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Deformation behavior of SiC particle reinforced Al matrix composites based on EMA model

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Deformation behavior of SiC particle reinforced Al matrix composites based on EMA model

    Deformation behavior of SiC particle reinforced Al matrix composites based on

    EMA model

    Science

    Press

    Availableonlineatwww.sciencedirect.corn

    ?ClENCEDIRECT0

    Trans.NonferrOUSMet.Soc.China17(2007)557

    DeformationbehaviorofSiCparticlereinforced

    AImatrixcompositesbasedonEMAmodel

    CHENGNan_pu(程南璞),ZENGSu.min(曾苏民),,

    YUWen.bin(于文斌),LIUZhi.yi(刘志义),CHENZhi.qian(陈志谦)

    Transactionsof

    NonferrousMetals

    SocietyofChina

    WWW.CSU.edu.cn/ysxb/

    1.SchoolofMaterialsScienceandEngineering,CentralSouthUniversity,Changsha410083

    ,China;

    2.SchoolofMaterialsScienceandEngineering,SouthwestUniversity,Chongqing400715,

    China;

    3.SouthwestAluminiumPlant,Chongqing401326,China

    Received28March2006;accepted12October2006

    Abstract:Effectsofthematrixproperties,particlesizedistribution behaviorinAImatrixcompositesreinforcedbySiCparticleswith andinterfacialmatrixfailureontheelastoplasticdeformation anaveragesizeof5pmandvolumefractionof12%were

    quantitativelycalculatedbyusingtheexpandedeffectiveassumption(EMA)mode1.Theparticlesizedistributionnaturallybrings

    aboutthevariationofmatrixpropertiesandtheinterfacialmatrixfailureduetothepresenceofSiCparticles.Thetheoreticalresults

    coincidewellwiththoseoftheexperiment.Thecurrentresearchindicatesthattheloadtransferbetweenmatrixandreinforcements,

    grainrefinementinmatrix.andenhanceddislocationdensityoriginatedfromthethermalmismatchbetweenSiCparticlesandAI

    matrixincreasetheflowstressofthecompositesbuttheinterfacialmatrixfailureisopposite.Italsoprovesthattheloadtransfer,

    grainrefinementanddislocationstrengtheningarethemainstrengtheningmechanisms.andtheinterfacialmatrixfailureandductile

    fractureofmatrixarethedominatingfracturemodesinthecomposites.Themechanicalpropertiesofthecompositesstronglydepend

    onthemetalmatrix.

    Keywords:SiCp/AIcomposites;deformationbehavior;EMAmodel

    1lntroduction

    Metalmatrixcompositesreinforeedbyceramic

    particles,withlowdensity,highstrengthandmodulus

    andflexiblefabricatingtechniques,haxrereceived

    particularattentioninthepastdecades[1].Some

    experimentalresearcheshaverevealedthatthe

    macroscopicbehaviorofthissortofcompositesdepends

    onthereinforcements(withdifferentvolumefraction,

    particlesizeandshape),thematrixpropertiesandthe

    metal/particleinterfaces.Meanwhile.theparticular

    preparationtechniquesofthecompositesrelyonthese

    factors[251.Inordertodescribetheeffectsofsuch

    factorsonthedeformationbehavioroftheparticle

    reinforeedmetalmatrixcomposites(PRMMC),the

    commonmethods.i.e.thedislocationplasticitytheory andthecontinuumplasticitycombinedwith

    Eshelby.inclusionapproachesorfiniteelementmethods, areoftenadopted[610].Theformertheoryissuccessful

    indescribingthedeformationbehaviorofmetalmatrix compositesreinforeedbysub.micronparticleswitha smallvolumefraction.whilethelatterisperfectforlarge reinforcements(>l0m).However,neithercan properlyexplainthecaseofreinforcementsizebetween 0.1and10.STROUD[1lproposedtheeffective

    mediumassumption(EMA)model,whichcanfully

    covertherangeofthereinforcementsizesandbringthe dislocationplasticitytheoryandthecontinuumplasticity intothismodelnaturally.NANandCLARKE[121

    modifiedthismodeltodescribetheeffectsoftheparticle size.shapeandfractureonthedeformationbehaviorOf PRMMC.

    Inthispaper,byconsideringtheeffectsofparticle size,particlesizedistribution,microstructurevarietyof metalmatrixandinterfacialmatrixfailure.theEMA Foundationitem:Project(10147207)supportedbytheNationalNaturalScienceFoundation

    ofChina;Project(201MDE4002)supportedbyChongqing CommissionofScienceandTechnology,China

    Correspondingauthor:CHENGNan-pu;Tel:+86

    23-68252747;Fax:+86-23-68254373;E-mail:cheng._np@swu.edu.cn

    52CHENGNan-pueta1.,'TransNonferrousMetSocCtlinall!(_{I modelwil1befurther

    stress.straincol-relationor

    expandedtocalculatethe

2.SiC(5.rim),"AIcomposites

    (vo[amefraction).Theaimofthetheorelicalresults comparedwiththoseofOH1e~:pelimentistohwestigate theelastoplasticdeformationbehaviorofPRMMCThe strengtheningmechanismandthefracturemodesof PRMMCwerealsodiscussed

