冲压模具英文翻译原文

journalhomepage:www.elsevier.com/locate/jmatprotec

Contactpressureevolutionatthedieradiusinsheetmetalstamping

MichaelP.Pereiraa,∗,JohnL.Duncanb,WenyiYanc,BernardF.Rolfed

a

CentreforMaterialandFibreInnovation,DeakinUniversity,PigdonsRoad,Geelong,VIC3217,AustraliaProfessorEmeritus,TheUniversityofAuckland,284GlenmoreRoad,RD3,Albany0793,NewZealandcDepartmentofMechanicalandAerospaceEngineering,MonashUniversity,Clayton,VIC3800,AustraliadSchoolofEngineeringandIT,DeakinUniversity,Geelong,VIC3217,Australia

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article

Articlehistory:

infoabstract

Thecontactconditionsatthedieradiusareofprimaryimportancetothewearresponseformanysheetmetalformingprocesses.Inparticular,adetailedunderstandingofthecon-tactpressureatthewearinginterfaceisessentialfortheapplicationofrepresentativeweartests,theuseofwearresistantmaterialsandcoatings,thedevelopmentofsuitablewearmodels,andfortheultimategoalofpredictingtoollife.However,thereisalackofinfor-mationconcerningthetime-dependantnatureofthecontactpressureresponseinsheetmetalstamping.Thisworkprovidesaqualitativedescriptionoftheevolutionanddistribu-

Received27March2008Receivedinrevisedform18July2008

Accepted17August2008

Keywords:ContactpressureSheetmetalstampingToolwear

Bending-under-tension

tionofcontactpressureatthedieradiusforatypicalchannelformingprocess.Throughananalysisofthedeformationconditions,contactphenomenaandunderlyingmechanics,itwasidentifiedthatthreedistinctphasesexist.Significantly,theinitialandintermediatestagesresultedinsevereandlocalisedcontactconditions,withcontactpressuressignif-icantlygreaterthantheblankmaterialyieldstrength.Thefinalphasecorrespondstoalargercontactarea,withsteadyandsmallercontactpressures.Theproposedcontactpres-surebehaviourwascomparedtootherresultsavailableintheliteratureandalsodiscussedwithrespecttotoolwear.

©2008ElsevierB.V.Allrightsreserved.

1.Introduction

Inrecentyears,therehasbeenanincreaseinwear-relatedproblemsassociatedwiththedieradiusofautomotivesheetmetalformingtools(Sandbergetal.,2004).Theseproblemshavemainlybeenaconsequenceoftheimplementationofhigherstrengthsteelstomeetcrashrequirements,andthereduceduseoflubricantsowingtoenvironmentalconcerns.Asaresult,formingtools,andthedieradiiinparticular,arerequiredtowithstandhigherformingforcesandmoreseveretribologicalstresses.Thiscanresultinhighcostsdue

tounscheduledstoppagesandmaintenance,andleadtopoorpartqualityintermsofsurfacefinish,geometricaccuracyandpossiblepartfailure.

Iftheside-wallofapartisexaminedafterforming,ademarcationknownasthe‘dieimpactline’iseasilyvisible(Karima,1994).Thislineseparatestheburnishedmaterialthathastravelledoverthedieradiusandthefreesurfacethathasnotcontactedthetooling,clearlyindicatingthatseveresur-faceeffectsexistatthedieradius.Itisthereforeimportanttounderstandthecontactphenomenaatthislocationofthetooling.

Correspondingauthor.Tel.:+61352273353;fax:+61352271103.E-mailaddress:michael.pereira@deakin.edu.au(M.P.Pereira).

0924-0136/$–seefrontmatter©2008ElsevierB.V.Allrightsreserved.doi:10.1016/j.jmatprotec.2008.08.010

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1.1.Bending-under-tensiontest

Thebending-under-tensiontest–inwhichastripisbentoveracylindricaltoolsurfaceandpulledagainstaspeci-fiedbacktension–hasbeenusedinthelaboratoryformanyyearstosimulateconditionsatthedieradius(Ranta-Eskolaetal.,1982).Theliteraturecontainsnumerousexperimentalinvestigationsthatexaminesurfacedegradationoverthedieradiusafterrepeatedorcontinuousbending-under-tensionoperations.Forexample,inindependentstudieswithdiffer-ingtestconditionsandmaterials,Mortensenetal.(1994),HortigandSchmoeckel(2001)andAttafetal.(2002),eachvisu-allyobservedwearintwolocalisedregionsonthedieradius.Moredetailedexaminationoftheworndieradiussurface,throughmeasurementofsurfaceroughness(ChristiansenandDeChiffre,1997),determinationofweardepth(Eriksen,1997)andscanningelectronmicroscopeimaging(Boheretal.,2005),hasalsoconfirmedtheexistenceofsimilarlocalisedwearregions.

