On forming limit stress diagram analysis

Abstract

Forming Limit Stress Diagrams (FLSDs) have been intensively studied and have been considered as being path-independent. This paper carries out a detailed study to examine the path-dependency of FLSDs based on different non-proportional loading histories, which are combinations of two linear strain paths. All simulations are based on crystal plasticity theory in conjunction with the M–K approach. It is confirmed that the Forming Limit Diagram (FLD) and the FLSD are two mathematically equivalent representations of forming limits in strain-space and stress-space, respectively. While the FLD is very sensitive to strain path changes, the FLSD is much less path-dependent. It is suggested that the FLSD is much more favourable than the FLD in representing forming limits in the numerical simulation of sheet metal forming processes. The nature of the effect of a strain path change on forming limits is investigated in terms of the transition work hardening behaviour upon the path change, and the concept of the FLSD.