MaterialsScienceandEngineeringA476(2008)178185EqualchannelangularextrusionofflatproductsV.M.SegalEngineeredPerformanceMaterials,11228LemenReceived19February2007；receivedinrevisedformAbstractAofItadv2007ElsevierB.V.Allrightsreserved.K1.tionAnmentinSuchfebetweenattractiSPDmationoptimizationofprocessingcharacteristics.Irrespectiveofpro-cessinggoal,materialandtemperaturestrainrateconditions,themechanicsofSPDshouldprovideintensiveanduniformstrains,simplesheardeformationmodeandlowstresses.Amonga(ECAE)trialimperfectimajoritywimposefolloproductsization.firstplates,calpracticalwellarepublicationsdetails2.LetsconsiderECAEofarectangularbillet(Fig.1)withthick-nessT,widthWandlengthLthroughsharpcornerchannelswithtoolangle90.Original1andfinal2billetpositionsareshowninFig.1bylongchainandsolidlines,correspondingly.Asthe0921-5093/$doi:fewknownmethodsofSPD,equalchannelangularextrusionispresentlyconsideredasthemostpromisingforindus-applications.However,realizationofECAEstillremainsve.Despiteofextensiveactivityinthefield,absoluteofthepublishedworksdealtwithelongatedbilletsasasoriginallydescribedin1.Thesebarsorrodslikebilletsrestrictionsonmaterials,characteristicsofECAEandwingprocessing.TheyaredifficulttouseassemifinishedTel.:E-mailaddress:.billetwidthWremainsthesameandthebilletismovedinsidethechannelsasarigidbody,theflowisnearplaneandtheplas-ticzoneislocalizedaroundacrossingplaneofchannels.Itisknown6thatthestressstrainstateandextensionoftheplas-ticzonestronglydependonboundaryconditionsimposedbyaninletchannel1andanoutletchannel2.Thus,correspondingconditionsshouldbeanalyzedfirst.2.1.InletchannelAtthebeginningofECAE,thewelllubricatedbilletisplacedintotheinletchannel.Anactualfrictionforcedependsonrealseefrontmatter2007ElsevierB.V.Allrightsreserved.10.1016/j.msea.2007.04.092Thepaperconsidersequalchannelangularextrusion(ECAE)ofsufficientlystressanalysisisperformedinsideplasticzoneandinletandoutletchannelstheprocessingmechanicsandstrategytodesigntoolsareformulated.antagesforprocessingofmassiveslab-likebilletsandtechnologycommercializationeywords:ECAE；Optimizationofprocessing；Flatproducts；LargescalecommercializationIntroductionThecontrolofmaterialstructuresbysevereplasticdeforma-(SPD)presentssignificantscientificandpracticalinterest.importantadvantageofthisapproachisstructurerefine-tothesub-micronscalethatcanbeattainedinbulkbillets,acosteffectivemannerandfordifferentmetalsandalloys.ultra-finegrainedstructures,usuallyintherangefromawmicronsto0.2micron,provideareasonablecompromisehighstrengthandsatisfactoryductilitythatisespeciallyveforstructuralapplications.Forcommercializationofsubstantialprogressshouldbemadeintherelateddefor-techniques.ThekeyfactorsaredeformationmethodandRd-SuiteA,WhitmoreLake,MI48198,USA20April2007；accepted24April2007longrectangularbilletswithdifferentwidth-to-thicknessratiosW/T.dependingoncontactfrictionandthebilletgeometry.OptimizationisshownthatflatbilletswithW/Tgreatermuch1provideimportanttechnicalonthelargemetallurgicalscale.andstilltherearenoreportsonprocesscommercial-Incontrast,ECAEofflatbilletsfollowedbyrolling,introducedin2,correspondstouniversalproductssuchassheets,stripsandfoils.Togetherwithothertechnologi-advantages,thisprocessingconceptofECAEpresentsgreatperspectives.WhileECAEofelongatedbilletsisnowinvestigated,specialfeaturesoftheECAEofflatbilletsnotunderstoodandwerenotdisclosedinjustafewrelated35.ThepresentpaperaddressessomeimportantoftheECAEtechnologyinthecaseofflatbillets.ProcessingmechanicsV.M.Segal/MaterialsScienceandEngineeringA476(2008)178185179Fig.1.ECAEofrectangularbillets.plasticnelsimilaronwherepplasticlocalpressurecontactlubricantmentpressurepwheresholinearsupposeandDelta1pHerefisafullcontactareabetweenbilletandwalls.When1isknownforspecificconditions,themaximumincrementoftheextrusionpressureinthestationaryrectangularchannelwithfourfrictionwalls(Fig.2a)is:Delta1pY=(2n1)(1+m)(1/Y)m(2)Hereparametersn=L/Tandm=W/Tdefinerelativebilletlengthandwidth.Inparticular,m=1correspondstotheordi-narycaseoflongbar-orrod-likebillets,mgreatermuch1correspondstoflatplate-likebilletsandmlessmuch1correspondstostrip-likebillets.Formulae(1)and(2)showthat,dependingonnandm,theextru-sionpressurepemaybesignificantlybiggerthanthematerialflowstressYevenforlowfriction1.Theeffectivewaytoreducecontactfriction,increasetoollifeandpunchstabilityisviamovablechannelwalls7.Inonepossiblecase(Fig.2b,fordetailsee7),theinletchannelisformedbyonestationarydiewallandrectangularslotoftheslider2,whichmovestogetherwiththebillet1.Thatwayfrictionincrementarewpressureallto-thicknessbeTheforpressureratiosureforfunctionlongbilletscontactandnormalpressurebetweenmaterialandchan-walls.Assumingthatastressstateinsidethechannelistolinearplasticcompression,thenormalpressurenchannelwallsis(Fig.2a)n(pY)pistheaxialpressureandYisthematerialflowstress.IfY,thepressuren0,andforlongbilletswithL/Tgreatermuch1thecontactisformedbytransversebuckling.Suchirregular,contactprovideslowfrictionforce.Ifp2Y,thenormalnY,andtheplasticcontactapproximatestothefullareabetweenbilletandchannel.Inthiscase,thesamewillresultinlargefrictionforceandsignificantincre-ofpressureDelta1palongachannellength.Then,theextrusionpeis:e=p1+Delta1p(1)p1istheaxialpressureatthechannelentry.ExperimentswthatinallcasestheincrementofpressureDelta1pchangesintheproportionwiththechannellengthL.Thatallowsonetothateffectiveplasticfriction1isuniformlydistributedtheDelta1pmaybecalculatedbytheformula:=1fFig.2.Distributionoffrictionininletchannelswith:(a)stationaryiseliminatedalongthreechannelwalls.Themaximumofextrusionpressureis:Delta1pY=(n1)parenleftBig1YparenrightBig(3)Inanothercase(Fig.2c),twosidewallsoftheinletchannelformedbymovablesliders2,3whereasbackandfrontdieallsarestationary.Correspondingly,theincrementofthepunchis:Delta1pY=(2n1)parenleftBig1YparenrightBig(4)Itisinformativetocompareresultsofformulae(2)(4).Incases,theextrusionpressureincreaseswiththebilletlength-ration.Foreffectiveprocessing,thisratioshouldsufficientlylarge.Practically,nisselectedbetween4and8.incrementDelta1p/YisalmosttwiceaslargeforFig.2cthanFig.2b.Forthestationarychannel(Fig.2a),theextrusionalsostronglydependsonthebilletwidth-to-thicknessm.However,thisratiodoesnotaffecttheextrusionpres-inbothcasesofmovablechannelwalls.Calculatedresultstypicalconditionsn=6,1/Y=0.15areshownonFig.3inofm.Threecharacteristicsituationsareoutlined:(I)billets(m=1)；(II)plate-likebillets(mgreatermuch1)；(III)strip-like(mlessmuch1).ItisevidentthatECAEoflongand,especially,walls；(b)threemovablewalls；(c)twomovablesidewalls.180V.M.Segal/MaterialsScienceandEngineeringA476(2008)178185Fig.3.Effectofbilletratiomontheincreaseofpressurealonginletchannel(L/T=6,1/Y=0.15)with:(1)stationarywalls；(2)threemovablewalls；(3)twomovablewalls.strip-likebilletsinstationarychannelsresultsinthemultifoldincreasestresshardchannelmoechannelsflat2.2.nelchangebottommaterialsticking7andusing7Fig.5.Sliplinesolutionwithdifferentfrictioninchannels.stitutedbyelasticfrictionbetweenslider1andguidePlate2.Duringextrusion,theslider1usuallyremainsfreeandsomeslipandshearstresses2shouldbedevelopedalongthebilletcontactguidethesliderstablemaybilletCorrespondingnottioncoef2.3.oftheextrusionpressureincomparisonwiththeflowY.Inthesecases,ECAEofsufficientlylargebilletsandmaterialscanbeperformedonlyindieswithmovablewallsatpowerfulpresses.However,forflatbillets,twovablechannelwallsprovideinsignificantreductionofthextrusionpressure.Therefore,simpledieswithstationaryinletandordinarypressescanbeusedinmanycasesoflargebillets.OutletchannelIncontrasttotheinletchannel,lubricationoftheoutletchan-isachallengingproblem(Fig.4a).Becauseofthesharpintheextrusiondirection,highnormalpressureatthewall,intensiveslipanduncoveringoftheatomiccleanalongabottomcontactsurfaceO1B,heavyscratches,andgallingcanbeobservedevenwiththebestlubricants.Thatleadstohighextrusionpressure,poorbilletsurfaceintensivediewear.Alltheseproblemscanbeeliminatedbyamovableslideralongthebottomchannelwall(Fig.4b).Thatwayplasticfrictionbetweenmaterialanddieissub-Fig.4.Stationaryoutletchannel(a)andoutletsurfaceO1Btoovercomefrictionbetweensliderandaplate:2fO1B=p1WT(5)HerefO1BisanareaofthecontactsurfaceO1BandiscoefficientofCoulombsfriction.Atnormalconditions,thespeedisclosetotheextrusionspeed.Asfrictionisnotaphenomenon,certaindeviationsintheslidermovementbeobserved.Ifstresses2exceedplasticfrictionbetweenandslider,theflowbecomessimilartothestationarydie.boundaryconditionsintheoutletchanneldoprovidealocalizedplasticzoneandsimplesheardeforma-modenecessaryforeffectiveprocessing6.Therefore,theficientshouldbesufficientlylow.PlasticdeformationzoneInletandoutletchannelsdefinefrictionboundaryconditions1,2fortheplasticzone.AsliplinesolutionisshownonFig.5channelwithmovablebottomwall(b).V.M.Segal/MaterialsScienceandEngineeringA476(2008)178185181forthecase121.Itissupposedthatthematerialbehaviorissimilartotheidealplasticbody28.ThesliplinefieldincludescentralfanFEDO,mixedboundaryareaCDEanddeadmetalareaO1CA.Thecentralangleofthedeadareais:1=1+2(6)Angles1,2arecalculatedbyformulae8:1=bracketleftbiggArccos(1/k)2bracketrightbigg,2=bracketleftbiggArccos(2/k)2bracketrightbigg,whereparticulartooutletlimitthefullhighLthatmaterialsnotplicityapplications.(ties.bewhenlineandorderandparametersinletpressurenel,or(withforsidefurthere3.3.1.tions,roducedmostdierotationserties.ofbeneficiallater3.2.oftheplasticzone(Fig.5)issmall.Inthiscase,materialstrainingduringcrossingtheplasticzoneincludesmainlytwosimpleshearsalongboundariesDOandAFO6.Approxi-mately,suchaccumulatedshearisequivalenttosingleshear=2alongsliplineO1Oofthecorresponding“zerosolution”when=0.Fig.6showstransformationofthe“unit”materialelementabcdintoparallelograma1b1c1d1causedbyshear3Inthepaper,wewillusethesamedesignationofrouteslikein7tounderlinethateachbasicrouteisindependentfromothers.Similarroutesbutwithdifferentdesignationwerealsousedin3.k=Y/3isthematerialshearflowstress.Solutionsforcasesof1,2wereconsideredin6.NowwecangatherresultsandoutlinetheoptimalstrategydesignECAEprocessing.Firstofall,notethatthestationarychannelalwaysinducesthelubricationproblem.Inthesituation2k,10,asliplineanalysis6,7givesforentrypressureattheinletchannelp1/Y2.3.Thatresultsincontactbetweenbilletandchannelwallsandleadstotheextrusionpressurepeinallpracticalcasesoflongchannels/Tgreatermuch1andfinitefriction10.Infact,publisheddatashowtheextrusionpressuremaybeashighasp/Y79.Formostatlowprocessingtemperatures,solargepressuresareadmissibleformoderntoolalloys.Therefore,despitesim-,stationaryoutletchannelsareunpracticalforindustrialWithapropermovablebottomwalloftheoutletchannelFig.4b),friction1,2andcoefficientaresmallquanti-Undertheseconditions,thesliplinefieldofFig.5canconsideredasasmallmodificationofthe“zerosolution”1=2=0andtheplasticzoneisthesingleslipO1O.Then,usingtheperturbationmethodforsliplines10omittingintermediateresults,withaccuracytothesecondofmagnitude,formulae(5)and(6)give:2Y,(1+Y)ktheentrypressureinsidetheinletchannelis:p1Y23+1Y+parenleftbigg1+122parenrightbigg(7)InaccordancewithEq.(7),thereisasufficientroomfor1andtoformthelocalcontactbetweenbilletandchannelwithlowfriction,iftheincrementoftheextrusionDelta1palsoremainsmoderate.Withmovableoutletchan-theinletchannelmaybe