A general forming limit criterion for sheet metal forming

The forming limit of sheet metal is defined to be the state at which a localized thinning of the sheet initiates during forming, ultimately leading to a split in the sheet. The forming limit is conventionally described as a curve in a plot of major strain vs. minor strain. This curve was originally proposed to characterize the general forming limit of sheet metal, but it has been subsequently observed that this criterion is valid only for the case of proportional loading. Nevertheless, due to the convenience of measuring strain and the lack of a better criterion, the strain- based forming limit curve continues to play a primary role in judging forming severity. In this paper it is shown that the forming limit for both proportional loading and non-proportional loading can be explained from a single criterion which is based on the state of stress rather than the state of strain. This proposed criteria is validated using data from several non-proportional loading paths previously reported in the literature for both aluminum and steel alloys. In addition to significantly improving the gauging of forming severity, the new stress-based criterion is as easy to use as the strain-based criterion in the validation of die designs by the finite element method. However, it presents a challenge to the experimentalist and the stamping plant because the state of stress cannot be directly measured. This paper will also discuss several methods to deal with this challenge so that the more general measure of forming severity, as determined by the state of stress, can be determined in the stamping plant.