The probability distribution of internal stresses in externally loaded 2D dislocationsystems

Abstract

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