Numerical simulation and experimental investigation of incremental sheet forming process

J. Cent. South Univ. Technol. (2008) 15: 581- -587DOI: 10.1007/511771- 008 -0109- 5包SpringerNumerical simulation and experimental investigation ofincremental sheet forming processHAN Fei(韩飞), MO Jian-hua(莫健华)(State Key Laboratory of Material Processing and Dic & Mould Technology,Huazhong University of Science and Technology, Wuhan 430074, China)Abstract: In order to investigate the process of incremental sheet forming (IlSF) through both experimental and numericalapproaches, a three-dimensional elasto-plastic finite element model (FEM) was developed to simulate the process and the simulatedresults were compared with those of experiment. The results of numerical simulations, such as the strain history and distribution, thestress state and distribution, sheet thickness distribution, etc, were discussed in details, and the influcnces of process parameters onthese results were also analyzed. The simulated results of the radial strain and the thickness distribution are in good agreement withexperimental results. The simulations reveal that the deformation is localized around the tool and constantly remains close to a planestrain state. With decreasing depth step, increasing tool diameter and wall inclination angle, the axial stress reduces, leading to lessthinning and more homogeneous plastic strain and thickness distribution. During ISF, the plastic strain increases stepwise under theaction of the tool. Each increase in plastic strain is accompanied by hydrostatic pressure, which explains why obtainable deformationusing ISF exceeds the forming limits of conventional sheet forming.Key words: incremental sheet forming (ISF); sheet metal forming; numerical simulation; finite element methodelement analysis(FEA). The most prominent analytical1 Introductionmodel is based on the sine lawl7. Unfortunately,analytical models are limited to the approximateIncremental sheet forming (ISF) is an innovative,prediction of strains. For further studies, the mostflexible sheet forming process that uses principles ofcommonly used tool was the finite element method.layeredmanufacturing for thproduction ofSHIM and PARK(8] performed a numerical simulation ofcomplex- shaped sheet metal parts. This process resolvesthe single layer in the forming of truncated pyramid tothe complicated geometry information into a series offind the deformation characters along the tool path.two-dimensional layers, and then the plastic deformationISEKI[9 modeled the incremental forming of a shell ofis carried out layer-by-layer through the computerizedthe frustum of a quadrangular pyramid based on the shellnumerical controlled movements of a simple sphericalelements without considering material anisotropy andforming tool to get the desired part!-1. Generall, twoBaushinger effects of shell material, and the formedmain variants of the incremental sheet forming processheight of the part was just 5 mm. AMBROGIO et al-"are known, i.e. the “negative forming process" and theshowed that the single point incremental sheet forming“positive forming” processlo. In negative incrementalprocess mainly depended on geometrical and processforming, a spherical tool moves on a sheet metal,conditions. Particularly， the accuracy of the finaaccording to a programmed tool path. The sheet isgeometry was mainly influenced by the tool depth step.clamped at the periphery by bolts on a support frame. lIn this paper, a three-dimensional elasto-plasticpositive forming (Fig.1), the blank is put on the generalfinite element model was adopted to simulate themandrel and fastened at its edges by a clamping plate,incremental sheet forming process. The truncated cone,which can move along the guide posts. The tool deformsas the benchmark part, was simulated for differentthe blank into the mandrel and moves along the contourprocessparameters.Thecomparisonbetweenlines until the required shape is formed. In the currentexperimental and FEM results was carried out.study, the latter technique was investigated.Additionally, the influence of the process parameters onISF has been investigated mainly by simplifedthe strain history and distribution, the stress state andanalytical deformation models and by full scale finitedistribution. sheet thickness distribution during forming中国煤化工Foundation