Hole flanging with ironing process of two-ply thick sheet metal Hole flanging with ironing process of two-ply thick sheet metal

Hole flanging with ironing process of two-ply thick sheet metal

  • 期刊名字:中国有色金属学会会刊(英文版)
  • 文件大小:174kb
  • 论文作者:HUANG Yuung-ming
  • 作者单位:Department of Mechanical and Computer-Aided Engineering
  • 更新时间:2020-11-11
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论文简介

Available online at www. sciencedirect.comSCIENCEz @oiREoT.Transactions ofonferrous M etalsSociety of ChinaScienceTrans. Nonferrous Met. Soc. China 17(2007) 221-227Presswww.csu.edu.cn/ysxb/Hole flanging with ironing process of two-ply thick sheet metalHUANG Yuung-ming(黄永明)Department of Mechanical and Computer-Aided Engineering, St. John's University,Taipei 25135, Taiwan, ChinaReceived 5 September 2006; accepted 31 December 2006Abstract: An incremental updated Lagrangian elasto-plastic finite element method(FEM) was employed to analyze the hole-flangingwith the ironing of circulate plates using a pre-determined smaller hole at the center of the two-ply sheet metals. An extended rmiantechnique was employed such that each incremental step size can be determined not only by the yielding of an element Gaussianpoint, but also by the change under the boundary conditions of penetration, separation, and the alternation of the sliding sticking stateof friction along the tool-sheet interface. Two-ply sheet metals are generally composed of metals that have different mechanicalproperties. Thus, the forming process of these materials is complicated. A number of experiments and simulations were performedusing a conical punch with a cone angle of 45*. The experimental results were compared with FEM simulated results. It is found thatusing the elasto-plastic FEM can effectively predict the generation process of the deformed shape until unloading. The calculatedsheet geometries and the relationship between punch load and punch travel are in good agreement with the experimental data.Key words: hole flanging; ironing; elasto-plasti; finite elerment method; sliding sticking friction .strain during the hole-flanging process. The result1 Introductionshowed that the strain path is independent of the punchshapes during the formation process, but that theHole-flanging is one of the important techniques ofmaximum punch load depends on the punch shapes.sheet metal forming, and has been used widely whenTAKUDA et al[4] used pure zirconium sheet to performmanufacturing industrial parts. After forming, thethe deep-drawing and bore expanding test in order toproducts are mainly offered for thread cutting to cary onobtain its basic formability. They also carried out awith second machining and coordinated as a strut whensimulation using the rigid-plastic FEM and the criterionconecting pipelines or supporting other parts[]. One of of ductile fracture to predict the forming limitation ofthe related studies is that of JOHNSON et al[2]. Theyzirconium sheet. The results showed that in the processperformed an experimental study on the deformation ofof deep-drawing and bore-expanding, the formingcircular plates leading to fracture of the lip in thelimitation of zirconium sheet would decreasehole-flanging process. They applied the plasticsignificantly along with the reduction in punch profileanisotropy of the Hill onto the plane stress condition toradius. The forming characteristics of hole-flanging withforecast the change in thickness along the edge ofironing for bimetal sheets have been studied recentlyexpanded hole on the sheet material and to discuss theusing a conical punch with a cone angle of 45° bydistortion patterm of the expanded hole of the curvingKUMAGAI et a[5]. Their experimental and simulatedflanged part after the sheet material was burst. They alsoresults demonstrate that rigid-plastic FEM candiscussed the influence of the plastic properties of theeffctively simulate the forming process. YAMADA etmaterial and processing geometry on hol-flanging.al[6] studied