相场法模拟凝固微观组织演化研究进展

:20101018;:20101126:(No.10872172)(No.G9KY101502):(1979),,,.:.Email:[e-mail].32No.3Mar.2011陈志,宋庆军,陈安琪,李阳,孔佑超,李峰(,710129):相场法是凝固组织模拟中最有潜力的方法之一,近年来已成为凝固领域研究的热点本文论述了相场法模拟凝固微观组织的原理,并分别介绍了无流动和流动条件下相场法模拟自由枝晶定向凝固界面及小平面枝晶在国内外的研究进展,指出了进一步的研究方向:相场法;流动;自由枝晶;定向凝固;小平面:TG113:A:10008365(2011)03038404RecentResearchandProgressonSolidificationSimulatedMicrostructuresbyPhaseFieldMethodCHENZhi,SONGQingjun,CHENAnqi,LIYang,KONGYouchao,LIFeng(DepartmentofAppliedPhysics,NorthwesternPolytechnicalUniversity,Xi'an710129,China)Abstract:Phasefieldmethodistheoneofpopularnumericalsimulationmethods.Recently,ithasbeenbecomearesearchfocusinsolidificationfield.Thispaperdiscussedtheprincipleofphasefieldmethodsimulationofsolidificationmicrostructureandintroducedresearchprogressinfreedendriteatfreeflow/flow,directionsolidificationinterface,andfacetdendriticgrowthathomeandabroad.Thetrendsinthefutureresearchhavealsoputforward.Keywords:Phasefieldmethod;Flow;Freedendritic;Directionalsolidification;Facet,,,,,,,/,,,,[1],1GinzburgLandau,(x,y,t),,=1,=-1,/-11,(x,y,t),/,,,,/,,/,,,,,,,3843/2011:22.1自由枝晶模拟研究进展,,1986,Langer[2]1993,Kobayashi[3],,1996,KarmaRappel(thininterfacelimit)[4],,,Loginova[5],,Karma[6]Kim[7],,,,,1997,Diepers[8],Al4%CuTong[9],2001,Jeong[10],1Beckermann[11],NS2,,21Fig.1Computedstreamtracesforflowoveragrowingthreedimensionaldendritic2,=0.55,U=1,=0.05,Pr=2.5,D=4,=6.383Fig.2Exampleofacomputeddendriticmorphologywiththreedimensionalflow,=0.55,U=1,=0.05,Pr=2.5,D=4,=6.383,,2006,Grns[12],,,Ai[13],,,,LatticeBoltzmann(LB),Mddvedev[14]LB,Zabaras[15],Quang[16],,2.2定向凝固界面模拟研究进展,,,1964,MullinsSekerka(MS)[17]WarrenLanger,[18],385FOUNDRYTECHNOLOGYVol.32No.3Mar.2011Boettinger[19],NiCuBeckermann[20]Karma,,[21]BiSekerka,,,,MS,Lan[22]SCN/ACE,:,,,,33Vp=6.5m/s,/Fig.3EffectofgravityforVp=5m/sontheflowandconcentrationfieldsandtheinterfaceshape2.3小平面枝晶模拟的研究进展1/15,1/15,,,2001,Eggleston[23]1/4Karma[24]1/4,=0[1+(|sinw|+|cosw|)],,4Kim[25],,0.10,,1/4,[26],,4=0.55,=1.0,1/4Fig.4Timeevolutionofaquarterfaceteddendriteforundercooling=0.55,anisotropy=1.03,,,,,,,,,,(LatticeBoltzmann),;[1]AstaM,BeckermannC,KarmaA,etal.Solidificationmicrostructuresandsolidstateparallels:Recentdevelopments,futuredirections[J].ActaMaterialia.2009,57:941971.[2]PietersR,LangerJS.Noisedrivensidebranchingintheboundarylayermodelofdendriticsolidification[J].PhysicalReviewLetter,1986,56:19481951.[3]KobayashiR.Modelingandnumericalsimulationsofdendriticcrystalgrowth[J].PhysicaD,1993,64(3):410423.[4]KarmaA,RappelWJ.Phasefieldmethodforcomputationallyefficientmodelingofsolidificationwitharbitraryinterfacekinetics[J].PhysicalReviewE,1996,53(4):R3017R3020.[5]LoginovaI,AmbergG,GrenJ.Phasefieldsimulations3863/2011:ofnonisothermalbinaryalloysolidification[J].ActaMaterialia,2001,49:573581.[6]KarmaA.Phasefieldformulationforquantitativemodelingofalloysolidification[J].PhysicalReviewLetters,2001,87(11):1157011.[7]KimSG,KimWT,SuzukiT.Phasefieldmodelwithareducedinterfacediffuseness[J].JournalofCrystalGrowth,2004,263:620628.[8]DiepersHJ,BeckermannC,SteinbachI.Simulationofconvectionandripeninginabinaryalloymushusingthephasefieldmethod[J].ActaMater,1999,47:36633678.[9]TongX,BeckermannC,KarmaA,etal.Phasefieldsimulationofdendriticcrystalgrowthinaforcedflow[J].PhysicalReviewE,2001,63:061601,116.[10]JeongJH,GoldenfeldN,DantzigJA.Phasefieldmodelforthreedimensionaldendriticgrowthwithfluidflow[J].PhysicalReviewE,2001,64:041602,114.[11]LuY,BeckermannC,RamirezJC.Threedimensionalphasefieldsimulationsoftheeffectofconvectiononfreedendriticgrowth[J].JournalofCrystalGrowth,2005,280:320334.[12]GrnsyL,PusztaiT,Brzsnyi.PhaseFieldTheoryofNucleationandPolycrystallinePatternFormation.HandbookofTheoreticalandComputationalNanotechnology[M].AmericanScientificPublishers,StevensonRanch,CAL,2006,9:525572.[13]AiX,ShuY,LiBQ.Discontinuousfiniteelementphasefieldmodelingofpolycrystallinegraingrowthwithconvection[J].ComputersandMathematicswithApplications,2006,52:721734.[14]MedvedevD,KassnerK.LatticeBoltzmannschemefordendriticgrowthinpresenceofconvection[J].JournalofCrystalGrowth,2005,275:e1495e1500.[15]TanLJ,ZabarasN.Alevelsetsimulationofdendriticsolidificationwithcombinedfeaturesoffronttrackingandfixeddomainmethods[J].JournalofComputationalPhysics,2006,211:3663.[16]QuangMD,AmbergG.Simulationoffreedendriticcrystalgrowthinagravityenvironment[J].JournalofComputationalPhysics,2008,227:17721789.[17]WheelerAA,AhmadNA,BoettingerWJ,etal.Recentdevelopmentsinphasefieldmodelsofsolidification[J].AdvSpceRes,1995,16(7):163172.[18],,,.[M].:,2008.[19]BoettingerWJ.WarrenJA.Simulationofthecelltoplanefronttransitionduringdirectionalsolidificationathighvelocity[J].JournalofCrystalGrowth,1999,200:583591.[20]BadilloA,BeckermannC.Phasefieldsimulationofthecolumnartoequiaxedtransitioninalloysolidification[J].ActaMaterialia,2006,54:20152026.[21],,,.[J].E:,2008,38(1):1623.[22]LanCW,LeeMH,ChuangMH,etal.Phasefieldmodelingofconvectiveandmorphologicalinstabilityduringdirectionalsolidificationofanalloy[J].JournalofCrystalGrowth,2006,295:202208.[23]Egg