MULTISCALE FRICTION MODELING FOR SHEET METAL FORMING

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1 MULTISCALE FRICTION MODELING FOR SHEET METAL FORMING Authors J. HOL 1, M.V. CID ALFARO 2, M.B. DE ROOIJ 3 AND T. MEINDERS 4 1 Materials innovation institute (M2i) 2 Corus Research Centre 3 University of Twente, Faculty of Engineering Technology, group of Surface Technology an Tribology 4 University of Twente, Faculty of Engineering Technology, chair of Forming Technology Please Note Care has been taken to ensure that the information herein is accurate, but Tata Steel an its subsiiary companies o not accept responsibility for errors or for information which is foun to be misleaing. Suggestions for or escriptions of the en use or applications of proucts or methos of working are for information only an Tata Steel an its subsiiaries accept no liability in respect thereof. Before using proucts supplie or manufacture by Tata Steel the customer shoul satisfy themselves of their suitability All rawings, calculations an avisory services are provie subject to Tata Steel Stanar Conitions available on request.

2 MULTISCALE FRICTION MODELING FOR SHEET METAL FORMING J. HOL 1, M.V. CID ALFARO 2, M.B. DE ROOIJ 3 AND T. MEINDERS 4 1 Materials innovation institute (M2i) P.O. box GA Delft The Netherlans 2 Corus Research Centre P.O. box CA IJmuien The Netherlans 3 University of Twente, Faculty of Engineering Technology, group of Surface Technology an Tribology P.O. box AE Enschee The Netherlans 4 University of Twente, Faculty of Engineering Technology, chair of Forming Technology P.O. box AE Enschee The Netherlans Abstract The most often use friction moel for sheet metal forming simulations is the relative simple Coulomb friction moel. This paper presents a more avance friction moel for large scale forming simulations base on the surface change on the micro-scale. The surface texture of a material changes if two surfaces are in contact uner a normal loa which is an effect of flattening ue to normal loaing an flattening ue to stretching. Shear stresses between the contacting surfaces, evelope by ahesion an ploughing effects between contacting asperities, will change if the surface texture change. A numerical proceure has been evelope which accounts for the change of the surface texture on the micro-scale an its influence on the friction behavior on the macro-scale. The numerical proceure is implemente in a finite element coe an applie to a full scale sheet metal forming simulation. Keywors: friction mechanisms, asperity contact, flattening, real contact area, ploughing, ahesion 1 INTRODUCTION The automotive inustry uses Finite Element (FE) software for formability analyses to reuce the cost an lea time of new vehicle programs. In this respect, FE analysis serves as a stepping stone to optimize manufacturing processes. An accurate forming analysis of an automotive part can however only be mae if, amongst others, the material behavior an friction conitions are moele accurately. For material moels, significant improvements have been mae in the last ecaes, but in the majority of simulations still a simple Coulomb friction moel is use. The Coulomb friction moel oes not inclue the influence of important parameters such as pressure, punch spee or eformation of the sheet material. Consequently, even using the latest material moels, it is still cumbersome to preict the raw-in of a blank uring the forming process correctly. To better unerstan contact an friction conitions uring lubricate sheet metal forming (SMF) processes, experimental an theoretical stuies have been performe in orer to escribe microscopic epenencies. On microscopic level, friction is ue to ahesion between contacting asperities [1,2], the ploughing effect between asperities [1,2] an the appearance of hyroynamic friction stresses [3,4]. Ploughing effects

