Sheet Metal Forming Processes Dorel Banabic Sheet Metal Forming Processes Constitutive Modelling and Numerical Simulation 123 Prof.Dr.Ing.DorelBanabic TechnicalUniversityofCluj-Napoca ResearchCentreonSheetMetal Forming–CERTETA 27Memorandumului 400114ClujNapoca Romania [email protected] ISBN978-3-540-88112-4 e-ISBN978-3-540-88113-1 DOI10.1007/978-3-540-88113-1 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2010927076 ©Springer-VerlagBerlinHeidelberg2010 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:FridoSteinen Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface The concept of virtual manufacturing has been developed in order to increase the industrialperformances,beingoneofthemostefficientwaysofreducingtheman- ufacturing times and improving the quality of the products. Numerical simulation of metal forming processes, as a component of the virtual manufacturing process, has a very important contribution to the reduction of the lead time. The finite element method is currently the most widely used numerical procedure for sim- ulating sheet metal forming processes. The accuracy of the simulation programs used in industry is influenced by the constitutive models and the forming limit curves models incorporated in their structure. From the above discussion, we can distinguish a very strong connection between virtual manufacturing as a general concept, finite element method as a numerical analysis instrument and constitutive laws, as well as forming limit curves as a specificity of the sheet metal forming processes.Consequently,thematerialmodelingisstrategicwhenmodelsofreality havetobebuilt. The book gives a synthetic presentation of the research performed in the field of sheet metal forming simulation during more than 20 years by the members of three international teams: the Research Centre on Sheet Metal Forming—CERTETA(TechnicalUniversityofCluj-Napoca,Romania);AutoForm Company from Zürich, Switzerland and VOLVO automotive company from Sweden. ThefirstchapterpresentsanoverviewofdifferentFiniteElement(FE)formula- tions used for sheet metal forming simulation, now and in the past. The objective of this chapter is to give a general understanding of the advantages and disadvan- tages of the various methods in use. The first section is dedicated to some of the necessaryingredientsofthefundamentalsofcontinuummechanicsforlargedefor- mation problems. These are needed for a better understanding of the forthcoming FE-formulations. A more extended chapter is devoted to the presentation of the phenomenologi- cal yield criteria. Due to the fact that this chapter is only a synthetic overview of the yield criteria, the reader interested in some particular formulation should also readtheoriginalpaperlistedinthereferencesection.Wehavetriedtousethesym- bols adopted by the authors, especially in the mathematical relationships defining v vi Preface theyieldstressesandthecoefficientsofplasticanisotropy.Thisdecisionhasbeen madeinordertofacilitatethereadingoftheoriginalpapers.Ofcourse,underthese circumstances,thecoherencyofthenotationscannotbepreserved.Asonemaysee inthelistofsymbols,severalidentifiershavedifferentmeanings.Thereadershould takethisaspectintoaccount.Thischaptergivesamoredetailedpresentationofthe yieldcriteriaimplementedinthecommercial programsusedforthefiniteelement simulation(emphasizingtheformulationsproposedbytheCERTETAteam—BBC models—implementedintheAutoFormcommercialcode)ortheyieldcriteriahav- ingamajorimpactontheresearchprogress.Toimprovethespringbackprediction a novel approach to model the Bauschinger effect has been developed and imple- mented in the commercial code AutoForm. Consequently, an extended section of thischapterhasbeendedicatedtothemodelingoftheBauschingereffect,especially intheAutoFormmodel. The sheet metal formability is discussed in a separate chapter. After present- ingthemethodsusedfortheformabilityassessment,thediscussionfocusesonthe FormingLimitCurves(FLC).Experimentalmethodsusedforlimitstrainsdetermi- nationandthemainfactorsinfluencingtheFLCarepresentedindetail.Asectionis dedicatedtotheuseofFormingLimitDiagramsinindustrialpractice.Theoretical