Generalized ultrasonic scattering model for arbitrary transducer configurations

Ultrasonic scattering in polycrystalline media is directly tied to microstructural features. As a result, modeling efforts of scattering from microstructure have been abundant. The inclusion of beam modeling for the ultrasonic transducers greatly simplified the ability to perform quantitative, fully calibrated experiments. In this article, a theoretical scattering model is generalized to allow for arbitrary source and receiver configurations, while accounting for beam behavior through the total propagation path. This extension elucidates the importance and potential of out-of-plane scattering modes in the context of microstructure characterization. The scattering coefficient is explicitly written for the case of statistical isotropy and ellipsoidal grain elongation, with a direct path toward expansion for increased microstructural complexity. Materials with crystallites of any symmetry can be studied with the present model; the numerical results focus on aluminum, titanium, and iron. The amplitude of the scattering response is seen to vary across materials, and to have varying sensitivity to grain elongation and orientation depending on the transducer configuration selected. The model provides a pathway to experimental characterization of microstructure with optimized sensitivity to parameters of interest.