Finite element modeling of grain size effects on the ultrasonic microstructural noise backscattering in polycrystalline materials

The numerical approach is proposed within the same unified theoretical framework as the classical analytical models, so it is possible to validate it in the cases of idealized microstructures for which the considered analytical models remain relevant. As an original result, assuming single phase, untextured and equiaxed microstructures, two-dimensional (2D) theoretical formulas are developed and a frequency-dependent coefficient is found compared to the classical three-dimensional (3D) formulas. 2D numerical simulations are then performed for idealized microstructures composed of hexagonal grains with a uniform grain-size. Three grain sizes are considered herein and involve different scattering regions. Good comparisons are obtained between theoretical and numerical estimates of the backscattering coefficient, which validate the numerical approach. Effects of the grain boundary orientations are analyzed by modeling an irregular hexagonal grain morphology and a random grain morphology generated by an established Voronoi approach. The origin of the significant oscillation level of backscattering is then investigated and discussed.