    2Experimentalmaterialsanddeformation

    behavior

    ThemetalmalrxmatedaIs1ntheeomposlteswere

    atom1zedpowders.whosenOnli'alCol'npositionswere

    Imassrraction,%)AI1.4Mg122Si-I19Cu0.92Mn

    0.5Fe.andthereinlbrcementswerchonw"SiCpalli1ms

    TheSCpavticlesizedlstribLitonisusualyexpressedby

    aloornlaIdstributonfunctioi1.ie.

    1

    

    2471t.lJl(il

    By'fittingEqn(1)totheSt('particlesize distribution,wegottheiHeanparticlesized=5pmand thestandarddeviation6=05.asshowninFig1

    TheSiCA1compositeswerefhbricatedbya

    powdermetallurgyandhotextrustunrouteForco01

    Fig.IDistributionotSt(parliclcsi/e

    paringexperimentalandtheoreticalcaleulation.the unstrengtl'Jenedalloy'n'latcrials'alsopl.eparedbythe samenlethudTheas.rece1ve(1i111tel1a1swerec?nducted

    10T^I1eattreati11enl(SO1I0I1trealedrillnal53()

    ?.waterquenchedat20?andauedIbr8l1tlt170?'1

    ThetensiIepropcrliesofthemater1aIswerenleasHiedon aSUN5testingnlac]lllid.

Thenletal0graph.fractureSUltheeandslressstrain

    COITealtonofthe1111[elialsurgSIIowninF1g2J11 Fig2fa1.thegraiiisizeormatrixinconlpositesissinai keV

    Fig2Microstructuresanddeformationbehaviororcomposites:(MetaltogtaphofSiC.

    A

    SiCp;A1composite;lc1EDXspectrumofSi(particlesttrface;)Stresssnaincurke~'iI,AI

    tenslletests

    composite;Ih)rmctLLresurlaceor

    alloyarMSi('r.AI~.'OlllposJ[edurhlg

    m

    CHENGNan-pu,etalFFrans.NonferrousMet.So~.China17(2007) andcomparativetotheaverageparticlesize.Thefracture surface(seeFig.2Co))ofthecompositesandEDX sDectrumanalysisinFig.2(c),revealthattheinterfacial matrixfailure(crackpropagationinthenearvicinityof theSiC/Almatrixinterface)andtheductilefractureofAl matrixarethedominatingfracturemodesinthe

    composites.ThefractureofSiCparticlesisn'tobserved. butafewclusteredparticlesarefoundonthefracture surface.InFig.2(d1,theexperimentalresultsshowthat theelasticmodulus,yieldstrengthandfracturestrength ofthecompositesarehigherthanthoseofthemarx alloy,whiletheductilitydecreasesroughlyby50%. 3EMAmodel[1l13

    Supposingthatthereinforcementiselasticand perfectlybondedtotheelastoplasticmetalmatrix.Both ofthenon..1inearstress..straincorrelationsofthematrix alloyandthePRMMCcanbedescribedbyaformulaas

=C(s)'s(2)

    wheretheelastoplasticsecantstiffnesstensorC(s)isa functionoftheinstantaneousstrains.Thentheeffective secantstiffnessCofthePRMMCcanbedefinedby =

    C().(3)

    wheI1eandaretheaveragestrainandstress. respectively.

    Forconvenienceincalculation,weseparatedC(c) intotwopartsas

    C()=c.(.)+c()(4)

    whereC^J()istheeffectivesecantmodulusofthe homogeneousreferencemediumandonlydependsonthe homogeneousstrainfield,andC)isthe

    instantaneousvariationfromC^Jf1.

    Tocalculatethedeformationbehaviorofthe PRMMC,themetalmatrixisthoughtofthe

    homogeneousreferencematerials.namelyC^J_Cm. Takingandasthesecantbulkandshearmoduliof thePIMMC,andastheelasticbulkandshear modulioftheparticles,andkmandasthesecantbulk andshearmoduliofthemetalmatrix,respectively,the moduliofthePRMMCcanbeobtainedfromEqn.f71 asl31

    (5)

    whereY.=

    53

    andisthevolume

    fractionofreinforcements.Theassumptionofplastic incompressibilityforthematrixmaterialsleads

tok=k.Theparticleswereconsideredtobe

    sphericalforconvenienceinthecalculationofEqn.f5). Bysplittingthestressandstraintensorsinto hydrostatic(O'kkandEkk)anddeviatoric(o-0.and)

    parts,theircomponentsfromEqn.(4)arewrittenas =

    =等等忍

    :=

    andthestresscomponentsinparticlesare

    等一kPmt-km%寺一

    =

    

    (6)

    (7)