Inadditiontotheexperimentalanalyses,Mortensenetal.(1994),HortigandSchmoeckel(2001)andAttafetal.(2002),eachconductedfiniteelementanalysesofthebending-under-tensionprocess.Inallcases,thefiniteele-mentmodelspredictedtheexistenceofdistinctcontactpressurepeaksonthedieradiussurface,correlatingwellwiththeregionsoflocalisedwear.UsinginsitusensorsHanakiandKato(1984)andmorerecentlyCoubroughetal.(2002)experimentallydemonstratedthatsimilarcontactpressurepeaksexistatlocationsonthedieradiusneartheentryandexitofthestripduringthebending-under-tensiontest.

Itisevidentthatdespitecoveringawiderangeofdiematerials(bothcoatedandun-coated),lubrication,surfaceroughness,bendratioandwork-piecematerials,eachofthe

studiesdiscussedintheprecedingparagraphswerefoundtoexhibitsimilarcharacteristictwo-peakcontactpressuredistributionsandlocalisedregionsofwearoverthedieradius.Theseresults,andthedocumentedpowerlawrela-tionbetweenwearandnormalloadforslidingcontacts(Rhee,1970),indicatethatcontactpressureisofprimarysignificancetothewearresponse.

1.2.Sheetmetalstamping

Thecontactconditionsoccurringduringsheetmetalstampingoperationshavenotbeenstudiedasextensivelyasthoseofthebending-under-tensionprocess.Throughfiniteelementanal-ysesofaxisymmetriccup-drawingprocesses,Mortensenetal.(1994)andJensenetal.(1998)identifiedthattime-dependantcontactconditionsoccuratthedieradius,asopposedtothe‘stationary’conditionsofthebending-under-tensiontest(HortigandSchmoeckel,2001).Inrecentnumericalstudiesonaplanestrainchannelformingprocess,Pereiraetal.(2007,2008)alsoreportedtime-dependantbehaviour.Complexcontactconditionsoverthedieradiuswerefoundtooccur,withregionsofhighlylocalisedandseverecontactpressure.SelectedresultsofthefiniteelementanalysisbyPereiraetal.(2008)aregiveninFig.1,wherethedynamicnatureofthecon-tactpressuredistributioncanbeseen.Additionally,theMisesstresscontoursshowthecorrespondingdeformationoftheblankandprovideanindicationofwhereyieldingoccurs.

Althougheachoftheaboveinvestigationsreporttime-dependantcontactconditionsforsheetmetalstampingprocesses,theauthorsineachcaseprovidelittleexplanationintothereasonsfortheidentifiedcontactbehaviour.Furtheranalysisofthisphenomenonhasnotbeenfoundintheliter-ature.

Fig.1–Misesstresscontoursandnormalisedcontactpressuredistributionspredictedbyfiniteelementanalysisatthethreedistinctstagesduringachannelformingprocess(seeSection4.1formoredetails).TheregionsinwhiteintheMisescontoursindicatevaluesofstressbelowtheblankmaterialinitialyieldstrength.

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1.3.

Motivation

Inordertounderstandtoolwearinsheetmetalstamp-ing,ortouserepresentativetests(bending-under-tension,slider-on-sheet,etc.)tocharacterisethewearresponseoftoolmaterialsandcoatings,knowledgeofthelocalcontactcondi-tionsthatoccurduringthestampingoperationisessential.Asdiscussed,thecontactpressureisofparticularsignificance.However,adescriptionoftheevolutionanddistributionofcontactstressesexperiencedbysheetmetalformingtool-ing,includinganexplanationforthisbehaviour,hasnotbeenfoundintheliterature.

Inthiswork,aqualitativedescriptionofthecontactpres-sureevolutionatthedieradiusandtheassociatedstressdistributionsintheblankduringachannelformingprocessisgiven.Thedescriptionisbasedonexperimentalobserva-tionsandtheresultsoffiniteelementanalyses.Throughananalysisofthedeformationconditions,contactphenomenaandunderlyingmechanics,itwillbeshownthatthreedis-tinctphasesexist.Duetotheuniquedeformationandcontactconditionsthatarefoundtooccur,theinitialandintermedi-atestagesexhibitlocalisedregionsofseverecontactpressure,withpeakcontactstressesthataresignificantlygreaterthantheblankmaterialyieldstrength.Thefinalstage,whichcanbeconsideredassteadystatewithregardstotheconditionsatthedieradius,correspondstoalargercontactareawithstableandsmallercontactpressures.

Itisnotedthatthemagnitudeofthecontactstresspeakswilldependonvariablessuchasbacktensiononthesheet,thedieradiustosheetthicknessratio,andtheclearancebetweenthepunchanddie.Theseeffectsarenotinvestigatedinthiswork.Theobjectiveofthisworkistoprovideanunderstandingofanimportantaspectofsheetmetalforming,ratherthanaquantitativeanalysisofaspecificcase.Thisshouldassistinunderstandingdiewear,whichisanincreasingproblemwiththeimplementationofhigherstrengthsheetinstampedautomotivecomponents.

