An efficient model for diffuse to localized necking transition in rate-dependent bifurcation analysis of metallic sheets

Abstract

A plastic instability model is extended to predict evolution of a bounded deformation in necking phenomenon. There are several studies to predict the plastic instability such as the vertex model proposed by Stören and Rice, which considers strain and stress rate discontinuities in the necking band. Here, the model is established on the J2 deformation theory of classical plasticity. Effect of stress triaxiality is investigated on the localization in bifurcation analysis. Also, a modified maximum force criterion is applied to predict diffuse necking considering loading conditions. Although considering the effect of strain rate hardening plays an important role to give accurate results, usually imposing it leads to emerging relatively the main complex constitutive equations. Therefore, a delicate bridge between the diffuse and localized models is made using the maximum force assumption to overcome on the complexity of the problem. Also, by investigating the strain rate behavior on the plastic instability, the forming limit diagrams are obtained illustrating more accurate results than other existing models. The anisotropy effect is studied by application of a quadratic Hill's criteria. The necking band angle will be investigated per different conditions through extending the vertex model coupled with the angle-dependent yield criterion.