Nonlinear Hysteretic Response of Piezoelectric Ceramics

Abstract

Ferroelectric materials, such as lead zirconate titanate (PZT), have been widely used in sensor, actuator, and energy conversion devices. In this paper, we are primarily interested in the electro-mechanical response of polarized ferroelectric ceramics subject to cyclic electric fields at various magnitudes and frequencies. There have been experimental studies on understanding the effect of electric fields and loading rates on the overall electro-mechanical response of PZT (see for examples Crawley and Anderson 1990, Zhou and Kamlah 2006). The electrical and mechanical responses of PZT are also shown to be time-dependent, especially under high electric field (Fett and Thun 1998; Cao and Evans 1993; Schaufele and Hardtl, 1996). Ben Atitallah et al. (2010) studied the hysteretic response of PZT5A and active PZT fiber composite at several frequencies and isothermal temperatures. They show the nonlinear and time-dependent piezoelectric constants of the PZTs and PZT fiber composites. In a review of nonlinear response of piezoelectric ceramics, Hall (2001) discussed experimental studies that show strong time-dependent and nonlinear behavior in the electro-mechanical response of ferroelectric ceramics. The time-dependent effect becomes more prominent at electric fields close to the coercive electric field of the ferroelectric ceramics and under high magnitude of electric fields a ferroelectric ceramics exhibits nonlinear electro-mechanical response. Furthermore, high mechanical stresses could result in nonlinear mechanical, electrical, and electro-mechanical responses of the ferroelectric materials. Within a context of a purely mechanical loading in viscoelastic materials, timedependent response is shown by a stress relaxation (or a creep strain). This results in stressstrain hysteretic response when a viscoelastic material is subjected to a cyclic mechanical loading. There are different types of viscoelastic materials, such as polymers, biological tissues, asphalts, and geological materials. It is understood that these materials possess different microstructural characteristics at several length scales; however the macroscopic (overall)1 mechanical response of these materials, i.e. stress relaxation and hysteretic response, especially for a linear response, follows similar trends. Experimental studies have shown that there are similarities with regards to the macroscopic time-dependent (or