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

Multiple Scattering from Assemblies of Dislocation Walls in Three Dimensions. Application to Propagation in Polycrystals. A.Maurel, V.Pagneux, F.Barra, F.Lund: Journal of the Acoustical Society of America, 2007, 121[6], 3418-31