Inhomogeneous deformation and residual stress in

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y201(2008)128–132j o u r n a l h o m e p a g e:w w w.e l s e v i e r.c o m/l o c a t e/j m a t p r o t ecInhomogeneous deformation and residual stress in skin-pass axisymmetric drawingHeng-Sheng Lin∗,Yuan-Chuan Hsu,Chia-Chow KehDepartment of Mechanical and Computer-Aided Engineering,National Formosa University,Hu-Wei,Yunlin632,Taiwana r t i c l e i n f oKeywords:Skin-passAxisymmetric drawing Inhomogeneous deformation Residual stress a b s t r a c tSkin-pass drawing is usually conducted in thefinal stage of wire,rod or shaped-section drawing or shape rolling.It helps improve shape accuracy and reduce residual stress of the drawn or rolled workpieces.However,its characteristic low reduction induces large -parameter,and causes significant inhomogeneous deformation in the workpiece.In this work,finite-element software DEFORM2D was utilized to investigate the effect of -parameter on inhomogeneous deformation and residual stress of mid-carbon steel through various combinations of area reduction and die semi-angle.The effect of the friction was also investigated.The results showed that the inhomogeneity factor of effective strain decreased with area reduction and increased with die semi-angle and friction.The level of inhomogeneous deformation could be reduced by drawing with small die semi-angle, and the influence of the friction was only substantial near the surface of the drawn work-piece.The axial and circumferential residual stresses would approach to compressive on the drawn surface in extreme light reductions.©2007Elsevier B.V.All rights reserved.1.IntroductionSkin-pass drawing is usually conducted in thefinal stage of wire,rod or shaped-section drawing or shape rolling.It helps improve shape accuracy and reduce residual stress of drawn or rolled workpieces.However,its characteristic low reduction induces large -parameter,and causes significant inhomo-geneous deformation in the workpiece.The -parameter is defined as=h(1)where h is the mean diameter of the workpiece and L is the contact length between the deforming workpiece and the die. The -parameter,though not perfectly,is a measure of the influence of the deformation geometry upon the drawn work-piece(Hosford and Caddell,1983).For axisymmetric drawing,∗Corresponding author.Tel.:+88656315311;fax:+88656315310.E-mail address:hslin@.tw(H.-S.Lin). can be expressed as=sin˛r(1+√1−r)2(2)where is the die semi-angle,r is the reduction of the cross-sectional area.Eq.(2)indicates that increases when ˛increases or r decreases.However,the small reduction used in skin-pass drawing intuitively bears a relatively large value and impairs its goal of improving shape accuracy.Backofen(1972)defines a hardness inhomogeneity factor to evaluate the level of inhomogeneous deformation asIF=H s−H cH c(3) where H s and H c are the Vickers hardness at the surface and center,respectively.This definition is suitable for experimen-tal approach,whereas in the FE simulation the distribution0924-0136/$–see front matter©2007Elsevier B.V.All rights reserved. doi:10.1016/j.jmatprotec.2007.11.126j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y201(2008)128–132129of hardness is not available.Since hardness is caused by thestraining of the material,and in order to facilitate the analysisof the data obtained from FE simulation,Backofen’s definitionof inhomogeneity factor is further modified asIFε=εs−εcεs(4)whereεs andεc are the effective strain at the surface and cen-ter,respectively.The denominator is replaced by the effective strain at the surface because the magnitude of the effective strain might approach to very small value for skin-pass draw-ing and cause the inhomogeneity factor of strain to approach to a quite large value.A larger IFεrepresents a larger discrep-ancy between the effective strain of the surface and center,i.e., a drawing condition with more inhomogeneous deformation. Through the definition of Eq.(4),the level of inhomogeneous deformation incurred by the process parameters can be read-ily analyzed by extracting the effective strain of the surface and center out of the FE simulation,without consorting to the experimental measurement of hardness.The definition of the inhomogeneity factor of hardness, Eq.