the effects of initial yield stress and strainTANG[3] proposed a finite element method(FEM) usinghardening on bore-expanding using the incrementalthe membrane shell theory while ignoring the bendingtheory. of nlastirity with 2 flat-headed cylindrical puncheffect. He used four different punch shapes, i.eto det中国煤化工tribution. WANG ethemispberical, ellipsoid, cylindrical and conical toal[7]|Y片C N MH G the flanged neck isanalyze the distribution of the sheet material's stress anddominanuy unuaxrdl accurung wU a utal strain membraneCorresponding nuthor: HUANG Yunng-ming; Tel: +86 886-28013131-6702; E-mail: hyming@milsu.du.cn222HUANG Yunng ming/Trans. Nonferrous Met. Soc. China 17(2007)theory of rigid-plasticity for analysing the stretch[K]{Ou}={OF}(2)flanging of a clamped sheet of anisotropic material usingwherea spherical punch. TAKUDA et al[8] examined thformability of bore expanding using the rigid-plastic[K]=Z {_[B][(DT]-[Q])[B]JV+FEM with the ductile fracture criterion to find thefracture initiation sites of sheets. JOHNSON et al[9- -10]E J.(E]T -[G)lE]dV(3)found that the lip always fractures at the outer edgeowing to excessive hoop tension and tensile instability{QF}=(S fs [N] idS)Ot(4)when a conical punch is used. Besides the plasticproperties of material, such as strain-hardening ananisotropy, which affect the formability in theIn these equations, [K] is the global tangent stiffnesshole-flanging process[1-12], other externa! influen-matrix, [D°] is the elemental elasto-plastic constitutivecing factors include the lubrication condition, the punchmatrix, [N] is the shape function matrix, [ B] is the strainshapes and the clearance between the punch andrate-velocity matrix, [叮] is the velocity gradient-velocitydie[13-15]. The effect of cone semi-angle of a truncatedmatrix, {Au} denotes the nodal displacement increment,conical punch on the limitation of formability in theand {△F} denotes the prescribed nodal force increment.process has not been explored.[Q] and [G] are defined as stress correction matrices dueIn this study, the elasto-plastic finite- element code,to the current stress states at any stage of deformation.developed from the updated Lagrangian formulation, wasadopted to simulate the hole-flanging with ironing2.3 Treatments of elasto-plastic and contact problemsprocess under variableparameter conditions. AnThe contact condition between tools and blank onexperiment from Ref.[5] was used to confirm theeach node should remain in the same state at the momentaccuracy of theoretical estimation and the formulaof one incremental deformation. In order to satisfy thisdeveloped using the elasto-plastic FEM.requirement, the r-minimum method proposed byYAMADA et al[17], is adopted and extended to treat the2 Description of basic theoryelasto-plastic and contact problem. The increment ofeach loading step is controlled by the smallest value from2.1 Variational principalr1 tor6, i.e.The variational principal, with respect to currentrmin* min{r, 2, r3, r4, r's, r6}(5)deformed material on the basis of an updated Lagrangianformulation using Jaumann rate of Cauchy stress, can bewhere r1 confirms that the state of the element stress isexpressed as[16]the same as that on the yielding surface when theelemental stress is greater than the yielding stress, r2 and「。-0emey)BegdV+ J,σxLa8LydV=r3 constrain the largest principal strain and the rotation」i8v,dS(1)increment, respectively, to the linear relation, r4 causesthe free nodes to contact the tools, rs causes the contactwhere σy=(σ;-Opσk +σxq) is the Jaumannnodes to depart from the tool surface, and re gives therate of Chaucy stress, σy is the Eluer stresses,altemation of a friction state from sliding to sticking for0g=-Ojp=+(i,j -ujs)is the anti- symmetricalthe contacted node along the tool-blank interface.rotation rate tensor, εy is the strain rate tensor,Ly=ijs =dv,/ax, the velocity gradient tensor, X is the3 Numerical analysisspatial fixed Cartesian coordinate, v;=i; is thevelocity