Nonlinear constitutive behavior of soft and hard PZT: Experiments and modeling

This work characterizes and models the nonlinear inelastic behavior of lead zirconate-titanate (PZT) ceramics. A detailed investigation of the hysteresis loop of the stress-strain curve shows that the process of ferroelastic non-180 degrees polarization switching and of switching saturation are, respectively, a smooth softening process and a gradual hardening process. The inflection point in the curve is found to be a boundary point that distinguishes the transition from a softening process to a hardening one. Based on underlying physical mechanisms, this nonlinear behavior is simulated by a mechanical model, consisting of several parallel-arranged Maxwell chains with each chain taking a main role in a different, successive stage of the switching process. Each chain includes a nonlinear spring and a frictional slider. The generalized displacement of the slider, indicating an internal variable, is introduced to describe the local process of the cooperative switching of the corresponding grain group. The hardening and softening processes are controlled by variations of stiffness of the nonlinear springs. Furthermore, the observed similarities between the hysteresis loop of the stress-strain curve and that of stress-electric displacement curve are used to develop an equivalent stress concept and to formulate constitutive laws for PZT ceramics. Comparisons between the experimental hysteresis loops and those calculated by the proposed model show satisfactory agreement for both hard PZT and C5800 and soft C5500. (C) 1999 Acta Metallurgica Inc. Published bl Elsevier Science Ltd. All rights reserved.