  The distribution of internal shear stresses in a 2D dislocation system is
investigated when external shear stress is applied. This problem serves as a
natural continuation of the previous work of Csikor and Groma (Csikor F F and
Groma I 2004 Phys. Rev. B 58 2969), where analytical result was given for the
stress distribution function at zero applied stress. First, the internal stress
distribution generated by a set of randomly positioned ideal dislocation
dipoles is studied. Analytical calculations are carried out for this case. The
theoretical predictions are checked by numerical simulations showing perfect
agreement. It is found that for real relaxed dislocation configurations the
role of dislocation multipoles cannot be neglected, but the theory presented
can still be applied.

Statistical Mechanics