Finite Element Investigation of Friction Condition in a Backward Extrusion of Aluminum Alloy

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1 Yong-Taek Im Professor, Fellow ASME Seong-Hoon Kang Jae-Seung Cheon Computer Aided Materials Processing Laboratory, Department of Mechanical Engineering, ME3227, Korea Advanced Institute of Science and Technology, Kusong-dong, Yusong-gu, Taejon , Korea Finite Element Investigation of Friction Condition in a Backward Extrusion of Aluminum Alloy Finite element simulations are being widely used to increase the efficiency and effectiveness of design of bulk metal forming processes. In such simulations, proper consideration of friction condition is important in obtaining reliable results. For this purpose, the shear friction factor is widely used for bulk deformation analyses. In the earlier work, it was found that a radial tip was formed on the extruded end of the workpiece and that the radial tip distance had a linear relationship with the forming load in the tip test. In order to characterize the global average shear friction factor, a linear relationship between the nondimensionalized radial tip distance and shear friction factor was numerically determined in this study for AL6061-O for various lubrication conditions. The global average friction condition at the bottom die interface was determined to be about 60 percent of the one at the punch in the backward extrusion under the present conditions. DOI: / Introduction With the recent increase in demand for net shape forming, necessity for more efficient design has become an important issue. Instead of using traditional design methods based on experiments, experience, and trial-and-error, the use of computers in the design of metal forming operations has become widespread to reduce both development time and cost. As such, the numerical analysis of metal forming processes based on the finite element method FEM has become a common tool in the process design and die design stages of product development. For such FE simulations to be reliable, it is crucial to accurately describe the friction condition, since it directly affects factors such as material flow, forming load, and tool wear. To date, the constant shear friction model is most widely used to quantitatively describe the global average friction condition in bulk metal forming operations. The shear friction factor must be determined based on lubrication conditions in order for the constant shear friction model to be used effectively. The ring compression test 1 4 has been widely used due to its simplicity of experimentation. However, due to its simplicity, the shear friction factor obtained from the ring compression test may not be always suitable for actual metal forming processes. Thus, friction testing methods based on other forming processes have been proposed. However, most of these methods such as spike forging test 5,6, bucket test 7, injection upsetting 8, and combined forward and backward extrusions 9 13 require nonlinear calibration curves and the test equipment is rather complex in design and operation. Nakamura et al. 14 proposed a friction testing method based on backward extrusion, but in this method, the dependency on forming load measurement was too high. Recently, Im et al. 15 proposed the tip test based on backward extrusion that can determine the global average friction condition from the radial tip distance from the side wall of the deformed workpiece. In this work, experimental tests revealed that by setting the initial workpiece diameter to be a value between the outer diameter of the punch and the inner diameter of the lower die cavity, the radial tip is formed on the extruded end of the workpiece deformed. From experiments with various lubricants, it was found that the radial tip distance and maximum forming load increase depending on the level of friction. Moreover, by plotting Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received July 2001; Revised November Associate Editor: S. Schmid. the radial tip distance and maximum forming load for each lubricant, it was found that the relationship between the two is in linear. This suggested that the simple geometrical measurement of this radial tip distance can be used effectively as an indicator of the global average friction condition. The current study is a following investigation to link the measured radial tip distance directly with the prediction of global average shear friction factor. Finite element analyses were performed with varying shear friction factors. Since the radial tip distance has a linear