An alternative model of the blocking of dislocations at grain boundaries

Abstract

The blocking of dislocations at a slip barrier, such as a grain boundary, is modelled by considering, in the domain of distribution of dislocations ahead of the slip band, a small zone representing a locked source or the width of the boundary itself. The ‘friction stress’ in this small zone is calculated so that no infinite stresses appear in the analysis. Hall–Petch type relationships are derived for the yield stress and the fatigue limit. When the length of the additional zone is sufficiently small in comparison to the total length of the array, the solution is very close to the one obtained by the common modelling of the block by an infinite delta-type function.