Available online at ScienceDirect. Procedia Engineering 81 (2014 )

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1 Available online at ScienceDirect Procedia Engineering 81 (2014 ) th International Conference on Technology of Plasticity, ICTP 2014, October 2014, Nagoya Congress Center, Nagoya, Japan Finite element analysis of deep piercing process Mansoo Joun a, Mincheol Kim a, Jongho Kim b, Wanjin Chung b,* a Dept. of Mechanical Engineering, Gyeongsang National University, 501 Jinju-daero,Jinju , Korea b Dept.of Mechanical System Design Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul, , Korea Abstract A finite element approach to analyzing a deep piercing process is presented. In the approach, the element deletion scheme after the element degradation scheme is employed to predict the piercing phenomenon because the time interval between piercing initiation time and final stroke is quite large. The normalized Cockcroft-Latham damage model is used and an assumed flow stress smoothing function is used to reflect the effect of cumulative damage on the flow stress, i.e., to designate the degree of element degradation due to damage. The approach is applied to a deep piercing process of which aspect ratio of plate thickness to hole diameter is 5.0. The comparison between simulation and experiment shows a good qualitative agreement with each other Published The Authors. by Elsevier Published Ltd. by This Elsevier is an Ltd. open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility of Nagoya University and Toyohashi University of Technology. Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University Keywords: Deep piercing; Finite element simulation; Element deletion Scheme; Element degration scheme 1. Introduction Pierced holes of most press formed parts are characterized by aspect ratios, defined by the thickness divided by hole diameter, ranging from 1.0 to 1.5. In precision piercing with fine-blanking dies, maximum aspect ratio can reach 2.0. Of course, a piercing process with aspect ratio of over 2.0 can be exposed to process failure due to punch buckling. Thus, in many cases, the deep holes of which aspect ratios are greater than 2.0 are being made by drilling process and the trial to remove the drilling process after press forming is one of hot issues in the related industries. *Corresponding author. Tel.: ;fax: address: wjchung@seoultech.ac.kr Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi: /j.proeng

2 Mansoo Joun et al. / Procedia Engineering 81 ( 2014 ) From almost two decades ago, numerical studies have been conducted extensively to investigate the mechanism and failure of conventional piercing and blanking processes (Jeong et al., 1996; Lee and Joun, 2000; Hatanaka et al., 2003; Farzin et al., 2006). However, for deep piercing, there have been quite few researches in spite of its industrial significance. Aoki et al.(1992) found that the mechanism of piercing process consists of simple indenting and traditional blanking. Sasada et al. (2006) showed the change of the mechanism from indentation to piercing with the aspect ratio. Even though the previous studies utilized the finite element analyses to investigate the mechanism, the separation of material had not been explored in deep piercing process. Recently Chung et al.(2014) conducted an experimental study on a deep piercing process of which aspect ratio is 5.0. Jeong et al. (2013) carried out the finite element analysis for this experiment, but it just demonstrated the possibility of numerical simulation for deep piercing and revealed many potential problems in the simulation. There are three approaches to analyze the material separation in piercing processes, i.e., crack propagation scheme (Hatanaka et al., 2003; Jeong et al., 2013), element deletion scheme (Jeong et al., 1996; Farzin et al., 2006) and element degradation scheme. The crack propagation scheme is most attractive but it has a limitation when the piercing stroke from initial crack generation to final stroke is large because frequent remeshings and materialmaterial contact problem are very difficult. This problem is true of the element deletion scheme. On the contrary, the element degradation scheme is not only far away from such problem but it is also simple. Nonetheless, it is not easy to find some applied examples from the literature. In a piercing process with high aspect ratio and with blank holding force exerted for delayed fracture, the tearing stroke as well as holistic piercing stroke are relatively large and it is thus inevitable to utilize the element degradation scheme to deviate the numerically difficult situations aforementioned. In this paper, a new approach to deep piercing process simulation based on element deletion scheme after element degradation scheme is proposed and a deep piercing process with large aspect ratio of 5.0 is analyzed to show the detailed plastic behaviors occurring in the deep piercing process. The predictions are compared with the experiments. 2. Finite element analysis Fig. 1 shows the finite element analysis model used for analyzing the deep piercing process of which punch diameter and plate thickness are 1.2 mm and 6.0 mm, respectively, i.e., the aspect ratio is 5.0. The clearance between punch and die is 0.12 mm and that between punch and blank holder 0.01 mm. The blank holding force is 1000 N and coefficient of Coulomb friction is assumed The blank holding force is dealt with by the force prescribing die (Jeong, 2013). 2~6 times of mesh densities compared with the normal mesh density are imposed around the die corners of the punch and die. Normalized Cockcroft-Latham damage model (1996) is employed. The material used is a round blank with 16.0 mm diameter. Flow stress of the material AA6061 is as follows: f( D) [MPa], (1) where, and D are effective stress, effective strain and damage, respectively and function f( D ) is a smoothing function to reflect the cumulative damage on the flow stress, i.e., to degrade the damaged material. Fig. 2 shows the assumed degrading function used. In the figure, D cr = 0.65 means critical damage value. Thus the degrading function reflects that the degrading occurs around the critical damage values, i.e., it starts when the cumulative damage reaches 0.60 and finishes when it reaches Non-zero value of the function for the large damage of over 0.7 implies that even fully damaged material can have 10% of normal flow stress so as to avoid occurrence of unpredicted stop of simulation due to zero Jacobian. Impact and strain rate effect was not considered in this study.

