Stainless steel in sheet metal forming processes show a hardening behavior, which can be described only in dependency of the deformation and temperature history. Because of the temperature influence to the material properties, the temperature dependence of the friction in the process has to be taken into account. Friction tests using different temperatures showed a change of the friction regime. From the experimental observation the temperature and velocity dependence of the friction was modeled and integrated in a finite element code for metal forming. On the macroscopic scale the temperature and velocity dependent friction was integrated in a FEM code of metal forming. The FEM simulation has been applied to the biaxial stretching test and compared with the experiment. The numerical results showed a good agreement with the failure behavior of the stainless stee

Grueebler, R.

Hora, P.

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TEMPERATURE DEPENDENT FRICTION MODELING FOR SHEETMETAL FORMINGR. Grueebler1∗, P. Hora11 ETH Zurich, Institute of Virtual Manufacturing (IVP), SwitzerlandABSTRACT: Stainless steel in sheet metal forming processes show a hardening behavior, which can be described only independency of the deformation and temperature history. Because of the temperature influence to the material properties,the temperature dependence of the friction in the process has to be taken into account. Friction tests using differenttemperatures showed a change of the friction regime. From the experimental observation the temperature and velocitydependence of the friction was modeled and integrated in a finite element code for metal forming. On the macroscopicscale the temperature and velocity dependent friction was integrated in a FEM code of metal forming. The FEM simulationhas been applied to the biaxial stretching test and compared with the experiment. The numerical results showed a goodagreement with the failure behavior of the stainless steel.KEYWORDS: Friction modeling, FEM simulation, Lubrication1 INTRODUCTIONIn the manufacturing of stainless sheet metal products pro-cess are optimized to the requirement for efficiency aswell as for quality improvement and for the augmentationof piece variety. Different lubrication regimes may occurin different areas of the interface or at different time dueto different factors influencing the friction like tempera-ture, normal force, velocity. Since strain distribution inthe workpiece is influenced by friction, the formability ofthe workpiece depends not only on the material propertybut also on the friction.There are different approaches to include the dependen-cies of the friction. Keum et al. [1] measured experimen-tally the effects of lubricant viscosity, surface roughnessand hardness of the sheet, punch velocity and die cornerradius on the friction. He suggested a mathematical modelof the friction coefficient as a function of friction parame-ters. This is an empirical model on the macroscale easy touse in a computer simulation but it does not consider thephysical processes. For a more theoretical approach theprocesses in the microscopic scale has to be considered. Inthis scale it’s possible to divide the friction in the differentregimes. For the boundary friction regime a lot of mod-els consider the asperity contact, most of them with thestatic equilibrium solution in pure flattening [2], [3], [4]and [5]. The asperity contact in sliding flattening is morecomplicated, because of the additional tangential stress.Lo and Yang [6] proposed a new concept of asperity flat-tening. The different friction regimes depends on the sur-face topography affecting the formation and transport oflubricant. Results of different textured surfaces modeled∗Corresponding author: Tannenstr. 3, 8092 Zurich, +41 44 632 2617, grueebler@ivp.mavt.ethz.chwith a finite element simulation on the microscopic scalewere presented in [7]. This model distinguishes explicitlybetween the different friction regimes by calculating theboundary friction at the real contact area and the hydrody-namic friction in between.The friction in sheet metal forming of autenitic stainlesssteel has an important impact because of the deformationand temperature dependent hardening behaviour becauseof the strain-induced martensitic transformation. For themodeling of the forming process the deformation, temper-ature and phase structure are essential factors for a properdescription of the material properties. So the influence oftemperature and velocity to the