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MATERIALSSCIENCEANDENGINEERINGA4762008178–185EQUALCHANNELANGULAREXTRUSIONOFFLATPRODUCTSVMSEGALENGINEEREDPERFORMANCEMATERIALS,11228LEMENRECEIVED19FEBRUARY2007；RECEIVEDINREVISEDFORMABSTRACTAOFITADV2007ELSEVIERBVALLRIGHTSRESERVEDK1TIONANMENTINSUCHFEBETWEENATTRACTISPDMATIONOPTIMIZATIONOFPROCESSINGCHARACTERISTICSIRRESPECTIVEOFPROCESSINGGOAL,MATERIALANDTEMPERATURE–STRAINRATECONDITIONS,THEMECHANICSOFSPDSHOULDPROVIDEINTENSIVEANDUNIFORMSTRAINS,SIMPLESHEARDEFORMATIONMODEANDLOWSTRESSESAMONGAECAETRIALIMPERFECTIMAJORITYWIMPOSEFOLLOPRODUCTSIZATIONFIRSTPLATES,CALPRACTICALWELLAREPUBLICATIONSDETAILS2LETSCONSIDERECAEOFARECTANGULARBILLETFIG1WITHTHICKNESST,WIDTHWANDLENGTHLTHROUGHSHARPCORNERCHANNELSWITHTOOLANGLE90◦ORIGINAL1ANDFINAL2BILLETPOSITIONSARESHOWNINFIG1BYLONGCHAINANDSOLIDLINES,CORRESPONDINGLYASTHE09215093/DOIFEWKNOWNMETHODSOFSPD,EQUALCHANNELANGULAREXTRUSIONISPRESENTLYCONSIDEREDASTHEMOSTPROMISINGFORINDUSAPPLICATIONSHOWEVER,REALIZATIONOFECAESTILLREMAINSVEDESPITEOFEXTENSIVEACTIVITYINTHEFIELD,ABSOLUTEOFTHEPUBLISHEDWORKSDEALTWITHELONGATEDBILLETSASASORIGINALLYDESCRIBEDIN1THESEBARSORRODSLIKEBILLETSRESTRICTIONSONMATERIALS,CHARACTERISTICSOFECAEANDWINGPROCESSINGTHEYAREDIFFICULTTOUSEASSEMIFINISHED∗TEL15175483417EMAILADDRESSVLADIMIRSEGALCOMCASTNETBILLETWIDTHWREMAINSTHESAMEANDTHEBILLETISMOVEDINSIDETHECHANNELSASARIGIDBODY,THEFLOWISNEARPLANEANDTHEPLASTICZONEISLOCALIZEDAROUNDACROSSINGPLANEOFCHANNELSITISKNOWN6THATTHESTRESS–STRAINSTATEANDEXTENSIONOFTHEPLASTICZONESTRONGLYDEPENDONBOUNDARYCONDITIONSIMPOSEDBYANINLETCHANNEL1ANDANOUTLETCHANNEL2THUS,CORRESPONDINGCONDITIONSSHOULDBEANALYZEDFIRST21INLETCHANNELATTHEBEGINNINGOFECAE,THEWELLLUBRICATEDBILLETISPLACEDINTOTHEINLETCHANNELANACTUALFRICTIONFORCEDEPENDSONREAL–SEEFRONTMATTER2007ELSEVIERBVALLRIGHTSRESERVED101016/JMSEA200704092THEPAPERCONSIDERSEQUALCHANNELANGULAREXTRUSIONECAEOFSUFFICIENTLYSTRESSANALYSISISPERFORMEDINSIDEPLASTICZONEANDINLETANDOUTLETCHANNELSTHEPROCESSINGMECHANICSANDSTRATEGYTODESIGNTOOLSAREFORMULATEDANTAGESFORPROCESSINGOFMASSIVESLABLIKEBILLETSANDTECHNOLOGYCOMMERCIALIZATIONEYWORDSECAE；OPTIMIZATIONOFPROCESSING；FLATPRODUCTS；LARGESCALECOMMERCIALIZATIONINTRODUCTIONTHECONTROLOFMATERIALSTRUCTURESBYSEVEREPLASTICDEFORMASPDPRESENTSSIGNIFICANTSCIENTIFICANDPRACTICALINTERESTIMPORTANTADVANTAGEOFTHISAPPROACHISSTRUCTUREREFINETOTHESUBMICRONSCALETHATCANBEATTAINEDINBULKBILLETS,ACOSTEFFECTIVEMANNERANDFORDIFFERENTMETALSANDALLOYSULTRAFINEGRAINEDSTRUCTURES,USUALLYINTHERANGEFROMAWMICRONSTO02MICRON,PROVIDEAREASONABLECOMPROMISEHIGHSTRENGTHANDSATISFACTORYDUCTILITYTHATISESPECIALLYVEFORSTRUCTURALAPPLICATIONSFORCOMMERCIALIZATIONOFSUBSTANTIALPROGRESSSHOULDBEMADEINTHERELATEDDEFORTECHNIQUESTHEKEYFACTORSAREDEFORMATIONMETHODAND∗RDSUITEA,WHITMORELAKE,MI48198,USA20APRIL2007；ACCEPTED24APRIL2007LONGRECTANGULARBILLETSWITHDIFFERENTWIDTHTOTHICKNESSRATIOSW/TDEPENDINGONCONTACTFRICTIONANDTHEBILLETGEOMETRYOPTIMIZATIONISSHOWNTHATFLATBILLETSWITHW/TGREATERMUCH1PROVIDEIMPORTANTTECHNICALONTHELARGEMETALLURGICALSCALEANDSTILLTHEREARENOREPORTSONPROCESSCOMMERCIALINCONTRAST,ECAEOFFLATBILLETSFOLLOWEDBYROLLING,INTRODUCEDIN2,CORRESPONDSTOUNIVERSALPRODUCTSSUCHASSHEETS,STRIPSANDFOILSTOGETHERWITHOTHERTECHNOLOGIADVANTAGES,THISPROCESSINGCONCEPTOFECAEPRESENTSGREATPERSPECTIVESWHILEECAEOFELONGATEDBILLETSISNOWINVESTIGATED,SPECIALFEATURESOFTHEECAEOFFLATBILLETSNOTUNDERSTOODANDWERENOTDISCLOSEDINJUSTAFEWRELATED3–5THEPRESENTPAPERADDRESSESSOMEIMPORTANTOFTHEECAETECHNOLOGYINTHECASEOFFLATBILLETSPROCESSINGMECHANICSVMSEGAL/MATERIALSSCIENCEANDENGINEERINGA4762008178–185179FIG1ECAEOFRECTANGULARBILLETSPLASTICNELSIMILARONΣWHEREPPLASTICLOCALPRESSURECONTACTLUBRICANTMENTPRESSUREPWHERESHOLINEARSUPPOSEANDDELTA1PHEREFISAFULLCONTACTAREABETWEENBILLETANDWALLSWHENΤ1ISKNOWNFORSPECIFICCONDITIONS,THEMAXIMUMINCREMENTOFTHEEXTRUSIONPRESSUREINTHESTATIONARYRECTANGULARCHANNELWITHFOURFRICTIONWALLSFIG2AISDELTA1PY2N−11MΤ1/YM2HEREPARAMETERSNL/TANDMW/TDEFINERELATIVEBILLETLENGTHANDWIDTHINPARTICULAR,M1CORRESPONDSTOTHEORDINARYCASEOFLONGBARORRODLIKEBILLETS,MGREATERMUCH1CORRESPONDSTOFLATPLATELIKEBILLETSANDMLESSMUCH1CORRESPONDSTOSTRIPLIKEBILLETSFORMULAE1AND2SHOWTHAT,DEPENDINGONNANDM,THEEXTRUSIONPRESSUREPEMAYBESIGNIFICANTLYBIGGERTHANTHEMATERIALFLOWSTRESSYEVENFORLOWFRICTIONΤ1THEEFFECTIVEWAYTOREDUCECONTACTFRICTION,INCREASETOOLLIFEANDPUNCHSTABILITYISVIAMOVABLECHANNELWALLS7INONEPOSSIBLECASEFIG2B,FORDETAILSEE7,THEINLETCHANNELISFORMEDBYONESTATIONARYDIEWALLANDRECTANGULARSLOTOFTHESLIDER2,WHICHMOVESTOGETHERWITHTHEBILLET1THATWAYFRICTIONINCREMENTAREWPRESSUREALLTOTHICKNESSBETHEFORPRESSURERATIOSUREFORFUNCTIONLONGBILLETSCONTACTANDNORMALPRESSUREBETWEENMATERIALANDCHANWALLSASSUMINGTHATASTRESSSTATEINSIDETHECHANNELISTOLINEARPLASTICCOMPRESSION,THENORMALPRESSUREΣNCHANNELWALLSISFIG2AN∼P−YPISTHEAXIALPRESSUREANDYISTHEMATERIALFLOWSTRESSIF∼Y,THEPRESSUREΣN∼0,ANDFORLONGBILLETSWITHL/TGREATERMUCH1THECONTACTISFORMEDBYTRANSVERSEBUCKLINGSUCHIRREGULAR,CONTACTPROVIDESLOWFRICTIONFORCEIFP2Y,THENORMALΣNY,ANDTHEPLASTICCONTACTAPPROXIMATESTOTHEFULLAREABETWEENBILLETANDCHANNELINTHISCASE,THESAMEWILLRESULTINLARGEFRICTIONFORCEANDSIGNIFICANTINCREOFPRESSUREDELTA1PALONGACHANNELLENGTHTHEN,THEEXTRUSIONPEISEP1DELTA1P1P1ISTHEAXIALPRESSUREATTHECHANNELENTRYEXPERIMENTSWTHATINALLCASESTHEINCREMENTOFPRESSUREDELTA1PCHANGESINTHEPROPORTIONWITHTHECHANNELLENGTHLTHATALLOWSONETOTHATEFFECTIVEPLASTICFRICTIONΤ1ISUNIFORMLYDISTRIBUTEDTHEDELTA1PMAYBECALCULATEDBYTHEFORMULAΤ1FFIG2DISTRIBUTIONOFFRICTIONININLETCHANNELSWITHASTATIONARYISELIMINATEDALONGTHREECHANNELWALLSTHEMAXIMUMOFEXTRUSIONPRESSUREISDELTA1PYN−1PARENLEFTBIGΤ1YPARENRIGHTBIG3INANOTHERCASEFIG2C,TWOSIDEWALLSOFTHEINLETCHANNELFORMEDBYMOVABLESLIDERS2,3WHEREASBACKANDFRONTDIEALLSARESTATIONARYCORRESPONDINGLY,THEINCREMENTOFTHEPUNCHISDELTA1PY2N−1PARENLEFTBIGΤ1YPARENRIGHTBIG4ITISINFORMATIVETOCOMPARERESULTSOFFORMULAE2–4INCASES,THEEXTRUSIONPRESSUREINCREASESWITHTHEBILLETLENGTHRATIONFOREFFECTIVEPROCESSING,THISRATIOSHOULDSUFFICIENTLYLARGEPRACTICALLY,NISSELECTEDBETWEEN4AND8INCREMENTDELTA1P/YISALMOSTTWICEASLARGEFORFIG2CTHANFIG2BFORTHESTATIONARYCHANNELFIG2A,THEEXTRUSIONALSOSTRONGLYDEPENDSONTHEBILLETWIDTHTOTHICKNESSMHOWEVER,THISRATIODOESNOTAFFECTTHEEXTRUSIONPRESINBOTHCASESOFMOVABLECHANNELWALLSCALCULATEDRESULTSTYPICALCONDITIONSN6,Τ1/Y015ARESHOWNONFIG3INOFMTHREECHARACTERISTICSITUATIONSAREOUTLINEDIBILLETSM1；IIPLATELIKEBILLETSMGREATERMUCH1；IIISTRIPLIKEMLESSMUCH1ITISEVIDENTTHATECAEOFLONGAND,ESPECIALLY,WALLS；BTHREEMOVABLEWALLS；CTWOMOVABLESIDEWALLS180VMSEGAL/MATERIALSSCIENCEANDENGINEERINGA4762008178–185FIG3EFFECTOFBILLETRATIOMONTHEINCREASEOFPRESSUREALONGINLETCHANNELL/T6,Τ1/Y015WITH1STATIONARYWALLS；2THREEMOVABLEWALLS；3TWOMOVABLEWALLSSTRIPLIKEBILLETSINSTATIONARYCHANNELSRESULTSINTHEMULTIFOLDINCREASESTRESSHARDCHANNELMOECHANNELSFLAT22NELCHANGEBOTTOMMATERIALSTICKING7ANDUSING7FIG5SLIPLINESOLUTIONWITHDIFFERENTFRICTIONINCHANNELSSTITUTEDBYELASTICFRICTIONBETWEENSLIDER1ANDGUIDEPLATE2DURINGEXTRUSION,THESLIDER1USUALLYREMAINSFREEANDSOMESLIPANDSHEARSTRESSESΤ2SHOULDBEDEVELOPEDALONGTHEBILLETCONTACTGUIDEΤTHESLIDERSTABLEMAYBILLETCORRESPONDINGNOTTIONCOEF23ΤOFTHEEXTRUSIONPRESSUREINCOMPARISONWITHTHEFLOWYINTHESECASES,ECAEOFSUFFICIENTLYLARGEBILLETSANDMATERIALSCANBEPERFORMEDONLYINDIESWITHMOVABLEWALLSATPOWERFULPRESSESHOWEVER,FORFLATBILLETS,TWOVABLECHANNELWALLSPROVIDEINSIGNIFICANTREDUCTIONOFTHEXTRUSIONPRESSURETHEREFORE,SIMPLEDIESWITHSTATIONARYINLETANDORDINARYPRESSESCANBEUSEDINMANYCASESOFLARGEBILLETSOUTLETCHANNELINCONTRASTTOTHEINLETCHANNEL,LUBRICATIONOFTHEOUTLETCHANISACHALLENGINGPROBLEMFIG4ABECAUSEOFTHESHARPINTHEEXTRUSIONDIRECTION,HIGHNORMALPRESSUREATTHEWALL,INTENSIVESLIPANDUNCOVERINGOFTHEATOMICCLEANALONGABOTTOMCONTACTSURFACEO1B,HEAVYSCRATCHES,ANDGALLINGCANBEOBSERVEDEVENWITHTHEBESTLUBRICANTSTHATLEADSTOHIGHEXTRUSIONPRESSURE,POORBILLETSURFACEINTENSIVEDIEWEARALLTHESEPROBLEMSCANBEELIMINATEDBYAMOVABLESLIDERALONGTHEBOTTOMCHANNELWALLFIG4BTHATWAYPLASTICFRICTIONBETWEENMATERIALANDDIEISSUBFIG4STATIONARYOUTLETCHANNELAANDOUTLETSURFACEO1BTOOVERCOMEFRICTIONBETWEENSLIDERANDAPLATE2FO1BP1WT5HEREFO1BISANAREAOFTHECONTACTSURFACEO1BANDISCOEFFICIENTOFCOULOMB’SFRICTIONATNORMALCONDITIONS,THESPEEDISCLOSETOTHEEXTRUSIONSPEEDASFRICTIONISNOTAPHENOMENON,CERTAINDEVIATIONSINTHESLIDERMOVEMENTBEOBSERVEDIFSTRESSESΤ2EXCEEDPLASTICFRICTIONBETWEENANDSLIDER,THEFLOWBECOMESSIMILARTOTHESTATIONARYDIEBOUNDARYCONDITIONSINTHEOUTLETCHANNELDOPROVIDEALOCALIZEDPLASTICZONEANDSIMPLESHEARDEFORMAMODENECESSARYFOREFFECTIVEPROCESSING6THEREFORE,THEFICIENTSHOULDBESUFFICIENTLYLOWPLASTICDEFORMATIONZONEINLETANDOUTLETCHANNELSDEFINEFRICTIONBOUNDARYCONDITIONS1,Τ2FORTHEPLASTICZONEASLIPLINESOLUTIONISSHOWNONFIG5CHANNELWITHMOVABLEBOTTOMWALLBVMSEGAL/MATERIALSSCIENCEANDENGINEERINGA4762008178–185181FORTHECASEΤ1Τ21ITISSUPPOSEDTHATTHEMATERIALBEHAVIORISSIMILARTOTHEIDEALPLASTICBODY28THESLIPLINEFIELDINCLUDESCENTRALFANFEDO,MIXEDBOUNDARYAREACDEANDDEADMETALAREAO1CATHECENTRALANGLEOFTHEDEADAREAISΨ1Η1Η2−Π6ANGLESΗ1,Η2ARECALCULATEDBYFORMULAE8Η1BRACKETLEFTBIGGΠ−ARCCOSΤ1/K2BRACKETRIGHTBIGG,Η2BRACKETLEFTBIGGΠ−ARCCOSΤ2/K2BRACKETRIGHTBIGG,WHEREPARTICULARTOOUTLETLIMITTHEFULLHIGHLTHATMATERIALSNOTPLICITYAPPLICATIONSTIESBEWHENLINEANDORDERΤANDPARAMETERSINLETPRESSURENEL,ORWITHFORSIDEFURTHERE331TIONS,ROTATIONSPASSINTRODUCEDMOSTDIEROTATIONSERTIESOFBENEFICIALLATER32ΨOFTHEPLASTICZONEFIG5ISSMALLINTHISCASE,MATERIALSTRAININGDURINGCROSSINGTHEPLASTICZONEINCLUDESMAINLYTWOSIMPLESHEARSALONGBOUNDARIESDOANDAFO6APPROXIMATELY,SUCHACCUMULATEDSHEARISEQUIVALENTTOSINGLESHEARΓ2ALONGSLIPLINEO1OOFTHECORRESPONDING“ZEROSOLUTION”WHENΨ0FIG6SHOWSTRANSFORMATIONOFTHE“UNIT”MATERIALELEMENTABCDINTOPARALLELOGRAMA1B1C1D1CAUSEDBYSHEARΓ3INTHEPAPER,WEWILLUSETHESAMEDESIGNATIONOFROUTESLIKEIN7TOUNDERLINETHATEACHBASICROUTEISINDEPENDENTFROMOTHERSSIMILARROUTESBUTWITHDIFFERENTDESIGNATIONWEREALSOUSEDIN3KY/√3ISTHEMATERIALSHEARFLOWSTRESSSOLUTIONSFORCASESOFΤ1,Τ2WERECONSIDEREDIN6NOWWECANGATHERRESULTSANDOUTLINETHEOPTIMALSTRATEGYDESIGNECAEPROCESSINGFIRSTOFALL,NOTETHATTHESTATIONARYCHANNELALWAYSINDUCESTHELUBRICATIONPROBLEMINTHESITUATIONΤ2→K,Τ1→0,ASLIPLINEANALYSIS6,7GIVESFORENTRYPRESSUREATTHEINLETCHANNELP1/Y∼23THATRESULTSINCONTACTBETWEENBILLETANDCHANNELWALLSANDLEADSTOTHEEXTRUSIONPRESSUREPEINALLPRACTICALCASESOFLONGCHAN
