Numerical Simulation of Sliding Contact during Sheet Metal Stamping

Transcription

1 Numerical Simulation of Sliding Contact during Sheet Metal Stamping Biglari F. R. * Nikbin K. ** O Dowd N. P. ** Busso E.P. ** * Mechanical Engineering Department, Amirkabir University of Technology, Hafez Ave., Tehran, Iran biglari@cic.aku.ac.ir ** Mechanical Engineering Department, Imperial College London, London SW7 2BX, UK k.nikbin@ic.ac.uk n.odowd@ic.ac.uk e.busso@ic.ac.uk ABSTRACT: The results of a computational study to examine the effects of design parameters on the life of a coated die used in sheet metal stamping are presented. The stress distributions within the coating under a range of conditions were evaluated and the stresses relevant to failure of the coating by fatigue crack growth identified. The analyses indicate that there is an increase in peak stress from approximately 500 to 800 MPa when the spacing between surface asperities increases from 10 to 200 microns. Based on the numerical results, the life of the coating under contact fatigue conditions was determined. KEY WORDS: Sliding contact, wear resistant coating, finite element analysis, fatigue, fracture 1. Introduction Stamping is a metal forming operation widely used in the automotive industry. In the stamping process, a sheet metal workpiece is formed between a pair of dies to achieve the desired component shape. To extend the life of the die, the surface may be protected by a wear resistant coating; sliding contact then occurs at the interface between the sheet metal and coating surfaces. Due to the high contact stresses, microcracks can initiate near the coating surface and propagate under cyclic fatigue leading to failure of the coating. In this work, the finite element method is employed to determine the magnitude of the stresses induced in the coating at the microscale during the stamping process. The work extends the approach followed in [1], where a failure mechanism based on a strain ratchetting mechanism, relevant to ductile coatings, was examined.

2 2 The cyclic contact between a workpiece and a coated metal may be represented as illustrated in Fig. 1(a). In coatings with high hardness (high yield strength), experimental observations suggest that the induced contact stresses during sliding contact leads to micro-crack initiation as shown in Fig. 1(b). These cracks subsequently propagate due to the fatigue loading, (Fig. 1c), and when they reach a sufficient size lead to final failure of the coating. (a) Sliding contact (a) Workpiece Unit Cell coating Substrate Coating Substrate L (b) Sliding contact (b) Direction of motion of the workpiece Asperity Microcracks at Surface R slide lines (c) Sliding contact t h Coating Substrate L Figure 1. Microcrack initiation during sliding contact of sheet metal on a coated steel die. Figure 2. (a) Periodic representation of the sliding contact problem (b) Unit cell used in the numerical analysis 2. Computational Framework The roughness of the highly polished die may be assumed to be negligible compared to that of the workpiece as illustrated in Fig. 1. In this work the workpiece roughness is represented as periodic with wavelength L. Therefore, as shown in Fig. 2, the problem may be analysed using a single unit cell of width L. In order to satisfy the periodic nature of the problem, the vertical boundaries of the unit cell illustrated in Fig. 2(b) must remain parallel. Thus the deformation of each point on the left hand vertical boundary must follow that of the right hand vertical boundary. The same concept applies to the asperity body. To account for interactions between the moving asperities and the coating and with each other, deformable slide lines are defined as illustrated in Fig. 2(b). Each of the slide lines must follow the deformation of the corresponding slide line on the asperity or coating surface, i.e. all lines of the same type indicated in Fig. 2(b) deform identically. The horizontal slide

3 Numerical Simulation of sliding contact 3 line, which represents the deformation of the surface of the coating, extends the length of three unit cells, which allows a total sliding distance of 3L to be examined in the analysis. This corresponds to the distance that a workpiece will travel along the die during a single stamping cycle. Note in Fig. 2(c) that the geometry of the unit cell is specified by four length scales radius of the workpiece asperity, R, height of the asperity, h, width of the unit cell, L and coating thickness, t. However, it may be seen that only three of these parameters are independent and from the geometry of 2 2 the unit cell (Fig. 2b), 2R = 4( R h) + L. To determine the pressure distribution to be applied to the unit cell, finite element simulations of the stamping process at the macro scale were carried out [2]; the sliding distance during a stamping cycle at different points along the die was also determined from these analyses. From these macro-scale calculations, the average pressure during stamping was found to be P =1000 MPa and this was the stress applied to the asperity in the unit cell calculations Material Properties The tensile properties of the workpiece steel have been determined from uniaxial tests at the operating temperature (60 o C) and the stress strain curve is illustrated in Fig. 3. The Young s modulus of the steel is 200 GPa and the yield strength is 320 MPa. In the analysis, the steel is assumed to be a rate dependent, Mises material with isotropic hardening (MPa) T = 60 o C Figure 3. Tensile properties of the workpiece material The die is coated with a thin multilayer Nb-TiN coating deposited by physical vapour deposition. The coating thickness is approx. 3 microns with each layer of the coating on the order of a few nanometers [3]. The Young s modulus of the coating was found to be E = 400 GPa, based on microindentation data. The yield strength of the coating is significantly higher than that of the workpiece material and therefore in the analysis the coating is assumed to deform elastically. The substrate die steel has a Young s modulus of E = 200 GPa. It may be noted that the coating is