relationship with the maximum forming load required, it might be construed that the radial tip distance and shear friction factor have a linear relationship as well. However, in the backward extrusion process the friction condition at the punch and lower die interfaces might not always be the same. In fact, it was observed that higher values of shear friction factor at the punch as compared to the die during numerical simulations of the backward extrusion process produced better result 13. Thus, in this study, the shear friction factor at the die was numerically determined by a certain percentage of the value assigned to the punch in order to make the slopes of the maximum forming load vs. radial tip distance curves obtained from simulations and experiments to be parallel. With this percentage value numerically determined, the linear relationship between the shear friction factor and radial tip distance was proposed to characterize appropriate shear friction factors for various lubricants used in experiments. Also, the predicted shear friction factors obtained from the linear relationship were compared to the values obtained from the ring compression test. 2 Numerical Simulation The dimensions of the punch and die used for experiments and FE simulations are given in Fig. 1. For numerical analyses, an in-house FE program for the metal forming analysis, CAMPform- 2D 16,17, was used. This program was developed based on the rigid-viscoplastic approach proposed by Lee and Kobayashi 18,19. In the current die-set, the initial cylindrical workpiece was made to have a diameter of 30 mm and a height of 15 mm. This workpiece was centered in the lower die by placing it in a shallow groove of depth 0.3 mm. It was found that the bottom surface of the workpiece remains in its original position inside the groove during deformation. Examination of the external shape of the deformed workpiece also revealed that this groove must be properly considered in numerical simulations. 378 Õ Vol. 125, MAY 2003 Copyright 2003 by ASME Transactions of the ASME

2 Fig. 1 Dimensions of the axisymmetric a punch and b die used for the tip test dimensions in mm Fig. 2 Stress-strain curve obtained from the compression test of an aluminum alloy AL6061-O FE simulations with various shear friction factors were carried out to examine its influence on formation of the radial tip distance and forming load. The flow stress for material characterization of AL6061-O was obtained through compression tests with grease as shown in Fig. 2. It was fitted to be MPa, where and are the effective stress and effective strain, respectively. In order to handle the rigid zone problem, the limiting strain of 10 5 was introduced in the present investigation as explained in reference 19. It should also be noted that the lubricants were simply applied to the raw workpiece material with a brush or sprayed as uniformly as possible for all compression and tip test experiments. Figure 3 a shows the simulation conditions for a typical case. The punch velocity and the stopping punch stroke were set as 5.0 mm/s and 8 mm, respectively. The initial workpiece, made to fit in the shallow groove of the lower die, was initially modeled by 1156 isoparametric nodes and 1089 quadrilateral elements. Only half of the workpiece dimension (15 mm 15 mm) was used due to symmetry of the axisymmetric problem. About 43 remeshings were required to finish the numerical calculation including the effect of the shallow groove. For this example, the shear friction factor was assumed to be 0.1 everywhere. The result of this simulation example is given in Fig. 3 b. Here, the deformed shape of the workpiece after extrusion is shown along with the distribution of effective strain. It can be confirmed that the current backward extrusion set-up results in the generation of the radial tip at the extruded end, and this radial tip is at a certain distance, d, from the external side surface of the specimen. Also, the thickness of the extruded end, t, is indicated Fig. 3 Example of FE simulation a conditions and b results showing the deformed shape and distribution of effective strain Journal of Manufacturing Science and Engineering MAY 2003, Vol. 125 Õ 379

