LONG-RANGE STRESS-FIELD FLUCTUATIONS INDUCED BY RANDOM DISLOCATION ARRAYS - A UNIFIED SPECTRAL APPROACH

We present a general and powerful formalism which allows one to determ ine the variance [Dr] of the stress field at a distance D from a rando m planar parallel distribution of dislocations. The problem is reduced to the calculation of two quantities: (1) the power spectrum of the d islocation density function in the low wavenumber limit and (2) the Fo urier transform of the elastic Green function for a single dislocation . We recover straightforwardly previous results that [D tau] scales wi th the distance D to the wall as D-3 for weak disorder and as D-1 for strong disorder. New results are derived for more general arrays of di slocations as well as in the presence of long range spatial correlatio ns. We illustrate the method by considering in details the case of wal ls of edge and screw dislocations.