Elastic Wave Scattering And Propagation

Author : Anubhav Roy
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (142 download)

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Download or read book Elastic Wave Propagation and Scattering in Polycrystals written by Anubhav Roy and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polycrystalline aggregates of randomly distributed grains are associated with a fluctuating elastic stiffness. These fluctuations or heterogeneities are potential scatterers to the elastic waves propagating through the polycrystalline microstructures. The scattering within these microstructures results in the attenuation of energy and a change in the phase velocity (wavespeed) of the incident wave. The attenuation and wavespeed are measurable quantities that reveal important information about the respective microstructure. Existing theoretical models apply a first-order Keller approximation or an equivalent first-order smoothing approximation (FOSA) to predict the attenuation and wavespeed in polycrystals. This dissertation presents a theoretical framework to investigate the effects of the third-order smoothing approximation (TOSA) on the attenuation and wavespeed estimates in transversely isotropic aggregates of randomly distributed cubic grains. \par The Keller approximation-based Unified Theory model is constructed in the spatial domain applicable to the propagation of plane waves. On the other hand, the equivalent FOSA-based model in the frequency domain, free from such plane wave assumptions, directly applies to modeling the diffuse fields as it considers a truncation of the mass operator series contained in an elastodynamic Dyson equation. This truncated Dyson series provides a statistical expectation of the Green's function dyadic used to model the respective mean field propagation. However, the existing FOSA-based model involves a Born approximation that limits its application to the stochastic scattering regime characterized by a transitional domain between the low and high frequencies. In this dissertation, the FOSA-based model has been extended for the first time to provide solutions beyond the Born approximation applicable for the full range of frequencies spanning from the Rayleigh (low frequencies) to the geometric regime (high frequencies). Independently generated FOSA-based estimates of wavespeed and attenuation in common metals like aluminum, iron, and lithium show reasonable agreement with the corresponding Unified Theory estimates. \par The FOSA-based model developed in the frequency domain is extended to incorporate two additional multiple scattering terms associated with the TOSA-based truncation to the Dyson series. The effects of including the TOSA-based terms are studied for the full range of frequencies from the Rayleigh to the geometric regime. These effects are quantified as a ratio between the estimates from the current model, including TOSA, and from the corresponding FOSA-based model. For low-frequency propagation under assumptions of Rayleigh limit, closed-form solutions of attenuation and wavespeed are obtained with and without considering Born approximation. The effects of including TOSA in the low frequencies have been studied for $758$ cubic metals with different degrees of elastic heterogeneities. The study in the low frequencies confirms a correlation between higher-order scattering and the degree of heterogeneity. Attenuation estimates are more sensitive than the wavespeed estimates to higher-order scattering. Moreover, the transverse or shear waves show a stronger sensitivity to higher-order scattering at low frequencies than longitudinal waves at the same frequencies. \par Significant effects of including the TOSA-based terms are observed in the high frequencies. Analogous to the FOSA-based estimates of wavespeed dispersion, the variation of attenuation in the geometric regime is found to be dependent on the incident mode while including the TOSA-based terms. Moreover, the attenuation and wavespeed dispersion in the geometric zone reveals a strong dependence on the degree of heterogeneity while including the TOSA-based terms. Nevertheless, both for longitudinal and transverse modes of propagation, the attenuation estimates start decreasing with increasing frequencies while considering the TOSA-based model. This can be attributed to a possible gain of resonance captured by the higher-order scattering events within the microstructure for propagation of high-frequency waves. This model can be applied to different microstructures possessing elastic heterogeneities to investigate the respective higher-order scattering effects. That may generate opportunities to offer a better agreement with the experimentally measured estimates in textured or porous microstructures. Beside the attenuation and wavespeed, analogous to the existing FOSA-based model, this model offers a direct scope of extension to provide other important estimates like the intensity of the scattered waves, diffusivity, etc.