A study was made of the coherent propagation of elastic waves through a 2-dimensional solid filled with randomly placed dislocations, edge and screw, in a multiple scattering formalism. The wavelengths were supposed to be large, as compared with the Burgers vector, and the dislocation density was supposed to be low. The basic mechanism of scattering of an elastic wave by a line defect was then quite simple: fluttering: An elastic wave hit each individual dislocation, causing it to oscillate. This oscillatory motion then generated out-going (from the dislocation position) elastic waves. When many dislocations were present, the resultant wave behavior could be complicated; because of multiple scattering. Under some circumstances, a coherent wave could exist which propagated with an effective wave velocity whose amplitude was attenuated because of the energy scattered away from the direction of propagation. A particular study concerned the determination of the coherent wave-number of an elastic wave which propagated through an elastic medium filled with randomly placed dislocations. The real part of the coherent wave-number gave the effective wave velocity, and its imaginary part gave the attenuation length (elastic mean free path). The calculations were performed by using a wave equation for the particle velocity with a right-hand-side term, which was valid in 2 and 3 dimensions. This accounted for the dislocation motion when forced by an external stress. In 2 dimensions, the motion of a dislocation was that of a massive particle driven by the incident wave. Both screw and edge dislocations were considered.

Elastic Wave Propagation through a Random Array of Dislocations. A.Maurel, J.F.Mercier, F.Lund: Physical Review B, 2004, 70[2], 024303 (15pp)