Elastic wave propagation through a polycrystal composed of anisotropic grains results in scattering-induced attenuation and velocity dispersion. The scattering response carries important information on the size, shape, and orientation of the grains, thus offering a possibility for estimation of the microstructural characteristics from ultrasonic measurements. To demonstrate the applicability of the advanced theoretical models for ultrasonic wave propagation in polycrystals, a series of comparative studies with 3D grain-scale finite element (FE) simulations have been performed for polycrystals with statistically equiaxed and elongated grains [1–6]. These have shown only a small difference between the FE and theoretical models for weakly scattering materials such as Aluminium (anisotropy index 1.24) across a wide frequency range. However, the difference increased systematically with the level of anisotropy and is distinctive for strongly scattering materials such as Inconel (anisotropy index 2.83). Since the FE results have achieved high accuracy [7], these observations suggest that the validity of the theoretical models may have been challenged for strongly scattering materials. In the present work, we significantly extend the range of materials to include polycrystals with anisotropy indices as high as 9.14. We demonstrate that the deviation of the theoretical models from the FE is, unexpectedly, more pronounced in the low-frequency Rayleigh regime than in the high-frequency stochastic regime as one would expect. We attribute this to the occurrence of multiple scattering in all directions from a grain, which is not accounted for by the existing theoretical models. To account for this, we propose a semi-analytical model based on the iteration of the dispersion equation for the far-field model [8]. We illustrate that the proposed model agrees remarkably well with the FE results across all studied equiaxed and elongated polycrystals of various microstructures with largely varying grain uniformities. Also, we demonstrate that its validity extends to the quasi-static velocity limit.REFERENCES 
[1] Van Pamel A, Sha G, Rokhlin SI, Lowe MJS. Finite-element modelling of elastic wave propagation and scattering within heterogeneous media. Proc R Soc A Math Phys Eng Sci. 2017;473(2197):20160738.&nbsp; 
[2] Van Pamel A, Sha G, Lowe MJS, Rokhlin SI. Numerical and analytic modelling of elastodynamic scattering within polycrystalline materials. J Acoust Soc Am. 2018;143(4):2394–408.&nbsp; 
[3] Ryzy M, Grabec T, Sedlák P, Veres IA. Influence of grain morphology on ultrasonic wave attenuation in polycrystalline media. J Acoust Soc Am. 2018;143(1):219–29.&nbsp; 
[4] Sha G, Huang M, Lowe MJS, Rokhlin SI. Attenuation and velocity of elastic waves in polycrystals with generally anisotropic grains: analytic and numerical modelling. J Acoust Soc Am. 2020;147(4):2422–65.&nbsp; 
[5] Huang M, Sha G, Huthwaite P, Rokhlin SI, Lowe MJS. Elastic wave velocity dispersion in polycrystals with elongated grains: theoretical and numerical analysis. J Acoust Soc Am. 2020;148(6):3645–3662.&nbsp; 
[6] Huang M, Sha G, Huthwaite P, Rokhlin SI, Lowe MJS. Longitudinal wave attenuation in polycrystals with elongated grains: 3D numerical and analytical modeling. J Acoust Soc Am. 2021;149(4):2377–94.&nbsp; 
[7] Huang M, Sha G, Huthwaite P, Rokhlin SI, Lowe MJS. Maximizing the accuracy of finite element simulation of elastic wave propagation in polycrystals. J Acoust Soc Am. 2020;148(4):1890–910.&nbsp; 
[8] Rokhlin SI, Li J, Sha G. Far-field scattering model for wave propagation in random media. J Acoust Soc Am. 2015;137(5):2655–69.&nbsp;&nbsp;

Elastic Wave Propagation in Strongly Scattering Polycrystals: Finite Element and Semi-Analytical Study

Paper Proceedings: https://asmedigitalcollection.asme.org/qnde/QNDE2021/volume/85529

ASME 2021 48th Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE2021)

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