, Volume 70, Issue 6, pp 906–911 | Cite as

Split-Ring Springback Simulations with the Non-associated Flow Rule and Evolutionary Elastic-Plasticity Models

  • K. J. Lee
  • Y. Choi
  • H. J. Choi
  • J. Y. Lee
  • M. G. Lee
Shaping & Forming of Advanced High Strength Steels


Finite element simulations and experiments for the split-ring test were conducted to investigate the effect of anisotropic constitutive models on the predictive capability of sheet springback. As an alternative to the commonly employed associated flow rule, a non-associated flow rule for Hill1948 yield function was implemented in the simulations. Moreover, the evolution of anisotropy with plastic deformation was efficiently modeled by identifying equivalent plastic strain-dependent anisotropic coefficients. Comparative study with different yield surfaces and elasticity models showed that the split-ring springback could be best predicted when the anisotropy in both the R value and yield stress, their evolution and variable apparent elastic modulus were taken into account in the simulations. Detailed analyses based on deformation paths superimposed on the anisotropic yield functions predicted by different constitutive models were provided to understand the complex springback response in the split-ring test.



MGL appreciates the support from the National Research Foundation of Korea (NRF) (2017R1A2A2A05069619) and (2012R1A5A1051500).

Supplementary material

11837_2018_2812_MOESM1_ESM.pdf (889 kb)
Supplementary material 1 (PDF 888 kb)


  1. 1.
    D. Banabic, H. Aretz, D.S. Comsa, and L. Paraianu, Int. J. Plast. 21, 493 (2005).CrossRefGoogle Scholar
  2. 2.
    F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, D.J. Lege, F. Pourboghrat, S.H. Choi, and E. Chu, Int. J. Plast. 19, 1297 (2003).CrossRefGoogle Scholar
  3. 3.
    T.B. Stoughton, Int. J. Plast. 18, 687 (2002).CrossRefGoogle Scholar
  4. 4.
    T. Park and K. Chung, Int. J. Solids Struct. 25, 3582 (2012).CrossRefGoogle Scholar
  5. 5.
    T. Kuwabara, S. Ikeda, and K. Kuroda, J. Mater. Process. Technol. 80, 517 (1998).CrossRefGoogle Scholar
  6. 6.
    H.J. Choi, Y. Choi, K.J. Lee, J.Y. Lee, K. Bandyopadhyay, and M.G. Lee, JOM 69, 915 (2017).CrossRefGoogle Scholar
  7. 7.
    L. Sun and R.H. Wagoner, Int. J. Plast. 27, 1126 (2011).CrossRefGoogle Scholar
  8. 8.
    J. Lee, J.Y. Lee, F. Barlat, R.H. Wagoner, K. Chung, and M.G. Lee, Int. J. Plast. 45, 140 (2013).CrossRefGoogle Scholar
  9. 9.
    J.Y. Lee, M.G. Lee, F. Barlat, and G. Bae, Int. J. Plast. 93, 112 (2017).CrossRefGoogle Scholar
  10. 10.
    F. Yoshida, T. Uemori, and K. Fujiwara, Int. J. Plast. 18, 633 (2002).CrossRefGoogle Scholar
  11. 11.
    J. Liao, X. Xue, M.G. Lee, F. Barlat, and J. Gracio, Int. J. Mech. Sci. 89, 311 (2014).CrossRefGoogle Scholar
  12. 12.
    R. Hill, Proc. R. Soc. Lond. 193A, 281 (1948).CrossRefGoogle Scholar
  13. 13.
    K.T. Lee, C.S. Park, and H.Y. Kim, Int. J. Automot. Technol. 18, 97 (2017).CrossRefGoogle Scholar
  14. 14.
    R.M. Cleveland and A.K. Ghosh, Int. J. Plast. 18, 769 (2002).CrossRefGoogle Scholar
  15. 15.
    H. Kim, C. Kim, F. Barlat, E. Pavlina, and M.G. Lee, Mater. Sci. Eng. A 562, 161 (2013).CrossRefGoogle Scholar
  16. 16.
    P.A. Eggertsen, K. Mattiasson, and J. Hertzman, J. Manuf. Sci. Eng. 133, 061021 (2011).CrossRefGoogle Scholar
  17. 17.
    J.Y. Lee, M.G. Lee, F. Barlat, K.H. Chung, and D.J. Kim, Int. J. Solids Struct. 87, 254 (2016).CrossRefGoogle Scholar
  18. 18.
    Y. Choi, H.J. Choi, K.J. Lee, and M.G. Lee, Manuscript in preparation.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  • K. J. Lee
    • 1
    • 2
  • Y. Choi
    • 1
    • 2
  • H. J. Choi
    • 1
    • 2
  • J. Y. Lee
    • 1
    • 2
  • M. G. Lee
    • 1
  1. 1.Department of Materials Science and Engineering & RIAMSeoul National UniversitySeoulSouth Korea
  2. 2.Department of Materials Science and EngineeringKorea UniversitySeoulSouth Korea

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