item: Prizt(s0175030) sppred by the National Natural Science FounduReceived date: 2007-12-14; Accepted date: 2008 01-21MHCNMHG.Corresponding author: HAN Fei, Doctoral candidate; Tel: +86 -13691060870; E-mail: hanre.nusudyanoo.com.cn582J. Cent. South Univ. Technol. (2008) 15: 581-587properties for input into the simulation. The mainBlankClamping|IToolmaterial parameters are shown in Table 1. Fig.2 showsplate>咖才the true stress- -strain curve for the blank material.BackingDieTable 1 Properties of blank for ISF simulationsplate_ItemValueMaterial08AlGuideFixedpostYield strengh/MPa175Utimate tensile strength/MPa303Ultimate elongation/%44Before formingDuring formingElastic modulus/MPa2.1X10°Fig,1 Positive incremental sheet forming processDensity(gcm2)7.83Poisson ratio0.30were carefully analyzed. Moreover, the reason why ISFgives higher forming limits than conventional sheetStrain-hardening exponent0.227forming processes was explained.Anisotropy coefficients, rro= 1.71,r4s-= 1.14,r90= 1.832 Experiment and simulation model5002.1 Experimental setupFor the experiments described in this paper, a00-special 3-axis numerical controlled machine was used asincremental sheet forming set-up. The blank wa300-fastened by a properly designed fixture. According to thefixture design, the blank with 330 mmX 330 mmX 1 mmE 200dimensions was 08AI in the annealed state. The circulardie used for the expecriments had a diameter of 80 mm100and a edge radius of 3 mm. A spherical nosed tool (toolsteel, Cr13) was used for all applied strategies. The code0.0.2 0.30.4 0.5for tool path was calculated using the computerautomated manufacturing module of Unigraphics NX.True strainThe tool speed was set to 200 mm/s. Oil was applied toFig.2 Stress strain curve of 08AI blankfurther minimizing the friction.ISF is a complex cold-forming process.Many2.2 Simulation setupfactors influence the forming process, such as verticalthree-dimensional, elasto-plastic finite elementstep down (Az) between the consecutive contours, themodel was set up for the simulation of the ISF process.wall inclination angle(a) and the tool diameter(D). InThe explicit finite element package Abaqus/Explicit wasorder to investigate the effects of control parameters onused in this work. Because of the nature of the process,the output values, a series of experiments andthere are several nonlinearities involved in the simulationsimulations were conducted. The final desired height ofof incremental forming. In addition, for the consideredhe cone was 20 mm. Fig.3 shows the ISF processapplications, incremental forming processes are typicallyparameters，and the processing parameters on thfully 3D without any symmetry plane. Usually, a largeinvestigated simulation are listed in Table 2.number of elements have to be used and the tool moves2.2.2 Finite element modelalong a relatively long trajectory, which will cause finiteIn the model, the 08Al-blank was meshed withelement analysis to be complicated and time to be14 400 4-node shell elements (Abaqus type S4R) withconsumed. In order to validate the model, similarfive integration points through the thickness. Theparameters and material property values have been usedmaterial was assumed to be planar anisotropic followingin both the simulation and the experimental study.Hill'中国煤化工atic hardening. The2.2.1 Material and process parameterstool,_backing plate wereA series of uniaxial tension tests at room:YC N M H G's friction law wastemperature with the tensile rate of 2.5 mm/min wereapplied with a tnction coetthclent of 0.05 between theconducted to experimentally determine the materialblank and the tool and of 0.15 between the blank and theJ. Cent. South Univ. Technol. (2008) 15: 581-587583partial die. The contact condition was implementedaverage value of Er from simulation was about 0.302. Thethrough a pure Master-Slave contact algorithm. Fig.4error between them is about 7.6%.shows the utilized FEM model for the process.PE 11CBlankt he"■n+1-rFig.3 ISF process parametersTable 2 Process parameters utilized for simulations(a)Process parameterValueTool depth step/mm0.5, 1.0, 1.5,2.0Tool diameter/mm10, 20, 30Region AWall inclination angle/(")45, 55, 65ClampingToolplateFig.5 Strain distribution comparison of numerical results withexperimental results: (a) Strain distribution in FEM simulation;bie, ，Backing(b) Strain