4 4 significantly stiffer than the substrate. This leads to a concentration of tensile stress in the coating as will be seen in Section 3. The asperity spacing typically varies from 10 to 200 µm in a rolled sheet metal [4, 5]. Six finite element analyses were carried out with a fixed coating thickness, t, of 3 µm and asperity spacing of 10, 15, 20, 40, 100 and 200 µm. In the analysis, the ratios, h /L and R/L are held fixed at 0.6 and 0.27 respectively. Thus the asperity height, h, ranges between 3 and 50 µm, typical values observed in sheet steel [4]. 3. Results from unit cell analysis Figure 4 shows an example of the principal stress distribution obtained from modelling the initial contact of the asperity with the coating. Full account is taken in the analysis of the large deformation changes associated with the contact loading. Coulomb friction is assumed between the die and the workpiece with µ = 0.1 Note that only a single unit cell has been modelled and the result has been mapped to a series of cells to illustrate the result. Although a compressive load is applied to the asperity it is seen that significant positive tensile stresses are generated in the coating. At high loads the neighbouring asperities may interact as illustrated in Fig. 4(b). It is seen that the boundary conditions specified in the analysis allow this effect to be fully accounted for. (Again only a single unit cell has been modelled and result mapped to the neighbouring cell.) σ 3 σ 1 (MPa) (a) (b) Figure 4. (a) Principal stress contours in the contact problem (b) Asperity deformation under large load 3.1. Effect of asperity spacing on principal stresses Figure 5 shows contours of maximum principal stress, σ 1, in a section of the coating for different asperity/cell sizes. For a given asperity height, h, and coating thickness, t, increasing the cell size, L, implies a reduction in the relative coating thickness, t/l. Thus when L increases the stresses become more concentrated in the coating as seen in Fig. 5. Figure 6 illustrates directly the dependence of the maximum

5 Numerical Simulation of sliding contact 5 principal stress on the asperity spacing, L. It is seen that the stress increases from 700 to 1000 MPa as the asperity spacing increases from 10 to 200 µm. (a) L = 10 µm (b) L = 40 µm σ 1 (MPa) (c) L = 100 µm (d) L = 200 µm Figure 5. Comparison of maximum principal stress contours in coating Maximum Principal Stress (MPa) t = 3 mm µ = 0.1 h/l = 0.6 R/L = Asperity unit cell width L [µm] Figure 6. Dependence of coating maximum principal stress on asperity spacing. 4. Contact fatigue life model of coating During its life the die is subjected to continuous sliding contact with the workpiece. This cyclic loading leads to the initiation and propagation of micro-cracks within the coating. Figure 7 illustrates the maximum principal stress history, obtained from the FE analysis, for three different regions of the coating as the asperity slides a distance of 3L. Here x measures distances from the right hand boundary of the unit cell. An initial sharp increase in stress can be seen at the beginning of the analysis where the normal loading on the asperity is first applied. A subsequent small variation in the peak stress values can be seen, which is due to the plastic deformation of the asperity while sliding over the die an elastic calculation

6 6 would provide a constant maximum principal stress throughout the analysis. As expected there is little difference in the peak stresses in the different regions, as under steady state conditions all regions of the unit cell experience near identical conditions as the asperity moves across the unit cell. Maximum Principal Stress (MPa) x Beginning = 0.5 µm x Centre = 5 µm x End = 9.5 µm Sliding Distance, s/l Figure 7. Stress history during sliding contact (asperity spacing, L = 10 µm). The stress data obtained from these analyses can be used to predict the life of the coating under fatigue conditions as discussed in the next section. σ 4.1. Determination of die lifetimes Fracture Mechanics Analysis The crack growth relation used in the analyses is of Paris-type form. The crack growth rate is expressed as a function of the stress intensity factor by a power law relation as follows, da dn m = C K [1] f where C and m are material parameters, K is the change in stress intensity factor and da/dn f is the rate of crack growth. The change in stress intensity factor is proportional to the change in stress, σ, via, K = Y σ π a, [2] where a is the microcrack size and Y is a geometry factor and depends on whether the initial microcrack is a surface defect or embedded within the coating region.

