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

TL;DR

This study compares theoretical, semi-analytical, and finite element models to analyze elastic wave scattering in strongly scattering polycrystals, revealing the semi-analytical model's effectiveness across various microstructures.

Contribution

The paper introduces a semi-analytical model that accurately predicts elastic wave scattering in strongly scattering polycrystals, extending the applicability of existing models.

Findings

Good agreement between models for A>1 in transition regions

Semi-analytical model matches FE results across diverse microstructures

Model validity extends to quasi-static velocity limit

Abstract

This work studies scattering-induced elastic wave attenuation and phase velocity variation in 3D 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 optimising 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.