Polycrystals under applied loads: Second-order grain statistics

The authors report results for the second-order statistics of the effective elastic moduli of polycrystals as a function of applied stress. These results are indicative of scattering behavior that occurs in such materials at ultrasonic frequencies. Numerical examples are given for materials of general interest with cubic symmetry subject to an applied uniaxial stress. The results suggest that the second-order statistics (scattering) may be more significantly affected than the first-order statistics (wave speed) with application of load for some materials. This work may be useful for development of techniques for monitoring changes in stress of loaded structures.