Effects of geometry and fillet radius on die stresses in stamping processes
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Effects of geometry and ®llet radius on die stresses in stamping processesJ.S.Sun,K.H.Lee *,H.P.LeeDepartment of Mechanical and Production Engineering,National University of Singapore,10Kent Ridge Crescent,Singapore 119260,SingaporeReceived 23February 1999AbstractThis paper describes the use of the ®nite element method to analyze the failure of dies in stamping processes.For the die analyzed in the present problem,the cracks at different locations can be attributed to a couple of mechanisms.One of them is due to large principal stresses and the other one is due to large shear stresses.A three-dimensional model is used to simulate these problems ®rst.The model is then simpli®ed to an axisymmetric problem for analyzing the effects of geometry and ®llet radius on die stresses.#2000Elsevier Science S.A.All rights reserved.Keywords:Stamping;Metal forming;Finite element method;Die failure1.IntroductionIn metal forming processes,die failure analysis is one of the most important problems.Before the beginning of this decade,most research focused on the development of the-oretical and numerical methods.Upper bound techniques [1,2],contact-impact procedures [3]and the ®nite element method (FEM)[4,5]are the main techniques for analyzing stamping problems.With the development of computer technology,the FEM becomes the dominant technique [6±12].Altan and co-workers [13,14]discussed the causes of failure in forging tooling and presented a fatigue analysis concept that can be applied during process and tool design to analyze the stresses in tools.In these two papers,they used the punching load as the boundary force to analyze the stress states that exist in the inserts during the forming process and determined the causes of the failures.Based on these con-cepts,they also gave some suggestions to improve die design.In this paper,linear stress analysis of a three-dimensional (3D)die model is presented.The stress patterns are then analyzed to explain the causes of the crack initiation.Some suggestions about optimization of the die to reduce the stress concentration are presented.In order to optimize the design of the die,the effects of geometry and ®llet radius are discussed based on a simpli®ed axisymmetric model.2.Problem de®nitionThis study focuses on the linear elastic stress analysis of the die in a typical metal forming situation (Fig.1).The die (Fig.2)with a half-moon shaped ingot on the top surface is punched down towards the workpiece which is held inside the collar,and the pattern is made onto the workpiece.Cracks were found in the die after repeated operation:(i)when the die punched the workpiece,there is crack initiation between the tip of the moon shaped pattern and one of the edges (Crack I);and (ii)after repeated punching,there is also a crack at the ®llet of the die (Crack II).The present work was carried out with the following objectives:(i)to establish the causes of the crack initiation;and (ii)to study the effects of geometry and ®llet radius.3.Simulation and analysis 3.1.3D simulationThe simulation is performed with the FEM code Abaqus [15].Two meshes are created for the die shown in Fig.3a and b.The 3D solid elements for the workpiece are C3D8(8-node linear brick)elements.There are about 4000nodes and 3343elements in the coarse mesh model,and 7586nodes and 6487elements in the ®ne mesh model.The boundary condition involves ®xing the bottom of the die,i.e.,U 2 0for all the nodes on the die bottom.A pressure of 200MPa is applied on the top surface of the half-moon pattern.Young's modulus is 200GPa and Poisson's ratio is0.3.Journal of Materials Processing Technology 104(2000)254±264*Corresponding author.Tel.: 65-874-2554;fax: 65-779-1459.E-mail address :mpeleekh@.sg (K.H.Lee).0924-0136/00/$±see front matter #2000Elsevier Science S.A.All rights reserved.PII:S 0924-0136(00)00540-9In order to analyze the principal stress concentration area in the region of Crack I,different cases are studied.Let the models shown in Fig.3a and b be Case 1.A new 3D model (Case 2)is used as shown in Fig.3c.The die is separated into three parts.The Abaqus command ÃCONTACT PAIR,TIED is used to tie separate surfaces together for joining dissimilar meshes.The advantage of this model is its convenience in changing the mesh of the half-moon pattern and its position.First,the half-moon pattern is moved 6mm towards the center (Case 3)as shown in Fig.3d.Second,the ®llet radius of the half-moon pattern is changed from 0to 0.5mm (Case 4)as shown in Fig.3e.3.2.Results and discussionFor the two meshes used in Case 1.The maximum principal shear stress (S12)distribution at the region of ®llet are shown in Fig.4a and b.The results show that the stress distribution patterns are the same for the two different meshes,and therefore,the convergence of the solutions is established.Altan and co-workers [14]have presented the stress analysis of an axisymmetric upper die.In their work,when the material of the workpiece ¯ows to ®ll the volume between the dies and collar,the contact surface of the die is stretched.At the area of the transition radius,the principal stresses change direction and reach high tensile values.According to their analysis,the fatigue failure is due to two factors:(i)when the stress exceeds the yield strength of the die material,a localized plastic zone generally forms during the ®rst load cycle and undergoes plastic cycling during subsequent unloading and reloading,thus micro-scopic cracks initiate;and (ii)tensile principal stresses cause the microscopic cracks to grow and lead to the subsequent propagation of the cracks.The V on Mises stress distribution is shown in Fig.5a.Very high stress occur in the half-moon and ®llet regions.If the contact pressure keeps increasing,plastic zones will form ®rst in these two regions.Fig.5b shows the maximum principal stress (SP3)dis-tribution pattern.In order to show the area of Crack I initiation,Fig.5c provides a zoomed view of the area.It is clear that a tensile principal stress (SP3)concentration of 25.5MPa exists between the half-moon pattern and the free edge and is the cause of crack initiation.Since Crack I propagates nearly normal to the 1±2plane,the direction of the stresses which cause the crack initiation must be parallel to that plane.Fig.5d shows the direction of the maximum principal tensile stress at node 145and con®rms Crack I is normal to the 1±2plane.Fig.1.A typical metal formingprocess.Fig.2.Die,Cracks I and II (unit:mm).J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264255Fig.3.Showing:(a)coarse mesh;(b)®ne mesh (top view);(c)parts of another mesh of the die;(d)moving the half-moon pattern to the center;(e)the half-moon pattern with varying ®llet.256J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264After repeated punching,Crack II initiates in the ®llet region,and gives rise to fatigue failure.The geometry in the local area is very similar to the case which Altan and co-workers [14]have analyzed.However,there are no contact stresses in that area for the present case,and Fig.5b shows that the maximum principal stresses are all compressive at the ®llet.Fig.5e shows that there is high shear stress (S12)concentration at the ®llet which is about 30MPa.The shear stresses seem to be the stresses which lead to the initiation and propagation of cracks.The results of the four cases (Cases 1±4)for the largest maximum principal stresses are listed in Table 1.When the number of elements for the half-moon pattern is increased from 10to 70,the largest principal stress at the position of Crack I initiation is increased by (30.5À25.5)/30.5 16%(Case 2).The principal stresses are very sensitive to the half-moon pattern.Cases 2±4show the effect of location of the half-moon and its ®llet radius.If the half-moon pattern is moved 6mm towards the center,the largest principal stress at the position of Crack I is reduced by (25.3À30.5)/30.5 À17%(Case 3).If the ®llet radius of the half-moon pattern