Elasto-Plastic Modeling of the Limit Strains in Metallic Sheets

Abstract:

In this work, the model of Marciniak and Kuczynski, hereafter referred to as the M-K model, was extended to account for the elastic strains to forecast the Forming Limit Curve (FLC) of metallic sheets. The return mapping algorithm is adopted where an elastic predictor step is performed with the generalized Hooke’s law and the plastic correction step is performed assuming the isotropic work-hardening together with the associated flow rule. The current M-K model predicted quite well both experimental and rigid-plastic results obtained for an IF steel sheet. Also, the principal stresses predicted by the elasto-plastic M-K model provided a good agreement with the experimental Forming Limit Stress Diagram (FLSD) of a Bake-Hardening steel sheet. Therefore, the elastic strains should be taken into account in the modeling of limit strains in metallic sheets, especially in the case of advanced high strength steels for which the Young modulus decreases with the plastic strain.

• Periodical: Materials Science Forum (Volume 869)
• Pages: 532-537
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.869.532
• Online since: August 2016
• Authors: M.C. Cardoso*, Luciano Pessanha Moreira, M.C.S. Freitas
• Keywords: Elasto-Plastic Modeling, Limit Strains, Metallic Sheets

References

[1] S.P. Keeler, W.A. Backofen: ASM Trans. Quart. Vol. 56 (1964), p.25.

[2] G.M. Goodwin: Application of strain analysis to sheet metal forming problems in press shop, SAE Paper No. 680093, (1968) 1-12.

DOI: 10.4271/680093

[3] R. Hill: J. Mech. Phys. Solids Vol. 1 (1952), p.19.

[4] Z. Marciniak, K. Kuckzinsky: Int. J. Mech. Sci. Vol. 9 (1967), p.609.

[5] M.C.S. Freitas, L.P. Moreira, R. Garcez: Materials Research Vol. 16 (2013), p.351.

[6] B. Molaei: Strain path effects on sheet metal formability. Doctoral (Thesis). Amirkabir University of Technology. Tehran, 1999. (IR).

[7] M.C. Butuc, Forming limit diagrams definition of plastic instability criteria. Doctoral (Thesis). Universidade do Porto. Porto, 2004. (PT).

[8] G. Ferron, R. Makkouk, J. Morreale: International Journal of Plasticity Vol. 10 (1994), p.431.

[9] R. Hill: A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the Royal Society of London, A 193 (1948) 281-297.