Ultrasonic scattering of elastic waves in polycrystalline materials with elongated grains: theoretical models and numerical simulation

The scattering of ultrasonic elastic waves is an interesting phenomenon that can be exploited by the Laser-Ultrasonics (LU) technique to characterize the polycrystalline microstructure of components produced by Wire and Laser Additive Manufacturing (WLAM). A polycrystalline microstructure is a heterogeneous medium due to the various crystal orientations from one grain to another (each being anisotropic), and the possible presence of multiple phases. Scattering resulting from the interaction of the propagating wave with the microstructure can be observed through wave amplitude decay and the variation in the wave phase/group velocity. Indeed, if one can correlate these scattering parameters with specific parameters of the microstructure (grain size/shape, degree of anisotropy, oriented texture, etc.), one can gain useful information that can be used in real-time non-destructive testing techniques. It is therefore important to have versatile and robust theoretical and numerical models capable of estimating the scattering of elastic waves in polycrystalline microstructures. In this work, a theoretical scattering model of bulk waves is developed based on previous models proposed by Bai and Tie [1], which is valid for grains varying from equiaxed to elongated shapes in the 3D and 2D cases. Ultrasonic scattering of bulk and surface waves in 3D and 2D polycrystalline microstructures is simulated using a space-discontinuous Galerkin framework. Ultrasonic attenuation and wave phase velocity in an Inconel 718 polycrystalline material are estimated thanks to theoretical and numerical results. First, our theoretical model is validated by comparing its prediction with numerical results obtained under the assumptions of untextured and single-phase medium. Moreover, 3D and 2D scattering phenomena are analyzed for pointing out the differences and the usefulness of 2D model to predict effects of 3D grain shape and rotation [2]. Then, the numerical model is extended to deal with the specific case of aligned crystallographic orientations in cases being found in WLAM components. It allows us to study the variations of attenuation and phase velocity with the angle of alignment of the principal crystallographic orientation. Acknowledgments This work was part of the COLUMBO project (ANR-21-CE08-0026) funded by the French National Agency for Research (ANR). References [1] X Bai, B Tie, J-H Schmitt, and D Aubry. Comparison of ultrasonic attenuation within two-and three-dimensional polycrystalline media. Ultrasonics, 100:105980, 2020. [2] J.C Victoria Giraldo, B Tie, J Laurent, A Lhémery, D Solas. Theoretical analysis of the dimensionality of ultrasonic attenuation in polycrystalline materials with elongated grains. Journal of Physics: Conference Series, 2024. ⟨hal-04485455⟩