Comparison of forming limit diagrams predicted with different localization criteria

Abstract

Automotive industries are more and more subject to restrictive environmental constraints. Weight reduction of structures seems to be an interesting way to satisfy these requirements. This can be achieved either by using new materials, such as high strength steels or by adopting appropriate dimensioning methods to predict the occurrence of strain localization. Forming Limit Diagram (FLD) is a concept widely used to characterize the formability of thin metal sheets. Analytical determination of FLDs is usually based on the use of localization criteria. Some of the existing material instability criteria are for example based on empirical observations, on the maximum load principle [1-3], on the existence of an initial defect in the sheet [4], on a perturbation method [5] or on bifurcation analysis [6]. Although numerous criteria have been developed, they all have advantages but also drawbacks and limitations. Their confrontation on a wide range of materials is still insufficiently developed to compare their respective capability of accurately predicting FLDs for new materials. Adaptations of some criteria to advanced constitutive laws are also made necessary by the use of new high strength materials. The aim of this paper is to give a general formulation of some localization criteria allowing the comparison of the predicted FLDs for a wide range of materials. An implementation of these criteria coupled with different phenomenological constitutive laws is presented and compared for different materials including an aluminium alloy, a brass and a dual phase steel.