Development of inter- and intragranular stresses during switching of ferroelectric polycrystals

Ferroelectrics are crystalline inorganic materials consisting of domains with different directions of spontaneous polarization. By application of sufficiently high electric fields, these domains can switch into a common direction, thus making the material piezoelectric. Due to ferroelasticity, the domains can be also switched into different states by the application of mechanical stress. In polycrystalline materials, as used in most applications, electric and stress fields interact so as to maintain compatibility. We study the influence of grain-to-grain interactions on the overall and local switching behavior and in particular the induced stresses inside grains and across grain boundaries. The behavior inside each grain is represented by the single-crystal model of [Huber, J.E., Fleck, N.A., Landis, C.M., McMeeking, R.M., 1999. A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids 47 (8), 1663–1697] and the polycrystal response is obtained through a two-dimensional multi-grain model in which grains are represented individually. We investigate the effect of random grain orientations, both in the plane of consideration and in three directions, and compare plane strain with plane stress conditions. It is found that the overall piezoelectric response under electric loading is not dependent only on the intra- and intergranular stresses in the plane but is also significantly affected by stresses in through-thickness direction.