got by coordinate grid method2.3.2 Blank thicknessFig.4 FEM model for ISF processKITAZAWA et al[l2-13] researched the aluminumblank thickness variation in ISF by experiments anIn order to synchronize the finite element simulationbased on the shear-dominant deformation model. Thewith the experiment, the NC file from the actualthickness variation was expressed as t=tqsin a withoutexperiment was imposed into the simulation to move theconsidering the material thickness anisotropy, where Iforming tool. The tool movement was controlled usingwas the current wall thickness, to was the initial blankpredefined displacerment constraints in several load steps.thickness and a was the inclination angle of the formedUsing an artifcially high tool velocity to substitute forpart.the real process is considered a potentially good methodThe experimental parts were formed under theto shorten the simulation time. So an artificiallyprocess parameters of D=20 mm, a=65° and Oz= I mm,increased tool feed rate of 2 m/s was utilized. Thethickness profiles of workpiece along the section cutssimulation time is reduced significantly with the increasewere measured and compared with those of numericalof tool velocity by 10 times.results (shown in Figs.6 and 7). It can be seen that a quitesatisfactory agreement is obtained. Values of thinnest2.3 Validation of simulation modelpoints in the two results are almost the same. The2.3.1 Radial strainabsolute error is small and the biggest value is only 0.018At the process parameters of D=10 mm, a=55* andmm, which confirms the effectiveness of the utilizedOz =1 mm, the experiments and numerical simulations ofnumerical model. The experimental result is alsothe truncated cone were performed. For the straincompared with the average theoretical value provided bymeasurements, a grid of 2.5 mm diameter circles, spacedthe sine law, showing that the sine law represents only a2.5 mm between centre-points, was used. The results ofcrude approximation.experiment and simulation are shown in Fig.5. The3 Nu中国煤化工。and discussionlength of circles is increased in the radial direction andremains nearly constant in the tangential direction. At aMYHCNMHGheight of 16 mm from the top of the truncated cone, the3.1 Strain history and distributionaverage radial strain Er was 0.325. At the same height, theIn the final deformed mesh model (shown in Fig.8),J. Cent. South Univ. Technol. (2008) 15: 581-587five selected nodes on the surface of the cone werenodes A, B, D and E indicated in Fig.8. During thehighlighted to examine the strain paths during thesimulation, four selected nodes are consecutivelyprocess.affected by the tool movement. The strain paths of nodesA, B, D and E are shown in Fig.10. As can be seen inFig.10, the strain paths are characterized by steps: eachstrain increment is directly due to the action of the toolwhen it passes the particular node. However, no strainoccurs when the tool continues its path along the samecontour and deviates from the node. As a result, thetypically small and localized strain can enhance theformability of the blank.Max284Fig.6 Numerical simulation of thickness dsributionMid1.00,Experiment-8Min; 0.98--12-0.51.0.96-Time/sSimulationFig9 Principal strains for node c during ISF process首0.94-器”).7厂0.920.6-Sine lawe[|o 20406080100120140马0BDistance from centre/mm0.4Fig.7 Thickness distibution comparison of numerical resultswith experimental results0.2).1 tA|1.52.0明”Fig.10 Strain history of nodes A, B, D and E during ISFprocessMoreover, node A that is close to the center of theFig.8 Selection of nodesblank, is the first to undergo deformation, but it reachesjust a limnited strain since it undergoes the tool action justAt process parameters of D=10 mm, a=55* and Az=for a few contours. Nodes B and D undergo the tool1 mm, the three principal strains for node C are presentedaction for the maximum number of contours anin Fig.9. The second principal strain is very close to zero,consequently the strains also reach the maximum there.which confirms the plane strain assumption for theAnd中国煤化工edge is not afcedeprocess as mentioned by ISEKI9. The strain componentby th-ind the deformationin the circunferential direction can be negligible.takeYHCNMHGIn order to investigate the strain history anThe selected node C on the blank was examined todistribution during ISF, the strain path was analyzed fordetermine the efct of process parameters on theJ. Cent. South Univ. Technol. (2008) 15: 581-587585equivalent plastic strain. At process parameters of D=accumulated strain decreaases. So, lower equivalent10 mm and a=4S*, as the step down increases (shown inplastic strain arises and greater deformation can beFig.11(a)),) the strain increments imposed at each loopachieved using a bigger tool. At process parameters ofincrease, and the total strain remains the same, since itD=10 mm and Oz=l mm, as the wall angle decreasesonly depends on the wall angle and height of the cone.