Investigation on ductile fracture in fine-blanking process by finite element method

Vol.12 No. 5Trans. Nonferrous Met. Soc. ChinaOct. 2002[ Article ID ] 1003 - 6326( 2002 )05 -0941 -06.Investigation on ductile fracture in fine-blanking process byfinite element method'LI Yu-ming(李昱明), PENG Ying-hong(彭穎紅)( National Die and Mould CAD Engineering Research Center , Shanghai Jiaotong University ,Shanghai 200030 , China )[ Abstract ] In order to continuously analyze the whole fine-blanking process , from the beginning of the operation up tothe total rupture of the sheet-metal , without computational divergence ,a 3-D rigid visco-plastic finite- element method basedon Gurson void model was developed. The void volume fraction was introduced into the finite element method to documentthe ductile fracture of the sheet-metal. A formulation of variation of the rigid visco-plastic material was presented accordingto the virtual work theory in which both the ffcts of equivalent stress and hydrostatic pressure in the deformation processwere considered. The crack initation of the sheet was predicted and the crack propagation was geometrically fufilled in thesimulation by separating the nodes according to the stress state. Furthermore ，the influences of different state-variables onthe deformation process were also studied.[ Key words ] fine-blanking ; ductile fracture ; finite element method ; Gurson plastic potential[CLCnumber]TG38.[ Document code ]A1 INTRODUCTIONinto three phases9. During the first phase the punchmoves downward and elastic and plastic deformationsSheet metal forming is a widely used process intake place. In the period of the second phase , the cut-manufacturing industries , among which fine-blankingting edge of the punch penetrates the material and theprocess is the most advanced technique that offers andeformation accumulates until the limit shear strengtheffective and economical metal cutting. Similar as allof the material is reached and the material is sheared a-other blanking processes , fine blanking process ends inlong the cutting edge. The third phase consists of cracktotal rupture of the sheet metal as opposed at othergrowth and propagation and the operation ends whenprocesses such as stamping and drawing which arethe material is completely separated. From a numericalaimed at deforming the sheet plastically without rup-point of view , the main difficulty to simulate the fine-ture. At the same time , fine-blanking process is imple-blanking process is to describe the material behaviormented with triple-action tools :a punch , an indent-continuously from the beginning of the operation up toed V-ring , and an ejector to generate a concentratingthe complete rupture. A good description of the abovecompressive stress state and nearly pure shearing forcesstages of fine-blanking process requires the develop-to perform a bulk deformation of the blank in the nar-ment of reliable algorithms. Finite element method hasrow clearance zone between the punch and the die.recently been applied extensively in the numerical a-Comparing with the conventional blanking process andnalysis and is proved to be a powerful means. Thereother metal forming processes , the material behavior inhave been several investigations into the understandingfine-blanking process is submitted to more complexof the mechanics of fine-blanking processt[10-12], butstress and strain state , and is subject to ductile fracturethese investigations did not consider the fracture andand crack propagation phenomenat 21the studied problem was of two dimensions. Therefore ,The ductile fracture phenomena exist in manythese investigations are not sufficient to clarify the me-metal-forming processes , and the ductile fracture oc-chanics of the process and haven' t well simulated thecurs when the material is subject to too large plastic de-bulk deformation. Based on the above situations , theformation and stresses beyond the yield point. A lot ofpurpose of this paper is to propose a 3-D finite elementresearches have been done on the ductile fracture bymethod that is capable of numerically analyzing all theboth experimental observations”and theoretical analy-phases of the fine-blanking process without computa-sis4-8. However , the knowledge obtained so far ofthe ductile fracture is far to be sufficient and the relat-中國煤化工ed investigations in the fine-blanking process are muchTYHiCNMHGless , there is still much to do in this field as the ductilefracture plays an important role in the fine blanking2.1 Modeling of ductile fractureprocess. Fine-blanking process can be broadly dividedAccurate knowledge of the fracture process helps①[ Reee格揭o1 -10 -16 ;[ Aceped date 12001-121 -29942.Trans. Nonferrous Met. Soc. ChinaOct.2002to select a suitable damage