is changed to 0.5mm,the principal stress is reduced (28.5À30.5)/30.5 À7%(Case 4).Therefore both these methodscanFig.4.Showing:(a)maximum principal shear stresses (S12)of course mesh in the ®llet region;(b)maximum principal shear stresses (S12)of ®ne mesh in the ®llet region.Table 1Comparison of the largest maximum principal stressesCase 1Case 2Case 3Case 4SP3max (MPa)25.530.525.328.5J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264257Fig.5.Showing:(a)the V on Mises stress distribution;(b)the maximum principal stress (SP3)distribution;(c)a zoomed view of maximum principal stresses (SP3);(d)displaying vectors of maximum principal stress (SP3);(e)shear stress (S12)distribution.258J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264reduce the stress concentration,the ®rst being more effec-tive.4.Effects of geometry and ®llet radius on die stress distribution 4.1.2D modelingIn order to optimize the die,the effects of geometry and ®llet radius on die stress distribution are discussed further.An axisymmetric model is used (Fig.6)for the analysis.Initially,the radius r 1of the inner cylinder is set to 10mm,the height h of the inner cylinder is set to 5mm,and the height H of the outer cylinder is set to 25mm.Also,r 2is the radius of the outer cylinder,and the ratio r 2/r 1is changed from 1.2to 1.5,2.0,3.0and 4.0.The radius R of the ®llet is changed from 2.0to 0.5mm,and h is changed from 5to 2and 0mm.The pressure is given as 200MPa at the top surface.The nodes at the bottom edge are ®xed,and all others are free to translate (except those on the axis in the radial direction).4.2.Results and discussionA total of 30cases were studied.Parameters that are varied include r 2/r 1ratio,h ,and ®llet radius R .These 30cases are shown in Table 2.For all cases,r 1is ®xed at 10mm and H is ®xed at 25mm.4.2.1.Effect of r 2/r 1The effect of varying the r 2/r 1ratio is examined for cases with the value of h ®xed at 5mm.Fig.7a±c with the value of h ®xed at 5mm and varying ratio of r 2/r 1shows that the maximum value of the principalstress (SP3)reduces with increasing r 2/r 1,and changes in position from a point on the surface to below the surface.This trend is re¯ected in Fig.8a.On the other hand,Fig.8b indicates that the maximum shear stress (S12)becomes larger with increasing ratio of r 2/r 1.The rate of this increase drops with increasing r 2/r 1.The shear stress patterns for some cases are shown in Fig.7f±h.4.2.2.Effect of height hThe effect of height h of the inner portion is examined for three cases with h 0,2and 5mm with R ®xed at 2mm.From Fig.8a,it can be seen that the maximum principal stress (SP3)increases marginally with increasing h up to r 2/r 1of 2,after which the trend is reversed.However,for large h ,the effect becomes less important.On the other hand,the maximum shear stress is higher with increasing h for the same r 2/r 1ratio.Stress patterns are shown in Fig.7a,d±f,i andj.Fig.6.Pro®le of the axisymmetric die model.Table 2List of the 30cases h (mm)R (mm)r 2/r 1 1.250.55220.52200.502r 2/r 1 1.550.55220.52200.502r 2/r 1 2.050.55220.52200.502r 2/r 1 3.050.55220.52200.502r 2/r 1 4.050.55220.52200.502J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264259Fig.7.Showing SP3for:(a)r 2/r 1 1.2,h 5mm,R 2mm;(b)r 2/r 1 1.5,h 5mm,R 2mm;(c)r 2/r 1 3.0,h 5mm,R 2mm;(d)r 2/r 1 1.2,h 2mm,R 2mm;(e)r 2/r 1 1.2,h 0mm,R 2mm;Showing S12for (f)r 2/r 1 1.2,h 5mm,R 2mm;(g)r 2/r 1 1.5,h 5mm,R 2mm;(h)r 2/r 1 3.0,h 5mm,R 2mm;(i)r 2/r 1 1.2,h 2mm,R 2mm;(j)r 2/r 1 1.2,h 0mm,R 2mm;Showing SP3for (k)r 2/r 1 1.2,h 5mm,R 0.5mm;Showing S12for (l)r 2/r 1 1.2,h 5mm,R 0.5mm.260J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264Fig.7.