(shown in Fig.11(c))， the final accumulated strainThus, with the decrease of the step down, theincreases. So, if the wall angle is too small, the straindeformation will be more uniform.will exceed the forming limit of the material, and then,At process parameters of a=45* and Qz=1 mm, withthe blank will be broken.increasing tool diameter (shown in Fig.1l(b)), the strainof one step is smaller and more uniform and the final3.2 Stress state and distributionIn order to investigate the stress conditions ir间)further detail, Fig.12 shows the equivalent plastic strainand the stress triaxiality ratio for the highlighted node C旨0.8(with process parameters of D=30 mm, a=45° and 0z-sZ=1.5mm| IJ NZ=0.5 mm1 mm). The stress triaxiality ratio q is the ratio of the0.6-AZ=1.0 mmphydrostatic pressure (σm) to the equivalent von Misesstress (σ ), where Om=(on+o2+o3)/3, σ (i=1, 2, 3) is0.4-principal stress in the integration points, and0.2-r=1√(0-02)2 +(02-03)2+(a5-)234It is generally recognized that damage behavior ofTime/ssheet metal depends strongly on stress triaxiality σm/ σ1.0F(6)and equivalent plastic strain ε [14-15]. It can be seen thatD=10 mmpositive peaks in the course of the stress triaxiality ratiocoincide with an increase in plastic strain. Thus,compressive stresses are superimposed whenever the toolD-20 mm.6-deformns the selected nodes, indicating that hydrostaticpressure plays a major role during the process.Compressive hydrostatic stress is thought to be thD-30 mmreasonthe high forming limits obtained“0.2experimentally.Node C on the blank was chosen to investigate theeffects of process parameters on the maximum principle0.51.01.52.0stress. With the tool diameter increasing (a=45", Oz=1mm) or the wall angle increasing (D= 10 mm, 0z=l mm),.00(C-45the maximum principal stress decreases (shown in Fig.13).县0.75-0.60.4.55"0.50-0.265岳0.25 |-0.40..1.5中国煤化工Fig.11 Effect of process parameters on equivalent plastic strain:YHCNMHG1.5(a) Strain history for different step downs; (b) Strain history fordifferent tool diameters; (c) Strain history for different wallFig.12 Equivalent plastic strain E and stress triaxiality ratio qangles586J. Cent. South Univ. Technol. (2008) 15: 581-587inclination angle (D=10 mm,△z=1 mm). So the lower700(a)一D=10mm.depth step, larger tool diamcter and wall inclination600D-20 mmangle will lead to more homogeneous thinning reduction. D-30 mmand thickness distribution.二400-0.950.90-100g 0.85-首1.02.0出0.80-AZ=0.5 mmTime/sAZ= 1.0 mm700pb)一459--- 0Z=2.0 mm0 20406080100120 140; 500Distance from centre/mm1.00F--(b)i 300-2000.900.51.01.5西0.80-一D= 10mm. D=20 mmFig.13 Effeet of process parameters on maximum principal--- D=30 mmstress: (a) Stress history for different tool diameters; (b) Stresshistory for different wall angle5 20406080100120140It is well known that the maximum principal stress ismainly responsible for necking and fracture inc)incremental sheet forming. Therefore, the blank materialexperiences a smaller axial stress and lower mechanicaldamage with a larger tool diameter and larger wall angle.3.3 Thickness distributionIt is worth pointing out that thinning plays a basicrole in incremental sheet forming process. “Safe"苗0.80|二5S"thinning in incremental forming (such as maximum--- 65°thinning before fracture) is much larger than that in0.75-conventional stamping due to the stress and strainconditions which characterize the process'o. It is quiteobvious that an effective design and control ofFig.14 Effect of process parameters on thickness distribution:incremental forming operations requires an accurate and(a) Thickness distribution for different step downs; (b) Thick-reliable modeling of thinning.ness distribution for different tool diameters; (C) ThicknessIn order to investigate