Investigation of some localization criteria and their relevance to prediction of forming limit diagrams

Abstract

Because prevention of forming defects has become one of the major industrial challenges, various experimental and theoretical approaches have been developed to predict sheet metal formability. The main theoretical models can be summarized as: the maximum force principle, according to which necking is associated with the maximum load in a uniaxial tensile test; Marciniak-Kuczyński (M-K) two-zone analysis, based on an initial thickness defect in the sheet; bifurcation theory, predicting diffuse necking with general bifurcation criterion or localized modes corresponding to loss of ellipticity; and more recently, linear stability analysis by means of linearization of perturbed equilibrium equations. Considering this variety of models, a careful comparison of numerical Forming Limit Diagrams (FLDs) along with in-depth understanding of their theoretical foundations is required to help select relevant localization criteria. In this paper, the theoretical bases of M-K and Rice's criteria are first reviewed, which are then applied to steels modeled by elasto-plastic constitutive equations coupled with damage. It is shown that the FLDs obtained with the M-K model tend to those yielded by Rice's criterion in the limit of vanishing initial imperfections.