3 2 4 th International Conference on Tribology in Manufacturing Processes - ICTMP 2010 between asperities an ahesion effects between bounary layers are the main factors causing friction in the bounary lubrication regime. If the contact pressure is carrie by the asperities an the lubricant flow, as in the mixe- an hyroynamic lubrication regime, hyroynamic shear stresses will become important. This paper will focus on the friction mechanisms present in the bounary layer regime: ploughing an ahesion. Wilson [1] evelope a friction moel which treate the effect of ahesion an ploughing separately. A more avance friction moel is evelope by Challen & Oxley [2] which takes the combining effect of ploughing an ahesion on the coefficient of friction into account. Challen & Oxley performe a slip-line analysis on the eformation of a soft asperity by a har asperity an erive expressions for the coefficient of friction an wear rates. Their friction moel assumes contact between a har wege-shape asperity an a soft flat material. Westeneng [5] extene the moel of Challen & Oxley to escribe friction conitions between a flat workpiece material an multiple, spherical shape, tool asperities. The influence of ploughing an ahesion on the coefficient of friction epens on the real area of contact. The coefficient of friction will change if the real area of contact changes. The real area of contact epens on ifferent flattening an roughening mechanisms of the eforming asperities. The three ominating flattening mechanisms uring SMF processes are flattening ue to normal loaing [6], flattening ue to stretching [7,8] an flattening ue to sliing [9]. Flattening increases the real area of contact representing a higher coefficient of friction. Roughening of asperities, observe uring stretching the eforme material [10], tens to ecrease the real area of contact resulting in a lower coefficient of friction. The two mechanisms outline in this paper are flattening ue to normal loaing an flattening ue to stretching. A large research area within the fiel of friction moeling is focuse on eveloping moels to preict the flattening behavior of asperities ue to normal loaing. Most of these moels are base on the pioneering work of Greenwoo & Williamson [6] which evelope a stochastic moel base on contact between a flat tool an rough workpiece surface. The moel mathematically escribes contact between two surfaces base on the assumption that summits of the rough surface are spherical, that summits only eform elastically an that the surface texture can be escribe by a istribution function. Over the past ecaes, moifications have been mae to this moel to account for arbitrary shape asperities, plastically eforming asperities an the interaction between asperities. Pullen & Williamson [11] evelope an ieal plastic contact moel base on conservation of volume uring plastic eformation an the assumption that isplace material reappears as a uniform rise in the non-contacting surface. The moel of Pullen an Williamson inspire Westeneng [5] to erive an ieal plastic an nonlinear plastic contact moel base on the conservation of volume an energy. Westeneng moele the asperities by bars which can represent arbitrarily shape asperities. The moels inclue a persistence parameter, work harening parameters an are able to escribe the interaction between asperities. A further increase of the real area of contact coul occur if uring normal loaing a bulk strain is applie to the material. The effective harness of the asperities can be largely reuce if a bulk strain is present in the unerlying material [7]. Wilson & Sheu [7] evelope an analytical upperboun moel to escribe the flattening behavior using

4 Multiscale friction moeling for sheet metal forming 3 wege-shape asperities with a constant angle. Westeneng [5] evelope a strain moel which escribes the influence of strain on a surface geometry with arbitrary shape asperities. The moel is applicable to both plain strain an plane stress situations epenent on the efinition of the non-imensional strain rate [5]. In this paper, a numerical proceure is propose which couples the ifferent friction mechanisms. A general overview of the numerical proceure is presente an the translation from micro to macro moeling is outline. The evelopment of the real area of contact is escribe by the flattening moels propose by Westeneng [5] an the effect of ploughing an ahesion on the coefficient of friction is escribe by the moifie friction moel of Challen & Oxley [5]. The numerical proceure has been applie to a full scale sheet metal forming simulation which shows the applicability of the numerical proceure. 2 THEORETICAL BACKGROUND 2.1 NUMERICAL PROCEDURE A numerical proceure, to be use in finite element coes, has been evelope to couple the ifferent micro friction moels. The numerical proceure starts with efining the process variables an material characteristics. Process variables are the nominal contact pressure an strain in the material which are calculate by the FE coe. The contact pressure carrie by the asperities equals the total nominal contact pressure since hyroynamic friction stresses will be neglecte. Material characteristics are the harness of the asperities an the surface properties of the tool an workpiece material. Once the input parameters are known, the real area of contact is calculate base on flattening ue to normal loaing an flattening ue to stretching. The amount of inentation of the harer tool asperities into the softer workpiece asperities can be calculate if the real area of contact an the contact pressure carrie by the asperities are known. Consequently, shear stresses ue to ploughing an ahesion effects between asperities an the coefficient of friction are being calculate. Friction moels encompassing micro mechanisms are generally regare as too cumbersome to be use in large scale FE simulations. Translation techniques are therefore necessary to translate microscopic behavior to macroscopic behavior. Using stochastic methos, rough surfaces are escribe on micro-scale by their statistical parameters (mean raius of asperities, asperity ensity an the surface height istribution). Assuming that the surface height istribution on the micro scale represents the surface texture on the macro scale, it is even possible to escribe contact problems between tool an workpiece of large scale FE problems [5]. Statistical parameters can be use uner the assumption that the surface texture is isotropic an can be represente by 2-imensional ranom noise. It is assume that these restrictions are true for the workpiece an tool material which makes the use of statistical parameters favorable to make the translation from micro to macro moeling. 2.2 CHARACTERIZATION OF ROUGH SURFACES The surface height istribution of the tool an workpiece material is obtaine from the surface profiles of the rough surfaces (Fig. 1). A iscrete surface height istribution will