2.Thesheetmetalstampingprocess

ThestampingordrawdieprocessisshownschematicallyinFig.2.Sheetmetalisclampedbetweenthedieandblank-holderandstretchedoverthepunch.Thesheetslidesoverthedieradiussurfacewithhighvelocityinthepresenceofcontactpressureandfriction,asitundergoescomplexbend-ing,thinningandstraighteningdeformation(Fig.2c).Inthemostrudimentaryanalysisofsheetmetalforming,bendingisneglectedandthedeformationisstudiedundertheactionofprincipaltensions(Marciniaketal.,2002).Thetensionistheforceperunitwidthtransmittedinthesheetandisaprod-uctofstressandthickness.Fortwo-dimensionalplanestraindeformationaroundthedieradius,thewell-knownanalysisindicatesthatthecontactpressurepisp=

TR=󰀆1R/t(1)

where󰀆1isthelongitudinalprincipalstress,Tisthelongitu-dinaltension,Risthedieradius,tisthesheetthickness,and

Fig.2–(a)Thebeginningofatypicalsheetmetalstampingprocess.(b)Themotionandforcesexertedbythetoolscausetheblanktobeformedintoachannelshapeduringthestampingprocess.(c)Forcesactingonthesheetatthedieradiusregion.

R/tthebendratio.Duetotheeffectoffriction,thelongitudinal

tensioninthesheetvariesalongthedieradius.Ifthetensionatonepoint,j,onthedieradiusisknown,thenthetensionatsomeotherpoint,k,furtheralongtheradiuscanbefoundaccordingto:Tk=Tjexp(󰀅Âjk)

(2)

whereÂjkistheangleturnedthroughbetweenthetwopoints,and󰀅isthecoefficientoffrictionbetweenthetoolandsheetsurfaces.

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Eq.(1)providesausefulrelationshipthatshowsthecontactpressureisinverselyproportionaltothebendratio.Giventhatthetensionisusuallyclosetotheyieldtensionandthatthebendratiointypicaltoolingisoftenlessthan10,Eq.(1)indi-catesthatthecontactstressisanappreciablefractionoftheyieldstress.Thisimpliesthattheassumptionofplanestressinthestripmaynotbevalid.Additionally,anumericalstudyofabending-under-tensionprocesswithabendratioof3.3revealedthattherestraintforcesattributedtobending(andunbending)werealmost50%ofthetotalrestraintforcesonthesheet(GrocheandNitzsche,2006).AlthoughEqs.(1)and(2)canbemodifiedtoincludetheworkdoneinbendingandstraightening,thesesimplemodelsareunlikelytoadequatelydescribethecontactpressuredistribution.

Furthermore,suchananalysisassumesthatthesheetslidescontinuouslyoverthedieradiusundersteady-state-typeconditionsanalogoustoabending-under-tensionprocess.However,asdiscussedinSection1,severalstudiesintheliteraturehaveshownthatthecontactconditionsarenotsteadyduringtypicalsheetmetalstamping.Forthesereasons,itisevidentthatamoredetailedanalysis,includingexamina-tionofthestressstatesandyieldinginthesheet,isrequiredinordertounderstandthecomplexandtime-dependantcontactconditionsatthedieradius.

3.Contactpressureatthedieradius

Inthiswork,aqualitativedescriptionofthedevelopmentofpeakcontactpressuresatthedieradiusforthechannelformingprocessshowninFig.2isgiven.Forsimplicity,thedeformationofthesheetisconsideredasatwo-dimensional,planestrainprocess.Alinear-elastic,perfectlyplasticsheetmaterialmodel,obeyingaTrescayieldcriterionisused.ThematerialcurveisshowninFig.3,wheretheflowstressisS,withzeroBauschingereffectonreverseloading.Itisassumedthatifthereisadraw-bead,itisatsomedistancefromthedieradiussothatthesheetenteringthedieradiusisundeformedbuthassometensionapplied.

Inthisstudy,thedeformationandcontactconditionsatthedieradiusforatypicalsheetmetalformingprocessaredividedintothreedistinctphases(Fig.4).Amaterialelementontheblank,PointA,isinitiallylocatedatthebeginningofthedieradius,asshowninFig.4a.Atthisinstant,contactislimited

Fig.3–Simplifiedplanestrainmaterialresponsewithreverseloading.

Fig.4–Threedistinctphasesofdeformationandcontact,whichoccurduringthechannelformingprocess:(a)initialdeformation,(b)intermediateconditions,and(c)steady-stateconditionsatdieradius.

toalineacrossthedieradius.Duringthenextstage,PointAhastravelledaroundthedieradius,buthasnotyetreachedtheexitortangentpoint(Fig.4b).Atthisinstant,thematerialintheside-wall(betweenthedieradiusandpunchradius)remainsstraightandhasnotpreviouslycontactedthetools.AstateofapproximatelysteadyconditionsatthedieradiusisreachedinFig.4c,wherePointAisnowintheside-wallregion.

