Modern piezoelectric transducers normally have complicated structures and work under severe loading conditions. Application of an external load in excess of a critical level will cause domain switching in the material and therefore lead to a significant nonlinearity and hysteresis in the polarization and strain response. To develop a constitutive model concerning the large-signal nonlinear behavior of ferroelectric piezoceramics, it is desirable to determine a switching criterion in the multiaxial stress and electric field states.
In this experimental work, "soft" lead zirconate titanate (PZT) specimens in initially unpoled state were subjected to a proportional electromechanical loading, in which a compressive stress and a parallel, proportional electric field were applied simultaneously. By varying the relative proportions of the stress and E-field between tests, a family of nonlinear polarization and strain responses were obtained. An attempt has been made to explain the experimental findings by simultaneously taking into account the contributions of dielectric response, elastic deformation, piezoeffects, and irreversible domain switching. Based on an offset method, switching (domain reorientation threshold) surfaces were mapped out in the biaxial stress and electric field space. Finally, several switching conditions existing in the literature were summarized and compared with the experimental data obtained in this work.
In the present paper a constitutive model for piezoceramics under
multiaxial electromechanical loadings is developed for the
engineering reliability analysis of piezoceramic components designed for so-called "smart" electromechanical sensor and actuator applications. At first a constitutive framework capable of representing general thermo-electromechnical processes is presented. This framework is established by using internal variables and is thermodynamically consistent with the Clasius-Duhem inequality for all admissible processes. Then, two scalar and two unit vector internal variables are introduced. One of the vectorial internal variables indicates the overall alignment direction of the c-axes of domains and the other variable represents the direction of the macroscopic irreversible polarization. The two scalar internal variables represent the fraction of domains whose c-axis is oriented in the alignment direction and the relative irreversible polarization, respectively. We indicate the microscopic foundation of the scalar internal variables in terms of an approximate orientation distribution function. A domain switching function is formulated in the driving force space to indicate the onset of the domain switching. The evolution equations of the internal variables are derived from the switching function by using the normality flow rule.
Remanent strain and polarization are calculated as functions of the internal variables.In order to verify the underlying assumptions and to examine the ability of the model indescribing the material responses to electromechanical loadings, we demonstrate the simulation of various uniaxial and multiaxial loading processes.