Effect of the electric conductivity on the modeling of the poling process of ferroelectric components

摘要

Piezoceramic materials, despite being semiconductors with a high but finite ohmic resistance, are generally modeled as perfect insulators. In this work the influence of the electric conductivity on the poling process of piezoceramic materials is investigated. To solve the electromechanically coupled boundary value problem, a reduced form of the Maxwell equations is implemented inside a hybrid finite element formulation. In this formulation the electric displacement is available as nodal quantity (i.e. degree of freedom) which is used instead of the electric field to determine the evolution of the remanent polarization. The material model is fully ferroelectric/ferroelastic coupled, whereas the material behavior is described by a set of yield functions and the history dependence is stored in internal state variables representing the remanent polarization and the remanent strain. The simulation of poling processes for three different components are presented. First and second, the poling of a radially poled hollow cylinder and of a stack actuator is investigated. Here, a residual electric field appears after poling, leading to significant time-dependent changes of stresses and deformation due to subsequent charge transportation processes. The third example is a bending actuator composed of two layers of hard-PZT and soft-PZT material. It is shown that considering the electric conductivity new strategies for the poling process can be developed in order to improve the bending actuation. In this way, we show the importance of considering charge transportation processes in simulations of the poling of ferroelectrics, which seems not to have been recognized so far.