Analysis of localized necking in anisotropic sheet metals

Abstract

The ductility of sheet metals during forming operations is limited by a plastic instability leading to necking in the thickness direction along a narrow band. The critical condition for the onset of localized necking depends on constitutive effects such as plastic anisotropy, strain hardening and softening due to damage growth. Using the classical bifurcation analysis of Rice and co-workers, we derive a general analytical solution for localized necking in elastic–plastic thin sheets obeying arbitrary yield criteria and the normality flow rule. The criterion is illustrated for the case of plastically orthotropic sheets obeying Hill-type yield criteria, for which the model predictions for the localization strains are compared with explicit finite element simulations of sheet necking. Existing results in the literature are recovered for the special case of materials that exhibit in-plane isotropy and power law strain hardening.