FE implementation of HAH model using FDM-based stress update algorithm for springback prediction of AHSS sheets

Abstract

The homogeneous anisotropic hardening (HAH) model was implemented into a finite element (FE) code in order to predict springback for an advanced high strength steel (AHSS) sheet sample after double-stage U-draw bending. The finite difference method (FDM) was utilized as an alternative way to calculate the derivatives of this advanced distortional plasticity model allowing the update of the equivalent plastic strain and stress tensor at each time step in the user-material subroutines (UMAT and VUMAT). The FDM makes it easier to derive the stress gradient of complex yield surfaces. The proposed FDM-based stress update algorithm was verified by comparing the springback profiles after the single- and double-stage U-draw bending tests for a DP980 sheet sample predicted with analytical and numerical approaches. In addition, the springback measurement parameters and computational efficiencies depending on both approaches were also compared. The results indicate that the computational efficiency and accuracy of the FE simulations with the FDM-based stress update algorithm were similar to those of the analytical method.