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JEURMDORMATERIALSPROCESSINGTECHNOLOGYELSEVIERJOURNALOFMATERIALSPROCESSINGRCCHNOLOG68199713ILOADINGOFFORMINGPRESSESBYTHEUPSETTINGOFOBLIQUESPECIMENSKCHODNIKIEWZ,SBPETERSEN,RBALENDRABPAFMARTINSLL2TRS,UNIRERITYO/TCIMOH,GVULVMHUTTA502524LVTRA,P,HMDHUTLIRCRSILDSTRALHCLVDC75LLOTLROSESTREETGLASGOWGIIXJ,IKBLTITULOSUPERIORTCCNICO41RORICOPAI1096LISHOAC,CORRESPONDINGAUTHORFAX351I847404509240136/97/171101997ELSEVIERSCIENCESAALLRIGHTSRESERVEDPLLS0924013696025174HENCE,THESELOADINGCONDITIONSWOULDHAVETOBESIMULATEDDURINGPRESSELASTICITYMEASUREMENTSITISPOSSIBLETOLOADTHEPRESSWITHAHYDRAULICJACKLOCATEDBETWEENTWOOBLIQUEWASHERSFIGIA,BUTFRICTIONBETWEENTHEPISTONANDTHECYLINDERRENDERSTHEMCTHODINACCURATEARECENTLYPROPOSED3ALTERNATIVEMETHODWHICHISBASEDONTHEUPSETTINGOFOBLIQUESPECIMENSFIGLBPROVIDESAMOREREPRESENTATIVELOADINGCONDITIONUNFORTUNATELY,THISFORMOFUPSETTINGISNOTCOMMONSOMEASPECTSOFTHISPROCESSHAVEBEENREPORTEDBYRAMAEKERSANDKAIS4,WHOCONSIDEREDTHEUNSTABLELIIIRAMIRAMILUPPERDIESPOI,FLIPIIIIIABFIG1METHODSOFLOADINGAPRESSWITHVERTICALANDHORIZONTALFORCESAUSINGAHYDRAULICJACKIBUSINGTHEUPSETTINGOFANOBLIQUESPECIMEN14KCHODNIKIEWICZETAL/JOURNALOJ“MATERIALSPROCESSHLGTECHNOLOGY6819971318THEFUNCTIONAL/75THEMODIFIEDFUNCTIONAL,/TIN,HAVTINGTHIVFRMJFS101I,“X/K,0O9FHT0DVK2EDVTJU/DS50808“I0WHEREKISALARGEPOSITIVEPENALTYCONSTANTNOW,IFTHE06O6FIRSTVARIATIONHINTHEFUNCTIONAL/VANISHES,THENO,FO,O,6/7G6DVKVT,DVTUJDSO60302ANDBOTHTHEEQUILIBRIUMEQUATIONSANDTHEVOLUMEOZCONSTANCYCONSTRAINTWILLBE,APPROXIMATELY,SATISFIED01P/GOSIMULTANEOUSLY5THEABOVEVARIATIONALEQUATIONIS023,5FIG2RELATIVEFRICTIONALSTRESSASAFUNCTIONOFNORMALSTRESSANDFRICTIONFACTOR71FLOWOFMATERIALWHICHRESULTSFROMTHEANGULARMISALIGNMENTOFTHETOOLSHOWEVER,RAMAEKERSANDKALSDIDNOTPROVIDEADETAILEDINSIGHTTOTHEPROCESS,THUSPRIORTOTHEUSEOFTHEUPSETTINGCFOBLIQUESPECIMENSFORPRESSELASTICITYEXPERIMENTS,AMORECOMPREHENSIVEPROCESSANALYSISISREQUIRED2METHODOFSOLUTIONTHEUPSETTINGOFOBLIQUESPECIMENSWASSIMULATEDUSINGTHE2DFINITEELEMENTPROGRAMPLAST2WHICHWASDEVELOPEDATLNSTITUTOSUPERIORTCNICO,LISBONTHISPROGRAMISBASEDONTHEVARIATIONALPRINCIPLEWHICHREQUIRESTHATALLADMISSIBLEVELOCITIESUJ,WHICHSATISFYTHECONDITIONSOFCOMPACTIBILITYANDINCOMPRESSIBILITY,MAKETHEFUNCTIONAL/7FVATDVSTJUJDSIFSTATIONARYINTHISEXPRESSION0ISTHEEFFECTIVESTRESS,ISTHEEFFECTIVESTRAINRATE,TJISTHESURFACETRACTION,SFISTHESURFACEONWHICHTRACTIONSAREPRESCRIBEDANDVISTHEVOLUMETHEEFFECTIVESTRESSANDEFFECTIVESTRAINRATEAREDEFINEDASFOLLOWS2,T120TAOAJ223EOE23WHEREAANDVARETHEDEVIATORICSTRESSANDTHEDEVIATORICSTRAINRATE,RESPECTIVELYWHENTHEFUNCTIONALHISGIVENASTATIONARYVALUE,ITSFIRSTORDERVARIATIONHVANISHESIE/0THEDEFINITIONOFINCOMPRESSIBILITYHASTHEFORM,KK04WHEREBISTHEVOLUMETRICSTRAINRATEINORDERTOTAKETHISCONDITIONINTOACCOUNT,THEPENALTYFUNCTIONMETHODWASAPPLIED,WHICHREQUIRESTHEMODIFICATIONOFPRESENTEDINDETAILIN6THEELASTICDEFORMATIONOFTHESPECIMENANDDIESISNEGLECTEDANDTHERELATIONSHIPBETWEENTHEEFFECTIVESTRAINRATEANDTHEDEVIATORICSTRESSESISPROVIDEDBYTHELEVYMISESFLOWRULE3,INWHICH0FORTHEPLASTICREGIONISEQUALTOTHEYIELDSTRESSAOWHICH,INTURN,ISDEFINEDBYTHEEQUATIONAOCG“8WHERECANDNDENOTETHEMATERIALCONSTANTS,ANDGISTHEEFFECTIVESTRAINGEE,/129INWHICHEEISTHESTRAINFURTHER,THEWANHEIMANDBAY7FRICTIONMODELWASAPPLIEDACCORDINGTOTHISMODEL,THEFRICTIONALSTRESSRISDESCRIBEDBYRJ“K10INWHICHFISTHEFRICTIONFACTOR,ISTHERATIOBETWEENTHEREALANDAPPARENTCONTACTAREAS,ANDKISTHESHEARYIELDSTRESSOFTHEWORKMATERIAL,DEFINEDBYKLLTHEFRICTIONAL,ANDNORMAL,P,STRESSESATTHEDIEWORKPIECEINTERFACEAREPROPORTIONALFORP/AO3THERELATIVEFRICTIONALSTRESSZ/KFAPPROACHESACONSTANTVALUEWHICHISEQUALTOFFIG2INORDERTOELIMINATETHESUDDENCHANGESOFTHEFRICTIONALSTRESSATTHENEUTRALPOINT,THEFOLLOWINGAPPROXIMATIONWASDEFINEDTANT12/RINWHICHJISTHEUNITVECTORINTHEDIRECTIONOPPOSITETOTHEVELOCITYUSOFTHEWORKMATERIALRELATIVETOTHEDIEANDVOISASMALLPOSITIVENUMBERINCOMPARISONWITHUS61DETAILEDINFORMATIONABOUTPLAST2ISPROVIDEDIN8METALFLOWANALYSISACHIEVEDUSINGPLAST2COMPARESWELLWITHTHERESULTSOFEXPERIMENT9KCHMHTIKWWICTTALLOURMDFTLMATERIALSPROCCSINGTECHMDOGY6G19971I31815,11/“I_,_OOAP/COZ/3,T,/OI,_,BBFIG3DISTORTEDMESHFORTHEUPSEUINGOFLAAPARALLELPECIMENANDBAEDGESHAPEDSPECIMENTOGETHERITHTHEDISTRIBUTIONOFNORMALPANDFRICTIONALRSTRESSES/1,JOAXNI“OQITTL“0304,500,Q0102“03I04B,OFIG4PRESENTINGASPECIMENSHAPESANDPOSITIONSOFTHENEUTRALPOINTNANDBTHEFUNCTIONXNEBOFORF05,FL10ANDH,B,053ASSUMPTIONSTHEFOLLOWINGASSUMPTIONSAPPLYTOTHEANALYSISIPLANESTRAINUPSETTINGCONDITIONSPREVAILITSTICKINGFRICTIONPREVAILSONTHELOWERDIESPECIMENINTERFACE,WHILSTTHEWORKMATERIALSLIDESRELATIVETOTHEUPPERTJIETHISASSUMPTIONCORRESPONDSTOEXPERIMENTALCONDI0ONSWHERETHELOWERDIEISROUGHWHILSTTHEUPPERDIEANDTHESPECIMENARESMOOTHANDWELLLUBRICATEDIIITHERELATIONSHIPBETWEENTHEYIELDSTRENGTHANDTHEEFFECTIVESTRAINRATEFORMILDSTEELHASBEENASSUMEDTOBEAO740“TMMPA13IVTHEINITIALGEOMETRYOFTHESPECIMENISCHARACTERISEDBYTHERATIOHO/BOINWHICHHOISTHEORIGINALAVERAGEHEIGHTMEASUREDALONGTHECENTRELINEOFTHESPECIMEN,B0ISTHEORIGINALWIDTHOFTHESPECIMENANDFLISTHEANGLEBETWEENTHEDIEANDTHESPECIMENREFERTOFIG1VTHERATIOHOHE“10014HOISUSEDTODEFINETHEREDUCTIONINHEIGHTOFTHESPECIMEN,WHEREHISITSCURRENTHEIGHTATTHECENTERLINEVITHEFOLLOWINGBASICPARAMETERSWEREUSEDFORTHEANALYSISHO/BO05,F0,5,FLI0FORTHEANALYSISEACHPARAMETERWASVARIEDABOUTTHESEPRESCRIBEDVALUES,WHILSTOTHERPARAMETERSWERERETAINEDCONSTANT16KCHODNIKIEWICZETAL/JOURNALOJMATERIALSPROCESSINGTECHNOLOGY6819971318,S7“FOO,_1111/I,FOOL,/LOO,I,I1OBAX_3_B002Z002505075,I17“OTL020304RIOFFIG5PRESENTINGASPECIMENSHAPESANDTHEPOSITIONOFTHENEUTRALPOINTNANDBTHEFUNCTIONXJ/BOFORE20,10ANDHO/BO05,/T/XN0“00III5“10LFI“ABFIG6PRESENTINGASPECIMENSHAPESANDTHEPOSITIONOFTHENEUTRALPOINTNANDBTHEFUNCTIONXNFL/BOFORE20“/,FL0ANDHO/BO054RESULTSTHEDEFORMATIONOFPARALLELANDOBLIQUESPECIMENS,THELATTERBEINGCHARATTERISEDBYBASICPARAMETERS,ARESHOWNINFIG3,TOGETHERWITHDISTRIBUTIONSOFRELATIVENORMALPRESSURESP/GOONTHEUPPERFACEOFTHESPECIMENGAPSWHICHCANBEOBSERVEDBETWEENSPECIMENSANDTHEUPPERDIESAREDUETOTHEDIFFERENCEINFRICTIONATTHECONTACTSURFACESTHEDEFORMATIONOFTHEOBLIQUESPECIMENMAYBEDESCRIBEDASFOLLOWSITHEFLOWPATTERNISNOTSYMMETRICALABOUTTHECENTERLINEIIALARGERVOLUMEOFMETALFLOWSTOWARDTHETHICKERSIDEOFTHEWEDGESHAPEDSPECIMENTHANTOWARDSITSTHINSIDEIIITHENEUTRALPOINT,N,ATWHICHMATERIALFLOWHASNOTANGENTIALCOMPONENTRELATIVETOTHEUPPERDIE,ISDISPLACEDTOWARDSTHETHINSIDEOFTHESPECIMENIVAGAPBETWEENTHEUPPERDIEANDTHEOBLIQUESPECIMENISCREATEDATTHETHICKSIDEOFTHESPECIMENTHEDEFORMATIONOFTHEOBLIQUESPECIMENISACOMPLEXFUNCTIONOFTHEREDUCTIONE,THEFRICTIONFACTORF,THEANGLEANDTHERATIOHO/BOSPECIMENSHAPESARESHOWNINFIG4AFORDIFFERENTREDUCTIONSANDCONSTANTF05,FL10ANDHO/BO05THELINENNREPRESENTSTHEPOSITIONOFTHENEUTRALPOINTOVERTHECOURSEOFTHEUPSETTINGWHILSTTHELINERRREFERSTOTHEDISPLACEMENTSLOCATIONOFTHERESULTANTFORMINGFORCEFORASMALLVALUEOFREDUCTION,THERELATIVECOORDINATEXN/BOOFTHENEUTRALPOINTREMAINSPRACTICALLYCONSTANTFIG4B,BUTFORGREATERREDUCTIONS,THERATIOXR/BOCHANGESSIGNIFICANTLYTHETRANSSECTIONALVALUEOFDEKCHODNIKIEWICETAL/JOURNALOFMATERIALSPROCESSINGIECHNOLOG,681997131817FORMATIONREFERSTOTHEDEVELOPMENTOFTHEGAPBET,VEENTHEUPPERDIEANDTHESPECIMENTHISISSHOWNMAGNIFIEDINFIG4ASINCETHEGAPCHANGESTHECONTACTAREABETWEENTHESPECIMENANDTHEUPPERDIE,THENEUTRALPOINTMOVESTOWARDSTHETHINSIDEOFTHESPECIMENSPECIMENFORMSTARE20,FL10ANDHO/BO05ARESHOWNINFIG5FORVARIOUSFRICTIONFACTORSTHEFOLLOWINGOBSERVATIONSAREMADEITHECREATIONOFTHEGAPDEPENDSONTHEFRICTIONFACTORFORF0THEGAPPREVAILSATANEARLYSTAGEOFTHEDEFORMATIONWHILSTFORF10THEFORMATIONOFTHEGAPISNOTINITIATEDFIFDFFH,RL,C2S02005XSA0DEG1C250205010050OOO,SELO20304050J1550X010XT02CBO,OC1SO025FJFV02_OTOO050OOS10O025X0750IISO,O20C,OEL02502/HO/BO025005O10O,OE1SO02OD0FIG7THERATIOF,/FVASAFUNCTIONOFPROCESSPARAMETERSTAFA/FVFLFORDIFFERENTVALUESOFEAND05,HO/BO05BFHFVXEFORDIFFERENTVALUESOFANDCONSTANTF05,HO/BO05CFH/FVXEFORDIFFERENTVALUESOFFANDCONSTANTFL10HO/BO05DFH/FVEFORDIFFERENTHO/8OANDCONSTANT10,F05IITHEFRICTIONFACTORHASAGREATERINFLUENCEONTHELOCATIONOFTHENEUTRALPOINTTHANTHESPECIMENFONNTHEPRACTICALLYLINEARFUNCTION,/S/B,FOICONSTANTE,FANDHO/BUISSHOWNINFIG6BACONCLUSIONDRAWNISSIMILARTOTHATINTHEPREVIOUSCASETHEANGLE/INFLUENCESTHEPOSITIONOFTHENEUTRALPOINTRATHERTHENTHEFORMOFTHEAXIALSECTIONOFTHEDEFONNEDSPECIMENTHERESULTANTUPSETTINGFORCEFFH,FVISINCLINEDRELATIVETOTHECENTRALLINESINCETHEWORKMATERIALSLIDESALONGTHEUPPERSURFACETOWARDSBOTHTHETHICKANDTHETHINSIDESOFTHESPECIMEN,ITFOLLOWSTHATTHEANGLEOFINCLINATIONOFTHERESULTANTFORCE7WOULDBESMALLERINVALUETHENTHEANGLEFLOFTHEINCLINATIONOFTHEUPPERDIE,IEFTANJFVL151THEFUNCTIONFH/FVFLLFORDIFFERENTVALUESOFE,CONSTANTFANDHO,BOISSHOWNINFIG7A,FROMHICHITCANBEOBSERVEDTHATTHERATIOFHFVDOESNOTDEPENDONTHELEVELOFEINTHISSPECIFICCASETHEFOLLOWINGEQUATIONAPPLIESF_H00132“FLDEG16FVTHISFEATURESUITSPRESSELASTICITYEXPERIMENTS,ASISIMPLIFIESTHEUSEOFDATAPERTAININGTOTHEFORCERATIOTHEFUNCTIONFH/FVEFORSELECTEDFLANDCONSTANFANDHO/BOFIG7BCONFIRMSTHEABOVEFEATUREFIG7CAND7DSHOWTHAT,DURINGTHEPRESSSTIFFHESSEXPERIMENTS,BOTHLOWFRICTIONANDALOWVALUOFHO/BOSHOULDBEENSUREDIFITISTHECASE,THERATKFH/FVREMAINSPRACTICALLYINDEPENDENTOFTHESPECIMENREDUCTIONTHEDEPARTUREOFTHETRENDFW“FVEFORHO/BO10FIG7DFROMTHEOTHERGRAPHSRESUITSFROMUSINGTOOLARGEASPECIMEN,THELATTERUNDERGOINGBENDINGATTHEEARLYSTAGEOFDEFORMATIONRELATIONSHIPSBETWEENTHEVERTICALCOMPONENTOTHEUNITFORMINGFORCERELATEDTOTHESPECIMELENGTHANDTHEREDUCTIONEARESHOWNSCHEMATICALLINFIG8ONTHEBASISOFFIG8B,ITCANBECONELUDEDTHAT,FORARELATIVELYSMALLDEFORMATION,THVERTICALCOMPONENTOFTHEFORMINGFORCEISPRACTICAILINDEPENDENTOFTHEANGLEBETWEENTHEDIES,INCLUDINTHECASE/0THISFEATURESIMPLIFIESTHEPROCEDMFORTHESELECTIONOFSPECIMENSFORPRESSELASTICITYMESUREMENTSTHEVERTICALCOMPONENTOFTHEFORMINFORCEMAYBECALCULATEDFROMTHECOMMONLYKNOWEQUATIONFORTHEUPSETTINGOFAPARALLELFACEDSPECMENTHETHIRDFEATUREOFTHERESULTANTFORCEISTHEPOINTOFIAPPLICATIONTHEPOSITIONOFTHISPOINTHASBEENDEFINEDFIG4AINAFORMOFLINERRTHEPOINTOFTHEFORAPPLICATIONFOLLOWSTHENEUTRALPOINTHENCE,CONCLUSIOWHICHHAVEBEENDRAWNFORTHENEUTRALPOINTAPPKCHODNIKIEWKETAL/JOURNALOFMATERIAL,PROCESSINGTECHNOLOGY681997131818FV/LKN/MMFV/LF106060TM075504030“20100005/1150O025/OOO/,4O2O10IILIT01020304050AKN/MMQ15E100_50/II,III1O20304050BFIG8THERELATI,C,RTICALCOMPONENTOFTHEFORMINGFORCEFV/LASAFUNCTIONOFPROCESSPARAMETERSAFORSELECTEDVALUESOFANDP10THO/BO05BFORSELECTEDVALUESOF/IANDF05,H,B,05EQUALLYWELLTOTHEPOINTOFAPPLICATIONOFTHERESULTANTFORCE5CONCLUSIONS1FORCONSTANTFRICTIONANDCONSTANTRELATIVEHEIGHTOFTHESPECIMEN,HO/BO,THERATIOBETWEENTHEHORIZONTALANDVERTICALCOMPONENTSOFTHEFORMINGFORCE,FH/FV,DEPENDSMAINLYONTHESPECIMEN/UPPERDIEINCLINATION2ITISPOSSIBLETOCHOSEANOBLIQUESPECIMENSOTHATTHERATIOF/FVREMAINSPRACTICALLYINDEPENDENTONTHESPECIMENREDUCTIONINORDERTOACHIEVETHIS,THEFOLLOWINGCONDITIONSSHOULDBEFULFILLEDITHESPECIMENREDUCTIONSHOULDBEKEPTRELATIVELYLOW,EGFOR,/05ITSHOULDNOTEXCEE