A quantitative theory of the elastic wave damping and velocity change due to interactions with dislocations was presented. It provided a firm theoretical basis and a generalization of the Granato-Lücke model. This was done by considering the interaction of transverse (T) and longitudinal (L) elastic waves with an ensemble of dislocation segments randomly placed and randomly oriented in an elastic solid. In order to characterize the coherent wave propagation using multiple scattering theory, a perturbation approach was used which was based upon a wave equation that took account of dislocation motion forced by an external stress. In these calculations, the effective velocities of the coherent waves appeared to first order in perturbation theory, while the attenuations have a first-order part due to internal viscosity and a second-order part due to the energy that was taken away from the incident direction. This led to a frequency-dependence law, for longitudinal and transverse attenuations, that was a combination of quadratic and quartic terms instead of the usual quadratic term alone. A comparison with resonant ultrasound spectroscopy and electromagnetic acoustic resonance experiments was proposed. The present theory explained the experimentally observed difference between longitudinal and transverse attenuations.

Wave Propagation through a Random Array of Pinned Dislocations - Velocity Change and Attenuation in a Generalized Granato and Lücke Theory. A.Maurel, V.Pagneux, F.Barra, F.Lund: Physical Review B, 2005, 72[17], 174111 (15pp)