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CONTENTSLISTSAVAILABLEATSCIENCEDIRECTTHINWALLEDSTRUCTURESJOURNALHOMEPAGEWWWELSEVIERCOM/LOCATE/TWSFULLLENGTHARTICLEFINITEELEMENTANALYSISOFMATERIALOWINDIELESSCLINCHINGPROCESSANDJOINTSTRENGTHASSESSMENTMOSTAFAKSABRAATIA,MUKESHKJAINDEPARTMENTOFMECHANICALENGINEERING,MCMASTERUNIVERSITY,HAMILTON,ONTARIO,CANADAL8S4L7ARTICLEINFOKEYWORDSCLINCHINGDIELESSCLINCHINGFESIMULATIONABSTRACTINTHEPRESENTWORK,ANUMERICALINVESTIGATIONOFTHEEECTOFTHEBLANKHOLDERPARAMETERSONMATERIALOWANDTHENALGEOMETRYOFTHEDIELESSCLINCHEDJOINTISCONDUCTEDVARIOUSBLANKHOLDERDESIGNSASWELLASDIERENTPROCESSPARAMETERSAREUSEDTOOBTAINCLINCHEDJOINTSAXISYMMETRICNITEELEMENTFEMODELWASDEVELOPEDTOSIMULATEDIELESSCLINCHINGEXPERIMENTSAHYBRIDMATERIALMODELWITHAWEIGHTFUNCTIONBETWEENTHETWOCOMMONUSEDHARDENINGLAWS,SWIFTANDVOCE,WASUTILIZEDTOBETTERREPRESENTTHEMATERIALBEHAVIORINTHEFEMODELANOTHERHYBRIDMATERIALMODEL,REFERREDTOASEXTENDEDVOCEMODEL,WASALSOUTILIZEDINTHEFESIMULATIONANDTHERESULTSCOMPAREDWITHTHEWEIGHTFUNCTIONAPPROACHTHEWEIGHTFUNCTIONMATERIALMODELRESULTEDINSMALLERGEOMETRICINTERLOCKCOMPAREDWITHTHEEXPERIMENT,WHEREAS,THEEXTENDEDVOCEMODELLEDTOBETTERPREDICTIONOFEXPERIMENTALGEOMETRICINTERLOCKWITHANERROROFLESSTHAN5THERESULTSSHOWEDTHATTHEINTERLOCKFORMSDUETOALARGEMATERIALOWINTHEAXIALANDRADIALDIRECTIONSTHEINTERLOCKCANBEMAXIMIZEDBYCONTROLLINGTHEMATERIALTOOWINRADIALDIRECTIONINSTEADOFAXIALDIRECTION,BYDECREASINGBLANKHOLDERDEPTHALSO,DISTORTIONOFTHEBOTTOMOFTHEDIELESSCLINCHEDJOINTCANBEAVOIDEDBYACHIEVINGABOTTOMTHICKNESSOFATLEAST10OFTHETOTALSHEETTHICKNESSLASTLY,NITEELEMENTMODELSWEREALSODEVELOPEDTOPREDICTTHEJOINTSTRENGTHINSHEARANDPEELFAILUREMODES1INTRODUCTIONADHESIVEBONDING,WELDING,ANDMECHANICALFASTENINGARETHEMAINTECHNIQUESFORJOININGOFSHEETMATERIALS1MECHANICALFASTENINGPROVIDESSOMEADVANTAGESOVERTHEOTHERTWOTECHNIQUESINTERMSOFECIENCY,COST,QUALITYANDAPPEARANCEOFTHEJOINTS2MECHANICALJOININGCANBEFURTHERDIVIDEDINTOTWOCATEGORIES,IJOININGBYUSINGCONSUMABLEPARTSSUCHASRIVETS,ANDIIJOININGBYFORMINGSUCHASHEMMINGANDCLINCHINGCLINCHINGISARAPIDANDCLEANPROCESSWHERETWOORMORESHEETSARELOCALLYDEFORMEDBYUSINGPUNCHANDDIETOFORMAGEOMETRICALINTERLOCK35CLINCHINGCANBECARRIEDOUTWITHORWITHOUTMETALCUTTING6INFACT,THERECENTCLINCHINGOPERATIONSINVOLVENOMETALCUTTINGANDONLYREDISTRIBUTIONOFTHEMATERIALBYPLASTICOWINTHEVICINITYOFTHECLINCHEDREGIONDURINGGEOMETRICALINTERLOCKINGASSHOWNINFIG1A,THENECKTHICKNESSN,INTERLOCKDEPTHUANDBOTTOMTHICKNESSXARETHEMAINGEOMETRICPARAMETERSOFTHECLINCHEDJOINT7THEXPARAMETER,RSTINTRODUCEDBYVARIES6,8,ISAUSEFULPARAMETERFORINSPECTIONOFTHEJOINTINGENERAL,THEMAINLIMITATIONOFCONVENTIONALCLINCHINGISTHECREATIONOFSURFACESTEPSONBOTHSIDESOFTHECLINCHEDJOINTMANYATTEMPTSHAVEBEENMADETODECREASETHEHEIGHTOFTHEPROTRUSIONOFTHECONVENTIONALCLINCHEDJOINTBYSUBSEQUENTRESHAPING1012INTHISREGARD,ACOUNTERMEASURETOOLINGWASEMPLOYEDBYWENETAL13TOREDUCETHEPROTRUSIONHEIGHTBY50OFTHECONVENTIONALLYCLINCHEDJOINTWITHOUTAECTINGTHESTRENGTHOFTHEJOINTLAMBIASEETAL14HAVECONVENTIONALLYCLINCHEDCARBONBERREINFORCEDPOLYMERCFRPTOALUMINUMUSINGEXTENSIBLEDIESANDFOLLOWEDTHEPROCESSBYASECONDSTEPOFRESHAPINGUTILIZINGAPUNCHANDAATDIEDICULTYOFALIGNINGTHEPREFORMEDJOINTWITHTHEATTENINGPUNCHREPRESENTSTHEMAINDISADVANTAGEFORTHISAPPROACH9BORSELLINOETAL3SUGGESTEDUTILIZINGTWOATANVILSINSTEADTHESTUDYSHOWEDAPROMISINGRESULTINNOTONLYINREDUCEDPROTRUSIONHEIGHTBUTALSOININCREASEDJOINTSTRENGTHCOMPAREDTOTHECONVENTIONALCLINCHEDJOINTWITHOUTRESHAPINGCHENETAL15,16USEDAPAIROFATDIESWITHORWITHOUTTHEADDITIONOFRIVETTODECREASETHEHEIGHTOFTHEPROTRUSIONOFTHECONVENTIONALCLINCHEDJOINTCHENETAL17HAVEUTILIZEDATANDBUMPEDDIESTORESHAPETHECONVENTIONALLYCLINCHED5052ALUMINUMSHEETSWITHDIERENTTHICKNESSESALLOFTHEABOVERESHAPINGTECHNIQUESRESULTEDINANINCREASEINTHEPROCESSINGTIMEBECAUSEOFTHEEXTRASTEPTHATUTILIZESADIERENTTOOLINGINORDERTOMAKECLINCHINGMOREAESTHETICALLYAPPEALING,ANDWITHOUTINCREASINGTHEJOININGTIME,ANEWCLINCHINGTECHNIQUECALLEDHTTPS/DOIORG/101016/JTWS201803001RECEIVED28AUGUST2017RECEIVEDINREVISEDFORM10FEBRUARY2018ACCEPTED1MARCH2018CORRESPONDINGAUTHOREMAILADDRESSATIAMMCMASTERCAMKSATIATHINWALLEDSTRUCTURES127201850051502638231/2018ELSEVIERLTDALLRIGHTSRESERVEDTDIELESSCLINCHINGHASBEENDEVELOPEDDIELESSCLINCHJOININGISAONESTEPJOININGBYFORMINGPROCESSINWHICHAPUNCH,BLANKHOLDER,ANDAATANVILAREUSEDASSHOWNINFIG1BINDIELESSCLINCHINGTHESURFACESTEPSOCCURONLYONONESIDEOFTHEFORMEDJOINT,OFTENONTHEPUNCHSIDEOFTHEJOINT9,18HOWEVER,ATINYPROTRUSIONMAYBEFORMEDONTHEANVILSIDEOFTHEFORMEDJOINT19,20THEDESIGNEDGROOVEINTHEBLANKHOLDERINDIELESSCLINCHINGPLAYSANIMPORTANTROLEINCONTROLLINGTHEOWOFTHEMATERIALTOFORMTHEGEOMETRICINTERLOCK9THEUSAGEOFATANVILINSTEADOFADIEINDIELESSCLINCHINGNOTONLYIMPROVESTHEAESTHETICAPPEALOFTHEJOINEDCOMPONENTSBUTALSOREDUCESTHEJOININGTIMEANDDIEALIGNMENTISSUESTHEMAINDISADVANTAGEOFDIELESSCLINCHINGISTHATTHEPROCESSREQUIRESACOMBINEDMOVEMENTOFBLANKHOLDERANDPUNCHTHATMAKESTHETOOLSETMORECOMPLEX13UNLIKECONVENTIONALCLINCHING,THESTRESSSTATEATTHEBOTTOMOFTHEDIELESSCLINCHEDJOINTSHOWEDAREDUCTIONINTHECRACKSENSITIVITYOFTHECOMBINEDSHEETSBYMINIMIZINGTHEAMOUNTOFTENSILESTRESSDURINGTHEDEFORMATIONTHISREGIONISINFACTUNDERCOMPRESSION21THECOMPARISONOFTHESTRESSDISTRIBUTIONSSHOWEDTHATTHEREISSIGNICANTFIG1SCHEMEDRAWINGSSHOWINGTHEVARIOUSGEOMETRICPARAMETERSINACONVENTIONALCLINCHINGANDBDIELESSCLINCHING9TABLE1MECHANICALPROPERTIESOFAA7075ALUMINUMSHEETINT6ANDOTEMPERSTATESMECHANICALPROPERTIESFROMUNIAXIALTENSIONTESTSTEMPERDESIGNATIONMATERIALSTATE02YIELDSTRENGTHMPAUTSMPATOTALELONGATIONT6ASRECEIVED5806959OANNEALED17529515FIG2DIELESSCLINCHINGTOOLSETUPAPHOTOGRAPHFORTHEINSTALLATIONOFTHETOOLINGANDBSCHEMATICDRAWINGSHOWINGTHEPUNCH,BLANKHOLDERSHAPEANDCOMPRESSIONURETHANESPRINGFIG3A2DDRAWINGOFDIELESSCLINCHINGTOOLSSHOWINGXEDANDVARIABLEDIMENSIONSOFPUNCH,BLANKHOLDERANDATANVILALLDIMENSIONSAREINMMMKSATIA,MKJAINTHINWALLEDSTRUCTURES1272018500515501COMPRESSIVESTRESSASSOCIATEDWITHDIELESSCLINCHINGWHEREASTENSILESTRESSISPREDOMINANTINTHECASEOFCONVENTIONALCLINCHING,ESPECIALLYATTHEBEGINNINGOFTHEPROCESSHOWEVER,THETENSIONINTHENECKREGIONOFTHEDIELESSCLINCHEDJOINTISCOMPARATIVELYLARGERTHANTHETENSIONOFTHENECKREGIONOFTHECONVENTIONALCLINCHEDJOINT22INORDERTOFORMAGEOMETRICALINTERLOCK,THEDIELESSCLINCHINGREQUIREDMUCHLARGERFORMINGFORCECOMPAREDWITHCONVENTIONALCLINCHING21SHEARANDPEELTESTSARECOMMONLYUSEDINTHECHARACTERIZATIONOFSTRENGTHOFCLINCHEDJOINTS20THEEXPERIMENTSREQUIREDTOOPTIMIZEJOINTPARAMETERSTHATYIELDHIGHERSTRENGTHJOINTSCANBECOSTLYANDTIMECONSUMINGNUMERICALSIMULATIONVIANITEELEMENTFEMETHODOERSACOSTEECTIVE,ECIENTANDSYSTEMATICMETHODOFANALYZINGTHEEECTOFTOOLDESIGNANDMATERIALPARAMETERSONCLINCHINGPROCESS23DUETOTHESYMMETRICCONDITIONSOFTHECLINCHINGPROCESSINTERMSOFLOADINGANDBOUNDARYCONDITIONS,A2DAXISYMMETRICFEMODELWASBUILTTOPREDICTTHENALSHAPEOFTHEFORMEDJOINTALSO,THIS2DSHAPEOFTHEJOINTWASUSEDTODEVELOPAMORECOMPLEX,NONAXISYMMETRIC3DFEMODELTOCHARACTERIZETHEJOINTSTRENGTH24MANYPAPERSHAVEBEENPUBLISHEDTODESCRIBETHEFESIMULATIONOFCONVENTIONALCLINCHINGPROCESS23THEDIELESSCLINCHINGPROCESSISQUITERECENTANDCONSIDEREDAMORECOMPLEXPROCESSCOMPAREDTOCONVENTIONALCLINCHINGTHEREFORE,VERYFEWSTUDIESHAVEBEENCARRIEDOUTTOSIMULATETHEDIELESSCLINCHINGPROCESSTHEMAXIMUMEQUIVALENTPLASTICSTRAININDIELESSCLINCHINGCANBEVERYLARGE,OFTHEORDEROF5,WHEREAS,INCONVENTIONALCLINCHING,THEPLASTICSTRAINSAREONLYOFTHEORDEROFUNITY9SPECIALPROCEDURESARENEEDEDINTHEFESIMULATIONTODEALWITHSOLUTIONCONVERGENCEPROBLEMSATLARGEPLASTICSTRAINSINVOLVEDINDIELESSCLINCHINGINTHEPRESENTSTUDY,THEFOCUSISONANALYZINGTHEEECTOFCLINCHTOOLDESIGNANDFORMINGFORCEONTHEMATERIALOWANDNALGEOMETRYOFTHEDIELESSCLINCHEDJOINTASWELLASPOSTCLINCHJOINTSTRENGTHABETTERMATERIALMODELTOCAPTURETHELARGESTRAINWORKHARDENINGBEHAVIOROFAA7075SHEETISPROPOSEDTHISMATERIALMODELISTHENUSEDTOBUILD2DASWELLAS3DFEMODELSTOSIMULATETHEDIELESSCLINCHJOININGANDASSESSTHEPOSTSTRENGTHCHARACTERISTICSRESPECTIVELY2MATERIALANDMETHODSTHEMATERIALCHOSENFORCLINCHJOININGWASANAA7075OALUMINUMSHEETOF127MMNOMINALTHICKNESSTHESHEETMETALWASINITIALLYRECEIVEDINTHEPEAKAGEDT6TEMPERSTATEINORDERTOENHANCEITSLOWDUCTILITYINTHEPEAKT6CONDITION,THESHEETWASPARTIALLYANNEALEDBYHEATINGTO413CFOR1HINAFURNACEUNIAXIALTENSILETESTSWERECONDUCTEDTOASSESSTHEMECHANICALPROPERTIESOFTHEMATERIALUSINGINSTRUMENTED,SCREWDRIVEN,INSTRONUNIVERSALTESTINGMACHINEOF100KNLOADCAPACITYATACROSSHEADSPEEDOF1MM/MINSUBSIZESAMPLEDIMENSIONSOF120MMLENGTH6MMWIDTH,ASPERTHEASTMSTANDARDE8M,WEREUTILIZEDFORTHEUNIAXIALTENSIONTESTSTHERESULTINGMECHANICALPROPERTIESINTHEASRECEIVEDT6ANDANNEALEDOTEMPERSTATESAREPRESENTEDINTABLE1CLINCHINGPRIMARILYRESULTSFROMFORMATIONOFGEOMETRICINTERLOCK,ORSSHAPE,WHICHMAINLYDEPENDSONTHETOOLCONGURATIONTHETOOLSETINTHEPRESENTWORKINVOLVEDANANVIL,PUNCHANDBLANKHOLDERMADEOFTUNGSTEN,TUNGSTENCARBIDE,ANDTOOLSTEELRESPECTIVELY,DESIGNEDTOCONTROLTHEOWOFMATERIALINADDITION,ACYLINDRICALURETHANESPRINGOF25MMLENGTHAND25MMAND125MMOUTERANDINNERDIAMETERSRESPECTIVELYWASINCORPORATEDINTOTHETOOLSETTOAPPLYTHECLAMPINGFORCESEEFIG2ADETAILEDDRAWINGOFTHETOOLINGUTILIZEDINTHISSTUDYISSHOWNINFIG3THETOTALCLAMPINGFORCEWASDETERMINEDBYTHESTINESSOFTHEURETHANESPRINGANDITSINTERACTIONWITHTHECASETHECLAMPINGFORCEWASMEASUREDEXPERIMENTALLYASAFUNCTIONOFPUNCHSTROKEBYUSINGAPUNCHWITHOUTATIPTOAVOIDINTERACTIONBETWEENPUNCHTIPANDSHEETSFIG4SHOWSTHEEXPERIMENTALLYMEASUREDCLAMPINGFORCEPROLEASWELLASTWOOTHERCLAMPINGFORCEPROLESUSEDFORSIMULATIONPURPOSESSEESUBSECTION43LATER3FEMODELINGMETHODOLOGYDIELESSCLINCHINGPROCESSWASSIMULATEDBYINCORPORATINGTHEFIG4EXPERIMENTALANDTWOOTHERFEMODELBLANKHOLDERFORCEPROLESUTILIZEDINTHEPRESENTSTUDYFIG5TWODIERENTBLANKHOLDERDESIGNSUTILIZEDINTHEFESIMULATIONOFDIELESSCLINCHING,ASTEPPEDEDGEBLANKHOLDERANDBROUNDEDEDGEBLANKHOLDERTABLE2BLANKHOLDERDESIGNPARAMETERSINTHEPRESENTSTUDYBLANKHOLDERTYPESTEPPEDEDGEROUNDEDEDGEPARAMETERRMMTMMRMMSMMRANGEOFVALUES47502125AND3515TABLE3MATERIALMODELPARAMETERSVOCEC1K1MPAM13194241904769SWIFT0K2MPAN0002485902071EXTENDEDVOCE0MPACMKMPAMPA14717160883424345MKSATIA,MKJAINTHINWALLEDSTRUCTURES1272018500515502FIG6EXTRAPOLATIONOFTHETRUESTRESSTRUEPLASTICSTRAINDATABYUSINGEXTENDEDVOCEASWELLASDIERENTWEIGHTFUNCTIONSFIG7AXISYMMETRIC2DFEMODELSETUPFORDIELESSCLINCHINGSIMULATIONWITHBLANKHOLDERCLAMPINGFORCEVERSUSTIMEPROLESHOWNABOVE,ASMODELINPUTDATAFIG8ACOMPARISONOFEXPERIMENTALANDFEPREDICTEDINTERLOCKSHAPESFROMDIERENTWEIGHTFUNCTIONSINTHESWIFTVOCEMIXEDHARDENINGLAWOFEQ2XPARAMETER10MKSATIA,MKJAINTHINWALLEDSTRUCTURES1272018500515503GEOMETRYOFTOOLING,SHEETTHICKNESS,SHEETELASTICANDPLASTICPROPERTIES,SHEETSHEETCONTACT,ANDFRICTIONBETWEENALLTOOLANDSHEETCONTACTINGSURFACESTHEABOVEGEOMETRIC,MATERIALANDPROCESSPARAMETERSCOULDBESTUDIEDBYSYSTEMATICALLYVARYINGTHEIRVALUESANDOBSERVINGTHEMATERIALOWANDTHEEVOLUTIONOFTHESTRESSSTATEOFTHESHEETWITHTHEPROGRESSIONOFTHEPUNCHGENERALLY,SUCHDETAILSAREQUITEDICULTTOSTUDYEXPERIMENTALLYDUETOVERYSMALLCLINCHINGAREA,NOTAMENABLETOCAMERAVIEWING,ANDTHEHIGHSPEEDOFTHEPROCESSTHECOMMERCIALFECODEABAQUSEXPLICITWASUSEDTOSIMULATETHEDIELESSCLINCHINGPROCESSTHISCODEWASPREFERREDOVEROTHERAVAILABLECODESDUETOITSABILITYTOSIMULATEMULTIPLETOOLSHEETANDSHEETSHEETINTERACTIONSTHATOCCURINCLINCHINGANDITSMOREROBUSTCONTACTALGORITHMANDSOLVERALSO,THEEXPLICITSOLVEREXHIBITSSIGNICANTTIMESAVINGOVERIMPLICITSOLVERASTHEMODELSIZEINCREASESANAXISYMMETRIC2DDIELESSCLINCHINGMODELWASDEVELOPEDDUETOTHEAXISYMMETRICNATUREOFTOOLING,THECLINCHGEOMETRY,ANDTHELOADINGCONDITIONSTHETOOLING,WITHTHEEXCEPTIONOFTHEURETHANESPRING,WASCONSIDEREDASRIGIDANDTHEBOUNDARYCONDITIONSWEREDENEDBYTOOLMOTIONSANDCONSTRAINTSTWODIERENTBLANKHOLDERTYPESWERECONSIDEREDINTHEANALYSIS,DENEDASSTEPPEDEDGEANDROUNDEDEDGEBLANKHOLDERS,ASSHOWNINFIG5,WHEREGROOVERADIUSRANDDEPTHT,ASRSTANDSECONDNUMBERSRESPECTIVELY,WEREUSEDTOREPRESENTVARIOUSSTEPPEDEDGEBLANKHOLDERSSIMILARLY,FORTHEROUNDEDEDGEBLANKHOLDER,RADIUSRANDLLETRADIUSSWEREUSEDASRSTANDSECONDNUMBERSRESPECTIVELYINTABLE2THESHEETMATERIALSWEREMODELEDUSING4NODEBILINEARAXISYMMETRICQUADRILATERALELEMENTSWITHREDUCEDINTEGRATIONCAX4RELEMENTINABAQUSEXPLICITANDENHANCEDHOURGLASSCONTROLOPTIONWASUTILIZEDTOAVOIDHOURGLASSINGPROBLEMSATLARGEPLASTICSTRAINSALARGENUMBEROFELEMENTSTHROUGHTHESHEETTHICKNESS,40INTOTAL,WEREUSEDTOMESHTHESHEETMATERIALSINTHECLINCHEDAREATOACCOUNTFORLARGETHROUGHTHICKNESSSTRAINGRADIENTPRESENTINTHEDIELESSCLINCHINGPROCESSALSO,ANASPECTRATIOOF13WASUTILIZEDTOMINIMIZEELEMENTDISTORTIONWHEREASPECTRATIOWASDENEDBYTHERATIOOFTHEELEMENTSIZEINAXIALANDRADIALDIRECTIONSTHEFEMESHSIZEINTHEAREAOUTSIDETHECLINCHINGREGIONWASKEPTRELATIVELYLARGE,TOTALING30ELEMENTSTHROUGHTHETHICKNESSWITHANASPECTRATIOOF025DUETOLARGEDEFORMATIONANDHIGHLYLOCALIZEDPLASTICSTRAININTHECLINCHREGION,ADAPTIVEREMESHINGOPTIONWITHVOLUMETRICSMOOTHINGWASUSEDTOPREVENTEXCESSIVEMESHDISTORTION,ANDANADVANCEDALGORITHMBASEDONEVOLVINGGEOMETRYWASIMPLEMENTEDTOATTAINSTABLENUMERICALSOLUTIONAMASSSCALINGFACTOROF100WASUSEDTOREDUCETHECOMPUTATIONALRUNTIMETHESHEETMATERIALWASASSUMEDTOBEISOTROPICELASTICPLASTICFOLLOWINGVONMISESYIELDCRITERIONANEXTENDEDVOCEHARDENINGLAWWASUSEDTOEXTRAPOLATETHEEXPERIMENTALPLASTICSTRESSPLASTICSTRAINDATAOBTAINEDFROMTHEUNIAXIALTENSILETESTBEYONDTHETENSILESTRESSSTRAINLIMITTOLARGESTRAINSCMEXPK1EQEQPEQP01WHERE,EQ,0ANDEQPAREEQUIVALENTSTRESS,INITIALYIELDSTRESSANDEQUIVALENTPLASTICSTRAINRESPECTIVELY,KISSTRESSCOECIENT,ANDCANDMARETWOOTHERMATERIALCONSTANTSTHETHIRDTERMONTHERIGHTSIDEOFEQ1,EQP,WASADDEDTODESCRIBECONTINUEDHARDENINGBEHAVIORATLARGERSTRAINS25THECOMMONLYUSEDSWIFTANDVOCEHARDENINGLAWSHAVEBEENFIG9ACOMPARISONOFEXPERIMENTALANDFEPREDICTEDSHAPEPROLESFORASTEPPEDEDGEBLANKHOLDER5/04ANDBSTEPPEDEDGEBLANKHOLDER5/02XPARAMETER10FIG10ACOMPARISONOFEXPERIMENTALANDFEPREDICTEDINTERLOCKREGIONSFORASTEPPEDEDGEBLANKHOLDER5/04ANDBSTEPPEDEDGEBLANKHOLDER5/02XPARAMETER10MKSATIA,MKJAINTHINWALLEDSTRUCTURES1272018500515504FOUNDTOBEINADEQUATEINREPRESENTINGTRUESTRESSSTRAINBEHAVIOROFMANYALUMINUMSHEETSMATERIALSATLARGESTRAINS26THEREFORE,AMODICATIONBASEDONUSEOFAWEIGHTFUNCTIONBETWEENTHESWIFTANDVOCEHARDENINGLAWSWASUSEDINTHISSTUDYASSHOWNBELOW|1|EQEQSWIFTEQVOCE2WHEREVOCECMEXPK1EQEQP1113ANDSWIFTKEQEQPN204INTHEABOVEEQUATIONS,K1ANDK2ARESTRENGTHCOECIENTSINEQS3AND4RESPECTIVELY,NISTHESTRAINHARDENINGEXPONENT,CANDMARETWOOTHERMATERIALCONSTANTS,ISAWEIGHTOFTHEFUNCTIONWITHVALUESINTHERANGE02509ITISTOBENOTEDTHAT,FORVALUESOF0AND1,THEMIXEDHARDENINGLAWOFEQ2REVERTSSIMPLYTOVOCEANDSWIFTLAWSRESPECTIVELYTABLE3PRESENTSTHEVALUESOFHARDENINGPARAMETERSFORAA7075OSHEETFIG6SHOWSTHEEXTRAPOLATIONOFSTRESSSTRAINCURVESTOLARGEPLASTICSTRAINSBYUSINGDIERENTWEIGHTFUNCTIONSINEQUATIONASWELLASANOTHEREXTENDEDVOCELAWTHEEXPERIMENTALLYMEASUREDCLAMPINGFORCEVERSUSPUNCHDISPLACEMENTPROLEASWELLASTWOOTHERTHEORETICALCLAMPINGFORCESWEREEMPLOYEDINTHEFESTUDYSEEEARLIERFIG4THEINTERACTIONBETWEENTOOLANDSHEETANDBETWEENTHETWOSHEETMATERIALSWASDESCRIBEDBYCOULOMBFRICTIONLAWFRICTIONCOECIENTVALUESOF015AND04WERECHOSENFORFRICTIONBETWEENSHEETTOOLSANDBETWEENTHETWOSHEETSRESPECTIVELYFROMTHELITERATURE27,28FIG7ILLUSTRATESTHEAXISYMMETRICMODELOFTHEDIELESSCLINCHINGSIMULATIONTHATALSOINCLUDESINPUTTHEAPPLIEDBLANKHOLDERCLAMPINGFORCEVERSUSTIMEPROLEATTHETOPFIG11EXPERIMENTALANDCORRESPONDINGFEPREDICTEDTHROUGHTHICKNESSCLINCHEDSHAPESFORASTEPPEDEDGEBLANKHOLDER5/04ANDBSTEPPEDEDGEBLANKHOLDER5/02XPARAMETER10FIG12ACOMPARISONOFPUNCHFORMINGFORCEVERSUSDISPLACEMENTTRACESFROMEXPERIMENTANDFESIMULATIONFORSTEPPEDEDGEBLANKHOLDER5/04XPARAMETER10FIG13FLOWSTRESSCURVESOFAA7075OSHEETATCROSSHEADSPEEDOF01AND10MM/MINMKSATIA,MKJAINTHINWALLEDSTRUCTURES12720185005155054RESULTANDDISCUSSION41FEMODELVALIDATIONFIG8DEMONSTRATESACOMPARISONBETWEENTHENALINTERLOCKSHAPEOFTHEDIELESSCLINCHEDJOINTOBTAINEDEXPERIMENTALLYANDFROMTHEFEMODELUSINGDIERENTWEIGHTFUNCTIONSINTHESWIFTVOCEMIXEDHARDENINGLAWOFEQ2ITISTOBENOTEDTHATALOWERVALUEOFTHEWEIGHTFUNCTIONIE,AHARDENINGBEHAVIORCLOSERTOTHEVOCEMODELRESULTSININCREASESINBOTHTHEPREDICTEDNECKTHICKNESS“N“ANDTHEINTERLOCKDEPTH“U“ANDCLOSERTOTHEEXPERIMENTALVALUES,WITHANERROROFABOUT35ALSO,FROMEARLIERFIG6ITCANBENOTEDTHATATAPLASTICSTRAINOF1THEDIERENCEINPOSTNECKINGBEHAVIORBETWEENTHEWEIGHTFUNCTIONOF025ANDEXTENDEDVOCEMATERIALMODELOFEQ1ISRATHERSMALLHOWEVER,ATHIGHERSTRAINSTYPICALOFDIELESSCLINCHINGTHEDIERENCEINTHEMECHANICALBEHAVIORBETWEENTHETWOMODELSDOESBECOMELARGERFIG9SHOWSACOMPARISONOFTHENALGEOMETRYOFTHEDIELESSCLINCHEDJOINTBETWEENFEMODELINGUSINGEXTENDEDVOCEMATERIALMODELANDTHEEXPERIMENTALLYOBTAINEDJOINTSBYUSINGTWODIERENTSTEPPEDEDGEBLANKHOLDERSALSO,FIG10SHOWSANEXPANDEDVIEWOFTHECRITICALINTERLOCKREGIONFROMEXPERIMENTSANDSIMULATIONSTHETWOGURESSHOWAGOODPREDICTIONINTHENALSHAPEOFTHEDIELESSCLINCHEDJOINTFROMTHEEXTENDEDVOCEBASEDFEMODELWITHANERROROFLESSTHAN5SPECICALLY,THEEXPERIMENTUSING5/04AND5/02STEPPEDEDGEBLANKHOLDERSRESULTEDININTERLOCKDEPTHSOF0065MMAND005MMRESPECTIVELYCOMPAREDTO0062MMAND0047MMFROMFEPREDICTIONFIG11ALSOPRESENTSRATHERGOODAGREEMENTINTHROUGHTHICKNESSPROLESFROMEXTENDEDVOCELAWBASEDFEMODELANDEXPERIMENTHOWEVER,THEGURESHOWSARELATIVELYLARGEDIERENCEBETWEENOBTAINEDFERESULTSANDTHEEXPERIMENTALLYMEASUREDNALSHAPEOFTHEJOINTINTERMSOFTHESHAPEOFTHELIFT,ASSHOWNBYANELLIPSEDRAWNATTHEBOTTOMOFFIG11THISLIFTLIKELYARISESFROMTHEASSUMPTIONOFTREATINGTHETOOLSASRIGIDORUNDEFORMABLEINTHEFEANALYSISLASTLY,PUNCHLOADVERSUSDISPLACEMENTTRACESCOMPARINGOVERALLPROCESSBEHAVIORFROMEXPERIMENTALANDSIMULATIONCLINCHESAREPRESENTEDINFIG12FIGS812COLLECTIVELYINDICATEGOODOVERALLAGREEMENTBETWEENEXPERIMENTALANDNUMERICALRESULTSEXPERIMENTALLYOBTAINEDUNIAXIALTENSILETESTSTRESSSTRAINDATAFORAA7075SHEETWASUTILIZEDFOREXTRAPOLATIONOFSTRESSSTRAINCURVESTHEREAREBETTERMETHODSAVAILABLEINTHELITERATUREFOREXPERIMENTALLYDETERMININGSTRESSSTRAINCURVESOFSHEETMATERIALSSUCHASHYDRAULICBULGETESTSTHATPROVIDELARGERSTRAINSPRIORTOFAILURECOMPAREDTOTHEUNIAXIALTENSIONTESTEXTRAPOLATIONFROMSUCHDATAWOULDHAVEBEENBETTERTHANTHEUNIAXIALTESTDATAUTILIZEDINTHEPRESENTWORKALTERNATIVELY,AMULTILAYERUPSETTINGTESTCOULDHAVEBEENUSEDTOREACHLARGEREXPERIMENTALSTRAINSANDEXTRAPOLATIONFROMSUCHADATACOULDFIG14PLASTICSTRAINSPL11LEFTCOLUMNANDPL22RIGHTCOLUMNINTHECLINCHEDREGIONATPOINTSCORRESPONDINGTOPOSITIONSADINFIG12,FORASTEPPEDEDGEBLANKHOLDERMKSATIA,MKJAINTHINWALLEDSTRUCTURES1272018500515506ALSOHAVEBEENBETTER29HOWEVER,ANUPSETTINGTESTISALARGELYACOMPRESSIONTESTANDITDOESNOTQUITESIMULATETHESTRESSSTATEOFTHEDIELESSCLINCHINGWHERELARGETENSILESTRAINSEXISTALONGWITHCOMPRESSIVESTRAINSASDISCUSSEDEARLIERINTHEMANUSCRIPTSEEFIG13ALSO,THETESTCANBEINUENCEDBYFRICTIONBETWEENTHEPLATENSANDTHETESTSPECIMENASWELLASBETWEENTH
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