5 4 4 th International Conference on Tribology in Manufacturing Processes - ICTMP 2010 be obtaine which has to be evaluate by a continuous function. A continuous function is require to eliminate the nee of integrating iscrete functions uring the numerical proceure. 6 4 Surface profile Real istribution Fourier fit z (µm) φ(z) (µm -1 ) x (µm) z (µm) Figure 1: Surface profile (left) an surface height istribution (right) An avance metho to escribe iscrete signals is by using Fourier series. Fourier series makes it possible to escribe non-smooth asymmetric istribution functions from which the accuracy of the evaluation epens on the number of expansions use. The results iscusse in this paper are obtaine by evaluating the surface height istribution functions by a half range sine Fourier function, given by: f Fourier ( x) = n= 1 nπ bn sin x L L n with b = 2 n f ( x)sin π x L L with n the number of expansions an L the evaluation omain. In Figure 1, a measure istribution function is evaluate by a Fourier function using 15 expansions. 2.3 FLATTENING MECHANISMS Two flattening mechanisms have been implemente in the numerical proceure to calculate the real area of contact of the workpiece: flattening ue to normal loaing an flattening ue to stretching. The moels of Westeneng are use for this purpose [5]. Westeneng moele the asperities of the rough surface by bars which can represent arbitrarily shape asperities, Figure 2. Westeneng introuce 3 stochastic variables as presente in Figure 2: The normalize surface height istribution function of the asperities of the rough surface φ ( z), the uniform rise of the non-contacting surface U (volume conservation) an the separation between the tool surface an the mean plane of the asperities of the rough surface. 0 (1)

6 Multiscale friction moeling for sheet metal forming 5 Inente asperities Rise non-contacting surface U Tool surface Mean plane z ø(z) Workpiece asperities U Figure 2: A rough soft surface inente by a smooth rigi surface Using the normalize surface height istribution φ ( z), the amount of flattening of the contacting asperities an the rise of the non-contacting asperities U can be calculate by solving the following set of equations: ( z ) φ( z) z ( z + U ) φ( z) z + ( z ) φ( z) z nom 0 = ξ 1+ η (2) = U U ( z + U ) φ( z) z U 0 (3) In which H represents the harness of the softer material, η is the persistence parameter (energy require to lift up the valleys) an ξ is a parameter which characterizes the ieal plastic contact moel. The value of the parameter η is boune between 0 (no energy neee to raise the valleys) an 1 (maximum amount of energy require to raise the valleys). In this paper, the value of η is taken equal to p nom H resulting in an increasing persistence parameter for increasing loa [5]. The parameter ξ can be etermine by equation 4: ξ = U U n n ( z + U ) φ( z) z + ( z ) φ( z) z n+ 1 n+ 1 ( z + U ) φ( z) z + ( z ) φ( z) z in which n represent an inentation parameter. For inente bars which eform iealplastically it is expecte that the value of n is close to one [5]. p H (4)

7 6 4 th International Conference on Tribology in Manufacturing Processes - ICTMP 2010 The ratio of real to apparent area of contact α can be foun by equation 5 once the amount of inentation an rise of the valleys U are calculate from equation 2, 3 an 4: U Ar α = = φ( z) z (5) A nom An extensive research on the influence of the parameters η an n on the real area of contact, amount of inentation an rise of the valleys can be foun in [5]. Besies an ieal-plastic contact moel for normal loaing, Westeneng erive an analytical contact moel which escribes the influence of strain on eforming, arbitrary shape, asperities. The harness of the eforming asperities will ecrease ue to stretching of the material resulting in a higher amount of inentation of the contacting asperities an rise of the non-contacting asperities U. The subscript s correspons s to the influence of strain on the parameters an U foun by the ieal plastic contact moel for normal loaing. Values for α, s an solution scheme, see Figure 3. s U can be foun by an iterative The parameter l in Figure 3 represents half the asperity istance an can be obtaine from equation 6 with Q representing the asperity ensity of the workpiece. The nonimensional strain rate E is escribe by Wilson & Sheu [7] for a plane stress eformation moe an by Sutcliffe [8] for a plane strain eformation moe. l 2 1 = (6) Qα s U, an from ieal plastic contact moel (Eq. 2 an 3) α l = φ U S S ε E ( ) α = α + α p nom an 0 = 0 = φ S U S S U S ( z) z α ( z ) φ( z) z U ( 1 α ) S S S an U S Figure 3: Calculation scheme for strain contact moel

