Computational modeling of intrinsically induced strain gradients during compression of c-axis-oriented magnesium single crystal

Abstract

A finite-deformation strain gradient crystal plasticity model is implemented in a three-dimensional finite-element framework in order to analyze the deformation behavior and the stress–strain response of magnesium single crystals under c -axis orientation. The potential-based and thermodynamically consistent material model is formulated in a non-local and non-linear inelastic context in which dislocation densities are introduced via plastic strain gradients. Experiments have shown that the internal length scale of the microstructure starts to affect the overall stress–strain response when the sample size decreases to the micron scale. As a consequence, strain gradients develop, leading to an additional energetic-like hardening effect which results in an increase of the macroscopic strength with decreasing crystal size. In the case of uniaxial compression of c -axis-oriented single-crystal micropillars, the model is able to predict the discrete dislocation glide in terms of a band-shaped slip zone. Two different pillar sample sizes are taken into account in order to investigate the intrinsic size effect during plastic deformation where the crystallographic orientation leads to the activation of pyramidal {112¯2}〈112¯3〉 slip systems as reported in various experimental studies. The interaction of those slip systems is expressed in terms of latent hardening and excess dislocation development. A comparison between numerical results and corresponding experimental data is presented.