(3),only takes into account the discrepancy of hardness between the surface and center of the drawn workpiece.It also assumes that the maximum hardness occurs on the surface and the minimum hardness occurs at the center.However, from the FE simulation of this work,it was observed that the effective strain does not necessarily increase monotonically from the center to the surface.The maximum effective strain might occur somewhere near the surface.Therefore a more objective definition,the mean variation of effective strain,was also applied to assess the level of inhomogeneous deformation which is defined as¯ε= ni=1|εi−¯ε|r2i−r2i−1r2f(5)where r i is the radius of the i th point,and i=0corresponds to the center and i=n corresponds to the surface;r f is the radius of the drawn workpiece.εi is the effective strain at point i, and¯εis the mean effective strain of the cross-section which is defined as¯ε= ni=1εi(r2i−r2i−1)r2f(6)Up to now,there has been abundant work reported for rod or wire drawing of medium reductions.However limited number of work was devoted to the drawing process of light reductions.This work focuses on investigating the relation-ship of the inhomogeneous deformation of effective strain as well as residual stress with the area reduction of the work-piece,the die semi-angle and workpiece/die friction condition byfinite-element simulation.2.Finite-element simulationFinite-element software DEFORM was used in simulating the skin-pass drawing process.Since the process is axisymmetric in nature,the2D Version8.0axisymmetric module was cho-sen.Mid-carbon steel AISI-1045was used as the workpiece material,and the built-in stress–strain relationship of elasto-plasticity at20◦C with yield strength640MPa was selected. Heat transfer effect was not considered.There were5000ele-ments used in meshing the workpiece,andfiner meshes were constructed close to the surface in order to better scope the “skin-pass”process.Billet length was20mm and the outlet diameter of the drawing die was10mm.Reduction of cross-section selected was from2to10%.Converging die was used and assumed to be rigid.Values of the die semi-angle are from 2to20◦.Die bearing length was4mm and the radius of thefil-let joining the bearing and the converging zone was0.2mm. The drawing speed wasfixed at67mm/s.The frictional law of constant shear strength was used and friction factors0.1,0.3 and0.5were ually drawing with a small friction factor corresponds to a forming condition of better lubrica-tion at the workpiece/die interface and vice versa.Drawing with the billet is unsteady at the beginning and near the end of the process.Steady values appear at the middle of the billet and satisfactory data acquisition of the drawing load,cross-sectional distributions of the effective strain and the residual stress can be obtained.3.Results and discussion3.1.Optimum die semi-angleThough minimizing drawing stress is not the primary consid-eration of skin-pass drawing,the evaluation of the optimum die semi-angle is still essential in understanding the char-acteristics of the process.Fig.1shows the variation of the normalized drawing stress with die semi-angle with area reductions ranging from2to10%.The normalized drawing stress was obtained by dividing the drawing load with the outlet area of the drawn workpiece and normalized with the yield strength of workpiece.The friction factor was0.1.For a selected reduction,the drawing stressfirst decreases and then increases with die semi-angle,as a consequence that the frictional work decreases and the redundant work increases with die semi-angle(Hosford and Caddell,1983).The angle which yields the minimum drawing stress is the optimum die semi-angle of the respective reduction.The optimum angle gradually increases from4to6◦as the reduction increases from2to10%.Same trends had been reported by Avitzur(1990)Fig.1–Variation of drawing stress with die semi-angle for various reductions.130j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 201(2008)128–132Fig.2–The influence of friction factor on the optimum angle.with larger reductions and incurring with larger optimum die semi-angles.The influence of friction on the optimum angle is shown in Fig.2with friction factors of 0.1,0.3and 0.5and for area reduc-tions of 2and 10%,respectively.A significant increase of the optimum angle from 6to 8and 10◦is observed in drawing with the higher reduction of 10%,whereas no significant increase of optimum angles is observed for the smaller reduction of 2%.In drawing with relatively low reduction,the decrease of the frictional work with die semi-angle becomes less sig-nificant because the contact length between the deforming workpiece and the die becomes relatively small.Therefore,the result suggests,on the basis of minimizing drawing stress,using a larger