The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials: theory, measurement and computation

Due to continuing miniaturization, characteristic dimensions of electronic components are now becoming of the same order of magnitude as the characteristic microstructural scales of the constituent materials, such as grain sizes. In this situation, it is necessary to take into account the influence of microstructure when studying the mechanical behaviour. In this paper, we focus on the relation between the (anisotropic) properties of individual grains and the effective elastic behaviour of polycrystalline materials. For large volumes of materials, the conventional averaging theory may be applied. This is illustrated with experiments on various barium titanates. For small volumes of material, we examine the relationship by means of micromechanical computations using a finite-element model, allowing the simulation of a real microstructure, based on a microscopic image of the grain structure. Various cubic and tetragonal materials are studied. The computational results clearly show the influence of the specific microstructural properties on the effective elastic behaviour.