Elastic properties of polycrystals in the Voigt-Reuss-Hill approximation

The problem of calculating polycrystalline elasticity from texture has been treated in the most general way in the framework of the Voigt–Reuss–Hill (VRH) approximation. The analytical solution involves only the even texture coefficients up to fourth order, which can be derived with a limited number of experimental pole figures (e.g. one pole figure for hexagonal polycrystals). The present analysis has been applied to the prediction of the fourth-rank elastic tensors and Young's modulus for a rolled zinc sheet.