On the effective physical properties of polycrystalline materials

An iteration method is presented for calculation of the gross physical properties of polycrystals in terms of the physical properties of the crystals. No assumptions are made concerning the shape or behaviour of the crystallites. The only mathematical condition to be fulfilled is that the product of the matrix of a gross physical property with its inverse must give a unit matrix if the same is valid for the crystals. The method is demonstrated by the calculation of the effective elastic tensor of a hypothetical texturized polycrystal consisting of Cu crystallites. The calculated upper and lower bounds of the Young modulus are extremely close to each other.