3 Fig. 6 Dependence of radial tip distance and maximum forming load on varied x with m fp fixed as 0.5 Fig. 4 Load vs. stroke curve obtained from the FE simulation with shear friction factor of 0.1 in the figure. The higher mesh density in the groove region that was used to improve the accuracy of simulations can be seen in the results as well. Figure 4 shows the change of forming load with the stroke for this simulation example. This curve shows that the forming load increases steadily during the upsetting phase phase I of the process, then sharply rises when the workpiece begins to be extruded backward, and finally begins to level off during extrusion phase II. The maximum forming load, indicated by L, is the load calculated at the stroke of 8 mm as shown in the figure. Ten simulations were carried out using shear friction factors in the range of with the increment of 0.1 to examine their influence on the radial tip distance formed and maximum forming load. Similar to the experiments, the simulation results showed that the relationship between the maximum forming load, L, and the radial tip distance, d, was linear as shown in Fig. 5. In this figure, nondimensionalized L/L 0.9 was plotted as a linear function of d/t. Here, L kn was the maximum forming load when using a shear friction factor of 0.9 and t 3.4 mm was the thickness of the extruded end of the deformed workpiece. As can be seen in Fig. 5, it was found that the slopes of the L/L 0.9 vs. d/t graphs were different for the simulation and experimental results. Also, it was found that the measured values of the radial tip distances from experiments were not all within the range of radial tip distances obtained from simulations. For example, the largest value of d/t obtained from the simulation using the shear friction factor of 0.9 was only 0.40, but the average measurement from the three experiments with lubricant WD 40 used was The lubricant was sprayed on the raw workpiece as uniformly as possible. Such discrepancies between the experimental and simulation results suggest that using the same shear friction factor for both the punch and die may not be appropriate. Thus, numerical studies were conducted in such a way that the shear friction factor of the die, m fd, was assumed to be a certain percentage of that assigned to the punch, m fp. That is, m fd /m fp x where 0.0 x 1.0. This approach was introduced in order to make the slopes of the maximum forming load vs. radial tip distance curves obtained from simulations and experiments to be parallel. In order to investigate the effect of x on the radial tip distance and maximum forming load, FE simulations were carried out. When m fp was assumed to be 0.5, x was varied among 1.0, 0.8, Fig. 5 Load vs. radial tip distance curves obtained from FE simulations with shear friction factors ranging from 0.0 to 0.9 and experiments using various lubricants Fig. 7 The procedure of obtaining the linear calibration equation for predicting the appropriate shear friction factor 380 Õ Vol. 125, MAY 2003 Transactions of the ASME

4 Fig. 8 Load vs. radial tip distance curves depending on the value of x for the various friction conditions of m fp ranging from 0.0 to and 0.4. This resulted in d/t values of 0.327, 0.341, and 0.375, respectively. Also, the resultant L/L 0.9 was 0.748, 0.717, and 0.658, respectively. Figure 6 shows the dependency of both d/t and L/L 0.9 on x. As can be seen in this figure, when the value of x decreases d/t becomes larger, while L/L 0.9 becomes smaller. These results indicate that the slope of the numerically obtained L/L 0.9 vs. d/t graph can be made parallel to the slope of the L/L 0.9 vs. d/t graph obtained from experiments depending on the value of x. 3 Relationship Between Shear Friction Factor and Tip Distance Figure 7 shows overall procedure used in the present investigation in predicting the global average shear friction factor. As mentioned previously, the load vs. radial tip distance curve in Fig. 5 was obtained by plotting the nondimensionalized maximum loads, L/L 0.9, and radial tip distances, d/t, for various shear friction factors. More specifically, the shear friction factors were varied in the range of with the increment of 0.1 for both the punch and die. In order to determine the influence of x on load vs. radial tip distance curves, further simulations were carried out in a similar manner except that x was changed to 0.8, 0.6, and 0.4 instead of 1.0. Figure 8 shows the result of these simulations. This figure clearly demonstrates that the slope of the curves depends on x. Also, it can be seen that the linearity between the radial tip distance and maximum forming load was maintained regardless of the value of x. As shown in Fig. 9, it was found that the simulation case of x 0.6 resulted in a slope that best matched the experimental one. From this result, it is notable that the friction level at the punch interface is higher than the one at the die interface in the backward