3.1.Initialdeformation

Atthestartoftheformingstroke,contactbetweentheblankanddieoccursnearthestartofthedieradiusatanangleofÂ=˛,asshowninFig.5a.TheMohrcircleofstressatthecon-tactinginnersurfaceandthestressdistributionthroughthethicknessofthesheetaregivenschematicallyinthisdiagram.Theregionsofplasticdeformationinthesheetareindicatedbyshading.

ThesheetisbentbythetransverseforceFshown,sothatacompressivebendingstress󰀆1existsontheuppersurface.Duetotheinitiallackofconformanceoftheblanktotheradius,contactoccursalmostalongaline,resultinginacontactpres-sureP˛thatcanbeveryhigh.Asaresult,thenormalstress󰀆3,whichisequalto−P˛,isgreatestatthesurfaceanddiminishestozeroattheouter,freesurface.Atthislocation,approx-

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Fig.5–(a)Schematicoftheblanktodieradiusinterfaceduringtheinitialdeformationstage—thestressdistributionthroughthethicknessandtheMohr’scircleatthesurfaceofthecontactzoneareshown.Correspondingdistributionsaroundthedieradiusof(b)contactpressureand(c)bendingmomentinthesheet.

imatelyplanestressconditionsexistandthesheetyieldsundertensionattheplanestrainyieldstressS.Thetransversestress󰀆2attheinnersurfacewillhaveanintermediatevalue,sincetheprocessisplanestrain.Intheplasticcase,thisisthemeanoftheotherprincipalstresses.Intheelasticcase,thisisonlyapproximatelyso.

Thebendingstressandcontactpressureattheinnersur-facegenerateahighcompressivehydrostaticstress,suchthatyieldingcanbesuppressed(thediameteroftheMohrcircleisregion,wheretheinhibitingcompressivehydrostaticstressislower.Theresultisthataveryhigh-pressurepeakoccursatthecontactline,greaterinmagnitudethanthesheetyieldstress(Fig.5b).Thisinitiallinecontact,causingalocalisedpeakcontactpressure,isamomentaryevent.

3.2.Intermediateconditions

Asthepunchdrawsthesheettoslideintothediecavity,PointAmovesawayfromthestartoftheradius,asshowninFig.6a.Duetotheplasticbendingofthesheetthatoccursnearthebeginningofthedieradius,inthevicinityofÂ=0◦,themate-rialenteringthedieradiushasgreaterconformancewiththe

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Fig.6–(a)Schematicoftheblanktodieradiusinterfaceduringtheintermediateconditions—thestressdistributionthroughthethicknessandtheMohr’scircleatthesurfaceofthecontactzonesareshown.Correspondingdistributionsaroundthedieradiusof(b)contactpressureand(c)bendingmomentinthesheet.dieradiussurface.Thiscausesareductionincontactpressure,duetothechangefromlinecontactinFig.5toabroadercon-tactareainFig.6.Consequently,thecompressivehydrostaticstressisreducedandplasticdeformationattheblanksurfaceoccurs(thediameteroftheMohrcircleisS).

ThebendingmomentonthesheetisgreatestnearthePointA,asshowninFig.6c,suchthatthestripmaybeover-bentatthispoint,causingalossofcontactbetweenthesheetandthedieradius.Asimilareffectcanexistoverthenoseofthepunchinvee-diebending(Marciniaketal.,2002).Assuch,asecondcontactpointwiththedieoccursfurtheralongtheradius,atÂ=ˇ.PointA,whichbeganatthestartoftheradius,hasnotyetreachedthetangentpointatˇ.Hence,thematerialcurrently

atˇislargelyundeformed,despitethefactthattheangleofwrapoftheblankoverthedieradiusisrelativelylarge.Withsimilarcontactconditionstotheinitialdeformationstage,linecontactoccursatˇ.Asseenpreviously,theseconditionsresultinhighcontactpressure,largecompressivehydrostaticstress,andcansuppressplasticdeformationattheblanksurfaceassupportedbythecasestudyinFig.1b.

Fig.6bshowsthecontactpressuredistributionfortheinter-mediatestage.Themagnitudeofthecontactpressureatthestartoftheradiusislessthantheyieldstress,wherecon-tactisdistributedoverawiderarea.Conversely,asharppeakexistsatthetangentpointatˇ,wherethesheetisstillbeingbentandthecontactareaissmall.Inmanypunchanddie

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configurations,thepunchdisplacementneededtodrawthematerialfromthebeginningofthedieradius(PointAinthiscase)aroundtothetangentpointissignificant.Therefore,theintermediatephasemaybelongandthemaximumcontactangle,ˇmax,quitelarge.