8 Multiscale friction moeling for sheet metal forming SHEAR STRESSES The friction moel of Challen & Oxley [2] takes the combining effect of ploughing an ahesion effects between wege-shape tool asperities an flat workpiece asperities into account. Westeneng [5] extene the moel of Challen & Oxley to escribe friction conitions between a flat workpiece material an multiple, spherical-shape tool asperities, Figure 4. This moifie friction moel of Challen & Oxley has been implemente in the numerical proceure to escribe friction conitions between the tool an workpiece material. Tool surface ø(s) Workpiece surface Figure 4: Inentation tool asperities Westeneng escribes the translation from friction forces occurring at single asperity contacts to the total friction force at multiple asperities by: F w t nom smax ( s) = ρ αa F φ s (7) w, asp t δ ρ represents the asperity ensity of the tool surface, α the ratio of real to In which t apparent area of contact of the workpiece, Anom the nominal contact area, φt the normalize surface height istribution function of the tool surface an F w, asp the friction force occurring at one single asperity. The friction force F w, asp is escribe by Challen & Oxley [2] for wege-shape asperities an Westeneng [5] for spherical shape asperities. The bouns of the integral are escribe by s max, the maximum height of the tool asperities, an δ, the separation between the workpiece surface an the mean plane of the tool asperities (Fig. 4). The amount of separation δ can be calculate base on force equilibrium by solving the equation: s max 0 = t ρt δ ( s δ ) φt ( s) sh pnom πβ (8) The term between brackets represents the ratio of real to apparent area of contact of the tool asperities penetrating into the workpiece material an β t is the mean raius of the tool asperities. If the shear stresses are known from Equation 7 the coefficient of friction can be calculate by equation 9: F w, asp µ = (9) F N s max

9 8 4 th International Conference on Tribology in Manufacturing Processes - ICTMP RESULTS The numerical proceure to etermine the friction coefficient is teste in a simulation of the cross-ie prouct (Fig. 5). The cross-ie prouct is a test prouct esigne by Renault which approximates process conitions of complex automotive parts. Simulations are performe using the in house FE coe Dieka, evelope at the University of Twente. Due to symmetry of the cross-ie prouct only a quarter of the workpiece was moele. The workpiece was meshe by 9000 triangular iscrete Kirchhoff shell elements using 3 integration points in plane an 5 integration points in thickness irection. The yiel surface was escribe by the Vegter moel [12] using the Bergström Van Liempt harening relation [13] to escribe harening behavior. Material parameters were use from DC04 low carbon steel, a typical forming steel use for SMF processes. Contact between the tools an the workpiece was escribe by a penalty metho using a penalty stiffness of 200 N/mm. The coefficient of friction use in the contact algorithm was calculate base on the numerical proceure presente in this paper. Moels to escribe flattening ue to normal loaing an flattening ue to stretching were inclue to etermine ploughing an ahesion effects between contacting asperities. The simulation was performe by prescribing the isplacement of the punch until a total isplacement of 60 mm was reache. The punch spee was set to 6 cm/sec an the applie blankholer force was 61 kn. Two simulations have been performe in orer to show the iniviual contribution of the two flattening mechanisms. The first simulation only escribes the influence of normal loaing on the coefficient of friction, Figure 5. The secon simulation use both flattening moels to escribe the evelopment of the coefficient of friction, Figure 6. Both figures show higher contact ratios an friction coefficients in areas where higher strains an contact pressures occur. 15% % 0.00 Figure 5: Development real area of contact (left) an coefficient of friction (right) for normal loaing only

