An Analytical Description of Slow Hysteresis in Polarized Ferroelectric Ceramic Actuators

Abstract

Recently, an existing system of electroelastic equations was extended to account for slow hysteretic effects in polarized ferroelectric ceramic plates by employing an internal variable in a thermodynamic state function. All material irreversibility was taken to be a consequence of the ferroelectric polarization-electric field irreversibility. Since only the slowest possible hysteresis is of concern, the evolution equation is ignored and the known irreversible thickness polarization-electric field saturation curve is taken as the starting curve. Since all experimental data available to us are from strain measurements on a thin wide beam forced by voltages applied to very thin polarized ferroelectric ceramic actuators on the surfaces, the linear strain, plane-stress version of the equations is employed in the description of the actuator. The new irreversible material coefficients for the case of plane-stress are obtained from data on one major hysteresis loop along with the coefficients in the saturation polarization-electric field relations. These now known coefficients are then used to calculate other hysteresis loops, which are shown to agree quite well with measurement.