Analytical attenuation and scattering models for polycrystals with uniform equiaxed grains

Abstract

This paper reports an explicit two-point correlation function (TPCF), associated with the mean grain size from a grain size distribution, which can well present the TPCFs of three-dimensional (3D) Voronoi polycrystals with uniform equiaxed grains. Analytical attenuation and scattering models applicable to polycrystals of uniform equiaxed grains of arbitrary symmetry are developed using this explicit TPCF. Additionally, a comparison is drawn between analytical attenuation model and available 3D finite element method (FEM) results in the literature, and it indicates that the analytical attenuation model has excellent agreement with 3D FEM. This work will facilitate the comparison between analytical modeling and 3D FEM.

Attenuation and velocity of elastic waves in polycrystals with generally anisotropic grains: Analytic and numerical modeling

“…In most prior theoretical work on wave propagation in polycrystals the exponential form of the TPC exp( ) ra − ( a is the mean grain radius) has been adopted for polycrystals with equiaxed [4,5,7,13,19,[28][29][30][31][32] and ellipsoidal grains [9,[12][13][14][15]29,30]. However, it was shown experimentally [30] that a polycrystal TPC may deviate significantly from a simple exponential form.…”

A far-field scattering model in textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry

“…Similarly, Figure 6 shows the phase velocity comparison between the SOA model and the FFA model for the textured Ti polycrystals with axisymmetric ellipsoidal grain crystallites (the same example as Figure 5). Phase velocity from the FFA model has been constantly shifted using the quasi-static velocity from the SOA model, Equation (20). In Figure 6, after correction the phase velocity from the FFA model has reasonable agreement with the SOA model except for the geometric region.…”

“…As explained in Section 3, the FFA model fails to produce correct phase velocities and one has to shift its phase velocity by a constant using Equation (20). Figure 4 indicates the normalized phase velocities from the FFA and SOA models on the textured Ti polycrystals with equiaxed grain where only dominant roots are shown and the phase velocity of the FFA model is corrected using Equation (20). Obviously, after correction the phase velocity of the FFA model is reasonably close to that of the SOA model below the geometric region.…”

“…Forward attenuation modeling is of great importance to study the interaction of elastic waves with aggregates of scatters, such as polycrystalline rocks and metals [2][3][4][5], and it has practical applications in seismology [6] and ultrasonic non-destructive evaluation [7][8][9][10]. For example, numerous studies have correlated the ultrasonic attenuation with polycrystalline microstructure characteristics [11][12][13][14][15][16][17][18][19][20][21], and in terms of these analytical models microstructure information can be retrieved non-destructively from attenuation measurements [22,23].…”

“…The derivation of Equation(20) is based on the counter integral, and the lengthy intermediate steps are not shown here. The sign of DV (p) is always negative (because the Voigt velocity V M (p) is the upper bound and the actual wave speed cannot surpass the Voigt velocity), which means that the phase velocity from the FFA model should be shifted down for correction.…”