Fig. 9 Comparison of load vs. radial tip distance plots between the experiments and simulations for xä0.6 extrusion process. Although the slopes of the graphs obtained from experiments and simulations are parallel, a small gap exists between the two in this figure. The overall load error between the experiment and simulation results was about 8.5%. This error might be due to material characterization, and machine and human errors involved with measurements of tip distance and forming load. Once a linear calibration curve fitted between these two simulation and experimental graphs is used, this error can be reduced further. Also, it should be noted that some error between experimental and simulation results is unavoidable when using the shear friction model without characterizing the actual friction condition that varies depending on position and time in reality. Since each dimensionless maximum forming load, L/L 0.9,in the load vs. radial tip distance curve has corresponding global average shear friction value, the result of the load vs. radial tip distance curve using x 0.6 condition can be directly converted into the shear friction factor vs. radial tip distance curve according to the linearity between these two. This conversion leads to the following linear equations: m fp 3.38 d/t 0.72 or m fd 2.03 d/t 0.43 (1) These linear expressions can now be used to predict the appropriate shear friction factors of the punch and the die for various lubrications. By inserting the dimensionless radial tip distances measured from the experiments into Eq. 1, the corresponding shear friction factors of the punch and die can be easily calculated. The shear friction factors calculated in this way according to various lubricants are summarized in Table 1. The radial tip distances obtained from experiments and simulations are also listed in this table. It can be seen that two values are very similar to each other. In order to confirm the validity of such friction factors calculated, the deformed shapes obtained from the experiments and simulations were compared as well in Fig. 10 for the case of tip test with industrial oil grade VG 100. As listed in Table 1, this Table 1 Predicted shear friction factors obtained by the tip test and ring compression test for various lubricants ring compression test method tip test test d/t lubricant experiment simulation m fp m fd m f Grease VG VG WD Journal of Manufacturing Science and Engineering MAY 2003, Vol. 125 Õ 381

5 Fig. 10 Comparison of deformed shapes between the experiment using the lubricant VG100 and simulation using m fp Ä0.38 and m fd Ä0.23 at strokes of a 4.9 mm and 8.0 mm simulation was carried out with m fp 0.38 and m fd This figure shows that the deformed shapes are in good agreement with each other for both strokes of 4.9 mm and 8 mm. Although the results are not shown here because of space limitation, it was found out that such agreement of deformed shapes was found for other lubricants investigated as well. The load-stroke curves obtained from the experiment and simulation for the same case is shown in Fig. 11. Two other cases with m fp m fd 0.38 and m fp m fd 0.23 were simulated as well. For the case with m fp m fd 0.38, it can be seen that the load error increases further. Also d/t for this case was found to be 0.292, while the case using m fp 0.38 and m fd 0.23 gave d/t as 0.314, which is in better agreement with the experiment. The case with m fp m fd 0.23 actually gives a similar result in terms of load prediction, but d/t was found to be 0.259, which is a larger deviation from the experimental result. In this approach, two global average shear friction factors, m fp and m fd are predicted for each lubricant. These values were compared to the results from ring compression tests for the same lubricants. The experimental results obtained from ring compression tests are shown in Fig. 12 along with the calibration curves. The shear friction factors determined by the ring compression tests are summarized in Table 1. As can be seen in this table, the predicted shear friction factor at the punch by the tip test is approximately two times the value of that obtained by ring compression test for each lubricant investigated. It might be construed that the global shear friction factor for the complex forming process will be the value between m fd and m fp determined by the linear relationship of Eqn. 1, depending on the level of new surface generation during deformation. 