Self-consistent, polycrystal rate-independent crystal plasticity modeling for yield surface determination

The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.