Propagation of elastic waves through polycrystals: the effects of scattering from dislocation arrays

Abstract

We address the problem of an elastic wave coherently propagating through a two-dimensional polycrystal. The main source of scattering is taken to be the interaction with grain boundaries that are in turn modelled as line distribution of dislocations-a good approximation for low angle grain boundaries. First, the scattering due to a single linear array is worked out in detail in a Born approximation, both for longitudinal and transverse polarization and allowing for mode conversion. Next, the polycrystal is modelled as a continuum medium filled with such lines that are in turn assumed to be randomly distributed. The properties of the coherent wave are worked out in a multiple scattering formalism, with the calculation of a mass operator, the main technical ingredient. Expansion of this operator to second-order in perturbation theory gives expressions for the index of refraction and attenuation length. This work is motivated by two sources of recent experiments: firstly, the experiments of Zhang et al. (Zhang, G., Simpson Jr, W. A., Vitek, J. M., Barnard, D. J., Tweed, L. J. & Foley J. 2004 J. Acoust. Soc. Am. 116, 109-116.) suggesting that current understanding of wave propagation in polycrystalline material fails to interpret experimental results; secondly, the experiments of Zolotoyabko & Shilo who show that dislocations are potentially strong scatterers for elastic waves.