Universal power-law strengthening in metals?

The strength of most metals scales with either an internal or external length scale. Motivated by the wide applicability of this phenomenon to material type and microstructure, we develop a model which gives quantitative insight into the scaling exponent using the known universal properties of a dislocation network and the leading order stress dependence of an underlying critical stress distribution. The approach is found to be equally valid for both Hall-Petch strengthening and the smaller-is-stronger paradigm of small scale plasticity.