On forming limit stress diagram analysis

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.