Abstract
Solutions for the distribution of dislocations representing a crack have previously been obtained both for the instances in which the stress field is totally bounded (Bilby-Cottrell-Swinden), and also where the leading dislocations are blocked (Taira-Tanaka-Nakai). This work evaluates a compact formula incorporating both solutions by considering a rectilinear crack transversing an arbitrary number of zones with different friction stresses. Symmetry is not required. The expressions for the dislocation density and the plastic displacement, as well as the stress distribution in the plane of the crack, are obtained.