Material characterization and modeling for piezoelectric actuation and power generation under high electromechanical driving levels

Abstract

High electromechanical loads parallel to piezoelectric polarization might result in depolarization of the material, depending on the material property itself and the external excitations such as electrical field, electrical driving frequency, stress and stress duration. In this work, material properties under these effects were first characterized experimentally. The experiments included monitoring general piezoelectric responses of PZT-5H and PZT-5A subjected to large electric excitations (butterfly curves) under various static compressions and measuring generalized piezoelectric constants under short and open circuit conditions for actuation of PZT-5A and power generation of PZT-5H, single crystals PZN-PT, and single crystals PMN-PT. To model these observed material behaviors, one- and three-dimensional rate dependent nonlinear constitutive models based on thermodynamic potentials for PZT-5H and PZT-5A piezoelectric materials were then developed. An internal variable, net remnant polarization D*, was used to simulate the hysteric behaviors of piezoelectric materials. An evolution law of D* was derived to specify the rate dependent responses of the materials. The parameters of the material models were determined by minimizing the error between the data and the models. The material models were capable of describing the responses subjected to large electric excitations under static compression, but incapable of predicting accurate piezoelectric constants under dynamic compression. This flaw was believed due to the absence of stress rate dependency in the models. It was also found that the PZT-5A model performed worse than the PZT-5H model because of its highly hysteretic strain-polarization relation.

(cont.) This hysteresis could be explained by the slow switching rate of 90-degree domain movement. Finally, to simulate devices under non-uniform field or with irregular geometries using these material models, differential algebraic equations for mixed finite element analysis of 3-D nonlinear rate dependent piezoelectric materials were formulated and solved numerically by DASPK solver. Using 4-node tetrahedral elements, this formulation was demonstrated by examples with uniform and skewed electric excitations. The combination of the nonlinear mixed FEM model and the material model provided a useful tool for modeling the response of active devices with complicated geometries and irregular boundary conditions.