Dynamical correlations near dislocation jamming

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 ${\chi }_4^{\ast }$ 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.