Theoretical and numerical comparison of the elastic ultrasonic wave scattering in polycrystalline materials with fiber texture

The physics of the elastic ultrasonic wave scattering is of interest for the non-destructive Laser-Ultrasonics (LU) technique to characterize polycrystalline materials. Generally, polycrystalline media are composed of multiple anisotropic single crystals that are randomly oriented. Components produced by Wire and Laser Additive Manufacturing (WLAM) can have a particular texture with single crystals having one aligned axis and known as fiber texture. It is therefore of interest to develop theoretical and numerical models to study the influence of this type of fiber texture on the wave scattering parameters such as attenuation and phase velocity, which is the subject of the study presented in this work. The theoretical study of the elastic wave propagation and scattering is developed here in terms of the Dyson equation for the average heterogeneous Green function, approach followed by Weaver [1]. Moreover, as the fiber texture results in a medium that macroscopically respects transverse isotropy, the Dyson equation is written in terms of the transversely isotropic reference homogeneous Green dyadic as was first proposed by Turner [2]. With a generalized two-point spatial correlation function for equiaxed and elongated grains, the real and imaginary parts of the solution are sought to obtain 2D and 3D expressions for the wave attenuation and phase velocity. As expected, these parameters are explicitly dependent on the wave propagation direction. Moreover, the phase velocity shows a clear, direct relationship with the distribution of the fastest and slowest axes in the propagation direction. Finite element numerical simulations with a space-discontinuous Galerkin framework are carried out to validate and find the limitations of the theoretical assumptions. It is found that both theoretical and numerical results are in good agreement with both results showing a stronger wave scattering when the wave propagates perpendicular to the fiber direction and no wave dispersion when the wave propagates in the fiber direction.