Influence of Texture and Grain Morphology on the Two-Point Correlation of Elastic Constants: Theory and Implications on Ultrasonic Attenuation and Backscattering

Abstract

The discontinuity in the elastic properties at the grain boundaries of a polycrystal controls the attenuation [1] and noise backscattered [2] by an elastic wave propagating through the material. In stochastic theories, which describe the propagation of the mean field in an ensemble of macroscopically identical microstructures, the effects of these discontinuities are quantified by the two-point correlation of elastic constants. It is well known that this correlation, and hence the attenuation and backscttering, is influenced by grain size [3--5] and shape [6], and recent experimental results of Hirao et al [7] imply a strong dependence on preferred grain orientation (texture). The purpose of this paper is to develop the theory necessary to describe these relationships.