Porous plasticity modeling of local necking in sheet metals

Abstract

Sheet metals subjected to biaxial plane stress loading typically fail due to localized necking in the thickness direction. Classical plasticity models using a smooth yield surface and the normality flow rule cannot predict localized necking at realistic strain levels when both the in-plane principal strains are tensile. In this paper, a recently developed multi-surface model for porous metal plasticity is used to show that the development of vertices on the yield surface at finite strains due to microscopic void growth, and the resulting deviations from plastic flow normality, can result in realistic predictions for the limit strains under biaxial tensile loadings. The shapes of the forming limit curves predicted using an instability analysis are in qualitative agreement with experiments. The effect of constitutive features such as strain hardening and void nucleation on the predicted ductility are discussed.