对流作用下镁合金凝固组织演变的数值模拟_杨满红

25420154Volume25Number4TheChineseJournalofNonferrousMetalsApril20151004-0609(2015)04-0835-09111,2(1.1000842.100084)TG111.4ANumericalsimulationofdendriticgrowthofmagnesiumalloywithconvectionYANGMan-hong1,GUOZhi-peng1,XIONGShou-mei1,2(1.SchoolofMaterialsScienceandEngineering,TsinghuaUniversity,Beijing100084,China;2.StateKeyLaboratoryofAutomobileSafetyandEnergy,TsinghuaUniversity,Beijing100084,China)Abstract:Amodel,whichisbasedonmodifiedcellularautomaton(CA)andmomentumtransport,wasusedtomodelequiaxedandcolumnardendriticgrowthofmagnesiumalloyswithconvection.TheCAmodelwasusedtosimulatedendriticgrowthofMgalloy(hexagonalclose-packedstructure).Themodifiedprojectionmethodwasusedtosolvetheflowfieldtransportmodelcoupledmassconservationequation,momentumconservationequationandsolutediffusionequation.Thegrowthlawsofthesingledendrite,multipledendritesandcolumnargraininMgalloyweresimulated,andthesolutedistributionsofdendriticsolidificationfrontwithdifferentinflowvelocitieswereanalyzedquantificationally.Thesimulationresultsshowthatthedendritegrowthattheupstreamtipisfasterthanthatatdownstream,andsecondaryarmsstretchesintensivelyontheprimaryarmsattheupstreamtip,ratherthanthatatthedownstreamwhereonlyafewweakornosecondaryarmsstretches.Theflowalsochangesthedistributionofthediffusionlayer,andthediffusionlayer,whichspreadsheavilyatthedownstream.Therefore,theconvectionhasamajorimpactontheevolutionofsolidificationmicrostructureofMgalloy.Keywords:magnesiumalloys;dendritegrowth;convection;cellularautomaton213C[1−2](51275269)(2012ZX04012011)(20121087918)2014-09-012014-12-11010-62789448E-mail:[e-mail]20154836(PF)(CA)PF[3−10]CA[11−12]CAAl-Cu[13−14]YIN[15]LBMCAYUAN[16][17−18][19]Ni-NbAl-SiAl-CuAl-CuNi-Nb(FCC)(HCP){0001}0211PF[9]PFAZ91DGUO[7][10]AZ91DCACAPFCANavier-Stokes11.10u(1)()ptuuuuS(2)upS1.2sss()ctDc(3)s111110()()1fccDcckttu(4)csclDsDlk0fs(4)sl0(1)fctk1.3[20]**slckc(5)*l,eq*l0ll(,)TTΓKfcckk(6)*sclcc0*Teq,1Tc0kl(,)fΓGibbs-ThomsonK254837(,)1cos[6()]f(7)s22ss/arccos(/)(/)fxfxfy(8)xx[21]K(9)s1()12/1NiffiKLN(9)LNN8(10)llss*l1()(1)DcDccknvn(10)vnn(11)sδδtflnv(11)δtlHCP[22]22.1AZ91AM60MgAlMg-Al1AZ91AM60[23−25]2.2[26][27]1AZ91AM60[23−25]Table1PhysicalpropertyparametersofAZ91andAM60magnesiumalloys[23−25]ParameterAM60AZ91Initialmassfractionofalloys,c0/%6.09.21Liquidustemperature,Tl,eq/K888868Solutepartitioncoefficient,k00.40.4Liquidusslope,kl/(K·%−1)−5.5−6.59Solutediffusioncoefficientinliquid,Dl/(m2·s−1)1.810−91.810−9Solutediffusioncoefficientinsolid,Ds/(m2·s−1)1.810−121.810−12Gibbs-Thomson’scoefficient,Γ/(K·m)6.210−76.210−7Density,ρ/(kg·m−3)1.741031.74103Dynamicviscosity,μ/(N·s·m−2)3.0810−33.0810−333.1CA2μm80K/s00.1mm/s40040060°60°60°60°1AZ911AZ91021160°PF[7,10]PFCA280K/s0.1mm/sAZ912AZ91201548381AZ91(0.1mm/s)Fig.1SimulatedresultsofequiaxeddendriticmorphologiesofAZ91magnesiumalloy(inletvelocityof0.1mm/s):(a)Withoutconvection;(b)Withconvection2AZ91Fig.2SimulatedsingledendriticgrowthofAZ91magnesiumalloywithconvectionatdifferenttimes:(a)t=0.40s;(b)t=0.72s;(c)t=0.88s;(d)t=1.04s[17]33254839443AZ91Fig.3RelationshipbetweentipvelocityofAZ91magnesiumalloyandsolidificationtime60°(4(a))60°(4(b)(c))60°(4(d))AZ91(1(a))4(d)60°5(5(a))(5(b))5(4(d))4AZ91Fig.4SimulatedresultsofequiaxeddendriticgrowthofAZ91magnesiumalloywithdifferentinletvelocities:(a)0.1mm/s;(b)0.2mm/s;(c)0.35mm/s;(d)0.5mm/s201548403.26AZ915005002μm480K/s0.2mm/s6(a)(6(b)~(d))[10][28]AZ91D65AZ91AlFig.5AlconcentrationprofilesofAZ91magnesiumalloyatupstreamanddownstreamdendritetipsalonghorizontaldirectionwithdifferentvelocities:(a)Upstreamdendritetips;(b)Downstreamdendritetips6AZ91Fig.6SimulatedresultsofequiaxeddendriticgrowthofAZ91magnesiumalloywithdifferentcrystalorientationsandconvectionatdifferenttimes:(a)t=0.384s;(b)t=0.584s;(c)t=0.784s;(d)t=0.884s25484140°()15°()30°()45°()0°15°0°(g0)g0t015°(g15)g15t15b15t0t15t15t0()t0t15t0t153.37AM603005002μm10K/mm42.5K/s12347(a)(b)360°(l3)3(r3)4r344832005004μm35673386575l55775r7YUAN[16]76.4sAM60(0.05mm/s)Fig.7SimulatedresultsofcolumnardendriticgrowthofAM60magnesiumalloyat6.4s(inletvelocityof0.05mm/s):(a)Withoutconvection;(b)Withconvection201548428AM60(10K/mm0.25mm/s0.05mm/s)Fig.8SimulatedresultsofcolumnardendriticgrowthofAM60magnesiumalloywithconvection(temperaturegradientof10K/mm,solidificationrateof0.25mm/sandinletvelocityof0.05mm/s):(a)t=0.8s;(b)t=5.6s;(c)t=10.4s;(d)t=14.4s41)CA2)3)4)REFERENCES[1]MORDIKEBL,EBERTT.Magnesium:Properties-applications-potential[J].MaterialsScienceandEngineeringA,2001,302(1):37−45.[2]KULEKCIMK.Magnesiumanditsalloysapplicationsinautomotiveindustry[J].TheInternationalJournalofAdvancedManufacturingTechnology,2008,39(9/10):851−865.[3]TONGX,BECKERMANNC,KARMAA,LIQ.Phase-fieldsimulationsofdendriticcrystalgrowthinaforcedflow[J].PhysicalReviewE,2001,63(6):061601.[4]LUY,BECKERMANNC,RAMIREZJC.Three-dimensionalphase-fieldsimulationsoftheeffectofconvectiononfreedendriticgrowth[J].JournalofCrystalGrowth,2005,