The mean free path length for dislocation movement during deformation of a polycrystal determines the storage term during strain hardening. The classical Mecking–Estrin model postulates additivity of the effects of substructure and grain boundaries. The present work considers the probability distribution of obstacles along the path and uses the laws of probability to derive an expression of which the Mecking–Estrin model was a good approximation. The physical implications of the approach and the extension of this method to particle hardening were briefly discussed.

A Probabilistic Derivation of the Effect of Grain Size on the Dislocation Free Path in a Deforming Polycrystal. R.Schouwenaars, M.Seefeldt, P.Van Houtte: Scripta Materialia, 2010, 62[8], 590-3