Stress integration method for a nonlinear kinematic/isotropic hardening model and its characterization based on polycrystal plasticity

Sheet metal forming processes generally involve non-proportional strain paths including springback, leading to the Bauschinger effect, transient hardening, and permanent softening behavior, that can be possibly modeled by kinematic hardening laws. In this work, a stress integration procedure based on the backward-Euler method was newly derived for a nonlinear combined isotropic/kinematic hardening model based on the two-yield’s surfaces approach. The backward-Euler method can be combined with general non-quadratic anisotropic yield functions and thus it can predict accurately the behavior of aluminum alloy sheets for sheet metal forming processes. In order to characterize the material coefficients, including the Bauschinger ratio for the kinematic hardening model, one element tension–compression simulations were newly tried based on a polycrystal plasticity approach, which compensates extensive tension and compression experiments. The developed model was applied for a springback prediction of the NUMISHEET’93 2D draw bend benchmark example.