The correlation between ultrasonic wave propagation and polycrystalline microstructures has significant implications in nondestructive evaluation. An original numerical approach using the finite element method to quantify in both time and frequency domains the ultrasonic noise scattering due to the elastic heterogeneity of polycrystalline microstructures is presented. Based on the reciprocity theorem, it allows the scattering evaluation using mechanical data recorded only on the boundary of polycrystal instead of within its volume and is applicable to any polycrystalline aggregate regardless of its crystallographic or morphological characteristics. Consequently it gives a more realistic and accurate access of polycrystalline microstructures than the classical analytical models developed under the assumption of single scattering and the Born approximation.
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.