Effective elastic constants of polycrystalline aggregates

A method is presented for the determination of the effective elastic constants of a transversely isotropic aggregate of weakly anisotropic crystallites with cubic symmetry. The results obtained generalize those given in the literature for the second and third order elastic constants. In addition, the second moments and the binary angular correlations of the second order stiffnesses are obtained. It is also explained how these moments can be used to find the two-point correlations of the elastic constants.