3.3.Steady-stateconditionsatthedieradius

Steady-stateconditionsatthedieradiusarereachedwhenPointA,whichbeganatthestartofthedieradius,hasmoved

aroundandbecomepartoftheside-wall,asshowninFig.7a.Newmaterialisplasticallybentasitentersthedieradiusfromtheblank-holderregion.Here,thecontactpressureandstressdistributionsaresimilartothoseoftheintermediatestage,duetothebendingandconformanceoftheblanktothedieradius.Beyondthisregion,thesheetremainsincontactwiththediewithoutfurtherplasticdeformation,andtheresultingcontactpressureissmall.

Furtheralongtheradius,undertheactionofanincreasingoppositemoment,thesheetispartiallystraightened,where

Fig.7–(a)Schematicoftheblanktodieradiusinterfaceduringthesteady-statedeformationstage—thestressdistributionthroughthethicknessandtheMohr’scircleatthesurfaceofthecontactzonesareshown.Thestressdistributionthroughthethicknessattwolocationsintheside-wallregionisalsoshown.Correspondingdistributionsaroundthedieradiusof(b)contactpressureand(c)bendingmomentinthesheet.

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itlosescontactwiththedieradius.Asecond,smallercon-tactpressurepeakoccursatthelocationÂ=󰀃.Thispeakcanbeexplained,atleastinpart,byexaminingthesim-plifiedanalysispresentedinSection2.AccordingtoEq.(1),thecontactpressureisproportionaltothetensioninthesheet—whichitselfincreaseswithincreasingangleÂalongtheradius,accordingtoEq.(2).Therefore,thecontactpressureincreaseswithanglealongtheradius,causingapeakpressurenearthesheetexitpoint,indicatedbyP󰀃inFig.7b.Here,thesheetunloadselasticallyandthestressdistributionisshown(thediameteroftheMohrcircleisBeyondthecontactpressurepeak,thebendingmomentonthesheetbecomesreversed,asshowninFig.7c,andstraighteningbeginsatthetangentpoint.Thestraighteningprocesscontinuesbeyondthecontactpoint;theextentofwhichdependsonthetoolingconditionsandthetensiongen-eratedbytheblank-holder.‘Side-wallcurl’isawell-knownphenomenoninchannelformingandisgreatestwithsmallerblank-holdertension.Asaresultofthecurlintheside-wall,theangleofcontactislessthanintheintermediatestage,wheretheentireside-wallwasapproximatelystraight.Thisindicatesthatthereisaregiononthedieradiusthatonlymakescontactwiththeblankduringtheintermediatestage—i.e.anintermediate-onlycontactregion.

Itisworthemphasizingthat,despitetheapproximatelysteadycontactconditionsthatoccuratthedieradiusduringthisstage,theformingprocessitselfdoesnotreachatruesteadystate.Thisisbecausetheblankcontinuestoexperi-encesignificantdeformationanddisplacementasitisdrawnoverthedieradiusbytheactionofthemovingpunch.Asaresult,therewillbeacontinualreductionintheflangelengthandasubsequentchangingofcontactconditionsintheblank-holderregion.

4.Discussion

InSection3,aqualitativedescriptionofthedeformationandcontactpressureresponseatthedieradiusofasheetmetalstampingprocesswasgiven.Thissectionwilldiscusstheidentifiedresponse,withparticularreferencetoresultsfromotheranalysesintheliterature,comparisontothebending-under-tensionprocess,andwearatthedieradius.

4.1.Correlationwithfiniteelementmodelpredictions

Inrecentstudies,Pereiraetal.(2007,2008)usedfiniteelementanalysistoexaminethecontactpressureatthedieradiusforachannelformingprocess.A2mmthickhighstrengthsteelblankwasformedoveranR5mmdieradius(R/t=2.5),withapunchstrokeof50mm.ThecontactpressureresponsepredictedbyPereiraetal.(2008)wasre-plottedatthreedis-tinctinstancesinFig.1.Inthisfigure,thecontactpressureisnormalisedbytheconstantY,whichcanbeconsideredastheflowstressoftheblankmaterialifaperfectlyplas-ticapproximationofthematerialstress–strainresponsewasadopted(seeMarciniaketal.(2002)foranexplanationoftheapproximationmethodandcalculationofY).Assuch,theuseofthenormalisedcontactpressureallowsbettercomparisonbetweentheanalysisemployingablankmaterialwithcon-

siderablestrainhardening(Fig.1)tothatwhichassumestheblankmaterialhaszerostrainhardening(Figs.5–7).

ThenormalisedcontactpressuredistributionsinFig.1clearlydemonstratetheexistenceofthethreephasesiden-tifiedinSection3.Notably,thefirsttwostagesinSection3correspondtothesingletransientphasereportedinthepre-viousnumericalstudy(Pereiraetal.,2008).Thediscrepancyiscausedbythefactthattheinitialcontactstage,whichisamomentaryevent,iseasilyoverlookedwithoutadetailedanalysisofthedeformationandcontactconditionsoccurringatthedieradius.