predictions of the FLCs are presented in an extended section. In this context, the authors emphasize their contributions to the mathematical modeling of FLCs. A special section has been devoted to present an original implicit formulation of the Hutchinson–Neale model, developed by the authors of this chapter, used for cal- culating the FLCs of thin sheet metals. The commercial programs (emphasizing theFORMCERTprogram)andthesemi-empiricalmodelsforFLCpredictionare presentedinthelastsectionsofthechapter. Theaspectsrelatedtothenumericalsimulationofthesheetmetalformingpro- cessesarediscussedinthelastchapterofthebook.Theroleofsimulationinprocess planning,partfeasibilityandquality,processvalidationandrobustnessarepresented based on the AutoForm solutions. The performances of the material models are provedbythenumericalsimulationofvarioussheetmetalformingprocesses:bulge andstretchforming,deep-drawingandformingofthecomplexparts.Asectionhas beendevotedtotherobustdesignofsheetmetalformingprocesses.Springbackis themajorqualityconcerninthestampingfield.Consequently,twosectionsofthis chapter are focused on the springback analysis and Computer Aided Springback Compensation(CASP). TheauthorswishtoexpresstheirgratitudetoDr.WaldemarKubli,founderand CEO, Dr. Mike Selig, CTO and Markus Thomma, CMD of AutoForm Company, fortheirsupportofthebookproject.Theyhavecreatedfavorableconditionsforthe AutoFormteaminordertomakethisbookpossible.Theauthorsalsowishtothank Dr.AlanLeacockfromUniversityofUlster(UK)forhishelpinproofingtheEnglish of the manuscript. Prof. Banabic wishes to express his thanks to his former PhD studentsDr.L.Paraianu,Dr.P.Jurco,Dr.M.Vos,Dr.G.Cosoviciandhiscurrent PhD students G. Dragos and I. Bichis for their help in preparing and editing this book. Preface vii Thebookwillbeofinteresttoboththeresearchandindustrialcommunities.Itis usefulforthestudents,doctoralfellows,researchersandengineerswhoaremainly interestedinthematerialmodelingandnumericalsimulationofsheetmetalforming processes. Cluj-Napoca,Romania DorelBanabic December2009 Contents 1 FE-ModelsoftheSheetMetalFormingProcesses. . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 FundamentalsofContinuumMechanics . . . . . . . . . . . . . . 3 1.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 StrainMeasures . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.3 StressMeasures . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 MaterialModels . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 FE-EquationsforSmallDeformations . . . . . . . . . . . . . . . 11 1.5 FE-EquationsforFiniteDeformations . . . . . . . . . . . . . . . 13 1.6 The ‘Flow Approach’—Eulerian FE-Formulations forRigid-PlasticSheetMetalAnalysis . . . . . . . . . . . . . . . 16 1.7 TheDynamic,ExplicitMethod . . . . . . . . . . . . . . . . . . . 18 1.8 AHistoricalReviewofSheetFormingSimulation . . . . . . . . . 21 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 PlasticBehaviourofSheetMetal . . . . . . . . . . . . . . . . . . . . 27 2.1 AnisotropyofSheetMetals . . . . . . . . . . . . . . . . . . . . . 30 2.1.1 UniaxialAnisotropyCoefficients . . . . . . . . . . . . . . 30 2.1.2 BiaxialAnisotropyCoefficient . . . . . . . . . . . . . . . 36 2.2 YieldCriteriaforIsotropicMaterials . . . . . . . . . . . . . . . . 39 2.2.1 TrescaYieldCriterion . . . . . . . . . . . . . . . . . . . . 41 2.2.2 Huber–Mises–HenckyYieldCriterion . . . . . . . . . . . 42 2.2.3 DruckerYieldCriterion . . . . . . . . . . . . . . . . . . . 43 2.2.4 HersheyYieldCriterion . . . . . . . . . . . . . . . . . . . 44 2.3 ClassicalYieldCriteriaforAnisotropicMaterials . . . . . . . . . 45 2.3.1 Hill’sFamillyYieldCriteria . . . . . . . . . . . . . . . . 45 2.3.2 Yield Function Based on Crystal Plasticity (Hershey’sFamilly) . . . . . . . . . . . . . . . . . . . . . 61 2.3.3 YieldCriteriaExpressedinPolarCoordinates . . . . . . . 74 2.3.4 OtherYieldCriteria . . . . . . . . . . . . . . . . . . . . . 75 2.4 AdvancedAnisotropicYieldCriteria . . . . . . . . . . . . . . . . 76 2.4.1 BarlatYieldCriteria . . . . . . . . . . . . . . . . . . . . . 77 2.4.2 Banabic–Balan–Comsa(BBC)YieldCriteria . . . . . . . 81 ix