Correlation Between Ultrasonic Scattering Coefficients and Orientation Distribution Coefficients (ODCs) in Textured Polycrystalline Materials with Arbitrary Crystallite Symmetry

Elastic wave scattering in polycrystalline materials has been a long-lasting topic in seismology and physical acoustics. Numerous analytical scattering models have been reported for polycrystals with random grain orientations. However, the elastic wave scattering in polycrystals with a preferred grain orientation (crystallographic texture) has not been well studied. This study develops a general ultrasonic scattering model that correlates the scattering coefficients and attenuation coefficients with orientation distribution coefficients (ODCs) for polycrystalline materials with a crystallographic texture. These models are valid for aggregates of triclinic grains with arbitrary texture symmetry. Since different terminologies for orientation distribution functions (ODFs) are adopted in quantitative texture analysis, the relations between different terminologies are also summarized in this study. Furthermore, for two special cases—hexagonal polycrystalline materials with a fiber texture and cubic polycrystalline materials with orthotropic texture symmetry—explicit expressions for the ultrasonic backscattering coefficient through ODCs are derived. The explicit relationship between ultrasonic backscattering and ODCs not only manifests how the individual texture coefficients impact ultrasonic scattering but also makes it possible to determine ODCs up to the eighth order experimentally from ultrasonic scattering measurements. This type of forward model also can be applied to the microstructure characterization of textured polycrystals.