Skip to main content
Log in

Calculations of forming limit diagrams

  • Published:
Metallurgical Transactions A Aims and scope Submit manuscript

Abstract

The right-hand side of the forming limit diagram (FLD) was calculated using a Marciniak-Kuczynski analysis with a nonquadratic anisotropic yield criterion. Effects of changing the strain-hardening exponent, n, strain-rate exponent, m, strain ratio, R, stress exponent in the anisotropic yield criterion, a, and the inhomogeneity factor, f, were explored. For a ≥ 6, the effect of R is negligible. The calculated forming limit for plane strain is raised by increased values of n, m, and f and is unaffected by R and a. The slope of the right-hand side is decreased by increased values of n, m, and a, whereas the slope increases with higher f The calculated FLDs agree well with experimental ones determined by in-plane stretching.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S.P. Keeler and W.A. Backofen:Trans. ASM, 1963, vol. 56, pp. 25–48.

    Google Scholar 

  2. S.P. Keeler: Sheet Met. Ind., 1965, pp. 683–91.

  3. S.S. HeckenSheet Met. Ind., 1975, vol. 52, pp. 671–75.

    Google Scholar 

  4. Amit K. Ghosh and Siegfried S. Hecker:Metall. Trans., 1974, vol. 5, pp. 2161–64.

    Article  CAS  Google Scholar 

  5. Z. Marciniak and K. Kuczynski:Int. J. Mech. Sci., 1967, vol. 9, pp. 609–20.

    Article  Google Scholar 

  6. K.S. Chan, D.A. Koss, and A.K. Ghosh:Metall. Trans. A, 1984, vol. 15A, pp. 323–29.

    CAS  Google Scholar 

  7. J. Lian and B. Baudelet:Mater. Sci. Eng., 1987, vol. 86, pp. 137–44.

    Article  Google Scholar 

  8. R. Sowerby and D.L. Duncan:Int. J. Mech. Sci., 1971, vol. 13, pp. 217–29.

    Article  Google Scholar 

  9. R. Hill:Proc. R. Soc., 1948, vol. 193A, pp. 281–97.

    Google Scholar 

  10. A. Parmar and P.B. Mellor:Int. J. Mech. Sci., 1978, vol. 20, pp. 385–91.

    Article  Google Scholar 

  11. D. Lee and F. Zaverl, Jr.:Int. J. Mech. Sci., 1982, vol. 24, pp. 157–73.

    Article  Google Scholar 

  12. K.S. Chan:Metall. Trans. A, 1985, vol. 16A, pp. 629–39.

    CAS  Google Scholar 

  13. A.K. Ghosh:Met. Eng. Q., 1975, vol. 15 (3), pp. 53–64.

    CAS  Google Scholar 

  14. J.W. Hutchinson and K.W. Neale: inMechanics of Sheet Metal Forming, D.P. Koistinen and N.-M. Wang, eds., Plenum Press, New York, NY, 1978, pp. 127–53.

    Google Scholar 

  15. R. Hill:Math. Proc. Cambridge Philos. Soc, 1979, vol. 75, pp. 179–91.

    Article  Google Scholar 

  16. F. Barlat:Mater. Sci. Eng., 1987, vol. 91, pp. 55–72.

    Article  CAS  Google Scholar 

  17. A.V. Hersey:J. Appl. Mech., 1954, vol. 76, pp. 241–49.

    Google Scholar 

  18. B. Paul: inFracture, An Advanced Treatise, Vol. 2, Mathematical Fundamentals, H. Liebowitz, ed., Academic Press, New York, NY, 1968, p. 346.

    Google Scholar 

  19. W.F. Hosford:J. Appl. Mech. (Trans. ASME Ser. E), 1972, vol. 39, pp. 607–09.

    Google Scholar 

  20. J. Lian, F. Barlat, and B. Baudelet:Int. J. Plast., 1989, vol. 5, pp. 131–47.

    Article  Google Scholar 

  21. W.F. Hosford:7th North American Metalworking Conf., SME, Dearborn, MI, 1979, pp. 191–97.

    Google Scholar 

  22. R. Logan and W.F. Hosford:Int. J. Mech. Sci., 1980, vol. 22, pp. 419–30.

    Article  Google Scholar 

  23. Aitor Galdos and William Hosford: Texture of Crystalline Solids, 1989, in press.

  24. Alejandro Graf and William Hosford: inForming Limit Diagrams: Concepts, Methods and Applications, R.H. Wagoner, K.S. Chan, and S.P. Keeler, eds., TMS-AIME, Warrendale, PA, 1989, pp. 153–63.

    Google Scholar 

  25. Morris Azrin and Walter A. Backofen:Metall. Trans., 1970, vol. 1, pp. 2857–65.

    Google Scholar 

  26. Arnit K. Ghosh and Walter A. Backofen:Metall. Trans., 1973, vol. 4, pp. 1113–23.

    CAS  Google Scholar 

  27. A.K. Ghosh: inMechanics of Sheet Metal Forming, D.P. Koistinen and N.-M. Wang, eds., Plenum Press, New York, NY, 1978, pp. 287–312.

    Google Scholar 

  28. T.J. McCarron, K.E. Kain, G.T. Hahn, and W.F. Flanagan:Metall. Trans. A, 1988, vol. 19A, pp. 2067–74.

    CAS  Google Scholar 

  29. D.J. Meuleman: Ph.D. Thesis, The University of Michigan, Ann Arbor, MI, 1980.

    Google Scholar 

  30. A.K. Ghosh:J. Eng. Mater. Technol. (Trans. ASME), 1977, vol. 99, pp. 264–74.

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Graf, A., Hosford, W.F. Calculations of forming limit diagrams. Metall Trans A 21, 87–94 (1990). https://doi.org/10.1007/BF02656427

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02656427

Keywords

Navigation