FINITE ELEMENT SIMULATION OF PORE CLOSING DURING CYLINDER UPSETTING

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1 Modern Physics Letter B World Scientific Publishing Company FINITE ELEMENT SIMULATION OF PORE CLOSING DURING CYLINDER UPSETTING MIN CHEOL LEE, SUNG MIN JANG, JU HYUN CHO School of Mechanical and Aerospace Engineering, Gyeongsang National Universit, 900 Gajwa-dong, Jinju-City, GyeongNam, , Republic of Korea MAN SOO JOUN* * Corresponding author, School of Mechanical and Aerospace Engineering, RRC/Aricraft Parts Technology, Gyeongsang National University, 900 Gajwa-dong, Jinju-City, GyeongNam, , Republic of Korea msjoun@gnu.ac.kr Received Day Month Day Revised Day Month Day Three-dimensional precision simulation of pore closing during cylinder upsetting is carried out in this paper. A matrix of pores on the longitudinal section of a cylindrical material is traced at the same time. Various ratios of pore-to-cylinder diameter are tested to reveal their effect on the pore closing phenomena. Hydrostatic pressure and effective strain as well as the order of pore closing are investigated in detail to find out major factors affecting pore closing. It is shown that the effective strain has a strong relationship with the pore closing phenomena and that the finishing time of pore closing increases as the ratio of pore-to-cylinder diameter increases but that the pore size effect becomes negligible if the ratio exceeds a critical value. An intelligent metal forming simulator AFDEX 3D is used. Keywords: Precision simulation; pore closing; cylinder upsetting; intelligent remeshing 1. Introduction In open die forging of large mechanical parts including ship engine parts, wind power generator parts and the like, the cast material, that is, the cast ingot, is progressively formed to the desired shape by a series of upsetting or cogging processes. The major purposes of the open die forging include improvement of product quality as well as material saving. In general, a large cast ingot has many cavities or defects especially near its central region. These may cause deterioration of product quality or decisive damage of the system. For this reason, the pore or cavity closing has attracted interests of the researchers on the open die forging of the large mechanical parts for a long time. In spite of its significance, the related research works are not sufficient enough to be a guide for process design engineers. The reason lies in that both experimental approaches 1-4 and analytical or numerical approaches 5-14 have their own limitations. That is, experiments of large-scaled materials are very costly and difficult and most conventional simulation 1

2 2 Min Cheol Lee, Sung Min Jang. Ju Hyun Cho and Man Soo Joun techniques are also poor at describing the pore closing phenomena due to their poor remeshing capability. Tomlinson and Stringer 1 and Kopp and Ambaum 2 carried out an experimental study on the pore closing phenomena. Erman et al. 3,4 studied a physical modeling for the experiments of metal flow during open die forging. Tanaka et al. 5 conducted analysis of pore closing during cogging process and proposed a pore closing criterion. Stahlberg et al. 6 studied rectangular cavity closing by the upper-bound method and they compared the predictions with experiments. From the late 1980s, finite element methods 7-14 have been used to study the pore closing phenomena in open die forging. Shah et al. 7 applied threedimensional rigid-plastic finite element method to simulating open die forging processes without considering the pore closing phenomena. In the early years of finite element method based researches on pore closing, most researchers had used two-dimensional approaches 8,10,11,12 in which the pore shapes were considered as pipes in plane strain approach or rings in axi-symmetric approach. On the contrary, in recent years, most researchers on these topics have used three-dimensional finite element methods 9,13,14. However, it is not easy to find research works on precise simulation of pore closing of small spherical pores even though several researchers have tried to apply them to solving the pore closing phenomena. The reason has caused from some difficulties in remeshing because geometries of the pores during being closed are too complex to be automatically remeshed. In recent years, Lee et al. 15 developed an intelligent mesh generation technique and applied it to an intelligent metal forming simulator AFDEX 3D 16, based on a rigidthermoviscoplastic finite element method and tetrahedral MINI-elements. In this paper, the pore closing phenomena is investigated using AFDEX 3D. 2. Simulation of Pore Closing in Cylinder Upsetting Detailed pore closing phenomena during cylinder upsetting in open die hot forging of large mechanical parts have not fully revealed until now, even though its major purpose is to improve product quality by closing the internal pores in a mechanical way. Large size of a material has discouraged the researchers to approach empirically to the problem and poor remeshing capabilities have also limited application of the simulation technologies to solving the problem. Recently Lee et al. 12 developed an intelligent remeshing technique and applied it to developing an intelligent metal forming simulator, called AFDEX 3D. The intelligent remeshing technique is based on various surface mesh quality optimization schemes 17,18, which is essential to solve the pore closing phenomena with higher accuracy. We thus applied AFDEX 3D to solving the pore closing phenomena in this study. Figure 1 shows the initial material of which diameter and height are all 300 mm. In the figure, all pores are located equally on the twelve planes of symmetry, evenly spaced by the circumferential angle of 30 and a matrix of ten pores having the same diameters is located on each plane. The diameters of the pores investigated involve 2.5 mm, 5.0 mm, 7.5 mm, 10.0 mm, 12.5 mm and 15.0 mm. The flow stress of the material was assumed as