    TheempiricalRamburg-Osgoodequation(ROE)is reasonableandoftenusedtodescribetheuniaxial stress-strainbehaviorforthemetalmaterials,namely :

    Gm

    +Gyf,,ll/,lEEj(8)

    whereE,vnlandaretheelasticmodulus,yield strengthandstrainworkingexponentofthematrix, respectivelyandisaconstant.Atiermeasuringthe stress--straincurveofthemamxmaterials,,and ncanbegotbyfittingtheexperimentalresultsinFig.2(c) throughEqn.(8).Thenthesecantelasticmodulusofthe matrixmetalmaterialsisrepresentedby

    (9)

    andthesecantshearmodulus,undertheconditionof plasticincompressibilityduringdeformation,iswritten

aS

    =(10)

    Thesecantshearmodulus.ofthematrix

    ,?????????,????????【

    一:一一

    杀差肘

    54CHENGNanpu,etal/Trans.NonferrousMet.Soc.China17(2007) materialundertheuniaxialtensileloado-l(theeffective

    stressinuniaxialdeformation)canbecalculatedfrom Eqns.(8)(10).SubstitutingitsvaluesintoEqn.(6),we gettheaveragestressstraincorrelationofthecomposites andplotitinFig.3.Theparametersfortheoretical calculationaresummarizedinTable1.

    

    凸一

    highertheflowstressisinPIMMC.

    ThegrainsizeofmatrixinPIMC.comparedwith themonolithicmatrixalloyproducedbythesame process,willberefinedmuchduetotheadditionoffine andtoughparticles.Thisisbecausethatthetough particlescancutthematrix,andatthesametime,their presenceincreasestheeffectiveextrusionratioduringthe hotextrusionprocess.Thethermalmismatchbetween particlesandmetalmatrixwillbringhigherdislocation densityintomatrixneartheparticlesurfacesduring coolinginprocess,andthesubgrainsinmatrixformed

    bythedislocationlinesareverysmal1.The0rwan mechanismofthereinforcementswillactduetotheir smallsize.Meanwhile,thestraingradienteffects,

    associatedwithgeometricallynecessarydistributionof dislocations(GND)thatarerequiredtoaccommodatethe plasticstrainmismatchbetweentheparticlesandthe surroundingmatrixduringtensiledeformation,will influencetheflowstress.Allthesefactorswillcertainly enhancethestrengthofmatrixinPIMMCr14-16]. Fig.3ComparisonbetweenEMApredictionandexperimental results4Effectofreinforcementsonmatrix

    Table1PropertiesofSiCandA1matrixmaterials InFig.3,thecalculatedelasticmodulusofthe PIMCagreeswellwiththatoftheexperiment.The reinforcementscanbearpartialloadandthenenhance theflowstressofthecomposites(that'stosay,thetensile loadcantransferbetweenmatrixandreinforcements), whichcanalsobederivedfromEqn.(61.However,the theoreticalresultsaremuchlowerthanthoseof experimentduringtheplasticdeformation.Thereasonis thatthemicrostructurevariationofmatrix,particlesize (distribution)andinterfacialmatrixfailureisnottaken intoaccount,onlythevolumefractionofthe

    reinforcementsisconsideredinthesimpleEMAmode1. Atthesametime,thismeansthattheplasticdeformation behaviorspredictedbytheEMAmodelofPIMCwith differentparticlesizesarethesame,whichdeviatesfrom thereality.Commonly,withthesamevolumefractionof thereinforcements,thesmallertheparticlesizeiS,the Forverysmallreinforcement,theOrwan

    mechanismlikelyactsandreads[17]

    ACrom:2m6//4Vy(11)

    whereandbaretheshearmodulus,Burgersvector

    ofthematrixmaterials.anddandaretheparticlesize andvolumefraction,respectively.

    Thecontributionofthestraingradienteffectstothe flowstressduringtheplasticdeformationisrepresented by[15-16]

    a=

    m『?

    where0.4and0.2aretwogeometricconstants associatedwiththeparticletopologyrespectively,andp representstheplasticstrain.

    Theeffectofthegrainrefinementofmatrixin compositesduringthehotextrusionontheflowstress canbedescribedbytheHallPatchcorrelation18191

    AO'remf(13)

    where0.IMPa.misastrengtheningfacto~

    Thehighdensitydislocationsstemmedfrom

    processingandthermalexpansionmismatchoncooling (suchaswaterquenching)wills~engthenthecomposites, \,????

    \,_

CHENGNan.pu,etal/Trans.NonferrousMet.Soc.China17(2007)55

    whichcanbeexpressedby[12,17

    Aaotm:6?=b(14)

    where2.7isaconstant(sameasRef.[12]),Aais thedifferenceofthermalexpansionmismatchandATis thedifferenceintemperaturefromheattreatment temperatureofmatrixtoroomtemperature. ThecontributionsdescribedbyEqns.(11)(14)are

    eventuallyascribedtotheadditionofSiCparticles

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