friction coefficient has tobe considered.2 FRICTION IN SHEET METAL FORM-INGThe tribosystem in metal forming processes consists of theelastic tool, the elasto-plastic sheet, and the visco-elasticlubricant in between. In the commonly used FEM sim-ulation the explicit consideration of the lubricant in thecalculation is ignored as well as the topography of thesurfaces. The friction is taken into account with simplefriction models such as the Amontons lawτF = µσN (1)or the shear friction modelτF = mk (2)with τF the shear friction, µ andm the friction coefficient,σN the normal pressure and k the shear stress of the softermaterial. With this equations the influence of the lubri-cant and the topography of the surfaces are integrated inDOI 10.1007/s12289-009-0548-z© Springer/ESAFORM 2009Int J Mater Form (2009) Vol. 2 Suppl 1:251–254the friction coefficient without the dependence of veloc-ity and temperature. However, the friction depends on thecontact formation of the tool and sheet metal with the lu-bricant in between. The force of the tool is applied by as-perities in contact as well as by the lubricant between theasperities in lubricant pockets. The first friction regime re-sults into boundary friction, where the size of this contactzone and the composition of the additives play an impor-tant role. For the boundary friction regime in the sheetmetal forming process the friction stress can be expressedas:τb = τaA + τpA (3)where A is the fractional contact area and τa and τp arethe adhesion and plowing friction stress components. Inthe case of smooth tool and relatively rough workpiece asthe normal condition in sheet metal forming, the plowingcomponent can be neglected.The full film lubrication or hydrodynamic friction regimedepends on the viscosity of the lubricant and can be writ-ten asτh = ηvrelh(4)where η is the viscosity, vrel the relative velocity and hthe thickness of the lubricant layer.Because in sheet metal processes local temperature vari-ations can occur, the temperature dependence of the vis-cosity has to be considered. The temperature dependencecan be described with the equation of Vogel[8]:η = AeBT+C (5)where A,B and C are constants and T the temperature inKelvin.The contact formation is directly connected to the viscos-ity of the lubricant. With lower viscosity the boundaryfriction is becoming more dominant because of the in-crease in the real contact area. This temperature-viscositydependence of the friction can be expressed similar to thetemperature dependence of the viscosity in equation 5:µ = 1− aebT+c (6).The velocity dependence of the friction is assumed as lin-ear decreasing:µ = k1vrel + k2 (7)where k1 and k2 are constants. This has been validated bythe friction tests later on.As mentioned in the introduction the friction in sheetmetal forming of stainless steel takes place in the mixedlubrication regime. This regime is the combination of theboundary friction and the hydrodynamic friction regimeand can be written asτF = τbA + τh (1−A) . (8)The problem is to determine the friction in the mixed lu-brication. So the real contact area AR has to be known. Inthe macroscopic finite element simulation the determina-tion of the real contact area AR is not possible, because thesurface geometry with the asperities are not considered.For this reason the mixed lubrication can not be simulatedfrom the hydrodynamic and boundary friction. Howevera way to model the friction regimes is to measure the fric-tion dependence of the velocity and temperature in the tri-bosystem and to use the measured friction dependencies inthe simulation with the according characteristics of equa-tion 6 and 7. The two equations are composed together bymultiplication:µ = (k1vrel + k2)(1 − avrelebT+c ) (9)This is an macroscopic friction description in contrast tothe equation 8 with 3 and 4. So it is not possible to distin-guish between the boundary and hydrodynamic friction.3 RESULTSThe determination of the friction for the macroscopic fi-nite element simulation of the sheet metal forming ofstainless steel has been done by pin-on-disk tests. Themeasured data have been approximated by the theoreti-cal model shown in section 2. Then the biaxial stretchforming process is used to compare the simulation withthe experiment.3.1 EXPERIMENTSSeveral Experiments were carried out to measure the fric-tion behavior of the stainless sheet metal forming. The hy-drodynamic friction depends on the viscosity, which itselfis strongly temperature dependent. This temperature de-pendence is important