of node, n is the rate of the nominal traction, VThe experimental setup and the analytical model ofand Sr are the material volume and surface where thehole-flanging with ironing process were developed undertraction is prescribed.axisymmetric condition. Because of the symmetry of theblank, only the right-half portions of the tools and work2.2 Finite element discretizationpieces were modeled. A conical punch with a cone angleAs the principle of virtual work rate equation andof 45° and a diameter (Dp) of 18.0 mm was used. Thethe constitutive relation are linear equation of rates, thesepunch had 2.0 mm land length and 1 mm punch cornercan be replaced by increments defined with respect toradiu中国煤化工n die profile radius.any monotonously increasing measure, such as the toolTheYHCNMHGFIch and the dies wasdisplacement increment.controdiameter of the diesFollowing the standard procedure of finite elements(Da). Setting the ratio of clearance to thickness (R=C/T)to form the whole global sifness matrix, we obtainat less than unity, ironing was applied to the blank.HUANG Yunng-ming/Trans. Nonferrous Met. Soc. China 17(2007)223An automatic mesh program was employed tocladding Cu faced the inner wall of the lip, while Type Agenerate the finite-element mesh grid. The finite-elementwas named for the process where the matrix Al faced themesh grids comprised the four-node-quadrilateralinner wall of the lip.element in four integration points for selective reducedintegration, which were efficient for axisymmetric metalCulforming. In this study, 96 elements and 125 nodes weremeshed. Fig.1(a) shows the profile of the die and punch,fAIand the initial shape and the finite- element mesh of theblank used in the calculation. In the local coordinates,a)(b)axis l denotes the tangential direction of the contactFig.2 Deformation types: (a) Type Cu; (b) Type Albetween the sheet material and the tool, while axis ndenotes the normal direction of the same contact.4 Results and discussionConstant coordinates (r, 2) and local coordinates (I, n)describe the nodal force, displacement and element'sFigs.3 and 4 indicate the relationship between thestress and strain.punch force and punch travel under Type Cu and TypeFig.1(b) shows the boundary conditions of theAl, respectively when the initial hole diameter Dm=9.0deformed geometry of the sheet at a certain stage of themm. Regarding Type Cu in Fig.3, when R-=0.99, thehole-flanging with ironing process. The boundaryFEM-simulated result is consistent with the experimentalcondition of the nodes will be changed as the hole-finding. When R=0.49 before the hole-flanging processflanging with ironing process proceeds.reaches the maximum punch load, the FEM- simulatedresult is consistent with the experimental finding.18.0mmNevertheless, after the drawing process reaches themaximum punch load, the FEM-simulated result is lowerthan the experimental finding. The reasons can be easilyBIexplained.PunchBlankbolder口一Experimental[5], R2=0.49土Specimen-FD下16- 0- - Experimental[s], R_=0.991一FEM, R=0.49.2- FEM, R~=0.66DieS: Punch_3一FEM, R2=0.99travelS=0DsS=10mmb)85/。时0wy2-Web4-Finished shape4812162024R=CITPunch travel/mmfig,1 Dimensions of tool geometry and initial shape withFig.3 Relation between punch force and punch travel (Type Cu,finite element mesh of sheet (田) and boundary conditions ofDm=-9.0 mm)deformed sheet geometry (b)After the hole-flanging process reaches theThe material characteristics of the bi-metallic sheetmaximum punch load, the ironing function is moremetals[5] analyzed in this simulation are listed in Table 1.obvious. In addition, paraffin base oil was used as theThe initial hole diameters (Dm) were 9.0, 10.0, 11.0,lubricating oil in the previous experiment[5]; with lower12.0, 13.0 and 14.0 mm. Fig.2 shows the deformationviscosity, this lubricating oil creates higher frictionaltypes, Type Cu was named for the process where theshear stress of iraninσ after the hnle-flanging process中国煤化工Table 1 Material characteristics of bi-metallic sheet metalsMH.CNMHG_.Sheet metalThickness/mmYield stress/MPaStress-- strain rciauon_ToIsson ranoclastic modulus/GPaCu0.8355σ=354(e+0.000 1)310.35115_A2.2030o=145(e+0.000 1).270.3224HUANG Yunng ming/Trans. Nonferrous Met. Soc. China 17(2007)20-Experimental[5], R-=0.49a)1一FEM, Dm=9.0 mm2- FEM, Dm=11.0 mm0一Experimental[5j, R_=0.9916-3一FEM, Dm=13.0 mm!