3 Finite Element Simulation of Pore Closing During Cylinder Upsetting in Open Die Hot Forging 3 = the opposite direction with the constant speed of 300 mm/sec. 0.2 σ 64.4ε MPa and the friction factor as 0.6. The upper die and lower dies moved in 300 mm/sec Pore 1 Pore 2 Pore mm Pore 3 Pore 6 15 O Pore mm 150 mm Symmetry plane Fig. 1. Schematic description of the workpiece Fig. 2. Analysis model of the process Using the symmetry of the process, only one forty-eighth of the cylinder was considered as the solution domain as shown in Figure 2. During simulation, the number of tetrahedral elements was controlled to be less than When mesh densities were calculated for remeshing, not only state variables including the effective strain and effective strain-rate but also geometrical features including the surface curvature were considered 15. However, user-intervention during the whole simulation and mesh density control using special user-defined mesh density functions 18 were excluded. During automatic simulation, when a node on the material surface penetrated into the material, then the related region was considered as closed. Overall procedure of pore closing and disappearing for the 15 mm pore diameter case is shown in Figure 3 and detailed pore closing history of Pore 1 is shown in Figure 4. As shown in these figures, mesh densities near the pores were well distributed and thus even small shrunk pores did not disappear artificially during remeshing. Throughout the whole simulation, 65 remeshings were conducted to obtain the solutions shown in Figure 3. Reduction = 0.00% 24.32% 32.43% Reduction = 37.84% 45.95% 54.05% Fig. 3. Pore closing history of the 15.0 mm pore diameter case

4 4 Min Cheol Lee, Sung Min Jang. Ju Hyun Cho and Man Soo Joun Reduction = 0.00% 13.63% 23.50% 36.43% 39.10% 47.30% Fig. 4. Detailed pore closing history of Pore 1 for the 15.0 mm pore diameter case Figures 5(a) and 5(b) show variation of the hydrostatic pressure and effective strain at all the pore locations with the stroke or reduction for the 15.0 mm pore diameter case, respectively. The lowest point of the pore was traced to measure those state variables. Figure 6 shows the reductions at which each pore disappeared for all the cases of six different pore diameters Hydrostatic pressure (MPa) Pore1 Pore2 Pore3 Pore4 Pore5 Pore6 Effective strain Pore1 Pore2 Pore3 Pore4 Pore5 Pore Reduction (%) Reduction (%) (a) Hydrostatic pressure (b) Effective strain Fig. 5. Variations of the hydrostatic pressure and effective strain with the reduction for the 15.0 mm pore diameter case Figure 5(a) shows that hydrostatic pressure changed drastically from negative to positive during pore closing. It can be seen from the figure that the hydrostatic pressures at all pores were narrowly distributed before pore closing started while they were relatively widely scattered to the contrary after pore closing finished. It is noted that the hydrostatic pressure at Pore 2 was relatively high in comparison with the other pores except Pore 6 even though Pore 2 closed last as can be seen in Figure 5(a) and Figure 6(a), indicating that the hydrostatic pressure has no direct influence on pore closing. On the contrary, the order of pore closing that can be seen in Figure 6(b) for the 15 mm pore diameter case is nearly the same with the order of pores having higher effective strain in Figure 5(b), implying that the effective strain has a strong and direct influence on pore closing. It can be seen from Figures 5(b) and 6(a) for the 15.0 mm pore diameter case that all pores but Pores 3 and 5 closed when their effective strains reached around

