Multiple scattering from assemblies of dislocation walls in three dimensions. Application to propagation in polycrystals.

The attenuation of ultrasound in polycrystalline materials is modeled with grain boundaries considered as arrays of dislocation segments, a model valid for low angle mismatches. The polycrystal is thus studied as a continuous medium containing many dislocation "walls" of finite size randomly placed and oriented. Wave attenuation is blamed on the scattering by such objects, an effect that is studied using a multiple scattering formalism. This scattering also renormalizes the speed of sound, an effect that is also calculated. At low frequencies, meaning wavelengths that are long compared to grain boundary size, then attenuation is found to scale with frequency following a law that is a linear combination of quadratic and quartic terms, in agreement with the results of recent experiments performed in copper [Zhang et al., J. Acoust. Soc. Am. 116(1), 109-116 (2004)]. The prefactor of the quartic term can be obtained with reasonable values for the material under study, without adjustable parameters. The prefactor of the quadratic term can be fit assuming that the drag on the dynamics of the dislocations making up the wall is one to two orders of magnitude smaller than the value usually accepted for isolated dislocations. The quartic contribution is compared with the effect of the changes in the elastic constants from grain to grain that is usually considered as the source of attenuation in polycrystals. A complete model should include this scattering as well.