Appraising scattering theories for polycrystals of any symmetry using finite elements

TL;DR

This study evaluates classical scattering theories for polycrystals using finite element simulations and proposes improved models that account for quadratic effects, enhancing accuracy especially in strongly scattering materials.

Contribution

The paper critically assesses classical scattering theories with FE simulations and introduces two new quadratic models for better accuracy across various symmetries.

Findings

Classical theory shows linear relation at quasi-static limit, FE results are quadratic.

New models improve attenuation and velocity predictions, especially for strongly scattering materials.

Models are invalid for materials with negative quadratic coefficients.

Abstract

This paper uses 3D grain-scale finite element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with statistically equiaxed grains belonging to the seven crystal symmetries. As revealed from the results of 10,390 materials, the classical theory has a linear relationship with the elastic scattering factor at the quasi-static velocity limit, whereas the reference FE and self-consistent (SC) results generally exhibit a quadratic relationship. As supported by the results of 90 materials, such order difference also extends to the attenuation and phase velocity, leading to larger differences between the classical theory and the FE results for more strongly scattering materials. Alternatively, two approximate models are proposed to achieve more accurate calculations by including an additional quadratic term. One model uses quadratic coefficients from quasi-static SC velocity fits and is thus symmetry-specific, while the other uses theoretically-determined coefficients and is valid for any individual material. These simple models generally deliver more accurate attenuation and phase velocity (particularly the second model) than the classical theory, especially for strongly scattering materials. However, the models are invalid for the attenuation of materials with negative quadratic coefficients.