For nondestructive evaluation using laser ultrasonics technique, it is of great interest to study the scattering of ultrasonic waves in polycrystalline materials, which contains useful microstructural information that can be used in inversion methodologies for characterization. The scattering-induced attenuation has already been studied in microstructures with equiaxed grains[1,2,3]. However, components with more complex microstructures involving elongated or columnar grains can be produced, such as those obtained by Wire and Laser Additive Manufacturing (WLAM). Therefore, it is relevant to consider in the analytical and numerical modeling the effect of such microstructures.

In the present work, phase velocity and attenuation coefficients are first obtained for longitudinal and transverse waves in untextured cubic polycrystalline materials with elongated grains. Theoretical 2D and 3D expressions are obtained by an analytical approach based on Stanke and Kino's model and the equations obtained by Bai et al.[3] under the Born approximation. The 3D model is validated with that of Yang et al.[4], whose work is based on Weaver's equations. The comparison of 2D and 3D models allows an analysis of the dimensionality of grain diffusion-induced attenuation, which involves more complex mechanisms with elongated grains. In parallel, numerical simulations are done with an in-house code using a space discontinuous Galerkin method. Both idealized (custom generated to respect theoretical hypothesis) and virtual (generated after the WLAM process in nickel-based superalloys) microstructures with elongated and columnar grains are simulated. The numerical and theoretical results are compared to study the influence of the grain shape/size and propagating wave direction on the attenuation coefficient. In addition, the domain of validity of theoretical models is estimated in comparison to the more realistic results obtained by numerical simulations.

References
[1] F. E. Stanke and G. S. Kino, “A unified theory for elastic wave propagation in Polycrystalline
Materials,” J. Acoust. Soc. Am. 75, (1984), 665–681.
[2] R. L. Weaver, “Diffusivity of ultrasound in polycrystals,” J. Mech. Phys. Solids, 38 (1990), 55–86.
[3] X. Bai, B. Tie, J.-H. Schmitt, and D. Aubry, “Comparison of ultrasonic attenuation within two- and three-dimensional polycrystalline media,” Ultrasonics 100 (2020), 105980.
[4] L. Yang, O. I. Lobkis, and S. I. Rokhlin, “Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials,” Ultrasonics, 5 (2011), 697–708.