Models for the Nonlinear Switching of Ferroelectrics


Robert M. McMeeking

Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, California 93106, U.S.A.

Ferroelectric ceramics such as lead-zirconate-titanate (PZT) and lead-lanthanum-zirconate-titanate (PLZT) are used as transducers in sensing devices and as actuators in active control systems. Actuation displacements and forces are generated by the piezoelectric effect, but ferroelectric/ferroelastic depolarization occurs when the forces generated become too high, thereby destroying the actuation of the device. Measurements of the processes of polarization, depolarization and switching for a polycrystalline ceramic have provided insight into the combined electromechanical response of ferroelectric ceramics. This response is modeled as the average of the domain wall motion controlled repolarization behavior of individual grains. The result is a constitutive law for the single crystal switching behavior of ferrolectric materials. Based on experimental results and a domain-averaged model of polycrystalline materials, a nonlinear constitutive law is developed for ferroelectric ceramics that accounts for switching. This model is phenomenological and contains internal variables representing the degree of strain and electrical polarization as well as their principal directions. There is a close connection to kinematic hardening laws in the plasticity of metals. The driving force for switching is phrased in terms of applied stress and field with critical conditions depending on the current state of polarization. Switching saturation occurs when all possible domains have experienced reorientation. The resulting constitutive law is useful in finite element calculations of the response of a ferroelectric ceramic in critical locations in devices such as at crack and electrode tips. Examples are given of switching zones around electrode and crack tips.