Journal of Zhejiang University-SCIENCE A

, Volume 8, Issue 2, pp 237–244 | Cite as

An analytical model for predicting sheet springback after V-bending

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


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 

CLC number



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Copyright information

© Springer-Verlag 2007

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

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