(Continued ).J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±2642614.2.3.Effect of ®llet radius RThe effect of ®llet radius R is examined for two cases with R 0.5and 2mm.The results are shown in Fig.8c and d.It can be seen that for r 2/r 1larger than 2,the maximum principal stress (SP3)is relatively insensitive to changes in the ®llet radius.For r 2/r 1ratio less than 2,a larger ®llet radius results in a larger principal stress.However,the changes in the principal stress are less drastic compared with the changes in the maximum shear stress (S12)shown in Fig.8d.From Fig.8d,it can be seen that the maximum shear stress nearly doubles when the ®llet radius is reduced from 2to 0.5mm for the same r 2/r 1ratio.Stress patterns are shown in Fig.7a,f,k andl.Fig.8.Showing:(a)SP3for r 2/r 1 1.2±4.0,h 0±5mm,R 2mm;(b)S12for r 2/r 1 1.2±4.0,h 0±5mm,R 2mm;(c)SP3for r 2/r 1 1.2±4.0,h 5mm,R 0.5and 2mm;(d)S12for r 2/r 1 1.2±4.0,h 5mm,R 0.5and 2mm.262J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±2644.2.4.Suggestion for optimum performanceBased on the above analysis,some possible optimum solutions for the axisymmetric model can be achieved,as below.1.Both the maximum principal stress (SP3)and maximum shear stress (S12)are larger with increasing h .Thus,h should be relatively small.2.With changes in R ,the values of SP3and S12show different trends.If the maximum principal stress is more likely the cause of die failure,R should be changed to a smaller value.Conversely,if the maximum shear stress is the cause,R should be larger.Generally speaking,the value of R should be between 1.5and 2.0for the dimensions used here.3.The effects of r 2/r 1on SP3and S12are signi®cant when r 2/r 1is less than 2.However,the trends are different.If the maximum principal stress is the cause of diefailure,Fig.8.(Continued ).J.S.Sun et al./Journal of Materials Processing Technology 104(2000)254±264263r2/r1should be changed to a larger value,otherwise r2/r1 should be smaller.5.ConclusionsThe®nite element code Abaqus has been used for die stress analysis.A3D model is used to analyze the different mechanisms of crack initiation.This method not only pre-dicts the causes of cracks,but also the direction of crack propagation.Subsequently,a2D model is used to study the effects of die geometry and®llet radius on the stress distribution. Some guidelines on die design are given.At the early stage of die design,the FEM can help to predict possible failure and to optimize die design so as to save cost and time.The results are valuable both in theoretical research and indus-trial application.References[1]W.Prager,P.G.Hodge,Theory of Perfectly Plastic Solids,Chapman&Hall,London,1951.[2]D.C.Drucker,Appl.Mech.Rev.7(1954)421.[3]Z.H.Zhong,Finite Element Procedures for Contact-impact Pro-blems,Oxford University Press,New York,1993.[4]C.H.Lee,S.Kobayashi,New solutions to rigid±plastic deformationproblems using matrix method,J.Eng.Ind.,Trans.ASME95(1973) 865.[5]S.Kobayashi,S.I.Oh,T.Altan,Metalforming and the Finite ElementMethod,Oxford University Press,Oxford,1989.[6]N.Rebelo,S.Kobayashi,A coupled analysis of viscoplasticdeformation and heat transfer.I.Theoretical consideration,Int.J.Mech.Sci.22(1980)699.[7]N.Rebelo,S.Kobayashi,A coupled analysis of viscoplasticdeformation and heat transfer.II.Applications,Int.J.Mech.Sci.22(1980)707.[8]J.J.Park,N.Rebelo,S.Kobayashi,Three-dimensional®nite elementanalysis of block compression,Int.J.Mech.Sci.26(1984)165. [9]J.J.Park,N.Rebelo,S.Kobayashi,A new approach to preformdesign in metal forming with the®nite element method,Int.J.Mach.Tool Des.Res.23(1983)71.[10]C.H.Toh,S.Kobayashi,Deformation analysis and blank design forsquare cup drawing,Int.J.Mach.Tool Des.Res.25(1985)15. [11]N.S.Kim,S.Kobayashi,Preform design in H-shaped cross sectionalaxisymmetric forging by the®nite element method,Int.J.Mach.Tools Manuf.30(1990)243.[12]B.B.Hwang,S.Kobayashi,Deformation characterization ofpowdered metals in compaction,Int.J.Mach.Tools Manuf.30 (1990)309.[13]M.Knoer,nge,T.Altan,Fatigue failure of cold forging:causesand possible solutions through fatigue analysis,J.Mater.Process.Technol.46(1994)57.[14]Y.Nagao,M.Knoerr,T.Altan,Improvement of tool life in coldforging of complex automotive parts,J.Mater.Process.Technol.47 (1994)73.[15]Hibbit,Karlsson,Sorensen Ltd.,Abaqus Manuals,Version5.7,1998.264J.S.Sun et al./Journal of Materials Processing Technology104(2000)254±264。