die semi-angle when the lubrication condition is poor,especially in drawing with larger reductions.However,the optimum angle remains unchanged with the lubrication condition in skin-pass drawing.3.2.Inhomogeneous deformation 3.2.1.Distribution of effective strainFig.3illustrates the distribution of effective strain for 2%reduction.Friction factor was fixed at 0.1.The distribution shows that the minimum effective strain occurs at the cen-ter and its value is close to its nominal cross-sectional area reduction.The maximum effective strain occurs near the sur-face of the drawn workpiece for the selected die semi-angle.The larger the maximum effective strain,the higher level of inhomogeneous deformation is produced by the drawing pro-cess.The difference in effective strain among therespectiveFig.3–Distribution of effective strain for 2%reduction.Fig.4–Distributions of effective strain for various reductions and frictionfactors.Fig.5–Variation of inhomogeneity factor with -parameter for various die semi-angles.die semi-angles is not significant near the center whereas near the surface the effective strain increases dramatically with larger die semi-angles.Such trend becomes less substantial when drawing with larger reductions.However,in drawing with smaller die semi-angles,e.g.2or 4◦,the increase in effec-tive strain is insignificant and the strain distribution becomes more uniform.The level of inhomogeneous deformation is hence reduced.The influence of friction on inhomogeneous deformation is illustrated in Fig.4.It shows the distributions of effec-tive strain in drawing with 6and 2%reductions,respectively and 8◦die semi-angle with various friction factors.The dis-tributions indicate that the effective strain at the center is not affected by the chosen friction factor,i.e.,the lubrication condition between the workpiece and the die.The influence becomes significant near the surface and the effective strain is the greatest with friction factor of 0.5,followed by that of 0.3and 0.1.The slight drop in the effective strain on the surface can reduce the discrepancy of the effective strain between the surface and center,and hence reduce the inhomogeneity of deformation.3.2.2.Correlating inhomogeneity factor with -parameterFig.5shows the inhomogeneity factor of effective strain plot-ted against -parameter for various die semi-angles.The definitions of the IF εand are given by Eqs.(4)and (2),respectively.The plot shows a monotonic increase of the inho-mogeneity factor of effective strain with -parameter for each die semi-angle selected.At large values of -parameter,all thej o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 201(2008)128–132131Fig.6–Variation of mean variation of effective strain with -parameter for various reductions.curves converge,indicating the level of inhomogeneous defor-mation is determined solely by the -parameter.However,at small values of -parameter,the curves diverge and the devi-ation becomes more obvious especially for drawing with 2◦die semi-angle.This indicates an identical -parameter would bear different levels of inhomogeneous deformation at small .Moreover,from the observation of the strain distribution of Fig.3,using the discrepancy of effective strain between the surface and the center was not an objective way in determin-ing the inhomogeneous deformation because the maximum effective strain might occur somewhere near the surface instead of at the surface.Therefore a statistical definition,the mean variation of effective strain,Eq.(5),is applied to assess the level of inhomogeneous deformation.Fig.6shows the mean variation of effective strain plotted against -parameter for various reductions.The plot shows that the statistical def-inition on the contrary leads to an even obvious deviation of inhomogeneity among each reduction selected,indicating the necessity of modifying the -parameter in correlating defor-mation inhomogeneity with the process parameters such as area reductions,die semi-angles and friction factor altogether.3.3.Residual stressResidual stress affects the geometrical precision of the drawn ually a residual compressive stress is desirable on the surface because it helps increase workpiece’s ability in resisting crack propagation and consequently increase work-piece’s service life.The distribution of residual stress is also affected by the selection of the process parameters like reduc-tion and die semi-angle and friction as well.Fig.7shows the distributions of axial residual stress of various die semi-angles at 6%reduction.The residual stress