- FEM, Re-0.492- FEM, R-=0.66子3- FEM, R-=0.99 p2-1。g824十000002a00g081262024416 20 24Punch travel/mmb).1一FEM, Dm=9.0 mmFig.4 Relation between punch force and punch travel (Type Al,2一FEM, Dm=1I.0 mm16Dm-9.0 mm)reaches the maximum punch load. Moreover, theexperimental load value calculated is larger than thesimulated one. The punch load value at R-=0.66 is closer3\2\1to the one when Re =0.99. However, the value is stillsituated between the correspondent values at R =0.49 andR=0.99.Regarding Type A1、 in Fig.4, when theclearance-thickness ratio Rc=0.99 and R_=0.49, the24FEM-simulated result is consistent with the experimentalfinding. In the experiment reported in Ref.[5], MoS2 wasFig.5 Punch force of hole-flanging with ironing process ofused as the lubricating oil because of its good lubricationType Cu (a) and Type Al (b) under different initial holeeect. Therefore, at R-=0.49 after the hole-flangingdiameters (R-=0.49)process reaches the maximum punch load, the frictionalshear stress almost maintains its definite value and theFig.6(a) shows the result of hole-langing ironingexperimental load will be lowered, thus keeping thprocess simulation of Type Cu when R-=0.49 andconsistency between the simulated computing value andDm=9.0 mm, indicating the deformed shape. The lastexperimental load value. There is another reason thatshape is the final shape using A and B as the unloadingaccounts for why the punch load of Type Cu in Fig.3 iscontraction points. Fig.6(b) denotes the nodal velocityhigher than that of Type A1 in Fig.4 when R=0.49. Atdistributions during forming. The last shape is the nodalthe end of the ironing process, partial aluminum, whichvelocity distributions after unloading. From the figure itis Type Cu's foundation will becorme the inner wall ofis clear that the sheet is slowly bent and slided into thehole- flanging, and cause the punch land to slide on thedies, then extruded and finally ironing formed by punchaluminum coated with the paraffin base oil to have aand die. The condition of the contact surface of sheet andpoor lubrication effect.tools, which may determine that the extended rmirFig.5 indicates the relationship between the punchtechnique can trace adequately the whole deformationforce and punch travel of hole-flanging ironing athistory of the hole- flanging with ironing process.different initial hole diameters when the clearance-Meanwhile,the correct deformation procedures ofthickness ratio of Type Cu and Type Al is Re=0.49. Withhole-flanging with ironing process can be obtained froma larger initial hole diameter, there is fewer sheet hangingthe nodal velocity dstributions. Fig 6(c) shows the resulton the die surface that will need ironing forming. So, theof hol-fanging with ironing process simulation of Typeforming can be accomplished with shorter punch travel.Comparing Fig6(c)At the same time, the maximum punch load receivedwith中国煤化Ieformation types andwith larger initial hole diameter is larger than that withclea:CHCNMH Gat influences on thesmaller initial hole diameter, because the hanging sheetformung cuuuluun.is shorter and has good rigidness, and thus will not beFig.7 shows the reltionship between the ironing lipbent or deformed easily.length (Hb), initial hole diameter, and clearance-thicknessHUANG Yunng ming/Trans. Nonferrous Met. Soc. China 17(2007)225(a(b)(c)(d)|S -2.0mm|S- 2.0mm|S-2.0mm|S-10.0 mmS= 10.0 mms=10.0mmS-10.0 mm|s-14.0mm1s-14.0mmS=14.0mm|S=14.0mmS-18.0mmS=18.0mmS 20.0mmAs 20.0mmS=19.2 mm/S-19.2 mm房s 20.0mm导s=20.0mmS-19.0mmJs-19.0mmFinishedFig.6 Hole-flanging with ironing process of Type Cu (R= -0.49, Dm-9.0 mm) and Type AI (R-=0.99, Dm=9.0 mm): (间) Deformedgeometries of Type Cu; (b) Nodal velocity distributions of Type Cu; (C) Deformed geometries of Type Al; (d) Nodal velocitydistributions of Type Ala)。