Journal of Zhejiang University-SCIENCE A

, Volume 8, Issue 2, pp 237–244

An analytical model for predicting sheet springback after V-bending

• Zhang Dong-juan
• Cui Zhen-shan
• Chen Zhi-ying
• Ruan Xue-yu
Article

Abstract

Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simulating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.

Key words

Springback V-bending Contact pressure Neutral surface shifting Transverse stress Bending ratio

TG386.3

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References

1. Buranathiti, T., Cao, J., 2004. An effective analytical model for springback prediction in straight flanging processes. International Journal of Materials and Product Technology, 21(1/2/3):137–153. [doi:10.1504/IJMPT.2004.004748]
2. Chen, Y.Z., 1962. Pure bending of exponential hardening wide sheet. Acta Mechanica Sinica, 5:107–115 (in Chinese).
3. Cho, J.W., Yang, D.Y., Chung, W.J., 2002. A simplified approach for incorporating thickness stress in the analysis of sheet metal forming using shell elements. International Journal for Numerical Methods in Engineering, 53(10):2311–2327. [doi:10.1002/nme.379]
4. Gardiner, F.J., 1957. The springback of metals. Journal of Applied Mechanics, 79:1–9.Google Scholar
5. Gerdeen, J.C., Duncan, J.L., 1986. Springback in Sheet Metal Forming. AISI Report, p.1201–465.Google Scholar
6. Hamouda, A.M.S., Khadra, F.A., Hamadan, M.M., Imhemed, R.M., Mahdi, E., 2004. Springback in V-bending: A finite element approach. International Journal of Materials and Product Technology, 21(1/2/3):124–136. [doi:10.1504/IJMPT.2004.004747]
7. Hill, R., 1950. The Mathematical Theory of Plasticity. Oxford, London.
8. Huang, M., Gerdeen, J.C., 1994. Springback of Doubly Curved Developable Sheet Metal Surface—An Overview. SAE Technical Paper No. 940938, p.718–728.Google Scholar
9. Johnson, W., Yu, T.X., 1981a. Springback after the biaxial elastic-plastic pure bending of a rectangular plate—I. International Journal of Mechanical Sciences, 23(10):619–630. [doi:10.1016/0020-7403(81)90042-4]
10. Johnson, W., Yu, T.X., 1981b. On springback after the pure bending of beams and plates of elastic work-hardening materials—III. International Journal of Mechanical Sciences, 23(11):687–695. [doi:10.1016/0020-7403(81)90022-9]
11. Li, K., Wagoner, R.H., 1998. Simulation of Springback. Proceedings of NUMIFORM’98, the Netherlands, p.21–31.Google Scholar
12. Robinson, M., 2000. An evaluation of the errors in the yield surface for a rotationally symmetric thin shell due to neglecting transverse normal stresses and shell curvature. International Journal of Mechanical Sciences, 42(6):1087–1095. [doi:10.1016/S0020-7403(99)00037-5]
13. Tekaslan, Ö., Şeker, U., Özdemir, A., 2006. Determining springback amount of steel sheet metal has 0.5 mm thickness in bending dies. Materials and Design, 27(3):251–258. [doi:10.1016/j.matdes.2004.10.006]
14. Tekiner, Z., 2004. An experimental study on the examination of springback of sheet metals with several thicknesses and properties in bending dies. Journal of Materials Processing Technology, 145(1):109–117. [doi:10.1016/j.jmatprotec.2003.07.005]
15. Wang, C.T., Kinzel, G., Altan, T., 1993. Mathematical modeling of plane-strain bending of sheet and plate. Journal of Materials Processing Technology, 39(3–4):279–304. [doi:10.1016/0924-0136(93)90164-2]
16. Wang, X.C., Shao, M., 1997. The Basic Principle and Numerical Simulation of Finite Element Method. Tsinghua University Press, Beijing (in Chinese).Google Scholar
17. Yu, T.X., Johnson, W., 1982. Influence of axial force on the elastic-plastic bending and springback of a beam. Journal of Mechanical Working Technology, 6(1):5–21. [doi:10.1016/0378-3804(82)90016-X]
18. Zhang, Z.T., Hu, S.J., 1998, Stress and residual stress distributions in plane strain bending. International Journal of Mechanical Sciences, 40(6):533–543. [doi:10.1016/S0020-7403(97)00075-1]

Authors and Affiliations

• Zhang Dong-juan
• 1
• Cui Zhen-shan
• 1
• Chen Zhi-ying
• 1
• Ruan Xue-yu
• 1
1. 1.National Mold & Die CAD Engineering Research CenterShanghai Jiao Tong UniversityShanghaiChina