Theoretical Prediction Of FLDs Of Sheet Metal Using Plastic Instability Criteria

A forming limit diagram(FLD) is wildly used in sheet metal forming for predicting forming behavior of sheet metal. It can be determined by mechanical test or theoretical calculation. The calculation is realized by using different constitutive models with plastic instability criteria that give a condition to determine occurrence of necking or rupture.We used an elastoplastic model and a damaged elastoplastic model in the calculation. Constitutive models were embedded into ABAQUS through UMAT, and a fourth-order Runge-Kutta method was used to update stress. Five instability criteria were used: Hill’s general bifurcation theory, Valanis’ s limit point bifurcation theory, Swift’s maximum force criteria, a hardening modulus theory used in small deformation conditions,and Rice’s localization criteria. Mathematical expression of instability condition of each criterion was given and then modeled in calculation.Result shows that Hill’s theory is almost equivalent to Swift’s theory in prediction of diffuse instability limit of sheet metal. In small deformation conditions, FLDs obtained with general bifurcation criteria, limit point bifurcation criteria and hardening modulus theory are the same, and in the expansion area, FLD predicted by Rice’s localization criteria is much higher than the other three. We also studied influence of isotropic hardening parameters and damage parameters on FLD of materials.