Stress-Based Forming Limits in Sheet-Metal Forming

A strain-based forming limit criterion is widely used throughout the sheet-metal forming industry to gauge the stability of the deformed material with respect to the development of a localized neck prior to fracture. This criterion is strictly valid only when the strain path is linear throughout the deformation process. There is significant data that shows a strong and complex dependence of the limit criterion on the strain path. Unfortunately, the strain path is never linear in secondary forming and hydro-forming processes. Furthermore, the path is often found to be nonlinear in localized critical areas in the first draw die. Therefore, the conventional practice of using a path-independent strain-based forming limit criterion often leads to erroneous assessments of forming severity. Recently it has been reported that a stress-based forming limit criterion appears to exhibit no strain-path dependencies. Subsequently, it has been suggested that this effect is not real, but is due to the saturation of the stress-strain relation. This paper will review and compare the strain-based and stress-based forming limit criteria, looking at a number of factors that are involved in the definition of the stress-based forming limit, including the role of the stress-strain relation.