7 Numerical Simulation of sliding contact 7 If the crack size reaches the critical size a > a c, rapid crack propagation will take place leading to failure of the coating. However, if the critical crack size, a c, is greater than the coating thickness, t, then coating failure corresponds to the situation when the crack length is equal to the coating thickness. The value of a c depends on the highest positive effective stress range (maximum principal stress) in the coating layer during a sliding cycle, σ, which is obtained from the finite element analysis discussed in the previous sections (see Fig. 7). The critical crack size is then given by 1 KIC a =, c [3] π Y σ where K IC is the fracture toughness of the coating. In Eq. 1 the parameters C and m are required and the fracture toughness, K IC is needed to obtain the critical crack size via Eq. 3. An extensive literature search was carried out to obtain the fracture and crack growth data for coating materials similar to the NbTiN coatings of interest in this work. In order to obtain appropriate values for C and m a set of data for a range of ceramic coating materials [6] was used. The fatigue crack growth sensitivity in ceramic materials are much greater that in metallic materials [6] so the predicted results will be sensitive to the values chosen for C and m. The mean value, in the Paris law in Eq. 1 for the ceramic coating data was used, giving m = 27 and C = (with stress in MPa and crack length in metres). The fracture toughness of the coating was taken to be K IC = 4 MPa m 1/2 which is an average value for a range of similar ceramic materials [7]. It has been found that surface defects are predicted to result in a shorter life than for a similar size defect within the coating and, based on the results of the finite element analysis of the previous section, that the critical crack size, a c, for the coating materials is greater than the coating thickness, t. Therefore, for a coating thickness, t, the failure of the coating will occur when a surface microcrack grows by an amount equal to the thickness, i.e. a = t Results of finite element die life predictions Figure 8 illustrates the dependence of the die life on the initial microcrack size for different asperity sizes using Eq. 3, the mean values for the fatigue growth parameters and the principal stress values given in Fig. 6. It was seen in Fig. 6 that the maximum stress in the coating is strongly dependent on L and therefore the life of the coating will depend on asperity spacing. It is also seen in Fig. 8 that as the initial microcrack size increases, the number of stamping cycles required for failure decreases. The life of the production dies used in the stamping operation under study is between 20,000 and 30,000 cycles [2]. This is close to the lower bound life prediction presented in Fig. 8 for L = 200 µm with a i = 0.5 µm. Therefore if an initial microcrack size on the order of 0.5 µm exists in the coating, the life of the coated die, will be between 20,000 and 30,000 cycles. Thus, based on the current analysis, the largest defect present in the coating at start of life should be less than 0.5 µm to avoid fatigue failure of the coating within the service life.

8 8 Ns [Cycles] 1.E+18 1.E+12 1.E+06 Asperity Asperity unit spacing, cell width L, L µm [µm] E+00 lifetime of production dies a i [ µm] Figure 8. Effect of initial crack size on the number of stamping cycles to failure. 5. Conclusions A computation study of sliding contact in sheet metal stamping was presented. The surface of the sheet metal was modelled by a series of periodic unit cells with cylindrical asperities and the stresses within the coating were determined from finite element analysis. The predicted minimum lifetime of the coated dies was seen to be comparable to the observed lifetimes for production dies if the largest flaw in the coating at start of life is less than 0.5 µm. 6. References [1] YAN, W., BUSSO, E.P. and O DOWD, N.P., A micromechanics investigation of sliding wear in coated components, Proc. R. Soc. Lond. A, Vol , [2] TUNVISUT, K., 2002, PhD Thesis, University of London. [3] BRITE EURAM project, BE , Development of Engineering Surface Coatings obtained by advanced, cost effective and environmentally friendly technologies, [4] BUTLER, R. D., and POPE, R. J., Surface Roughness and Lubrication in Sheet Metal Working, Proc. Inst. Mech. Engineering, Vol. 182, p , [5] ROIZARD, X. and VON STEBUT, J., Surface Asperity Flattening in Sheet Metal Forming, A 3-D relocation stylus profilometric study, International Journal of Machine Tools and Manufacture, Vol. 35, No. 2, p , [6] RITCHIE, R. O. and DAUSKART, R. H., Cyclic Fatigue of Ceramics, Journal of Ceramic Society, Japan, Vol. 99, pp , [7] ASHBY, M. F. and JONES, D.R.H. Engineering Materials I, Pergammon Press, England, 1980.