This paper explores the right-hand side of the forming limit diagram for a body-centered cubic material in order to test the crystallographic slip assumptions. Body-centered cubic crystals were considered with either 24 or 48 slip systems. Identical uniaxial stress responses were assumed in order to compare the predicted forming limit diagrams. The latter were derived using a rate-dependent polycrystal viscoplastic model together with the Marciniak–Kuczynski approach. It was verified that the predictions of the limit strains carried out using the Marciniak–Kuczynski full-constraints model were strongly affected by the selected deformation modes, showing unrealistically high limit strains in balanced-biaxial tension. Much more reliable values were found using the Marciniak–Kuczynski viscoplastic self-consistent approach using either a 24 slip or 48 slip system assumption, enhancing the relevance of the selected transition scale model. Discrepancies between the numerical results, obtained using Marciniak–Kuczynski full-constraints and Marciniak–Kuczynski viscoplastic self-consistent methods, were interpreted in terms of the differences in the active slip systems selected by each model, and consequently, in the predicted lattice rotations and local curvature of the yield locus. Finally, it was found that calculation of the forming limit diagram using Marciniak–Kuczynski viscoplastic self-consistent assumptions, using 48 slip systems, successfully predicted the right-hand side experimental tendency observed in a low carbon steel sheet metal obtained by bulge testing.

Investigation of the Dislocation Slip Assumption on Formability of BCC Sheet Metals. M.J.Serenelli, M.A.Bertinetti, J.W.Signorelli: International Journal of Mechanical Sciences, 2010, 52[12], 1723-34