Scaling laws in plastic deformation

Abstract

In crystalline materials, plastic deformation is driven by the non-local long-range interaction of dislocations. This interaction is responsible for a series of features that obey scaling laws, such as the formation of fractal cellular structures, the intermittent plastic flow with scale-free avalanches following a power law and the Hall–Petch relation in which the yield stress depends on the sample size following a power law. A phase-field model of dislocations is described. The present theory is able to reproduce the jerky character of dislocation motion as well as size dependence in small-scale plasticity.