Theoretical and numerical modeling of ultrasonic scattering in polycrystalline materials: from elongated grains to columnar grains

International audienceFor nondestructive evaluation using laser ultrasonics technique, it is of great interest to studythe scattering of ultrasonic waves in polycrystalline materials, which contains usefulmicrostructural information that can be used in inversion methodologies for characterization.The scattering-induced attenuation has already been studied in microstructures with equiaxedgrains[1,2,3]. However, components with more complex microstructures involving elongated orcolumnar grains can be produced, such as those obtained by Wire and Laser AdditiveManufacturing (WLAM). Therefore, it is relevant to consider in the analytical and numericalmodeling the effect of such microstructures.In the present work, phase velocity and attenuation coefficients are first obtained forlongitudinal and transverse waves in untextured cubic polycrystalline materials with elongatedgrains. Theoretical 2D and 3D expressions are obtained by an analytical approach based onStanke and Kino's model and the equations obtained by Bai et al.[3] under the Bornapproximation. The 3D model is validated with that of Yang et al.[4], whose work is based onWeaver's equations. The comparison of 2D and 3D models allows an analysis of thedimensionality of grain diffusion-induced attenuation, which involves more complexmechanisms with elongated grains. In parallel, numerical simulations are done with an in-housecode using a space discontinuous Galerkin method. Both idealized (custom generated torespect theoretical hypothesis) and virtual (generated after the WLAM process in nickel-basedsuperalloys) microstructures with elongated and columnar grains are simulated. The numericaland theoretical results are compared to study the influence of the grain shape/size andpropagating wave direction on the attenuation coefficient. In addition, the domain of validity oftheoretical models is estimated in comparison to the more realistic results obtained bynumerical simulations.References[1] F. E. Stanke and G. S. Kino, “A unified theory for elastic wave propagation in PolycrystallineMaterials,” 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- andthree-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 inpolycrystalline materials,” Ultrasonics, 5 (2011), 697–708