the thickness distribution indistribution for different wall anglesfurther detail, with varying the process parameters (ie.tool depth step, tool diameter and wall inclination angle),4C中国煤化工the thickness distributions are plotted respectively(shown in Fig.14). It can be seen that thickness increasesYHc N M H Ghkness dsrbutinio ofwith the decrease of tool depth step (D=10 mm, a=45"),the simulation results are in good agreement withthe increase of tool diameter (a= -45*;, Oz=1 mm) or wallexperimental results, so the FEM in this work is provedJ. Cent. South Univ. Technol. (2008) 15: 581-587[6] ZHOU Liu-nu. Study on principle and process of NC incrementalto be effective.sheet metal forming [D] Wuhan: College of Materials Science and2) The second principal strain is very close to zeroEnineering. Huazhong University of Science and Tchnology, 2004.through the ISF proces, and the deformation pattern of(in Chincsc)ISF can be simplifed as plane-strain deformation.[7] KIM τ」, YANG D Y. lmprovement of formobility for the3) During incremental sheet forming, the platicincremental sheet metal forming proess小Intemational Jounal ofMechanical Sciencs, 2000 42(7): 1271-1286.strain increases stepwise under the action of the tool, and[8] SHIM M s, PARK J J. The fomablity of aluminum sheet inthe typically small and localized strain can enhance thincremenal forming [I. Journal of Materials Proessing Technology,formability of the blank.2001, 1313);654 658.4) Each increase in plastic strain is accompanied by[9] ISEKI H. An pproximate deformation analysis and FEM analysishydrostatic pressure, which explains why ISF exceedsfor he icememel blging odl sh metal uingasof sheet metal using a spherial rller小the forming limits of conventional sheet forming.Journal of Matcrials Processing Technology.2001，11(13): .5) With decreasing depth step, increasing to[10] AMBROGIO 0, FILICE L, FRATINI L MICARI F. Procesdiameter and wall inclination angle, the axial stesmechanics analysis in single point incremental forming (CV Materilreduces and leads to thinning reduction and morePoessing and Design Modeling Sinulation and Application,homogeneous plastic strain and thickness distribution.Columbus: AIP, 2004: 922 -927.Moreover, the deformation is more uniform and failure is11] AMBROGIO a COzzA V, FILICE L MICARI R. An analyticalmodel for improving preision in single point increnental formingless likely to occur.n Jourmal of Malerials Pcssin Technology. 2007, 1(0/3);92- -95.References[12] KITAZAWA K, OKAKU H. Posiblit of CNC incrementalsrech-expanding of sheet metal by sigleoo-path process [0[] KITAZAWA K. Ineremental sheet metal setch.expading withNiokieaiGaknunshu, 196.62(597; 2012- 2017.CNC machine ools (CV Advanced Technology of Paticity. Bejing; [13] YOUNG D, JESWIET J. Wall thickness varations in single-pointIntermational Academie Publisher, 1993: 1899-1904.incremental forming [0]. Journal of Engincering Manufacture, 2004,[2] MATSUBARA M, TANAKA s, NAKAMURA T. Development of218(11): 1453-1459.incemental seet metal forming system using clastic tols Pinciple14] HARTLEY P, HALL F R, CHIOU 」M. PILLINGER Lof forming process and formation of some fundamentally curvedElstic-lastes fnitefinite-element modelling of metal forming withshapes un. ISMEintral Journal, Series C, 1996, 39(): 156-damage evolution [n Studis in Applied Mechanics, 1997, 45:135-142.[3] LEACH D, GREEN AJ. BRAMLEY AN. Anew incremental sheet (15] MEDIAVILLA J, PEERLINGS R H I, GEERS M GD. A nonlocalforming procss for small batch and prototype pars [CW 9thtiaiaitydependent ducile damage model for fnite strain platicityIntermational Conference on Sheet Metal. Leuven: Elsevier ScienceComputer Methods in Applied Mechanics and Engineering. 2006,Publisher, 2001:211-218.19(33/36);: 4617- 4634.[4] HAGAN E, JESWIET J. A review of conventional and moderm[16] AMBROGIO o, FILICE L, GAGLIARDI F, MICARI F. SheeJounw Sheetsingl-point sheet metal forming methods 0 Jourmal of Engineeringthining prediction in single point incremental formingManufacture, 2003. 2172):213-225.Meal 205.-Procedings of the 11th Intemational Conference.[5] JESWIET J, MICARI F, HRT 0, BRAMLEY A, DUFLOU I,Erlangen-Nuremberg Trans Tch Pbicaions LId.2005 479- 486.ALLWOOD J. Asymnetric single point incremental forming of sheet(Edited by ZHAO Jun)metal [I]. CIRP Annals, 2005, 54(2); 623- 649.中国煤化工MHCNMHG