for the contact formation betweensheet metal and tool. With increasing temperature the vis-cosity decreases and the real contact area grows. The tem-perature dependence of the viscosity was measured on aPaar Physica MCR 300 Rheometer and approximated withthe equation 5.In the sheet metal forming of stainless steel the contactconditions are varying among others in temperature andspeed. According to this the friction is changing depend-ing on the conditions. With the pin-on-disk test it is possi-ble to measure the friction coefficient at different veloci-ties and temperatures. However the pin-on-disk test simu-lates rather the boundary lubrication regime. It exists onlya small contact area and the influence of the hydrodynamicfriction is low compared to the contact condition in sheetmetal forming. This results in a higher friction coefficientfor the pin-on-disk test compared to the sheet metal form-ing.To get the velocity and temperature dependency of the tri-bosystem stainless steel - lubricant - tool, several pin-on-disk tests were carried out.The friction coefficient of this tribosystem was measuredfor three different velocities v1 = 0.0007 m/s, v2 = 0.01m/s and v3 = 0.16 m/s and for three different tempera-tures T1 = 23◦ C, T2 = 60◦ C and T3 = 100◦ C. In figure2521 the results of the measured friction coefficients are plot-ted.280 300 320 340 360 3800.110.120.130.140.150.160.170.180.19Temperature [K]Friction coefficient []  Velocity 0.0007 m/sVelocity 0.01 m/sVelocity 0.16 m/sFigure 1:temperature measured with the pin-on-disk testFor the temperature dependence of the hydrodynamic lu-brication regime the parameter of equation 6 can be ap-proximated by the data of the Pin-on-disk tests in figure1.In sheet metal forming the full film lubrication regimecontributes more to the mixed friction than in the pin-on-disk test. This test shows the dependency of the influenc-ing parameters.3.2 MODELINGIn order to investigate the friction the biaxial stretch form-ing process is simulated and compared with experimentaldata. The temperature dependence of the friction was im-plemented in a finite element code for sheet metal formingand compared with the experimental measurement of thestretch forming process. The blank is 1.4301 (AISI304)steel of 0.7 mm thickness. The diameter of the punch is100 mm. The setup of the biaxial stretching test is shownin figure 2.Figure 2: Setup of the biaxial stretching testFigure 3 shows the radial strain distribution predicted bythe simulation for the two different velocities. With thelower velocity and therefore the higher friction the high-est strain appears at the side. However with the highervelocity the highest strain arises at the pole.The biaxial stretch forming process had been conductedby two different velocities to simulate two different tribo-0 10 20 30 40 50 600.10.150.20.250.30.350.40.450.5Punch radius [mm]radial strain  velocity 0.167 mm/svelocity 0.83 mm/sFigure 3: Radial strain distribution in the simulation for thetwo velocities.logical conditions. A punch speed of 0.167 mm/s and 0.83mm/s has been used. Due to the different velocities thereis a difference in the temperature due to the heat flux.The punch speed of 0.167 mm/s simulates the mixed lu-brication with more importance of the boundary friction.Besides the slow speed results in moderate temperaturebecause of the heat conduction. With a punch speed of0.83 mm/s the higher velocity implies more importanceof the hydrodynamic friction.For the slow punch speed the failure occures at the side ofthe sphere. But for the faster speed the sheet metal failsat the pole of the biaxial stretching test. In figure 6 thefailure for the two different speeds are shownThe finite element simulation were conducted by using themacroscopic friction model. In figure 4 the radial strainfor the simulation with a constant friction coefficient isshown. The distribution is similar for the two differentvelocities, for the higher velocity the highest strain valuestends to move toward the side of the punch.Figure 4: Radial strain distribution of the simulation withmm/sThe influence of the temperature and velocity dependentfriction is shown in figure 5. For the slow velocity thehighest strain appears at the side of the punch. In the caseof the higher velocity the highest strain occurs at the pole.This behaviour has been confirmed by the biaxial stretch-ing test in figure 6.Friction coefficient for three velocities and threeconstant friction coefficient: left 0.167 mm/s, right 0.83253Figure 5: Radial strain distribution of the simulation withthermal and velocity dependent friction: left 0.167 mm/s,right 0.83 mm/sFigure 6: Failure of the biaxial stretching test for differentspeeds and different lubrication: left 0.167 mm/s, right 0.83mm/s4 DISCUSSIONThe tribological tests show the temperature and velocitydependence of the friction. In the hydrodynamic lubri-cation regime the friction has a similar temperature de-pendence as the viscosity. For slow velocities, i.e. in theboundary friction regime the temperature dependency isvery low and tends to decrease with higher temperature(figure 1). This can be explained by the temperature de-pendence of the material in the interface layer.In the biaxial stretching test the temperature and velocityhave an important influence to the friction. For the slowpunch speed the temperature is low. The failure occur atthe side of the specimen. With the simulation this can beexplained by the high friction because of the low veloc-ity. The temperature influence is small because of the lowheating of the sheet metal due to the slow forming veloc-ity. In the case of the higher punch speed the friction islower because of the higher velocity. The higher temper-ature is less important for the friction than the velocity.Because of the lower friction the sheet metal fails at thepole. The peak value of the radial strain is greater in theslow velocity case and the position of the peak value ofthe radial strain is about 22 mm. For the higher velocitycase the peak value of the radial strain is smaller and theposition of the peak value of the radial strain is near thecenter of the punch. The distribution of the friction co-efficient due to the velocity and temperature dependenceeffects the strain distribution significantly. The lower fric-tion results in a lower peak value of the radial strain.The failure behaviour of the biaxial stretching test usingthe two velocities can be explained with the temperatureand velocity dependent friction.5 CONCLUSIONSThe temperature dependence of friction has been found tobe connected to the temperature dependence of the vis-cosity. The pin-on-disk test showed this dependence forhigh relative velocities. This shows the higher impor-tance of the hydrodynamic friction for higher velocitiesin the mixed lubrication. In contrast for slow velocitiesthe boundary lubrication regime contribute more to thefriction. With the finite element simulation these two ef-fects could be shown in the biaxial stretching process. Forslow velocities and therefore low temperature the frictionis high and the radial strain shows the highest values atthe side of the punch. The higher velocity causes lowerfriction and the highest strain values moves to the pole.Hence it is important to consider the temperature and ve-locity dependence of the friction for stainless sheet metalforming. It is possible to implemente the dependencies byempirical models in the FE-simulation. However it is notpossible to calculate the exact fraction of hydrodynamicfriction and the boundary friction with the macroscopicfriction model.REFERENCES[1] Y. T. Keum, R. H. Wagoner, and J. K. Lee. Frictionmodel for fem simulation of sheet metal formingoperations. Materials Processing and Design:Modeling, Simulation and Applications,Numiform2004, pages 989–994, 2004.[2] A. Majumdar and B. Bhushan. Fractal model ofelastic-plastic contact between rough surfaces.ASME J. Trib., 113:1–11, 1991.[3] Y. Ju and L. Zheng. A full numerical solution for theelastic contact of three-dimensional real roughsurfaces. Wear, 157:151–161, 1992.[4] W.R.D Wilson and S. Sheu. Real area of contact andboundary friction in metal forming. Int. J. Mech.Sci., 30:475–489, 1988.[5] M.P.F. Sutcliffe. Flattening of random rough surfacesin metal forming processes. ASME J. Trib., 121:433–440, 1999.[6] S. W. Lo and T. S. Yang. A new mechanism ofasperity flattening in sliding contact - the role ofelastic tool microwedge. ASME J. Trib., 125:713–719, 2003.[7] R. Grueebler and P. Hora. Modeling of surfacetexturing of sheet metal and tool in sheet metalprocesses. In Proceedings of ICTMP07, pages31–34. Yokohama National University, 2007.[8] H. Vogel. Das Temperaturabhaengigkeitsgesetz derViskositaet von Fluessigkeiten. PhysikalischeZeitschrift, XXII:645–646, 1921.254

Temperature dependent friction modeling for sheet metal forming

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Temperature dependent friction modeling for sheet metal forming

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