相场法凝固组织模拟的研究进展

:(59971037):2000203224,2000207218:(1974-),,,,1,1,1,1,Akarma2,CBeckermann3(11,710072;21,,02115,;31,,52242,):,;,:;;:TG21239:A:100124977(2000)0920507205Progressinnumericalsimulationofsolidificationmicrostructureusingphase2fieldmethodYUYanmei1,LYili1,ZHANGZhenzhou1,YANGGencang1,AKarma2,CBeckermann3(1.Statekeylaboratoryofsolidificationprocessing,NorthwesternPolytechnicalUniversity,Xian710072;2.DepartmentofPhysicsandCenterforInterdisciplinaryResearchonComplexSystems,NortheasternUniversity,Boston,Massachusetts02115,USA;3.DepartmentofMechanicalEngineering,TheUniversityofIowa.Iowacity,IA52242,USA)Abstract:Nowthenumericalsimulationofsolidificationmicrostructureisamostinterestedresearchfieldandphase-fieldmethodisaneffectivetoolofsimulatingsolidificationmicrostructure.Thepaperintro2ducedtheprincipleofnumericalsimulationusingphase-fieldmethod,reviewedthepresentdevelopmentconditioninthisareaathomeandabroad,andpointedoutthedevelopmentdirectionsinthefuture.Keywords:phase2fieldmethod;solidificationmicrostructure;numericalsimulation,,,,:(DeterminsticMethod)(StochasticMethod)(Phase2fieldMethod),,,,,12(=1;=-10,),,,,,,,,,,,,1-(r,t),705Vol149No19Sept2000FOUNDRY©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(r,t)0-1,;(r,t)1,,2,01(-11),,Helmholtz3-67-11,:(1),(2)(),(3)6,:Û=Ms(1)ÛC=-(¨Mc¨sc)cfixed(2)Ûe=-(¨Me¨se)efixed(3)ceÛÛcÛeMMcMeS,S=(s(,e,c)-22|¨|2)d(4)s(1)(4),,€,:()=€(1+cos(k))(5)¨€,k(46)4,12,,7„m55=(1-)[-12+30„u(1-)]+„¨2(6)5u5+1p()55=¨2u(7)=(T-TM)cuL(8)uTTMcLm„p(),,(Peclet),,X,,100XX10(0)21974,HalperinHohenbergMa13ModelC80,Collins14Langer3Caginalp15ModelC,Cagi2nalp16-18FifeGill19-20,,(Sharpinterfacemodel),1983,Fix21,Fix21Caginalp161993,Kobayashi,4,,Kobayashi,,WheelerMurry7Wang8FifePoul9(Thermodynamically2805Sept2000FOUNDRYVol149No19©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.)Ni,1:,018,,I2vantsov1996,KarmaRappel22-23(thin2interfacelimit),Gibbs2Thomson,,,,Karma,2Karma(a)(b)1Ni17Fig.1Asimulationofthedendriticgrowthofnickelinundercooledmelts17221Fig.2Asimulationofathree2dimensionalequiaxeddendrite21,WheelerBoettingerMcFad2den5(isothermal),,,,,WarrenWheelerBoet2tingerMcFadden10,24-25(¨c)2(¨c),CaginalpXie26(¨c)2,Conti27,,,:McCarthy28LeeSizuki29KimSizuki30Cu2Ni,Fe2C,Al2Si,,31,,,Con2ti32Ni2Cu:t,-VVt1/2,,WarrenBoettinger,Karma,,,,Karma,,1998,TÊnhardt33(shearflow),,,AndersonWheelerMcFadden,,,(),,TongBeckermann34Karma,,,3,,905:©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:1135Fouri2erCollocationMethod36FourierGalerkinMethod37,,,,:MatthiasHeinkerschloss,TÊnhardt,,,(MassivelyParallelMethods)Sandia,(,),,20,,3,,311,,,,,312,,,,Karma,42GDEC2AL2PHA30002700140,,,,,4,,,,:1.J.,1999,(8):40452,.J.,1999,(5):41473BraunRJ,McFaddenGB,CoriellSR.Morphologicalinstablityinphase2fieldmodelsofsolidiflcationJ.PhysicalReviewE,1994,49(5):433643524KobayashiR.Modelingandnumericalsimulationsofdendriticcrys2talgrowthJ.PhysicaD,1993,63(10):4104235WheelerAA,BoettingerWJ,McFaddenGB.Phase-fieldmodelforisothermalphasetransitioninbinaryalloysJ.PhysicalReviewE,1992,45(10):742474396CharachC,FifePC.Phasefieldmodelofsolidificationinbinaryal2loys:capillarityandsolutetrappingJ.JournalofCrystalGrowth,1999,198/199:12671277WheelerAA,MurrayRJ.ComputationofdendritesusingaphasefieldmodelJ.PhysicaD,1993,66(10):2432628WangSL,SekerkaRF,WheelerAAetal.Thermodynamically-consistentphase2fieldmodelsforsolidificationJ.PhysicaD,1993,69(10):1892009PenroseO,FifePC.ThermodynamicallyconsistentmodelsofphasefieldtypeforthekineticsofphasetransitionsJ,PhysicaD,1990,43(10):446210WarrenJA,BoettingerWJ.Predictionofdendriticgrowthandmicrosegregationpatternsinabinaryalloyusingthephase2fieldmethodJ.PhysicalReviewA,1991,43(10):1310131711WangSL,SekerkaRF.Computationofthedendriticoperating015Sept2000FOUNDRYVol149No19©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(7):3760377612BeckermannC,DiepersHJ,KarmaA,etal.Modelmeltconvec2tioninphase2fieldsimulationsofsolidificationJ.JournalofCom2putationPhysics,1999,154(1):46849613HalperinBI,HohenbergPC,MaSKJ.PhysicalReviewB,1974,(10):2016202414CollinsJB,LevinH.Diffuseinterfacemodelofdiffusion-limitedcrystalgrowthJ.PhysicalReviewB,1985,31(9):6119612215CaginalpG,FifePC.DynamicsoflayeredinterfacesarisingfromphaseboundariesJ.SIAMJournalofApplyMathematics,1988,48(3):50651016CaginalpG,FifePC.PhasefieldmethodsforinterfacialboundariesJ.PhysicalReviewB,1986,33(11):7792779417CaginalpG,FifePC.High2orderphasefieldmodelsanddetailedanisotropyJ.PhysicalReviewB,1986,34(7):4940494318CaginalpG.StefanandHele2Shawtypemodelsasasymptoticlimitsofthephase2fieldequationsJ.PhysicalReviewA,1989,39(11):5887589019FifePC,GillGS.Thephase2fielddescriptionofmushyzonesJ.PhysicaD,1989,35:26727520FifePC,GillGS.Phase2transitionmechanismsforthephase2fieldmodelunderinternalheatingJ.Ph