Experiment[5], R.=0.49。Experiment[5], R。=0.49口Experiment[Si, R=0.66口Experiment[Sj, R-=0.666s Experiment[5], R-=0.826卜1ns Experiment[s], R~=0.82i 一FEM, R-=0.491- FEM,- FEM; Rc=0.49二FEM, R-0.662一FEM, R-=0.66FEM, R-=0.823- FEM, R-=0.82昌4 2°--g.。2-3'中国煤化工.'8 910市1213 1415.FHCNMHG- 14 15Dm/mmDm/mm .Fig.7 Relation between ironing lip lengths (H2) and itial hole diameter (Dm): (a) Type Cu; (b) Type AI226HUANG Yunng-ming/Trans. Nonferrous Met. Soc. China 17(2007)ratio. For Type Cu and Type A1, when R-=0.99, thethat for Type Cu, since partial matrix A1 opposed theironing lip length Hp is zero because the clearance (C)pressing of punch.between the punch and die is bigger than the thickness ofFig.9 indicates the cross-section of the simulatedsheet metal (T). Therefore, there is no ironing functionfinished lip with different clearance-thickness ratios Rctoward the outer wall. When R.=0.49, H of Type Cu andwhen Dm=9.0 mm. When R.=0.99, since C is large, onlyType A1 are almost equal because C; is much smallerpartial sheet will fit with the shoulder angle of dies.than T. With the sheet metal extruding between theWhen R-=0.99 and Re -0.82, it is observed that the innerpunch and die, ironing functions on the entire surface ofwall of the finished lip is curved; but when R-0.66 andthe flanging outer wall. H of Type Cu and Type A1 areR_=0.49, this curving disappears because the sheet isincreased along with the decrease in Dm and R. Whenextruded ironing between the punch and die. Therefore,R=0.66 and R-=0.82, H of Type Cu is greater than thathe ironing function can improve the shape ofof Type A1. In other words, ironing with Type Cu ishole-flanging process.easier than that with Type A1 because when ironing TypeAl, the aluminum of the flanging inner wall and punchwill do a whole process contacting forming.Fig.8 shows the respective impact of Type Cu and厂厂厂厂Type Al ironing on the drawing length Hs. As can be seen,the experimental results agree considerably well with theR2=0.49 R_=0.66 Rc=0.82 R=0.99(aFEM-simulated ones. The drawing length H, is inverselyproportional to R. In other words, ironing function iseffective in improving product's shape. Generallyspeaking, the chance of Type Cu's H, decreasing along厂厂厂尸with the increase in initial hole diameter is smaller thanR_-0.49R2=0.66 R-=0.82R_=0.99that of Type A1's. For Type A1, the chance of Hs(bdecreasing along with the decrease in Re is greater thanFig.9 Cross-sectional views of finished lip at variousclearance-thickness ratios (R) when Dm= 9.0 mm: (a) Type Cu;“间), Experiment[5], R_=0.49(b) Type Al。ExperimentiS]R=066. Experiment[siR-0.82- FEM, R_=0.49Fig.10 shows the cross-section of the simulated-FEM, R 0.66finished lip with change of Dm when R_=0.49. RegardingFEM, R_=0.82昌the forming of sheet with different initial hole diameters,3the thickness of cladding Cu sheet of Type Cu afterforming is thinner than that of Type A1. The explanationof the above result is that the material of Type A1 is in2contact with the punch during the forming consistentlyand burnished by the punch. The thickness of thecladding Cu in the finished lip of Type A1 tends todecrease with decreasing Dm. This tendency is caused byDm/mmthe burnishing of the hole edge in the early formingb), Experiment[5], Rc=0.49stages.。Experiment(5,, R-=0.66Experiment[s5], R:=0.826-- FEM, R=0.49- FEM, R-=0.66- FEM, R_=0.82直4Dm=9.0 Dm=10.0 Dm=12.0 Dm=14.02--____22f中国煤化工0g9101市12131415CN M H G.0 Dm=14.0Fig.8 Relation between drawing length (H) and initial holeFig.10 Cross-sectional views of finished lip at various initialdiameter (Dm): (a) Type Cu; (b) Type Alhole diameters when R-= 0.49: (a) Type Cu; (b) Type AlHUANG Yunng-ming/Trans. Nonferrous Met. Soc. China 17(2007)227Fig.11 shows the effects of R。