIUMSTACKINGFAULTENERGY,SUCHASFCCMETALS,COPPERALLOYSANDNICKELALLOYSININDUSTRIALPRODUCTION,DYNAMICRECRYSTALLIZATIONISUSEDASANIMPORTANTMETHODTOIMPROVEMICROSTRUCTUREANDTOOBTAINFINEANDHOMOGENOUSGRAINSTHEREFORE,ITISSIGNIFICANTTOREVEALTHEEVOLUTIONMECHANISMOFDYNAMICRECRYSTALLIZATIONOFMETALSORALLOYSFORMANUFACTURINGPARTSWITHTHEFINEMICROSTRUCTUREANDEXCELLENTMECHANICALPROPERTIESSOFARDYNAMICRECRYSTALLIZATIONBEHAVIORSOFMETALSORALLOYSHAVEBEENEXTENSIVELYSTUDIED,ANDSEVERALMODELSFORTHERECRYSTALLIZATIONKINETICSANDMICROSTRUCTUREEVOLUTIONWEREPROPOSEDREF14THESEMODELSCANBEMAINLYDIVIDEDINTOTWOCATEGORIESPHENOMENOLOGICALMODELANDPHYSICALLYBASEDINTERNALVARIABLEMODELPHENOMENOLOGICALMODELDESCRIBESTHEEVOLUTIONOFTHERECRYSTALLIZATIONVOLUMEINTHEFORMOFTHEAVRAMIEQUATION,INWHICHPARAMETERSTOBEDETERMINEDAREUSUALLYREPRESENTEDASAFUNCTIONOFINITIALGRAINSIZE,TEMPERATURE,STRAINANDSTRAINRATEPHENOMENOLOGICALMODELSHAVEBEENWIDELYADOPTEDBYCOMMERCIALFEMSOFTWARE,SUCHASFORGEANDDEFORM3D,TOSIMULATERECRYSTALLIZATIONEVOLUTIONOFMETALSORALLOYSLOYDAETALREF5ESTABLISHEDKINETICSMODELSOFDYNAMICRECRYSTALLIZATIONDRX,METADYNAMICRECRYSTALLIZATIONMDRX,STATICRECRYSTALLIZATIONSRXANDGRAINGROWTHFORANIFEBASEDSUPERALLOYANDEVALUATEDTHEAVERAGEGRAINSIZEANDRECRYSTALLIZATIONFRACTIONOFTHENIFEBASEDSUPERALLOYDURINGTHEROTARYFORGINGPROCESSBYIMPLEMENTINGTHEPREVIOUSPHENOMENOLOGICALMODELSINTOTHECOMMERCIALPLATFORMDEFORM3DCHENETALREF6PROPOSEDTHESEGMENTEDKINETICSMODELSTODESCRIBEDYNAMICRECRYSTALLIZATIONBEHAVIOROFATYPICALNICKELBASEDSUPERALLOYDURINGHOTDEFORMATION,ANDTHEPROPOSEDSEGMENTEDMODELSCANGIVEANACCURATEANDPRECISEESTIMATIONOFTHEVOLUMEFRACTIONSOFDRXFORTHESTUDIEDSUPERALLOYBASEDONTHEINTERNALVARIABLEMODELOFDRXTHATDESCRIBESDISLOCATIONDENSITYEVOLUTION,NUCLEATIONANDGRAINGROWTH,THECELLULARAUTOMATACAAPPROACHCANREPRESENTTHEGROWTHKINETICSANDMICROSTRUCTUREEVOLUTIONINTHETIMEANDSPACESCALEREF7CAALGORITHMFORRECRYSTALLIZATIONUSESSTATEVARIABLESSUCHASDISLOCATIONDENSITYTOCREATEMOREREALISTICREPRESENTATIONSOFRECRYSTALLIZATIONKINETICSREF8,ANDWHETHERDRXGENERALLYTAKESPLACECANBEJUDGEDBYCOMPARINGTHEDISLOCATIONDENSITIESINTHEGRAINBOUNDARIESWITHACRITICALDISLOCATIONDENSITYREYESETALREF9SUCCESSFULLYMODELEDDRXOFINCONEL718ALLOYBYUSEOFTHECELLULARAUTOMATAMETHOD,ANDTHEINFLUENCEOFLOCALCHANGESOFINITIALGRAINWITHFULLYANDPARTIALRECRYSTALLIZEDMICROSTRUCTURESWASSIMULATEDBYCAANDCOMPAREDWITHISOTHERMALHOTCOMPRESSIONRESULTSLIUETALREF10STUDIEDTHEDYNAMICRECRYSTALLIZATIONBEHAVIOROFINCONEL718ALLOYBYEXPERIMENTSANDCELLULARAUTOMATONMODELANDFOUNDTHATTHEDRXGRAINSGRADUALLYBECOMEHOMOGENEOUSWHENTHEVOLUMEFRACTIONOFDYNAMICRECRYSTALLIZATIONISINCREASEDCHENETALREF11INVESTIGATEDTHEDYNAMICRECRYSTALLIZATIONINAUSTENITICSTAINLESSSTEELUSINGCELLULARAUTOMATONMETHODHUANGETALREF12REVIEWEDTHEDYNAMICRECRYSTALLIZATIONDRXMECHANISMSOCCURRINGINDIFFERENTTHERMOMECHANICALPROCESSINGCONDITIONSFORVARIOUSMETALLICMATERIALSITINCLUDESTHEFOLLOWINGTHREECATEGORIESDISCONTINUOUSDYNAMICRECRYSTALLIZATIONDDRX,CONTINUOUSDYNAMICRECRYSTALLIZATIONCDRXANDGEOMETRICDYNAMICRECRYSTALLIZATIONGDRXCHENANDLINREF13INVESTIGATEDTHEEVOLUTIONOFDYNAMICRECRYSTALLIZEDDRXGRAINANDDISLOCATIONSUBSTRUCTUREOFANICKELBASEDSUPERALLOYITISFOUNDTHATTHEDISLOCATIONSUBSTRUCTUREISALSOVERYSENSITIVETOTHEDEFORMATIONDEGREE,STRAINRATEANDDEFORMATIONTEMPERATUREWITHTHEINCREASEINGUOLIANGJI,FANGLIQIN,LIYUANZHU,ANDQIANGLI,SCHOOLOFMATERIALSSCIENCEANDENGINEERING,HENANPOLYTECHNICUNIVERSITY,JIAOZUO454000,CHINAANDLEILI,SCHOOLOFMECHANICALENGINEERING,SHANGHAIDIANJIUNIVERSITY,SHANGHAI201306,CHINACONTACTEMAILSJICHENMIAO126COMANDLEILI_HPU163COMJMEPEG20172626982707C211ASMINTERNATIONALDOI101007/S116650172701Z10599495/19002698VOLUME266JUNE2017JOURNALOFMATERIALSENGINEERINGANDPERFORMANCEDEFORMATIONDEGREE,THEEVOLUTIONOFDISLOCATIONSUBSTRUCTURECANBECHARACTERIZEDASHIGHDISLOCATIONDENSITYFIDISLOCATIONNETWORKFISUBGRAINFIDRXGRAINLINETALREF14INVESTIGATEDMICROSTRUCTUREEVOLUTIONDURINGDRXOFATYPICALNICKELBASEDSUPERALLOYITISFOUNDTHATTHEMICROSTRUCTURALCHANGESINDICATETHATBOTHCO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OUSPOWEROFFEREDBYINSTRUMENTSANDEQUIPMENTISDISSIPATEDDURINGHOTCOMPRESSIONATAUNIFORMTEMPERATUREANDACONSTANTSTRAINRATE,GLEEBLE3500THERMOMECHANICALSIMULATORREGULATESTHETEMPERATUREOFSPECIMENSBYTHEREALTIMECLOSEDLOOPSERVOCONTROLSYSTEMHOWEVER,HEATPRODUCEDATHIGHSTRAINRATESCOULDNOTBECONDUCTEDIMMEDIATELYDUETOANEXTREMELYSHORTSPANOFTIME,WHICHLEADSTOAREMARKABLETEMPERATURERISEINSPECIMENSSO,INFACTTHEHOTCOMPRESSIONATHIGHSTRAINRATESISANADIABATICPROCESSHENCE,TOUNDERSTANDREALMICROSTRUCTURALCHANGES,ITISNECESSARYTOREMOVETHEHEATINGEFFECTINTHEMEASUREDSTRESSSTRAINCURVESTHECORRECTEDISOTHERMALSTRESSRCANBEOBTAINEDBYCALCULATINGTHEDERIVATIVEOFMEASUREDSTRESSC22RWITHRESPECTTOACTUALTEMPERATURETATAGIVENSTRAINANDSTRAINRATE,ANDITISEXPRESSEDASFOLLOWSRC22RDC22RDTC12C12C12C12_EEDTEQ2FORTUNATELY,DURINGTHEHOTCOMPRESSIONONAGLEEBLE3500THERMOMECHANICALSIMULATOR,DATAOFSTRESS,STRAINANDTEMPERATURECANBERECORDEDAUTOMATICALLYSOTHEYCANBEUSEDTOCALCULATETHECORRECTEDISOTHERMALSTRESSBYDIRECTLYAPPLYINGEQ2HERE,ITSHOULDBENOTEDTHATMEASUREDSTRESSESC22RSHOULDBESUBSTITUTEDWITHFRICTIONCORRECTEDONESRECORDEDTEMPERATUREDATAINTHISTESTINDICATETHATSTRAINRATESOF1AND20SC01CANCAUSEMAXIMUMTEMPERATURECHANGESOF5AND35C176C,RESPECTIVELYSO,AFTERFRICTIONCORRECTIONOFMEASUREDTRUESTRESSSTRAINCURVES,WEFURTHERCARRIEDOUTTEMPERATURECORRECTIONFORTRUESTRESSSTRAINCURVESATSTRAINRATESOF1,10AND20SC01TEMPERATURECORRECTEDFLOWSTRESSESAREPRESENTEDINFIG2ITISFOUNDTHATFRICTIONAND/ORTEMPERATURECORRECTEDTRUESTRESSTRUESTRAINCURVESOFCU036CR003ZRALLOYEXHIBITTHETYPICALCHARACTERISTICSOFDYNAMICRECOVERYORDYNAMICRECRYSTALLIZATION,ASSHOWNINFIG332THEMICROSTRUCTUREEVOLUTIONOFDURINGDYNAMICRECRYSTALLIZATIONFIGURE4SHOWSTHEOPTICALMICROSTRUCTURESOFCU036CR003ZRALLOYAFTERDEFORMATIONATATEMPERATUREOF900C176CANDFIG2FRICTIONAND/ORTEMPERATURECORRECTEDSTRESSSTRAINCURVESATSTRAINRATESOFA20SC01,B10SC01ANDC1SC012700VOLUME266JUNE2017JOURNALOFMATERIALSENGINEERINGANDPERFORMANCEATSTRAINRATESFROM0001TO20SC01THEAVERAGEGRAINSIZESAREMEASUREDAS4635,4148,3099,2274,168AND1717LMFORTHESTRAINRATEOF0001,001,01,1,10SC01AND20SC01,RESPECTIVELY,WHICHINDICATESTHATTHEDYNAMICALLYRECRYSTALLIZEDGRAINSIZEISESSENTIALLYREFINEDWITHINCREASINGTHESTRAINRATETHISISMAINLYBECAUSEHIGHERSTRAINRATESCANLEADTOHIGHERDEFORMATIONSTOREDENERGY,THEREFOREINCREASINGTHENUCLEATIONRATEFORDYNAMICRECRYSTALLIZATIONANDLEAVINGLITTLETIMEFORRECRYSTALLIZEDGRAINTOGROWUPHOWEVER,WITHRAREEXCEPTIONSINTHISEXPERIMENT,THEAVERAGEGRAINSIZEAT20SC01ISLARGERTHANTHATAT10SC01SINCETHEHOTCOMPRESSIONATHIGHSTRAINRATESISANADIABATICPROCESS,THEGREATERTHESTRAINRATESDURINGHOTCOMPRESSION,THELARGERTHEACTUALTEMPERATURESITMAYBERESPONSIBLEFORDEVIATIONOFVERYFEWEXPERIMENTALRESULTSOFGRAINSIZEFROMGENERALCHANGELAWOFGRAINSIZEWITHSTRAINRATESFIGURE5SHOWSMICROSTRUCTURESOFTHISALLOYAFTERDEFORMATIONATSTRAINRATEOF001SC01WITHTHETEMPERATURESOF800AND950C176C,RESPECTIVELYITISOBVIOUSTHATTHEDEFORMEDSIZEINCREASESWITHINCREASINGTHETEMPERATURESTHEAVERAGEGRAINSIZESAREMEASUREDAS1546AND4036LM,FORTEMPERATURESOF800AND950C176C,RESPECTIVELYTHISISMAINLYBECAUSEHIGHERTEMPERATURESCANLEADTOLOWERDEFORMATIONSTOREDENERGY,THEREFOREDECREASINGTHENUCLEATIONRATEFORDYNAMICRECRYSTALLIZATIONANDLENDINGSTRONGERDIFFUSIONCAPACITYFORRECRYSTALLIZEDGRAINTOGROWUPOCCURRENCEOFRECRYSTALLIZATIONCANBEJUDGEDFROMVARYINGCHARACTERISTICSOFTRUESTRESSSTRAINCURVESTHISMEANSTHATFLOWSTRESSRAPIDLYINCREASESTOCRITICALSTRESSDUETOTHEWORKHARDENINGANDCONTINUESTOSLOWLYINCREASETOTHEPEAKSTRESSDUETOTHEOCCURRENCEOFRECRYSTALLIZATIONTHEN,FLOWSTRESSBEGINSTODECREASEUNTILITREACHESASTEADYSTRESSANDKEEPSCONSTANTMEANWHILE,SHAPEANDSIZEOFRECRYSTALLIZEDGRAINSREMAINUNCHANGEDHOWEVER,NOTALLTHETRUESTRESSSTRAINCURVESUNDERDIFFERENTHOTDEFORMATIONCONDITIONSEXHIBITTYPICALCHARACTERISTICSOFDYNAMICRECRYSTALLIZATION,EVENIFMETALMATERIALSHAVEUNDERGONEDYNAMICRECRYSTALLIZATIONINORDERTOMODELTHEKINETICSOFDYNAMICRECRYSTALLIZATION,ITISNECESSARYTODETERMINETHESOFTENINGMECHANISMSBYVERIFICATIONOFMICROSTRUCTURESINTHISEXPERIMENTJUDGINGFROMTRUESTRESSSTRAINCURVESANDCORRESPONDINGMICROSTRUCTURES,ITCANBECONCLUDEDTHATDYNAMICRECRYSTALLIZATIONOCCURSINALLPROCESSPARAMETERSOTHERTHANAT800C176CWITHSTRAINRATESOF1,10AND20SC0133DETERMINATIONOFCHARACTERISTICPARAMETERSFORDRXOFTRUESTRESSSTRAINCURVESACCORDINGTOTHEDYNAMICSOFTENINGMECHANISMSDURINGHOTDEFORMATION,THETRUESTRESSSTRAINCURVESFORCU036CR003ZRALLOYCANBEDIVIDEDINTOTWOTYPES,IE,DYNAMICRECOVERYANDDYNAMICRECRYSTALLIZATION,ANDTHEYAREMARKEDWITHC212AC213ANDC212B,C213FIG3FRICTIONAND/ORTEMPERATURECORRECTEDSTRESSSTRAINCURVESATA800C176C,B900C176CANDC950C176CJOURNALOFMATERIALSENGINEERINGANDPERFORMANCEVOLUME266JUNE20172701RESPECTIVELY,ASSHOWNINFIG6GENERALLY,THETRUESTRESSSTRAINCURVESCHARACTERISTICOFDYNAMICRECRYSTALLIZATIONCANBEDIVIDEDINTOTHREESTAGESSTAGEIWORKHARDENINGANDDYNAMICRECOVERY,STAGEIIWORKHARDENING,DYNAMICRECOVERYANDDYNAMICRECRYSTALLIZATIONANDSTAGEIIISTEADYDYNAMICRECRYSTALLIZATIONTHEDISLOCATIONDENSITYTHEORYANDTHEMODIFIEDAVRAMIEQUATIONCANBEUSEDTODESCRIBETHEFLOWBEHAVIOROFMETALFIG4MICROSTRUCTURESDEFORMEDAT900C176CWITHSTRAINRATESOFA0001SC01,B001SC01,C01SC01,D1SC01,E10SC01,F20SC01FIG5MICROSTRUCTURESDEFORMEDATASTRAINRATEOF001SC01WITHA800C176CANDB950C176C2702VOLUME266JUNE2017JOURNALOFMATERIALSENGINEERINGANDPERFORMANCEMATERIALSDURINGHOTWORKING,IE,WORKHARDENING,DYNAMICRECOVERYANDDYNAMICRECRYSTALLIZATIONASSHOWNINFIG6,THECURVEMARKEDC212AC213REPRESENTSTHETRUEWORKHARDENINGANDDRVBEHAVIOROFMETALMATERIALS,ORTHEASSUMEDWORKHARDENINGANDDRVBEHAVIOROFMETALMATERIALSINWHICHTHEREOCCURWORKHARDENING,DRVANDDRXSIMULTANEOUSLYRRECREPRESENTSTHEFLOWSTRESSOFMETALMATERIALSATTRIBUTABLETOWORKHARDENINGANDDRVTHECURVEMARKEDC212BC213REPRESENTSTHETRUEWORKHARDENING,DRVANDDRXBEHAVIOR,ANDITSSTAGEIIISCONSIDEREDTOBETHENETRESULTOFTHESIMULTANEOUSOPERATIONOFWORKHARDENINGANDDRVANDDRXREF34RDRXREPRESENTSTHEFLOWSTRESSINTHESTAGEII,ANDTHEDIFFERENCEDRBETWEENRDRXANDRRECISTHENETSOFTENINGDIRECTLYATTRIBUTABLETODRXVOLUMEFRACTIONOFDRXREF2931CANALSOBEREPRESENTEDASXDRXDRRSATC0RSSEC21ECEQ3THECRITICALSTRAINEC,PEAKSTRAINEP,SATURATIONSTRESSRSATANDSTEADYSTRESSRSSNEEDTOBEDETERMINEDFIRSTLYTOESTABLISHTHEKINETICSMODELOFDRXASSHOWNINFIG6,THEPEAKSTRAINEPANDPEAKSTRESSRPANDSTEADYSTRESSRSSCANBEOBTAINEDDIRECTLYFROMTRUESTRESSSTRAINCURVESHOWEVER,DIRECTDETERMINATIONOFCRITICALSTRAINECISDIFFICULT,ANDITCANBEATTAINEDWHENTHEVALUEOF|C0DH/DR|,WHERESTRAINHARDENINGRATEHDR/DE,REACHESTHEMINIMUM,WHICHCORRESPONDSTOANINFLECTIONOFDR/DEVERSUSRCURVEREF35THEN,SATURATIONSTRESSRSATCANBEDETERMINEDASTHEHORIZONTALINTERCEPTOFTHETANGENTLINEOFHC0RPLOTTHROUGHTHEINFLECTIONPOINTASANEXAMPLE,FIG7SHOWSTHEPLOTOFHVERSUSRATATEMPERATUREOF900C176CANDASTRAINRATEOF01SC01,FROMWHICHITISEASYTODETERMINETHEVALUESOFTHECRITICALSTRESSRCANDTHECRITICALSTRAINEC,THEPEAKSTRESSRPANDTHEPEAKSTRAINEP,SATURATIONSTRESSRSATANDTHESTEADYSTATESTRESSRSSWHENMETALMATERIALSAREDEFORMEDINSOMEPROCESSPARAMETERS,STEADYFLOWSTRESSMAYNOTAPPEARINTHETRUESTRESSSTRAINCURVES,SOONECANEXTRAPOLATETHECURVEOFHVERSUSRATTHEENDTOOBTAINTHESTEADYSTRESSTHEEFFECTOFTEMPERATUREANDSTRAINRATEONHOTDEFORMATIONBEHAVIOROFMETALMATERIALSCANBEREPRESENTEDBYZENERHOLLOMONPARAMETERZINANEXPONENTTYPEEQUATIONREF3234ASFOLLOWSZ_EEXPQRTC18C19EQ4WHERERISTHEUNIVERSALGASCONSTANT8314JMOLC01KC01TISTHEABSOLUTETEMPERATUREKQISTHEACTIVATIONENERGYJMOLC01_EISSTRAINRATESC01MOREOVER,ZCANBEFURTHEREXPRESSEDASAFUNCTIONOFSTRESSINTERMSOFTHEPOWERLAW,THEEXPONENTIALLAW,ORTHEHYPERBOLICSINELAWASFOLLOWSZAFREQ5FRRN0AR12SINHARC138NFORALLR8EQ14EQUATION14DESCRIBESTHEEVOLUTIONLAWOFTHEDRXVOLUMEFRACTIONWITHTEMPERATURE,STRAINRATEANDSTRAININCU036CR003ZRALLOYWHENSTRAINRATEISACONSTANT,EC0ECT_E,WHERETISTIMESUBSTITUTINGEC0ECT_EINTOEQ14,THEEVOLUTIONOFDRXVOLUMEFRACTIONWITHTIMETCANBEOBTAINED,ASSHOWNINFIG12,WHICHSHOWSTHATTHEKINETICSOFDRXISDESCRIBEDINTERMSOFSCURVESOFTHEDRXVOLUMEFRACTIONFIGURE12ASHOWSTHATFORAGIVENSTRAINRATE,TIMENEEDEDTOCOMPLETETHEDYNAMICRECRYSTALLIZATIONDECREASESWITHINCREASINGDEFORMATIONTEMPERATURES,VICEVERSAFIGURE12BSHOWSTHATFORAGIVENTEMPERATURE,TIMENEEDEDTOCOMPLETETHEDYNAMICRECRYSTALLIZATIONDECREASESWITHINCREASINGSTRAINRATES,VICEVERSA35GRAINSIZEOFCOMPLETEDRXTHEMEANGRAINSIZEDDRX,ITSSTANDARDDEVIATIONSDANDCORRESPONDINGZPARAMETER