Modélisation et simulation des mécanismes de diffusion des ultrasons dans les composants WLAM en vue d'une caractérisation multi-échelle

The scattering of elastic waves in polycrystalline materials is a physically interesting phenomenon that is widely exploited in the field of Non-Destructive Testing (NDT), as the Ultrasound-Laser Technique. Polycrystalline materials often exhibit complex morphological and crystallographic variations, leading to fluctuations in acoustic impedance. Individual grains, each characterized by their own elastic anisotropy, can be misoriented relative to the sample reference frame, resulting in different types of macroscopic anisotropy. For example, macroscopic isotropy arises from a random distribution of grain orientations.This thesis focuses on nickel-based superalloy produced by Wire Laser Additive Manufacturing (WLAM), a process that often yields a microstructure characterized by columnar grains and a pronounced macroscopic fiber texture caused by the alignment of a single crystallographic axis across all grains.For ultrasonic characterization, it is essential to understand the correlation between the coherent waves and the microstructure under investigation. The multiple scattering of elastic waves by the grains are commonly quantified in terms of the wave amplitude attenuation, phase velocity dispersion and backscattered noise. These quantities provide valuable information on grain morphology and elastic properties, enabling their use in inversion methodologies for quantitative microstructure characterization.In this thesis, theoretical and numerical models are developed to investigate the influence of WLAM-specific microstructural features on elastic wave amplitude attenuation and phase velocity dispersion. Two two-dimensional theoretical models are proposed, based on classical multiple-scattering theory, perturbation theory, and the Dyson equation for heterogeneous and anisotropic elastic media. Analytical expressions are derived for macroscopically isotropic media and transversely isotropic media with elongated grains.These models are further generalized by incorporating numerically computed average elastic and covariance tensors, as well as spatial correlation function, obtained from either synthetic or real microstructures. The developed frameworks provide a physically consistent basis for analyzing elastic wave scattering in virtually any type of polycrystalline material.Nevertheless, the theoretical models are constrained by certain idealized assumptions. To overcome these limitations, a space-discontinuous Galerkin finite element method is implemented, enabling the simulation of elastic wave propagation in polycrystals exhibiting arbitrary macroscopic anisotropy and morphological complexity, and capturing the complete multiple-scattering phenomenon.The theoretical and numerical results together provide an in-depth analysis showing that attenuation and phase velocity dispersion exhibit a strong directional dependence in fiber-textured and elongated microstructures. These findings offer valuable insights for ultrasonic characterization of the polycrystalline microstructures typical o WLAM-produced components.