22-09-2012, 12:52 PM
Three-dimensionalfiniteelementsimulationofmediumthickplatemetal
forming andspringback
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ABSTRACT
Degeneratedshellelementandmembraneelementhavebeenwidelyappliedinthinsheetmetal
forminganalysis.However,formediumthickplatemetalforming,especiallyinthecaseoftypical
double-sidedcontactproblemssuchaslocalbulgeformingorpurebendingwithasmallradius,these
two elementmodelscannotaccuratelysimulatenormalextrusiondeformationofthesheetmetal.In
this paper,anewfiniteelement(FE)solverbasedonthesolid-shellelementdynamicexplicitalgorithm
and implicitalgorithmisdevelopedforthesimulationofmediumthickplatemetalformingand
springback.Thesolid-shellelementmodelconsidersbendingeffectswithathickness-direction
multiple-pointintegrationapproach.Theviscousdampinghourglasscontrolalgorithmeliminatesthe
spuriousdeformationmodesactivatedbyin-planereducedintegration(RI).Thedoublesidedcontact
analysisconsideringthicknessvariationdescribestheextrusiondeformationinthethicknessdirection
accurately.Animprovedplane-stressconstitutivemodelinco-rotationalconfigurationtogetherwith
Hill’squadraticanisotropicyieldcriterionisemployedtoupdatethestressfield.Thesolid-shell
elementobtainsbothsolid-likeandshell-likebehaviourstosimulatelargemembranedeformation,
sheardeformationandrotation.Totesttheperformanceofthesolid-shellelement,somenumerical
examplesaretakenandcomparedwithexperiments.Thecomparisonresultsdemonstratethatthe
solid-shellelementmodeliscompetitiveenoughinthesimulationofmediumthickplatemetal
formingandspringback.
Introduction
In thefieldofthinsheetmetalformingsimulation,degener-
ated shellelementandmembraneelementarealwaysresearch
focuses fortheirhighcomputationalefficiencyandprecision.
However, intheprocessofmediumthickplate(T/R41/20, T is
the thickness,and R denotes theminimumcurvatureradiusofthe
middle surface)metalforming,theeffectsofnormalextrusion
deformation onformabilitypredictioncannotbeignored.In
recent years,a3Dsolid-shellelementmodelconsideringnormal
extrusion deformationofthesheetmetalhasattractedextensive
interests. Comparedwithdegeneratedshellelementandmem-
brane element,thesolid-shellelementhasseveralremarkable
characteristics asfollows:itemploysthesamegeometryconfig-
uration assolidelementandcontainstwomodes:hexahedron
and triangularprism;eachnodehasonlytranslationaldegreesof
freedom (DOF)butnorotationalDOFandthereforeitsgeometric
and kinematicdescriptionsaresimpler.
Hourglasscontrol
The applicationofRIintheplane xZ is themosteconomic
method forreducingcomputingtimeandmemoryconsumption.
In addition,thisintegrationschemeiseffectiveininhibiting
the transverseshearlockingandvolumelockingphenomena.
However, ontheotherhand,theuseofthelowerquadraturerule
leads torank-deficiencyofthestiffnessmatrix,whichwould
activate theundesirablezeroenergymodes.Here,theviscous
damping hourglasscontrolalgorithm [14] is adoptedtoeliminate
the spuriousdeformationmodesforitshigheffectiveness.The
essence ofthedampingalgorithmisthatastabilizingmatrixis
implicitly addedintothestiffnessmatrixtomakeitfullrank
Predictionofspringback
Two commonmethodsofpredictingspringbackareasfollows:
(1) Aftertheformingprocess,thediesmovealongthereverse
direction untiltheyareallseparatedfromtheblank,therefore,
the movementofdiesanddeformationofblankarefactually
simulated. Inthismethod,theexplicitincrementalmethodis
employed ingeneral.(2)Aftertheformingprocess,theeffectof
dies onblankdeformationisnotconsideredduringthespring-
back prediction.
Conclusions
A newFEsolverbasedonthesolid-shellelementdynamic
explicit algorithmandimplicitalgorithmisdevelopedforthe
simulation ofmediumthickplateformingandspringback.The
comparisons ofsimulationresultsandexperimentalmeasure-
ments demonstratethatthenewlydevelopedsolvershowsan
excellent performanceinlargedeformationanalysisandspring-
back predictionofthinsheetandmediumthickplatemetal.