TheresultsbyPereiraetal.(2007,2008)verifythattheini-tialandintermediatephasesoftheprocessresultinthemostsevereandlocalisedcontactloads.Fig.1showsthatattheregionsoflinecontact,identifiedinSections3.1and3.2,thepeakcontactpressuresarewellinexcessofY.Infact,themaximumcontactpressurefortheentireprocesswasfoundtooccurduringtheintermediatestage,withamagnitudeofapproximately3timesthematerial’sinitialyieldstrength(Pereiraetal.,2008).ExaminationoftheMisesstressplotsinFig.1attheregionsoflinecontactalsoconfirmthehypothesisofsuppressedplasticityduethelocalisedzonesoflargecon-tactpressure,andhencelargecompressivehydrostaticstress.

TheresultsinFig.1cconfirmthatthecontactpressureissignificantlyreducedduringthesteadyphase,withthemag-nitudeofpressurelessthanYduetotheincreasedcontactarea.Thefiniteelementresultsalsoshowthatthemaximumanglesofcontactbetweentheblankanddieradiusduringtheintermediateandsteadyphasesareapproximately80◦and45◦,respectively(Pereiraetal.,2008).Thisconfirmstheexis-tenceofanintermediate-onlycontactregion,correspondingtotheregionof45◦<Â≤80◦forthecaseexamined.

4.2.Comparisontothebending-under-tensiontest

Theidentifiedsteady-statebehaviouratthedieradiusduringthestampingprocessshowsnumeroussimilaritiestoatypicalbending-under-tensiontest.Forexample,thestressdistribu-tionsthroughthethicknessofthesheetshowninFig.7a,comparewelltothoseproposedbySwift(1948),inhisanalysisofaplasticbending-under-tensionprocessforarigid,per-fectlyplasticstrip.Additionally,theangleofcontactandshapeofcontactpressuredistributionspresentedinFigs.7band1c,showgoodcorrelationwiththeresultsrecordedbyHanakiandKato(1984)forexperimentalbending-under-tensiontests.

Theseparatefiniteelementstudiesofbending-under-tensionprocessesbyHortigandSchmoeckel(2001)andbyBoheretal.(2005)alsoshowsimilarlyshapedtwo-peakcontactpressuredistributions.Thedistributionsarechar-acterisedbylargeandrelativelylocalisedpressurepeaksatthebeginningofthecontactzone,withsmallerandmoredistributedsecondarypeaksattheendofthecon-tactzone.Additionally,theseinvestigationseachshowthattheangleofcontactissignificantlylessthanthegeomet-ricangleofwrap,confirmingtheexistenceoftheunbendingoftheblankandcurlthatoccursintheside-wallregion.Theseattributesofthebending-under-tensiontesthavedirectsimilaritiestothecontactpressureresponsepredictedbyPereiraetal.(2008)anddescribedpreviouslyinSection3.3,despitetheobviousdifferencesinmaterials,processes,

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bendratiosandbacktensionsconsidered.Althoughtherearenumeroussimilarities,directquantitativecomparisonbetweenthebending-under-tensiontestandthesteady-statephaseofthechannelformingprocesscannotbemade,duetothedifferencesintheapplicationofthebackandforwardtensions.

4.3.Contradictionswithfiniteelementmodelpredictions

AsstatedinSection1,therearealimitednumberofotherinvestigationsintheliteraturethatexaminethetime-dependantcontactpressureresponseofsheetmetalstampingprocesses.FiniteelementanalysesbyMortensenetal.(1994)andJensenetal.(1998)predictedthattime-dependantcontactconditionsdooccur.However,theseresultsdonotshowthesametrendsaspresentedinthisstudyandshownbyPereiraetal.(2007,2008)inpreviousfiniteelementinvestigations.Thissectionwillbrieflydiscussthepossiblereasonsforsuchdiscrepancies.

Firstly,consideringthefiniteelementanalysisofacup-drawingprocessbyMortensenetal.(1994),thepredictedcontactpressureoverthedieradiuswaspresentedatonlythreedistinctintervalsduringtheprocess.Bycomparison,Pereiraetal.(2008)recordedthecontactpressureatapprox-imately140intervalsthroughoutthefiniteelementresultshistory,inordertocompletelycharacterisethecomplexpressureevolution.Therefore,itislikelythatthetransienteffects,whicharereportedinthisstudy,werenotcapturedbyMortensenetal.(1994)duetothelimitednumberofinstancesatwhichthecontactpressurewasrecorded.