3 2496 Mansoo Joun et al. / Procedia Engineering 81 (2014) Note that the critical damage value of 0.65 is assumed comparing the predictions and experiments. It can be observed from the experiments that the length of distinct fractured region is about one-fourth of the hole height or thickness of the material. We considered the starting point of distinct fractured region the fracture starting stroke. 1.2 Punch Blank holder f D 0.8 Blank 0.6 (0.65, 0.5) 0.4 Die Fig. 1. Geometry of a test deep piercing process Damage D cr 1.0 Fig. 2. Smoothing function to reflect the effect of damage value on flow stress Unit: MPa (a) Damage (b) Hydrostatic pressure Fig. 3. State variables at fracture starting stroke. (a) 4.57 mm (b) 4.69 mm (c) 4.76 mm (d) 4.83 mm Fig. 4. Predictions of softening process by element degradation scheme. (e) 4.90 mm

4 Mansoo Joun et al. / Procedia Engineering 81 ( 2014 ) Fig. 3 shows the predictions at the stroke where the distinct fractured surface can be first observed from the experiments. Maximum damage value at the fracture starting stroke occurring around the lower die corner is 0.65, as shown in Fig. 3(a), which was assumed the critical damage value. On the contrary, it can be seen from Fig. 3(a) that the damage value at almost all the deforming region except the most damaged region around the lower die corner is negligible due to high hydrostatic pressure shown in Fig. 3(b), i.e., positive value of the minimum principal stress causing from the blank holding force. It can be thus expected that the crack around the punch side does not occur for a quite long time or stroke after the initial crack is generated around the lower die corner. Thus, a number of remeshings are inevitable. This is quite different from simple piercing process in cold forging (Jeong, 2013). It should be noted that when a crack growth or crack propagation approach is employed, automatic remeshing is almost impossible especially when quadrilateral finite element mesh system is employed. It should be also noted that material-material interaction after fracture occurrence under high hydrostatic pressure is too complicated to be solved. Therefore, an element degradation scheme which can avoid the difficult problems of remeshing as well as material-material interaction is employed for the tearing stroke from initial crack generation to full shear-band generation. The finite element predictions obtained by the element degradation scheme are shown in Fig. 4. Note that 15 remeshings were made during the element degrading stroke. The damaged element deletion scheme was applied just after a full shear-band was formed from the punch corner to the lower die corner as shown in Fig. 4(e). Fig. 5 shows the comparison between prediction and the corresponding experiment with respect to the shape of hole. The comparison shows an acceptable agreement between the two results. However, it should be noted that this paper focused on the methodology of simulating the whole deep piercing process. Much more attempts to study on damage model and fracture starting stroke should be made to decrease the difference between the predictions and experiments. Fig. 5.Comparison of predictions with experiments in final stage. 3. Conclusion In a deep piercing process, the tearing stroke from initial crack generation to shear-band formation is quite large. It is noted that simulation of such long tearing stroke of deep piercing process using element deletion scheme or

5 2498 Mansoo Joun et al. / Procedia Engineering 81 ( 2014 ) crack propagation scheme is almost impossible because of complexity of remeshing and material-material interaction along the sheared surface under high hydrostatic pressure. In this paper, a methodology of simulating the holistic deep piercing process was presented, which is composed of two stages. In the first stage, the simulation continues using the element degradation scheme until the shear band due to cumulative damage is formed. To degrade damaged element, flow stress of a damaged element was multiplied by an assumed smoothing function of damage value. In the second stage, element deletion scheme or crack propagation scheme is used to achieve visualization of crack or separation of pierced part. The approach is applied to a deep piercing process of which aspect ratio is 5.0. The predictions are compared with experiments. The comparison showed a qualitative agreement with each other. Acknowledgement The research was supported partially by National Research Foundation of Korea and Korea Research Foundation (Ministry of Education and Science Technology ) under grant No and partially by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF ). References Aoki, I., Blanking and shearing of precision micro-components, Journal of the Japan Society for Technology of Plasticity, 33(379), Cockcroft, M. G., Latham, D. J., National Engineering Laboratory, Report No Farzin, M., Javani, H. R., Mashayekhi, M., Hambli, R., Analysis of blanking process using various damage criteria, Journal of Materials Processing Technology, 177(1-3), Hatanaka, N., Yamaguchi, K., Takakura, N., Finite element simulation of the shearing mechanism in the blanking of sheet metal, J. Mater. Process. Technol. 139 (1-3) Jeong, S. H., Kang, J. J., Oh, S. I., A study on shearing mechanism by FEM simulation, Proceedings of the Fifth ICTP II, Jeong, S. W., Lee, S. W., Chung, W. J., Joun, M. S., Finite element analysis of fine blanking process using force prescribed die, Proceedings of the Korean Society for Technology of Plasticity Conference, Kim, J. G., Kim, J. B., Kim, J. H., The influence of process parameters in piercing with a high aspect ratio for thick aluminum sheet, Transactions of Materials Processing, 23(1), Lee, S. W., Joun, M. S., Rigid-viscoplastic finite element analysis of the piercing process in the automatic simulation of multi-stage forging processes, Journal of Materials Processing Technology, 104(3), Sasada, M., Kobayashi, H., Aoki, I., Study on piercing mechanism of small holes, Journal of Materials Processing Technology, 177(1-3),