Sizeeffectondeformationbehaviorandductilefracturei

Materials&Design83(2015)400–412ContentslistsavailableatScienceDirectMaterials&Designjournalhomepage:⇑DepartmentofMechanicalEngineering,TheHongKongPolytechnicUniversity,HungHom,Kowloon,HongKongarticleinfoArticlehistory:Received2April2015Revised29May2015Accepted6June2015Availableonline19June2015Keywords:Micro-scaledplasticdeformationFlowbehaviorDuctilefractureSizeeffectFreesurfacerougheningabstractInmeso/micro-scaledplasticdeformation,materialdeformationandductilefracturearequitedifferentfromthoseinmacro-scale.Theroughnessofthefreesurfacesofworkpieceincreaseswithdeformationandthedecreaseofgrainnumberinthesamplethicknessdirection,leadingtothenonuniformityofspec-imenthickness.Theso-calledsizeeffectandfreesurfacerougheningmayinturnaffectthedeformationbehavior,ductilityandfracturemorphologyofthesamples.Toexplorethecoupledeffectofworkpiecegeometryandgrainsizeonmaterialflowbehaviorinmeso/micro-scaledplasticdeformation,uniaxialtensiletestofpurecoppersheetswithdifferentthicknessesandcomparablemicrostructurewasper-formed.Theexperimentalresultsrevealthatthematerialflowstress,fracturestressandstrain,andthenumberofmicrovoidsonfracturesurfacearegettingsmallerwiththedecreasingratioofspecimenthicknesstograinsize.Inaddition,themodifiedSwift’sequationandthecorrecteduniformstrainareclosertotheexperimentalonesconsideringthethicknessnonuniformcoefficientinducedbythefreesur-faceroughening.Furthermore,theobservationoffracturemorphologiesconfirmsthatthelocaldeforma-tioncausedbythefreesurfacerougheningleadstostrainlocalizationandadecreasedfracturestrainwhenthereareonlyafewgrainsinvolvedinplasticdeformation.©2015ElsevierLtd.Allrightsreserved.1.IntroductionWiththeubiquitoustrendofproductminiaturization,meso/micro-scaledpartshavebeenwidelyusedinmanyindustryclusterssuchaselectronics,automobiles,healthcare,aerospace,andbiomedicine[1–3].Particularly,thecopperalloymicropartsarewidelyusedinelectronicandcommunicationindustriesduetotheexcellentconductivityandgoodductilityofcopperalloy.Tofabricatecopperalloymicropartsefficiently,microformingisusedduetoitshighproductivity,lowcost,andthegoodmechan-icalpropertiesofmicroformedparts[4–6].However,whentheworkpiecegeometryisscaleddownfrommacro-scaletomeso/micro-scale,thematerialdeformationbehavior,fracturetoughnessandsurfacerougheningmayalsochangeaccordingly.Thedeformationbehaviorandductilefracturecanfurtheraffecttheformingperformanceanddefectformationduetothefewergrainsinthedeformationzoneandtherandomorientationandpropertydistributionsofindividualgrains.Thus,understandingofthesizeeffectanditsaffectedmaterialdeformationbehavior⇑Correspondingauthor.E-mailaddress:[e-mail](M.W.Fu).iscrucialtoproductqualityanddefectavoidanceinmeso/micro-scaledsheetmetalforming.Toexplorethesize-dependentmaterialflowandfracturebehavior,manyattemptshavebeencarriedout.Fan[7]investi-gatedthegrainsizeeffectontheductilefracturetoughnessofpolycrystallinemetalsandalloys,andproposedasemi-empiricalequationtodescribethedependenceoffracturetoughnessongrainsize.MichelandPicart[8]conductedthetensileandhydrau-licbulgingteststoevaluatethethickness-dependentflowstressofbrasssheets,andestablishedaconstitutivemodelbytakingintoaccountthesizeeffect.Kimetal.[9]studiedthefeature/specimensizeeffectandquantifieditviarelatingthesizeeffecttothefunda-mentalpropertiesofsingleandpolycrystallinedeformation.Sinclairetal.[10]exploredthegrainsizedependentwork-hardeningofcopperpolycrystals.Theyfoundthatthegrainsizeeffectisrelatedtotheinteractionbetweendislocationandgrainboundary,andthiseffectonworkhardeningdisappearsatalargestrainowingtothedynamicrecovery.Pengetal.[11,12]developeddifferentmaterialmodelsconsideringthesizeeffectinmicroformingprocess.Theybelievedthattheflowstressinmeso/micro-scalefallsinbetweenthoseofsinglecrystalandpoly-crystal.Inaddition,Molotnikovetal.[13,14]establishedaphysi-callybasedconstitutivemodeltorepresentthesizeeffectontensilestrengthconsideringbothmaterialmicrostructureandB.Meng,M.W.Fu/Materials&Design83(2015)400–4122©2015ElsevierLtd.Allrightsreserved.sheetthickness.Theystudiedtheeffectofsheetthicknessinmicrodeepdrawingprocessofcoarse-grainedandultrafine-grainedcop-persheets.Vollertsen[15]summarizedthesizeeffectonflowstress,tribology,sheetformabilityandformingprocessesinmeso/micro-scaledplasticdeformation.ChanandFu[16,17]exam-inedthegeometryandgrainsizeeffectsonthedeformationbehav-iorandductilefractureofcoppersheetviauniaxialtensiletest.Theyfoundthatflowstress,fracturestressandstrain,andthenumberofmicrovoidsdecreasewiththeratioofsheetthickness(t0)tograinsize(d0).ChenandNgan[18]investigatedthecoupledeffectofgrainandspecimensizesonthetensilestrengthofAgwires.Theyrevealedthatthestrengtheningeffectdependsonthespecimenshapeastheratiooft0/d0decreasesfromabout3.Luetal.[19]presentedanewmaterialmodelformicro-scaledplasticdeformationb