THEORY OF ULTRASONIC SCATTERING BY GRAINS IN POLYCRYSTALS

A theory of ultrasonic scattering by a polycrystal, valid for a wide range of ratios of wavelength and grain‐size, is presented. The present treatment concerns the study of wave equations with random elements to take account of the fact that the elastic constants of the crystal change values abruptly at grain boundaries. The solutions of the wave equations, which are valid for weak inhomogeneities, are given in terms of the spatial correlation function of elastic moduli. Appropriate modelling of this correlation function yields closed expressions for the ultrasonic attenuation coefficient. These can be studied in the limiting cases of large and small wavelengths in order to make contact with existing theoretical results. Satisfactory agreement of the present theory with experimental data in Al is also obtained. Copyright © 1979 WILEY‐VCH Verlag GmbH & Co. KGaA