LAUSR

Hexagonal close-packed (HCP) metals show highly anisotropic mechanical responses due to twinning, slip and the interaction among various slip and twin systems. Each HCP metal shows different sets of activated slip and twin systems. The interaction among slip and twin systems causes highly nonlinear and rapidly changing hardening behaviors in the critical resolved shear stress (CRSS) of each slip/twin system. To accurately understand the anisotropic mechanical response of HCP metals, both single-crystal and polycrystal tests must be performed. The interaction among different slip and twin systems shows different behaviors in the single-crystal and polycrystal settings since the interacting environments are different. The fitting process of the single crystal and polycrystal stress–strain data involves a series of trials and errors to find the correct interaction patterns among various slip and twin systems. The fitting procedures used in previous researches take a lot of times of trials and errors and are not guided by any physical property. Therefore, this study employs a recently proposed new fitting procedure, which is based on a physical property, the saturation strength of the material, to fit magnesium experimental data more efficiently with a less number of trials and errors. Compared to the slip process, twinning is computationally more difficult to take into account due to the directionality of the twin process, i.e., twinning occurs only in one direction, not in the opposite direction unlike the slip process. The rapidly changing highly nonlinear interaction hardening behaviors among various slip and twin systems are computationally challenging. Both of the above computational difficulties require a more robust and accurate numerical scheme than previously used ones to obtain accurate representations of experimental data. Therefore, this study proposes a more accurate and robust numerical scheme for the hardening strengths (CRSS) of twin/slip systems and interaction hardening. The newly proposed scheme is based upon implicit time integration, which enhances accuracy and stability. Using the proposed fitting procedure and the implicit integration scheme for hardening strength (CRSS) and interaction hardening, the experimental stress–strain data of polycrystal magnesium shown in Kelley and Hosford (The plastic deformation of magnesium. Technical report, 1967, Trans Metall Soc AIME 242:5–13, 1968) are successfully reproduced.