Dynamical correlations near dislocation jamming

Abstract

Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value \(\sigma=\sigma_c\). Nevertheless the nature of this transition has not been ascertained. Here we study the heterogeneous and collective nature of dislocation dynamics within a crystal plasticity model close to \(\sigma_c\), by considering the first-passage properties of the dislocation dynamics. As the transition is approached in the moving phase, the first passage time distribution exhibits scaling, and a related peak {\it dynamical} susceptibility \(\chi_4^*\) diverges as \(\chi_4^* \sim (\sigma-\sigma_c)^{-\alpha}\), with \(\alpha \approx 1.1\). We relate this scaling to an avalanche description of the dynamics. While the static structural correlations are found to be independent of the external stress, we identify a diverging dynamical correlation length \(\xi_y\) in the direction perpendicular to the dislocation glide motion.