ThefiniteelementinvestigationbyJensenetal.(1998)examinedthecontactconditionsatapproximately100inter-valsduringacup-drawingprocess,butalsodidnotobserveasevereandlocalisedtransientresponse,asseeninthisstudy.(Significantlyvariedandlocalisedcontactconditionswereobservedattheendoftheprocess,butthesewereidenti-fiedtobeduetotheblank-rimeffect,andarenotrelevanttothisstudy.)CloseexaminationoftheresultsbyJensenetal.(1998)showthatsomelocalisedcontactconditionsdooccuratthebeginningoftheprocess—however,theseappearrela-tivelymildandwerenotdiscussedinthetext.Thisreducedseverityofthetransientresponse,comparedtothatpredictedbyPereiraetal.(2008),canbepartlyexplainedbythefactthattheactualcontactpressureatthedieradiuswasnotshownbyJensenetal.(1998).Instead,Zxt,whichwasdefinedtobeafunctionofcontactpressureandslidingvelocity,wasusedtocharacterisethecontactconditions.Thiscouldhaveeffec-tivelyreducedtheappearanceoftheinitiallocalisedcontactconditions,duetotheslowerslidingvelocityshowntoexistduringtheinitialstage.Additionally,Jensenetal.(1998)used20finiteelementstodescribethedieradiussurface,comparedto240elementsusedbyPereiraetal.(2008).Thereducednum-berofelementsatthedieradiussurfacecanhavetheeffectofaveragingtheextremelylocalisedcontactloadsoveralargerarea,thusreducingthemagnitudeoftheobservedcontactpressurepeaks.Finally,thedifferentprocessesexamined(cupdrawingvs.channelforming)mayalsoresultinadifferenttransientresponse.

4.4.Relevancetotoolwear

Wearisrelatedtocontactpressurethroughapowerlawrela-tionship(Rhee,1970).Therefore,theregionsofseverecontactpressureduringtheinitialandintermediatestagesmaybeparticularlyrelevanttotoolwearatthedieradius.ThefiniteelementinvestigationsbyPereiraetal.(2007,2008)showedthatthemaximumcontactpressurefortheentireprocessoccursintheintermediate-onlycontactregion,atapproximatelyÂ=59◦,indicatingthattheintermediatestageislikelytobeofprimarysignificancetothewearresponse.Thisresultwasval-idatedbylaboratory-basedchannelformingweartests,fortheparticularcaseexamined(Pereiraetal.,2008).

However,foreachstampingoperation,itcanbeseenthattherelativeslidingdistancebetweentheblankanddieradiusassociatedwiththeinitialandintermediatestagesissmall—i.e.nogreaterthanthearclengthofthedieradiussurface.Incomparison,thesteadycontactpressurephasecor-respondstoamuchlargerslidingdistance—i.e.theslidingdistancewillbeapproximatelyinthesameorderofmagnitudeasthepunchtravel.Therefore,despitethesmallercontactpressures,itispossiblethatthesteadyphasemayalsoinflu-encethetoollife;dependingontheprocessconditionsused(e.g.materials,surfaceconditions,slidingspeed,lubrication)andtheresultingwearmechanismsthatoccur.

Theexistenceofanintermediate-onlycontactzone(i.e.theregion󰀃<Â≤ˇmax),isconvenientforfuturewearanalyses.Duetothelackofslidingcontactinthisregionduringthesteady-statephase,anysurfacedegradationofthedieradiusatanglesofÂ>󰀃mustbeattributedtotheintermediatestageofthesheetmetalstampingprocess.Therefore,itisrecommendedthatfuturewearanalysisexaminethisregiontoassesstheimportanceoftheintermediatecontactconditionsontheoveralltoolwearresponseofthesheetmetalstampingpro-cess.

Theexistenceoftheinitialandintermediatestageshigh-lightthatthebending-under-tensiontest,duetoitsinherentlysteadynature,isunabletocapturethecompletecontactcon-ditionsthatexistsduringatypicalsheetmetalstampingprocess.Therefore,theapplicabilityofthebending-under-tensiontestforsheetmetalstampingwearsimulationmaybequestionable.

5.Summary

Inthiswork,aqualitativedescriptionofthedevelopmentofpeakcontactpressuresatthedieradiusforasheetmetalstampingprocesswasgiven.Itwasshownthatthreedistinctphasesexist:

(i)Atthestartoftheprocess,theblankisbentbytheaction

ofthepunchandahighcontactpressurepeakexistsatthestartofthedieradius.

(ii)Duringtheintermediatestage,theregionofthesheet

thatwasdeformedatthestartofthedieradiushasnotreachedtheside-wall.Therefore,theside-wallremainsstraightandthearcofcontactisamaximum.Thelargestpressure,whichissignificantlygreaterthanthesheetmaterialflowstress,existstowardstheendofthedie

journalofmaterialsprocessingtechnology209(2009)3532–31

31

radius,atthetangentpointbetweenthedieradiusandtheside-wall.