10 Multiscale friction moeling for sheet metal forming 9 99% % Figure 6: Development ratio of real to apparent area of contact (left) an coefficient of friction (right) for normal loaing + stretching If only flattening ue to static loaing is assume (Fig. 5), rather low values for the real area of contact are obtaine resulting in low values for the coefficient of friction. This result is questionable, but it shoul be notice that only one flattening mechanisms has been taken into account uring the simulation. If the secon flattening mechanism is taken into account (flattening ue to stretching) much higher values for the real area of contact are obtaine (Fig. 6). The higher amount of contact ratios results in higher values of the coefficient of friction which eventually leas to a friction istribution lying within the range of expectation. Expecte values of the coefficient of friction are foun in regions where high strains an contact pressures occur an low values of the coefficient of friction are obtaine in low pressure regimes. 4 CONCLUSIONS This paper presents a numerical proceure to calculate the coefficient of friction uring large scale FE simulations. The numerical proceure inclues two flattening mechanisms to escribe the real area of contact, a friction moel incluing ploughing an ahesion effects to calculate the coefficient of friction an statistical parameters to make the translation from micro- to macro moeling. The numerical proceure has been applie to a full scale sheet metal forming simulation which shows the applicability of the evelope algorithm. Results of the simulations have shown that relatively low values of the coefficient of friction are foun in case of normal loaing only, the first flattening mechanism. If a secon flattening mechanism is applie, flattening ue to stretching, much more promising results are obtaine. Besies the friction mechanisms iscusse in this paper, other mechanisms exist which are expecte to have a large influence on the real area of contact an coefficient of friction. The influence of sliing an roughening ue to stretching on the real area of contact shoul not be neglecte, as well as hyroynamic friction stresses occurring in the mixe lubrication regime. Therefore more research is require to inclue these epenencies into the numerical proceure to obtain a reliable an accurate multi-scale friction moel. 0.00

11 10 4 th International Conference on Tribology in Manufacturing Processes - ICTMP ACKNOWLEDGMENTS This research was carrie out uner the project number MC in the framework of the Research Program of the Materials innovation institute M2i ( 6 REFERENCES [1] W.R.D. Wilson, Friction moels for metal forming in the bounary lubrication regime, American Society of Mechanical Engineers 10 (1988) [2] J.M. Challen an P.L.B. Oxley, An explanation of the ifferent regimes of friction an wear using asperity eformation moels, Wear 53 (1979) [3] N. Patir an H.S. Cheng, An average flow moel for etermining effects of threeimensional roughness on partial hyroynamic lubrication, Journal of Lubrication Technology 100 (1978) [4] W.R.D. Wilson an D.F. Chang, Low spee mixe lubrication of bulk metal forming prcesses, Journal of Tribology 118 (1996) [5] J.D. Westeneng, Moelling of contact an friction in eep rawing processes, PhD thesis, University of Twente (2001) [6] J.A. Greenwoo an J.B.P. Williamson, Contact of nominally flat surfaces, Proceeings of the Royal Society of Lonon. Series A, Mathematical an Physical sciences 295 (1966) [7] W.R.D Wilson an S. Sheu, Real area of contact an bounary friction in metal forming, International Journal of Mechanical Science 30 (1988) [8] M.P.F. Sutcliffe, Surface asperity eformation in metal forming processes, International Journal of Mechanical Science 30 (1988) [9] S.W. Lo an T.S. Yang, A new mechanism of asperity flattening in sliing contact the role of tool elastic microwege, Journal of Tribology 125 (2003) [10] H-C. Shih, W.R.D Williamson an P.K. Saha, Moeling the influence of plastic strain on bounary friction in sheet metal forming, Proceeings of the North American Manufacturing Research Conference 24 (1996) [11] J. Pullen an J.B.P. Williamson, On the plastic contact of rough surfaces, Proceeings of the Royal Society of Lonon. Series A, Mathematical an Physical sciences 327 (1972) [12] H. Vegter an A.H. van en Boogaar, A plane stress yiel function for anisotropic sheet material by interpolation of biaxial stress states, International Journal of Plasticity 22 (2006) [13] A.H. van en Boogaar an J. Huétink, Simulation of aluminium sheet forming at elevate temperatures, Computer Methos in Applie Mechanics an Engineering 195 (2006)