Elastic properties of polycrystals - a review

A lot of technically important materials are polycrystalline. Their elastic properties depend on the single-crystal constants of the crystallites which build up the polycrystal and on the manner in which the crystallites are connected. Effective elastic constants polycrystalline materials can be calculated from single-crystal and structure properties. To solve this problem exactly, orientation and shape of each grain must be known. From these informations, the means values of stress and strain in the whole polycrystal and thus is effective elastic constants are to be determined taking into account the boundary conditions of stress and strain at the grain boundaries. But this technique is not practicable because the calculations whole become too complicated. Futhermore, in most cases the exact orientations and shapes of the grains are not known. This problem can be overcome while using orientation and grain shape distribution functions. The orientation distribution function indicates th e statistical probability to find the different orientations within the polycrystal. It can be determined by texture measurements. In this case orientation correlations of different grains are neglected. For the grain shape different assumptions more or less realistic are used. This paper gives a review concerning the most important theories and methods to calculate effective elastic constants of polycrystals from single-crystal and structure properties and points out its validity limitations