Averaging of elastic constants for polycrystals

Many materials of interest are polycrystals, i.e., aggregates of single crystals. Randomly distributed orientations of single crystals lead to macroscopically isotropic properties. Here, we briefly review strategies of calculating effective isotropic second and third order elastic constants from the single crystal ones. Our main emphasis is on single crystals of cubic symmetry. Specifically, the averaging of third order elastic constants has not been particularly successful in the past, and discrepancies have often been attributed to texturing of polycrystals as well as to uncertainties in the measurement of elastic constants of both poly and single crystals. While this may well be true, we also point out here shortcomings in the theoretical averaging framework. Published by AIP Publishing.