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This paper uses 3D grain-scale finite element (FE) simulations to appraisethe classical scattering theory of plane longitudinal wave propagation inuntextured polycrystals with statistically equiaxed grains belonging to theseven crystal symmetries. As revealed from the results of 10,390 materials, theclassical theory has a linear relationship with the elastic scattering factorat the quasi-static velocity limit, whereas the reference FE andself-consistent (SC) results generally exhibit a quadratic relationship. Assupported by the results of 90 materials, such order difference also extends tothe attenuation and phase velocity, leading to larger differences between theclassical theory and the FE results for more strongly scattering materials.Alternatively, two approximate models are proposed to achieve more accuratecalculations by including an additional quadratic term. One model usesquadratic coefficients from quasi-static SC velocity fits and is thussymmetry-specific, while the other uses theoretically-determined coefficientsand is valid for any individual material. These simple models generally delivermore 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 negativequadratic coefficients.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Appraising scattering theories for polycrystals of any symmetry using finite elements