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()12311(1.,110004;2.,471000;3.725,471000):(CA),,:,,JMAKAvrami2.5,,:;;;;:TG111:ACelluarAutomatonSimulation(I)inStaticRecrystallizationProcessMicrostructureEvolutionandDynamicsResearchGuoJuan1,WangYanmin2,LiWei3,WuDi1,ZhaoXianminAbstract:Microstructureevolutionmodelofstaticrecrystallizationduringhotmachiningprocesshasbeenestab2lishedbymeansofthecellularautomation(CA)madeupofregularhexagoncells,andthenearestneighbortypeandtheperiodicboundaryconditionaswell.Thedeformedmicrostructureandthemicrostructureevolutionwereanalyzed,andtherecrystallizationdynamicsandthevariationofstorageenergyaswellwereconcludedonthatbasis.Itturnsoutthatthelargerdeformationdegree,themoregrainshapedeviatedfromequiaxialmictrostrcture.TheCAmodelwasabletoreappearacethemictrostructureevolutiondynamicallyandthegrainshapeandsizewerejustaccordantwiththebasiclawsofstaticrecrystallization.ThedynamicsagreedwithJMAKtheoryandtheslopeofAvramicurvewascloseto2.5.Therateofdecreasingofstorageenergywasacceeratedandthetimeforrecrystallizationwasshortenwithincreasingde2formationdegree.Thevariationofstorageenergywasjustaccordanttotheenergydegradationprinciple.ThisanalysisfullyindicatedthatthestaticrecrystalliztioncanbesimulatedfairlywellinpresentCAmodel.Keywords:staticrecrystallization;cellularautomaton;computersimulation;microstructure;dynamics,,,[114][15,16][17,18],1991,Hessel2barth[1]PezzeeDunand[2]:20081103:(1981),,,Davies[35]GoetzSeetharaman[6],MarxGottstein[7],,[8,9]Raabe[1013],[14](CPFEM)(CA),,,,,02No.1January2009HEAVYCASTINGANDFORGING,,,11.1:,,abm2,(1)(2)XmaxYmax:Xmax=3a3L(1)Ymax=[2b3L],[2b3L][2b3L]+1,[2b3L](2),[]Ymax,,Ymax,,Err(3):Err=XmaxYmaxSab-1100%(3),SErr1%Err,L,StateEnergyOri(Ori1OriOrimax)State,0,1,2Energy,OriOri,,State=0Energy,,,:(1),,,,,(2),,2,31.21.2.1,,,,[19]:N=N0exp-QNkT(4),N,N0,QN,kBoltzmann,T,,NtXt:Xt=NtrecXmaxYmax(5)NtrectXmax,Ymax(t+1)CasNnucNXNt+1nuc=NXmaxYmax(1-Xt)ab(6),Nt+1nuct+1[],,X,0,12No.1HEAVYCASTINGANDFORGINGJanuary2009(t+1)Cas,Nnuc,Nnuc,Nnuc,State02,Energy0Ori(Ori),Nnuc,,1.2.2,06,,,vv[19]:v=v0exp-QvkT(7),QN,QvQNv0v,PG(0PG1),:(1)44,,State1,Ori,Energy0(2)33,p,pPG,,,,,,,t,,,State1,Ori22.1,T=1273K,ab=200200m2,e=0.250.50.75,D0=20m2,200m230m,Err=-0.407%,1,e,e,,,,,,1c,,,30%50%70%[20],(a)e=0.25(b)e=0.5(c)e=0.751Figure1Deformedmicrostructure22No.1January2009HEAVYCASTINGANDFORGING(a)10Cas(b)15Cas(c)30Cas2e=0.5Figure2Evolutionprocessofmicrustructurewithe=0.52.2e=0.52,,,,,,,,,2.3Avrami33a,S,JMAK,,;,;50%,;,,,;90%,,,3b,ln(ln(1/(1-X)))ln(t),,k2.5Johnson,k2.03.0(a)(b)Avrami3AvramiFigure3KineticcurveandcorrespondingAvramicurveofstaticrecrystallization2.4,,4,,,,0,,,32No.1HEAVYCASTINGANDFORGINGJanuary20094Figure4Deformationenergychangedwithtime3(1),e,e,,(2),,,,,,(3)JMAKAvrami,k2.5Johnson(4),,,e,,,[1]HesselbarthHW,GobelIR.SimulationofRecrystallizationbyCellularAutomata[J].ActaMetallurgicaetMaterialia.1991,39(9):2135-2143.[2]PezzeeCF,DunandDC.TheImpingementEffectofanInertImmobileSecondPhaseonheRecrystallizationofaMatrix[J].ActaMetallurgicaletMaterialia.1994,42(5):1509-1524.[3]DaviesCHJ.TheEffectofNeighbourhoodonTheKineticsofaCellularAutomatonRecrystallisationModel[J].ScriptaMet2allurgicaletMaterialia.1995,33(7):1139-1143.[4]DaviesCHJ.GrowthofNucleiinaCellularAutomatonSimu2lationofRecrystallisation[J].ScriptaMaterialia.1997,36(1):35-40.[5]DaviesCHJ,HongL.TheCellularAutomatonSimulationofStaticRecrystallisationinCold2RolledAA1050[J].ScriptaMaterialia.1999,40(10):1145-1150.[6]GoetzRL,SeetharamanV.StaticRecrystallizationKineticswithHomogeneousandHeterogeneousNucleationUsingaCel2lularAutomataModel[J].MetallurgicalandMaterialsTransac2tions.1998,29A:2307-2321.[7]MarxV,ReherFR,GottsteinG.SimulationofPrimaryRe2crystallizationUsingaModifiedThree2DimensionalCellularAu2tomaton[J].ActaMaterialia.1999,47(4):1219-1230.[8]GottsteinG,MarxV,SebaldR.Integralrecrystallizationmod2eling[J].JournalofShanghaiJiaotongUniversity.2000,5(1):4957.[9]GottsteinG,MarxV,SebaldR.Integralrecrystallizationmod2eling:fromcellularautomatatofiniteelementanalysis[A].ThefouthInternationalConferenceonRecrystallizationandRe2latedPhnomena.EditedbySakaiTandSuzukiHG.TheJa2panInstituteofMetals,Japan,1999:1524.[10]RaabeD.IntroductionofaThree2DimensionalCellularAu2tomatonwithaProbabilisticSwitchingRulefortheDiscreteMesoscaleSimulationofRecrystallizationPhenomena[J].Phil.Mag.1999,79(10):2339-2358.[11]RaabeD.DiscreteMesoscaleSimulationofRecrystallizationMicrostructureandTexyureUsingaStochasticCellularAu2tomatonApproach[J],MaterialsScienceForum.1998,273-275:169-174.[12]RaabeD,BeckerR.C.Couplingofacrystalplasticityfiniteelementmodelwithaprobabilisticcellularautomatonforsimu2latingprimarystaticrecrystallizaitoninAluminium,modelingsimulation[J].MaterialsScienceandEngineering.2000,8:445-462.[13]RaabeD.Cellularautomatainmaterialsciencewithparticularreferencetorecrystallizationsimulation[J].AnnualReviewofMaterialsResearch.2002,32:53-76[14],,,,.[J]..2006,42(05):474-480.[15]DingR,GuoZX.Coupledquantitativesimulationofmicro2structuralevolutionandplasticflowduringdynamicrecrystalli2zation[J],ActaMaterialia.2