5 Finite Element Simulation of Pore Closing During Cylinder Upsetting in Open Die Hot Forging while Pores 3 and 5 closed when they reached around 0.6. This fact might be associated with the effect of hydrostatic pressures because they are lowly ranked as seen in Figure 5(a). The hydrostatic pressure may also play an important role in determining the order of pore closing if the effective strains of two pores are nearly the same, as can be seen from Figures 5 and 6(a) for Pores 1 and 5. It is thus concluded that the hydrostatic pressure plays an indirect but non-negligible role in pore closing. It can be also seen from Figure 6(a) that the finishing time of pore closing increased on average as the pore diameter increased but that the pore size effect became negligible when the pore diameter exceeded 7.5 mm 20 Pore diameter (mm) Pore1 Pore2 Pore3 Pore4 Pore5 Pore6 Pore 1 Pore Pore 2 Pore Reduction (%) Pore 5 Pore (a) Reductions at which pore closing took place (b) Order of pore closing, 15.0 mm pore diameter Fig. 6. Reductions when pore closing took place and the order of pore closing for the 15.0 mm pore diameter case 3. Conclusions In this paper, three-dimensional finite element simulations of pore closing in cylinder upsetting was carried out using AFDEX 3D, a general-purpose intelligent metal forming simulator based on the rigid-thermoviscoplastic finite element method and tetrahedral MINI-elements. Various ratios of pore-to-cylinder diameter, that is, 2.5/300.0, 5.0/300.0, 7.5/300.0, 10.0/300.0, 12.5/300.0 and 15.0/300.0, were considered and a matrix of pores located on the longitudinal section of the cylindrical material was investigated. It was observed that the finishing time of pore closing increases as the ratio of poreto-cylinder diameter increases but that the pore size effect becomes negligible if the ratio exceeds 7.5/ It was found out that the effective strain has strong and direct relationship with the pore closing phenomena but that the hydrostatic pressure has indirect and secondary influence on pore closing.

6 6 Min Cheol Lee, Sung Min Jang. Ju Hyun Cho and Man Soo Joun Acknowledgments This work was supported by grant No. RTI from the Regional Technology Innovation Program of the Ministry of Commerce, Industry and Energy(MOCIE). References 1. A. Tomlinson and J. D. Stringer, J. Iron Steel Inst., March, (1958), pp R. Kopp and E. Ambaum, Stahl und Eigen, 96, (1976), pp E. Erman, N. M. Medei, A. R. Roesch and D. C. Shah, J. Mech. Working Tech. 19, (1989), pp E. Erman, N. M. Medei, A. R. Roesch and D. C. Shah, J. Mech. Working Tech. 19, (1989), pp M. Tanaka, S. Ono, M. Tsuneno and T. Iwadate, Proc. 2nd Int. Conf. Adv. Tech. Plast. 2, (1987), pp U. Stahlberg, H. Keife, M Lundberg and A. Melander, J. Mech. Working Tech. 4, (1980), pp K. N. Shah, B. V. Kiefer and J. J. Gavigan, Adv. Manuf. Proc. 1, (1986), pp S. P. Dudra and Y. T. Im, J. Mat. Proc. Tech. 21, (1990), pp B. V. Kiefer and K. N. Shah, ASME Trans., J. Eng. Mat. and Tech., 112, (1991), pp C. Y. Park, J. R. Cho, D. Y. Yang, D. J. Kim and I. S. Park, Trans. Korean Soc. Mech. Engnrs. 16 (10), (1992), pp J. R. Cho, D. K. Kim, Y. D. Kim and B. Y. Lee, Korean Soc. Tech. of Plast. 5 (1), (1996), pp C. Y. Park and D. Y. Yang, Proc. Korea Soc. Prec. Eng Spring Annual Meeting, (1996), pp M. S. Chun, J. S. Ryu and Y. H. Moon, Korean Soc. Tech. Plast. 13 (2), (2004), pp Y. C. Kwon, J. H. Lee, S. W. Lee, Y. S. Jung, N. S. Kim and Y. S. Lee, Trans. Mat. Proc. 16 (4), (2007), pp M. C. Lee, M. S. Joun and June K. Lee, Finite Elem. Anal. Des. 43 (10), (2007), pp M. C. Lee and M. S. Joun, Adv. in Soft. Eng. 39 (1), (2008), pp M. C. Lee and M. S. Joun, Adv. in Soft. Eng. 39 (1), (2008), pp M. S. Joun, H. K. Moon, J. S. Lee, S. J. Yoo and J. K. Lee, ASME Trans., J. Eng. Mat. and Tech. 129, (2007), pp