(iii)Thefinalstage,whichexhibitssteadycontactconditions

atthedieradius,occurswhenthematerialinitiallyatthestartoftheradiusreachestheside-wall.Thearcofcontactisreducedandthegreatestcontactpressureoccursatthestartofthedieradius.Thepeakpressureissignificantlylessthaninthepreviousstages.Thisanalysisallowsabetterunderstandingofthecontactconditionsthatoccuratthedieradiiofsheetmetalstamp-ingprocesses.Theresultswillassistfutureresearchintodevelopingandapplyingsuitableweartests,whichcorrectlyreplicatethecontactanddeformationconditionsoccurringintheactualstampingprocesses.Furtherworkisrequiredinordertoassesstheimportanceoftheidentifiedtransientcontactpressureresponseonthewearofthesystem.

Acknowledgments

ThisresearchwassupportedbyFordMotorCompanyUSA,FordofAustralia,VolvoCarsSwedenandbyanAustralianResearchCouncilLinkageProject(LP0776913).TheauthorsextendtheirgratitudetoProf.PeterHodgsonfromtheCen-treforMaterialandFibreInnovationatDeakinUniversityforhissupport.

references

Attaf,D.,Penazzi,L.,Boher,C.,Levaillant,C.,2002.Mechanical

studyofasheetmetalformingdieswear.In:Bergström,J.,Fredriksson,M.,Johansson,M.,Kotik,O.,Thuvander,F.(Eds.),Proceedingsof6thInternationalToolingConference.Karlstad,Sweden,pp.209–221.

Boher,C.,Attaf,D.,Penazzi,L.,Levaillant,C.,2005.Wear

behaviourontheradiusportionofadieindeep-drawing:identification,localisationandevolutionofthesurfacedamage.Wear259,1097–1108.

Christiansen,S.,DeChiffre,L.,1997.Topographic

characterizationofprogressivewearondeepdrawingdies.Tribol.Trans.40,346–352.

Coubrough,G.J.,Alinger,M.J.,VanTyne,C.J.,2002.Angleof

contactbetweensheetanddieduringstretch-bend

deformationasdeterminedonthebending-under-tensionfrictiontestsystem.J.Mater.Process.Technol.130–131,69–75.Eriksen,M.,1997.Theinfluenceofdiegeometryontoolwearin

deepdrawing.Wear207,10–15.

Groche,P.,Nitzsche,G.,2006.Reductionoffrictionindeep

drawingofaluminiumalloysbygeneratinglocal

hydrostatic-pressurelubrication.Proc.Inst.Mech.Eng.B220,43–48.

Hanaki,K.,Kato,K.,1984.Pressurepeakinbendingand

unbendingprocess.Adv.Technol.Plast.1,581–586.

Hortig,D.,Schmoeckel,D.,2001.Analysisoflocalloadsonthe

drawdieprofilewithregardtowearusingtheFEMand

experimentalinvestigations.J.Mater.Process.Technol.115,153–158.

Jensen,M.R.,Damborg,F.F.,Nielsen,K.B.,Danckert,J.,1998.

Applyingthefinite-elementmethodfordeterminationoftoolwearinconventionaldeep-drawing.J.Mater.Process.Technol.83,98–105.

Karima,M.,1994.Practicalapplicationofprocesssimulationin

stamping.J.Mater.Process.Technol.46,309–320.

Marciniak,Z.,Duncan,J.L.,Hu,S.J.,2002.MechanicsofSheet

MetalForming,2ndedition.Butterworth-Heinemann,Oxford.Mortensen,J.,Dirks,J.,Christensen,P.,1994.Acombinedphysical

andnumericalsimulationoftoolperformancein

conventionaldeep-drawingoperations.In:ProceedingsofIDDRG18thBiennialCongress,Lisbon,Portugal,pp.233–240.Pereira,M.,Yan,W.,Rolfe,B.F.,2007.Modelingofcontactpressure

insheetmetalforming.Mater.Sci.Forum561–565,1975–1978.

Pereira,M.P.,Yan,W.,Rolfe,B.F.,2008.Contactpressureevolution

anditsrelationtowearinsheetmetalforming.Wear.doi:10.1016/j.wear.2008.04.042.

Ranta-Eskola,A.,Kumpulainen,J.,Sulonen,M.,1982.Comparison

ofstripdrawingtestsusedformeasuringsurfaceinteractionsinpressforming.In:Ligure,S.M.(Ed.),ProceedingsofIDDRG12thBiennialCongress.Italy,pp.165–174.

Rhee,S.K.,1970.Wearequationforpolymersslidingagainst

metalsurfaces.Wear16,431–445.

Sandberg,O.,Bustad,P.-Å.,Carlsson,B.,Fällström,M.,Johansson,

T.,2004.CharacterisationoftoolwearinstampingofEHSandUHSsteelsheets.In:ProceedingsofRecentAdvancesinManufacture&UseofTools&DiesandStampingofSteelSheets,Olofström,Sweden,pp.127–146.

Swift,H.W.,1948.Plasticbendingundertension.Engineering166,

333–359.