Derivation of a forming limit stress diagram from an experimental FLC, and comparison of the two criteria when applied to FE simulation of a pressing using different yield functions

Abstract

The concept of a Forming Limit Curve (FLC), introduced in the sixties, has been widely used in the sheet metal industry, both to check out die designs at the design stage, using FE simulation techniques, and also to sign off stamped parts in the press shop. However, this approach should be strictly limited to stamping processes where the strain path is proportional during the stamping process. An alternative concept, the Forming Limit Stress Diagram (FLSD), was proposed back in the eighties. This FLSD concept is path independent, and solves the problem of possible non-linearity of the strain path during a press forming operation. The following paper uses a procedure for the transformation of an experimental path dependent strain based FLC into a stress based path independent FLSD, for three different yield functions, von Mises, Hill’48 and Hill’s 90. Having derived the FLSD criterion, this paper then shows a comparison between the FE stamping simulations carried out on a selected component, using both the standard FLC approach and the more recent FLSD approach, using each one of the three different yield criterion considered. The FE simulation results using the FLSD transformation and the original FLC approach show good agreement for each of the yield functions considered. Some differences between the yield functions are also highlighted and discussed, in particular the limitations of Hill’s 48 in the balanced bi-axial stress state for materials with an r value less than one, i.e. aluminium alloys.