Time-dependent and energy dissipation effects on the electro-mechanical response of PZTs

In this study, we formulate a constitutive model for coupled thermo-electro-mechanical behavior of piezoelectric ceramics, i.e. lead zirconate titanate (PZT) that takes into account time-dependent behavior and heat generation due to energy dissipation from the electro-mechanical response. Experimental studies show that PZTs dissipate energy when subjected to cyclic electric fields. The dissipated energy is, in some part, converted into heat and raises the temperature of the PZTs. The hysteretic dielectric and strain responses are also dependent on the amplitude and frequency of the applied electric field. The aim of this study is to investigate the energy dissipation and time-dependent effects on the electro-mechanical responses of polarized PZTs. The thermodynamics of irreversible processes for modeling dissipative material responses is adopted to incorporate the time-dependent electromechanical coupling effect. A Gibbs free energy is defined in order to account for the different time-dependent and dissipation behaviors in piezoelectric materials under combined electro-mechanical stimuli. Experimental data on polarized PZTs and PZT based composites at applied electric field magnitudes lower than the coercive electric field, are used to examine the model. The constitutive equations along with the energy equations are solved numerically and used to predict the creep, hysteretic and heat generation responses of PZTs and composites at different frequencies and cyclic electric fields.