  The strength of most metals used in daily life scales with either an internal
or external length scale. Empirically, this is characterized by power-laws
persisting to six orders of magnitude in both strength and length scale.
Attempts at understanding this scaling have generally been based on a specific
mechanism. However the wide applicability of material type and microstructure
to this phenomenon suggests a single mechanism is unlikely to capture the
observed trend. Here 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. This approach justifies a value for the scaling exponent
for virtually any experimental data set within the frameworks of both
Hall-Petch strengthening and the "small is stronger" paradigm of small scale
plasticity.
