A representative grain size for the mechanical response of polycrystals

In this note we propose a geometric parameter of a lognormal grain size distribution, denoted here as the representative grain size, that provides a natural link between the yield strength and work hardening response of a polycrystal and its grain size distribution. It is shown that using this representative grain size in place of the arithmetic mean of the grain size distribution produces a Hall–Petch slope that is independent of the size distribution. The utility of the proposed parameter in describing the work hardening behaviour of metals is also examined in the context of a viscoplastic self-consistent micromechanical model.