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.
Highlights
Elastic waves scatter as they travel through inhomogeneous media and exhibit scatteringinduced attenuation and phase velocity dispersion
A small discontinuity can be observed as we look along sequential FE model (FEM) points for each material, which is more evident from the phase velocity points for A = 5.0 and lithium at around 2k0La = 1
Taking the frequency at 2k0La = 1 as an example, the relative difference in attenuation between the second-order approximation (SOA) and FEM results increases from −10% for aluminium to −66% for lithium, while the relative difference in phase velocity increases from 4 × 10−4% for aluminium to 2.4% for lithium
Summary
Elastic waves scatter as they travel through inhomogeneous media and exhibit scatteringinduced attenuation and phase velocity dispersion. All three regimes can be predicted if the far-field approximation (FFA) [20] is invoked in the SOA model but the strongly scattering geometric regime vanishes if the single-scattering Born approximation is employed The validity of these model approximations has recently been evaluated by three-dimensional grain-scale finiteelement (FE) simulations which are capable of accurately describing the interaction of waves with grains [16–19,21–23]. We shall see that the proposed model works remarkably well in the Rayleigh, transition and stochastic regimes for various cubic polycrystals with largely differing anisotropies and greatly contrasting grain uniformities The development of this semi-analytical model is to some extent empirical, but we expect that these promising simple closed-form solutions would stimulate future rigorous theoretical development.
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