Simple prediction of sheet metal forming limit stresses and strains

Forming limit curves or diagrams (FLCs or FLDs) are widely used for troubleshooting purposes in sheet metal stamping industry. Their prediction using analytical approaches has assumed significant importance recently since the FLCs obtained experimentally pose several limitations while the former provides a high level of flexibility in adopting a variety of conditions. Generally, FLCs indicate the maximum strain achievable for a constant strain ratio path during forming operations. However, constant strain ratio condition does not exist in practical situations, particularly, when pressing complex shapes involving multiple stages of forming. This is mainly due to variations in material properties like strain hardening, strength and anisotropy that often lead to deviations in strain path. Equally important are the imposed process conditions that also exert considerable influence on the forming limits. A method is proposed to predict FLCs from tensile test data of sheet materials. A single limit yield stress is first obtained from simple tensile test. Following Hill's anisotropic yield criteria, a continuous limit yield locus is obtained, which can be termed as Forming Limit Stress Curve (FLSC). If necessary, it can be linearized following a regression method, and FLCs are obtained using relevant hardening equation, normality flow rule and Hill's anisotropic yield criterion. It has been found that the predicted FLCs with this approach have yielded consistently fair results in the case of several deep-drawing-quality steels. The second aspect addressed is on establishing the forming limit bands, which could be achieved by considering the tensile properties of a material in the three important directions and subsequently applying the prediction model. Results obtained with the model for brass are presented, and have been verified using the strains obtained in experiments on a dome-shaped cup formed in predominantly stretch type deformation mode.