Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals

Abstract

This work studies scattering-induced elastic wave attenuation and phase velocity variation in three-dimensional untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation models and the grain-scale finite-element (FE) model, pushing the boundary towards strongly scattering materials. The results for materials with Zener anisotropy indices A > 1 show a good agreement between the theoretical and FE models in the transition and stochastic regions. In the Rayleigh regime, the agreement is reasonable for common structural materials with 1 < A < 3.2 but it deteriorates as A increases. The wavefields and signals from FE modelling show the emergence of very strong scattering at low frequencies for strongly scattering materials that cannot be fully accounted for by the theoretical models. To account for such strong scattering at A > 1, a semi-analytical model is proposed by iterating the far-field Born approximation and optimizing the iterative coefficient. The proposed model agrees remarkably well with the FE model across all studied materials with greatly differing microstructures; the model validity also extends to the quasi-static velocity limit. For polycrystals with A < 1, it is found that the agreement between the SOA and FE results is excellent for all studied materials and the correction of the model is not needed.

Appraising scattering theories for polycrystals of any symmetry using finite elements

“…Most importantly, the applicability extends exceptionally well to the quasi-static velocity limit. This is further supported by the fact that the quadratic coefficient q of π3/2 obtained in our prior work [36] is essentially the same as that from the quasi-static SC fit in table 3 for cubic materials with Anormaleq>1.…”

“…The SC results have an excellent agreement with the FEM results for all seven symmetries, showing a relative difference at the level of 0.1% (max 1%, for orthorhombic Sr 1 Mg 6 Ga 1 ). In addition to this evidence, the exceptionally high degree of accuracy of the SC theory was also extensively supported by prior FE results [32,36,73]; the underlying reason for this is that the SC theory satisfies the continuity of stress and strain throughout the polycrystal [61,62]. Therefore, in addition to FE calculations, we use the SC results in this paper as the reference to appraise the classical SOA theory at the quasi-static limit (this allows us to reduce the amount of very computationally intensive FE calculations).…”

“…We use these three geometric samples to simulate all materials in table 1 that belong to the seven crystal symmetries. The materials are taken from [36,50–58], and their equivalent Anormaleq [47] (Anormaleq=A for cubic materials), universal AU [48] and log-Euclidean A L [49] anisotropy indices and elastic scattering factor QL→T are given in table 1.…”

“…The resulting expression for mM can be found in Refs. [32,36] for polycrystals with statistically equiaxed grains and in Refs. [33,34] for those with statistically elongated grains.…”

“…The authors of this paper carried out the evaluation work to a deeper extent to see how the classical theory performs for strongly scattering cubic polycrystals [36,37] (an equally important topic as for other inhomogeneous media [38,39]). In the low-frequency Rayleigh regime, we observed that the classical theory has a growing difference from three-dimensional FE results as the elastic scattering factor (equivalent to the degree of inhomogeneity ξ2 [15,40]) increases; their agreement remains good in the Rayleigh-stochastic transition region and the stochastic regime.…”