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.
Highlights
In various industrial fields, the demand for advanced high strength steels (AHSS) has increased because of the outstanding properties of these materials: high strength leading to low structural weight, and costeffectiveness in manufacturing
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 results indicate that the computational efficiency and accuracy of the FE simulations with the finite difference method (FDM)-based stress update algorithm were similar to those of the analytical method
Summary
The demand for advanced high strength steels (AHSS) has increased because of the outstanding properties of these materials: high strength leading to low structural weight, and costeffectiveness in manufacturing. In order to implement an advanced constitutive model such as HAH into a FE code, the stress at each time step should be calculated through a stress update (or integration) algorithm in which the equivalent plastic strain and stress components are obtained based on the gradient of the yield surface usually derived analytically. A numerical differentiation method was utilized to calculate the gradient of the yield surface generated by the HAH model, which makes the implementation of this constitutive description much easier than before [2]. The springback profiles after single- and doubleU-draw bending tests for a dual-phase (DP) steel grade (DP980) sheet by computing the plastic equivalent strain and stress tensors with the introduced FDM method were compared with those computed with the analytical expressions. The computational performance of the FDM-based approach was assessed
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