Effect of texture and grain shape on ultrasonic backscattering in polycrystals

An ultrasonic backscattering model is developed for textured polycrystalline materials with orthotropic or trigonal grains of ellipsoidal shape. The model allows us to simulate realistic microstructures and orthotropic macroscopic material textures resulting from thermomechanical processing for a broad variety of material symmetries. The 3-D texture is described by a modified Gaussian orientation distribution function (ODF) of the crystallographic orientation of the grains along the macroscopic texture direction. The preferred texture directions are arbitrary relative to the axes of the ellipsoidal grains. The averaged elastic covariance and the directional anisotropy of the backscattering coefficient are obtained for a wave propagation direction arbitrary relative to the texture and grain elongation directions. One particular application of this analysis is the backscattering solution for cubic crystallites with common textures such as Cube, Goss, Brass and Copper. In our analysis, in the texture-defined coordinates the matrix of elastic constants for cubic crystallites takes the form of orthotropic or trigonal symmetry. Numerical results are presented, discussed and compared to the experimental data available in the literature illustrating the dependence of the backscattering coefficient on texture and grain shape.