4 Conclusion In the present investigation, finite element investigations were made to determine the global average friction conditions at the punch and bottom die interfaces. It was revealed that the global average friction level at the punch interface is higher than that at the die interface as m fd /m fp 0.6. Finite element simulation results also clearly confirmed that the relationship between the radial tip distance and shear friction factor is in linear. This demonstrates the simplicity of the proposed tip test to determine the global average shear friction factor. Fig. 11 Comparison of load vs. stroke curves between the experiment using VG100 and simulations using various combinations of m fp and m fd various lubricants along with calibration Fig. 12 Experimental results of ring compression tests for curves 382 Õ Vol. 125, MAY 2003 Transactions of the ASME

6 Acknowledgment The authors wish to thank for the grant of Basic Research Fund from KAIST and BK21 project. Nomenclature d distance of the radial tip from the workpiece side wall L maximum forming load calculated at the stroke of 8 mm L 0.9 maximum forming load when using a shear friction factor of 0.9 m fp shear friction factor at the punch interface m fd shear friction factor at the die interface t thickness of the extruded end of the workpiece x ratio of die shear friction factor and punch shear friction factor effective stress effective strain References 1 Male, A. T., and Cockcroft, M. G., 1964, A Method for the Determination of the Coefficient of Friction of Metals Under Conditions of Bulk Plastic Deformation, J. Inst. Met., 93, pp Nagpal, V., Lahoti, G. D., and Altan, T., 1978, A Numerical Method for Simultaneous Prediction of Metal Flow and Temperature in Upset Forging of Rings, ASME J. Eng. Ind., 100, pp Chen, C. C., and Kobayashi, S., 1978, Rigid-plastic Finite-element Analysis of Ring Compression, H. Armen and R. F. Jones, Jr., eds., Applications of Numerical Methods of Forming Processes, AMD, New York, Vol. 28, pp Petersen, S. B., Martins, P. A. F., and Bay, N., 1998, An Alternative Ring-Test Geometry for the Evaluation of Friction under Low Normal Pressure, J. Mater. Process. Technol., 79, pp Im, Y. T., Vardan, O., Shen, G., and Altan, T., 1988, Investigation of Metal Flow in Non-Isothermal Forging Using Ring and Spike Test, CIRP Ann., 37, pp Isogawa, S., Kimura, A., and Tozawa, Y., 1992, Proposal of an Evaluation Method on Lubrication, CIRP Ann., 41, pp Shen, G., Vedhanayagam, A., Kropp, E., and Altan, T., 1992, A Method for Evaluating Friction Using a Backward Extrusion-type Forging, J. Mater. Process. Technol., 33, pp Nishimura, T., Sato, T., and Tada, Y., 1995, Evaluation of Frictional Conditions for Various Tool Materials and Lubricants using the Injection-Upsetting Method, J. Mater. Process. Technol., 53, pp Sanchez, T. R., Weinmann, K., and Story, J. M., 1985, A Friction Test for Extrusion based on Combined Forward and Backward Flow, Proceedings of the 13th North American Manufacturing Research Conference, pp Ohinishi, K., Gotho, H., Wadabayashi, R., Idemizu, T., and Shimabara, H., 1986, Evaluation of Lubricants for Warm Forging By Forward-Backward Extrusion, The Proceedings of the 1986 Japanese Spring Conference for the Technology of Plasticity, pp Popilek, M. E., Weinmann, K. J., and Majlessi, S. A., 1992, A Friction Test based on Combined Backward Can-Forward Bar Extrusion with Emphasis on Backward Flow, Trans. NAMRI/SME, 20, pp Buschhausen, A., Weinmann, K., Lee, J. Y., and Altan, T., 1992, Evaluation of Lubrication and Friction in Cold Forging Using a Double Backward- Extrusion Process, J. Mater. Process. Technol., 33, pp Nakamura, T., Bay, N., and Zhang, Z., 1998, FEM Simulation of a Friction Testing Method Based on Combined Forward Conical Can-Backward Straight Can Extrusion, ASME J. Tribol., 120, pp Nakamura, T., Zhang, Z. L., and Kimura, H., 1996, Evaluation of Various Lubricants for Cold Forging Processes of Different Aluminum Alloys, ICFG Do. No 2/ Im, Y. T., Cheon, J. S., and Kang, S. H., 2002, Determination of Friction Condition by Geometrical Measurement of Backward Extruded Aluminum Alloy Specimen, ASME J. Manuf. Sci. Eng., 124, pp CAMPform2D Users Manual version 1.5, 2002, campseries. 17 Kim, H. S., Im, Y. T., and Geiger, M., 1999, Prediction of Ductile Fracture in Cold Forging of Aluminum Alloy, ASME J. Manuf. Sci. Eng., 121, pp Lee, C. H., and Kobayashi, S., 1973, New Solutions to Rigid-Plastic Deformation Problems Using a Matrix Method, ASME J. Ind., 95 3, pp Kobayashi, S., Oh, S. I., and Altan, T., 1989, Metal Forming and the Finite Element Method, Oxford University Press, New York. Journal of Manufacturing Science and Engineering MAY 2003, Vol. 125 Õ 383