A polycrystal model for the anisotropic behavior of a fully poled ferroelectric ceramic

When an initially isotropic ferroelectric ceramic is fully poled with application of an axial electric field, it turns into a transversely isotropic one. The nonlinear response of such a material is then orientation dependent. Such an anisotropic behavior is studied by a self-consistent polycrystal model in this article. The model makes use of two separate levels of micromechanical analysis: the first one involves domain switch inside the constituent grains and the second one involves the transition from the grains to the polycrystal level. Domain switch inside the grains is taken to be a thermodynamic-driving process, and the self-consistent transition from the grain to the polycrystal is accomplished through a secant-modulus approach. This polycrystal model is applied to calculate the nonlinear electric displacement versus electric field relations (D vs E) of a PZT-5H along several loading directions from the original poling axis. This calculation takes into account the intercrystalline heterogeneity, and the results indicate that, as the loading direction changes from 0° to 45°, 90°, 135°, and finally to 180°, the magnitude of the electric displacement and the change in remnant polarization of the polycrystal all increase. These theoretical results are found to be consistent with the test data. In order to reveal the heterogeneity of the switching process among the constituent grains, the evolution of new domain concentration c1 in some selected grains is also illustrated.