Rate dependent properties of perovskite type tetragonal piezoelectric materials using micromechanical model

In this paper, a three-dimensional micromechanical model is presented for simulation of the rate dependent properties of certain perovskite type tetragonal piezoelectric materials. The model is based on linear constitutive, nonlinear domain switching, and linear kinetics theories. The simulation starts with a virgin bulk material of randomly oriented grains. Then the material is electrically loaded with an alternating voltage of various frequencies, which are in the order of 0.01 Hz to 1 Hz. An energy equation in combination with a probability function is used to determine the onset of the domain switching inside the grains. Such a probability function leads to a better phenomenological model for the domain switching even for electrical loadings, which are in a range far below the coercive fields. The propagation of the domain wall during the domain switching process in grains is modeled by means of linear kinetics relations after domain nucleation. The response of the bulk ceramic is predicted by averaging the response of individual grains using Euler angles for the transformation from local coordinates of the grains to global coordinate. Electric displacement hysteresis loops for different frequencies and amplitudes of the alternating electric fields are simulated. A simple micromechanical model without the probabilistic approach is compared with the one that takes it into account. Both models give important insights into the rate dependency of piezoelectric materials, which was observed in some experiments reported in the literature.