on web angle andthe decrease in thickness of the cladding Cu is larger forflange angle. With small R, the spring-back of web andType Cu than for Type Al.flange will also be small, because the ones with small Rc3) Ironing can effectively improve the finishedwill have greater ironing effects on metal sheet thatshape of the hole- flanging.makes the spring-back of web and flange small to have4) The results of a forming load, coming from thebetter perpendicular look, which improves the shape ofinitial shape to the last deformed shape, demonstrate aproduct.suitable approximation between experimental findingsand theoretical calculations, which indicates that the20[(aentire deformation history can be succesflly traced.This information can be used as references for improving15the manufacturing process and the design of tools.References10-1] LANGE K. Handbook of the Metal Forming [M]. New York:McGraw-Hill, 1985: 512-516.5°二TypeCu2] JOHNSON w, CHITKARA N R, MINH H v. Deformation mode andtip facture during hole-flanging of circular plates of anisotropicmaterials [J]. Trans ASME J Eng Ind, 1977, 99: 738-748.3] TANG s C. Large clasto-plastic strain analysis of flanged hole0.40.60.81.01.2forming [0]. Comp Struct, 1981, 13: 363- -370.4] TAKUDA H, HATTA N. Numcrical analysis of formability of aRcommercially pure zirconium sheet in some sheet forming processes20| (b[]. Mater Sci Eng A, 1998, A242: 15-21.[5] KUMAGAI I, SALKI H, MENG Y. Hole flanging with ironing oftwo-ply thick sheet metals [0]. J Mater Pro Tech, 199, 89/90: 51-57.15-6] YAMADA y, KOIDE M. Analysis of the bore expanding test by theincremental theory of plasticity []. hnt J Mech Sci, 1968, 10: 1-14.7] WANG N M, WENNER M L. An analytical and experimental studyof stretch flanging [凹]. Int J Mech Sci, 1974, 16: 135 -143.8] TAKUDA H, MORI K, FUJIMOTO H, HATTA N. Prediction offorming limit in bore expanding of sheet metals using ductilefracture criterion []. J Mater Pro Tech, 1999, 92/93: 433-438.9] ,JOHNSON W, CHITKARA N R, IBRAHIM A H, DASGUPTA AK.s。- TypeCus- Type AIHole flangiging and punching of crclar plates with coially beadedcylindrical punches [J]. J Strain Analysis, 1973, 8: 228 -241.10] CHITKARA N R, JOHNSON w. Hole flanging and piercing of0.1.circular plates [J]. Sheet Metal Industries, 1974, 51: 635-637.1] LEU D. Finite-element simulation of hole-flanging process ofcircular sheets of anisotropic materials [0 Int J Mech Sci, 1996, 38:Fig.11 Effect of clearance-thickness ratio (R) on web angle (@)917-933.and flange angle (b)I2] TAKUDA H, KJKUCHI s, HATTA N. Formability of acommercially pure zirconium sheet [D. J Mater Pro Tech, 1998, 84:117-121.5 Conclusions13] LEU D, CHEN T, HUANG Y. lnfuence of punch shapes on thecllar-drawing process of seet metal [0]. J Mater Pro Tech, 199, 84:134-146.1) When producing Type A1, its matrix A1 sheet is[14] HUANG Y, CHIEN K. Influence of punch profile on the limitation ofalways the inner wall formed by hole flanging andformability in the hol-langing process [D. J Mater Pro Tech, 2001,burnished by a punch. When producing Type Cu,113: 720-724.although the cladding Cu is the inner wall of the lipI5] HUANG Y, CHIEN K. The formability limitation of thehole- flanging process [J]. J Mater Pro Tech, 2001, 117:43-51.formed by hole-flanging, partial matrix A1 will be turned16] MCMEEKING R M, RICE J R. Finite element formulations forto the same side of the cladding Cu. This overhang isproblems of large elatic-plastic deformation ]. Int J Solids601-606.increased when increasing initial hole diameter.Structures,1975,11- 606.2) During the process, the thickness of cladding Cu[17] YAMADA y, YOSHIMURA N, SAKURAI T. Plastic stress strainmatrix and is application for the solution of elasti-plastic problemswill decrease along with the increase in initial holeby the finite element method [J]. Int J Mech Sci, 1968, 10: 343 - 354.diameter, regardless whether it is Type Cu or Type Al.(Edited by CHEN Wei-ping)Apart from that, even with the same initial hole diameter,中国煤化工MHCNMHG

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