model. Numerous authorsposed , and the elastic effect is neglected. Based on thehave studied different physical mechanisms leading toresolution of virtual work functional , the formulation ofthe final rupture't is well known that ductilevariation is expressed as : of all permissible kinematicfracture occurs on the micro-scale mainly by voids nu-compatible velocity fields v that satisfy the strain-ratecleation , growth and coalescence. In this study , thevelocity equations and the velocity boundary conditionsyield function proposed by Gurson' 20developed byat the loading surfaces , the real velocity field yieldsTvergarrd and Needleman' 21 ~23 ] by introducing materialthat the one-time functional of the work rate π is zero ,constants 91 ,92 , and 93 into the yield equation on con-that issidering the voids coalescence is written as :δπ=0(4 )andφcm(σj,σμ f)=(二)-(1 +qsf"(fY )+π=|σ_εwdV+→σmendV- |。 P'vds (5)2qJf*(f )cosh( 2 )=0(1 )where V is the plastic deformed volume of the materi-where σis the average macroscopic Cauchy stressal IEeq is the equivalent strain rate ,σm is the averagetensor , σM represents the equivalent tensile flow stressstress ,P is the force vector on the given force surfacein the matrix material disregarding local stress varia-S。. In the above formula , both the shearing force andthe hydrostatic pressure are considered. The void vol-tions ,σq= ( 3/2 )s;$; , is the macroscopic equiva-ume fraction is integrated into this formulation by usinglent stress ,where s; =σj-( 1/3 )σk , is the macro-the visco-plastic flow law :scopic Cauchy tress deviator ,and f is the current voidvolume fraction. 91 ,92 ,and 93 are material constantsεj=λ0φcrN( 6)dσjand their values are here suggested as 1.5 , 1.0 ,1.5where A is the visco-plastic multiplicative factor.respectively by Tvergarrd and Needleman.Functionf"( f ) that models the material fracture2.3 Matrix flow stressis expressed asThe rigid viscous-plastic material is adopted in(f≤f.)this analysis , and the isotropic flow stress of the matrixf"={f。+K(f-f.) (f.fr )σm=X εM)"(7)where f。 is the value of void volume fraction when thewhere C is the material constant ,m is the strain rateconnection of the voids start fr is the value of the voidcofficient. The parameters of the chosen material arevolume fraction when the material is fully damaged andtaken as C=814MPa ,and m=3. 50.K。is the voids growth acceleration factor. When thevoid volume fraction f approaches fp , the material lo-2.4 Modification of tool displacementcally loses its stress carrying capacity. The failureIn the rigid visco- plastic finite element method ,mentioned above is implemented in the numerical pro-the speed of the tool is set constant in all iterationcedure by freezing the evolution off after it reaches a .steps. Thus the current tool displacement of each itera-value close tofr , the conditionf =0.95fr is used in-tion step depends on the time increment △t of the cur-stead off =fr because as f- fF the macroscopic equiva-rent step. The time increment△t is an important factorlent stress σ一+0 causing numerical difficulties.that determines the coordinates of the nodes and theThe evolution of voids is presented by the com-state of the elements after each iteration step. In themonly used strain controlled criterion[24 ,25 ]which isrigid FEM , the time increment depends on the permis-proposed by Chu and Needleman(26] :sible volume loss rate , the most permissible strain and. f=(1 -f)esm +fthe stability of the convergenceIn this paper , thesa/2πbiggest time increment△tmx is designated to satisfy thecondition that the volume-loss rate is less than 3% andexp[Ey ]Je(3)guarantee the convergence stability of the FE program.The time increment△t is dependent on two aswhere fv is the volume fraction of the uniformly dis-pects :tributed small size particles , sn is the standard devia-中國煤化工nd the tool boundarytion of the distribution , εM is the equivalent plasticnost one node is allowedstrain-rate of the matrix , and ε。is a mean nucleationto tMYHC N M H Gools. The shortest timestrain. The values of.fv ,s。 ,and En are here set as 0.01 ,that the nodes need to touch the boundary of the tools0.1 and 0.3.is denoted as△t. If no node touch the boundary of thetools ,Otq =∞.2.2 Formulation of variation2 ) Fracturing of elementsIn thi3 n據s a rigid viscous-plastic FEM is pro-In each iteration step , at most one element is al-Vol. 12 No. 5Investigation on ductile fracture in fine-blanking process by finite element method . 943.lowed to fracture. If one element fractures ，fd= 0.95fp , which means after Ot2 from the beginningR4of the nth step , the element fractures. If no elementsfracture ,Ot2 =∞.On considering both the above aspects , the timeincrement can be determined by the following formula :If min( △t| ,Ot2 )