A general and powerful formalism was presented which permitted the determination of the variance of the stress field at a given distance from a random planar parallel distribution of dislocations. The problem was reduced to the calculation of 2 quantities. These were the power spectrum of the dislocation density function in the low wave-number limit, and the Fourier transform of the elastic Green’s function for a single dislocation. It was then straightforward to obtain the known result that the variance scaled with the distance, D, to the wall as D-3 for weak disorder and as D-1 for strong disorder. New results were derived for more general arrays of dislocations, and for the effect of long-range spatial correlations. The method was illustrated by considering walls of edge or screw dislocations.

Long-Range Stress Field Fluctuations Induced by Random Dislocation Arrays - a Unified Spectral Approach. G.Saada, D.Sornette: Acta Metallurgica et Materialia, 1995, 43[1], 313-8