Constitutive modeling based on non-associated flow rule for anisotropic sheet metals forming

For the finite element analysis of anisotropic sheet metals forming, the Hill48 function was developed into an anisotropic constitutive model based on the non-associated flow rule under general three-dimensional stress conditions. Under the non-associated flow rule, the anisotropic parameters of the yield function were calibrated by the directional planner yield stress, the biaxial tensile yield stress and the shear yield stress, respectively, while those of the potential function were calibrated by the directional R-values. The explicit analysis and solid element were employed, and the model was embedded into the finite element software ABAQUS by the VUMAT user subroutine. The capability of the model to predict the yield stress and R-values for different materials was evaluated. To further verify the representational ability of constitutive models on plastic deformation under different stress conditions, cylindrical cup drawing and thin-walled tube torsion tests were performed. The results show that the developed model can improve the prediction accuracy of anisotropic sheet metal forming to a certain extent and can adapt to plastic deformation under different stress conditions. This simple and effective anisotropic constitutive model can provide a flexible reference scheme for sheet metals forming problems.