Effect of multiaxial loading on evolution of {101¯2} twinning in magnesium single crystals

Abstract

We employ molecular dynamics (MD) simulations to investigate the evolution of $\left\{10\overline{1}2\right\}$ twinning in magnesium single crystals with an initial crack. The focus is on discerning the effect of multi-axial loading (resulting in c-axis extension) on the evolution of variant twin volume fraction and number of twins. Both these quantities fully describe the evolution of the overall twin volume fraction. In all the five loading conditions considered here, the evolution of variant volume fraction clearly shows the signature of twin coalescence through discrete jumps, which coincide with decrease in the number of twins that belong to the variant pair. Interestingly, coalescence occurs between twins that belong to conjugate variants, in addition to coalescence between twins of the same variant. The activation of twin variants is consistent with the Schmid factor. However, variants with identical Schmid factors do not necessarily activate simultaneously. Further, active twin variants with identical Schmid factors do not evolve at the same rate and as a result they do not contribute equally to the overall twin volume fraction. The evolution of N_T occurs a discontinuous manner through the competition of nucleation, coalescence and detwinning processes. Each of these processes is strongly influenced by the details of the loading states. A general rule is – the fewer the nucleation events of twins belonging to different variants, larger the overall volume fraction attained leading up to saturation (f_sat). Incipient non-basal slip precedes twinning ahead of the crack tip. Significant dislocation plasticity evolves during and after twinning and it occurs on basal and prismatic $〈a〉$ slip systems. Prior to the dominance of twin coalescence, f exhibits an exponentially decaying distribution with respect to N_T at a given strain. We present expressions for the evolution of volume fraction and number of twins that qualitatively reproduce the observed features observed for the loading conditions investigated in this work. These should serve as a starting point for constructing improved models for modeling twinning evolution at continuum length scales.