Strain localization analysis using a multiscale model

In order to analyze the formability of steels in sheet metal forming, a ductility loss criterion is coupled with a multiscale model. The behavior at the mesoscopic (grain) scale is modeled by a large strain micromechanical constitutive law, which is then used in a self-consistent scale transition scheme. Hardening at the slip system level is taken into account through mean dislocation densities considered as internal variables. The determination of active slip systems and the calculation of plastic slip activity are achieved with help of a regularization technique drawn from viscoplastic formulations. The model is shown to be able to correctly simulate the macroscopic behavior for single-phase steels during both monotonic and sequential loading paths. Finally, Rice’s localization criterion, based on the ellipticity loss of the elastic–plastic tangent modulus, is introduced and applied to determine forming limit diagrams (FLDs). The model allows us to obtain correct FLDs for monotonic as well as sequential loading paths. Pre-strain impact on FLDs is qualitatively reproduced as well.