Crystalline materials deform in an intermittent way with slip-avalanches that are power-law distributed.
In this work we study plasticity as a pinning-depinning phase transition employing a discrete dislocation
dynamics (DDD) model and a phase eld crystal (PFC) model in two dimensions. Below a critical (
ow)
stress, the dislocations are pinned/jammed within their glide plane due to long-range elastic interactions
and the material exhibits plastic response. Above this critical stress the dislocations are mobile (the depinned/
unjammed phase) and the material constantly
ows.
We employ discrete dislocation dynamics to resolve the temporal pro les of slip-avalanches and extract
the nite-size scaling properties of the slip-avalanche statistics, going beyond gross aggregate statistics of
slip avalanche sizes. We provide a comprehensive set of scaling exponents, including the depinning exponent
. Our work establishes that the dynamics of plasticity, in the absence of hardening, is consistent with the
mean eld interface depinning universality class, even though there is no quenched disorder.
We also use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress
grows with the square root of the dislocation density (Taylor's relation). Consequently, dislocations jam at
any density, in contrast to granular materials, which only jam above a critical density.
Finally, we utilize a phase eld crystal model to extract the size, energy and duration distributions of
the avalanches and show that they exhibit power law behavior in agreement with the mean eld interface
depinning universality class
