On the statistical behavior of homogenized properties and ultrasonic phase velocities in random

Most theoretical studies on homogenized properties of polycrystals consider infinite textureless media with orientations characterized by independent Euler angles. However, microstructural analyses of polycrystals reveal spatially correlated orientations of grains whose sizes often follow lognormal distributions. Moreover, experimental investigations show that the single-crystal elastic constants (SEC) in the crystallite's local coordinates could exhibit variabilities. To the best of our knowledge, in the context of our study, these have never been considered in the literature. In this paper, the crystal orientations are simulated using random fields (RFs) with different correlation parameters. A maximum entropy principle is used to simulate realizations of the local stiffness matrices. Numerical results indicate that generating Euler angles using independent random variables is legitimate when correlation lengths of orientations are close enough to the average grain size. Analytical formulas are derived to estimate the statistical behavior of effective elastic moduli and the phase velocities considering either unimodal or bimodal grain size distributions and fluctuations in local tensors for both two-and three-dimensional polycrystals. The former highlight the important roles of the coefficient of variations of the grain sizes and that of the elastic constants. This work contributes to microstructural characterization research associated with ultrasonic phase velocity measurements.