is normalized with yield strength,and the simulation also showed axial stress was more dominant than the circumferential stress.The axial residual stress exceeds its yield strength near the center and the surface of the drawn workpiece because of the work hard-ening effect.Residual stress becomes compressive near the center and tensile near the surface,and the level of resid-ual stress on the surface is minimum in drawing with 2◦diesemi-angle.Fig.7–Distribution of axial residual stress of various diesemi-angles.Fig.8–Residual stress becomes compressive on the surface at light reductions.Kuntani and Asakawa (2000)reported that axial residual stress was maximum in drawing with medium die semi-angle or medium reduction,which are the ordinary operation con-ditions in drawing.The axial residual stress would become compressive when the reduction is small.Fig.8shows the axial residual stress on the surface plotted against the -parameter of various friction factors in drawing with die semi-angle 8◦.The figure shows that the axial residual stress becomes compressive at reduction less than 0.4%,and the simulation also showed that the circumferential stress became compressive at reduction less than 0.3%.However,the relation between residual stress and friction factor was hardly to observe.The conditions of drawing with large die semi-angles were not simulated because of little relevancy in skin-pass drawing.4.ConclusionSeveral points can be drawn from the results of the simulation with DEFORM 2D as follows:(1)The evaluation of the optimum die semi-angle suggestedusing a large die semi-angle at high reductions and using a smaller angle at low reductions.When the lubrication condition was poor,the optimum die semi-angle would increase especially in drawing with larger reductions.132j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y201(2008)128–132However,the optimum angle remained unchanged with the lubrication condition in skin-pass drawing.(2)The minimum effective strain occurred at the center andwas close to its nominal cross-sectional area reduction of the drawn workpiece.The maximum effective strain occurred near the surface.The differences in effective strain in drawing with various die semi-angles were not substantial near the center whereas near the surface the effective strain increased dramatically in drawing with larger die semi-angles.In drawing with very small die semi-angles,the increase in effective strain was insignifi-cant and the strain distribution became more uniform.The level of inhomogeneous deformation was hence reduced.The effective strain at the center was not affected by the friction but increased significantly with the friction near the surface.The larger the friction,the more inhomoge-neous deformation was incurred on the drawn workpiece.(3)The plot of inhomogeneity factor of effective strainagainst -parameter showed all the curves converged at large values of -parameter,indicating the level of inho-mogeneous deformation was determined solely by the -parameter.However,the curves diverged at small val-ues of -parameter,indicating an identical -parameter would bear different levels of inhomogeneous deforma-tion at small .The deviation became more obvious when the mean variation of effective strain was plotted against -parameter,indicating the necessity of modifying the -parameters in correlating deformation inhomogeneity with the process parameters.(4)Residual stress was compressive near the center andbecame tensile near the surface of the drawn workpiece, and the level of residual stress on the surface was min-imum in drawing with2◦die semi-angle.The residual axial stress was more dominant than the circumferential stress.The axial residual stress became compressive on the drawn surface at reduction less than0.4%,and the circumferential stress became compressive at reduction less than0.3%.The relation between residual stress and friction factor was hardly to observe.AcknowledgementThe authors would like to thank thefinancial support of the National Science Council of the R.O.C.under the grant of NSC 93-2212-E-218-006.r e f e r e n c e sAvitzur,B.,1990.The use of the personal computer for simulation of the process of wire drawing and extrusion in an interactive, user-friendly mode.Wire J.Int.23,48–60.Backofen,W.A.,1972.Deformation Processing.Addison-Wesley, Reading,Mass,p.140.Hosford,W.F.,Caddell,R.M.,1983.Metal Forming:Mechanics and Metallurgy.Prentice-Hall.Kuntani,N.,Asakawa,M.,2000.Analysis of the residual stress induced by bar and wire drawing.SEAISI Q.(July),35–41.。