Jmj. Den Toonder et al., The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials: theory, measurement and computation, MODEL SIM M, 7(6), 1999, pp. 909-928
Due to continuing miniaturization, characteristic dimensions of electronic
components are now becoming of the same order of magnitude as the character
istic microstructural scales of the constituent materials, such as grain si
zes. 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 g
rains and the effective elastic behaviour of polycrystalline materials. For
large volumes of materials, the conventional averaging theory may be appli
ed. This is illustrated with experiments on various barium titanates. For s
mall volumes of material, we examine the relationship by means of micromech
anical computations using a finite-element model, allowing the simulation o
f a real microstructure, based on a microscopic image of the grain structur
e. Various cubic and tetragonal materials are studied. The computational re
sults clearly show the influence of the specific microstructural properties
on the effective elastic behaviour.