Localized necking analysis by the subloading surface model with tangential-strain rate and anisotropy

A rational approach to the localized necking problem was given by Storen and Rice [J. Mech. Phys. Solids 23 (1975) 421] but this approach is limited to the description of monotonic loading behavior near a proportional loading of the isotropic, rigid-plastic materials with von Mises yield surface. In this article it is extended so as to be applicable to the arbitrary loading behavior of elastoplastic materials with an arbitrary yield surface by introducing the subloading surface model with the tangential-stress rate effect [Met. Mater. 4 (1998) 652; Int. J. Plasticity 17 (2001) 117]. The localized necking condition under biaxial stretching of a uniform and homogeneous thin sheet subjected to biaxial stretching in the plane stress state is formulated in such a way that elastic deformation and compressibility are allowed. Based on this condition, the localized necking for metals is analyzed showing the forming limit diagrams (FLDs). It becomes clear that not only the tangential-strain rate but also the inherent/induced anisotropy due to the kinematic hardening intensely influence the onset of localized necking.