A thermodynamically and microscopically motivated constitutive model for piezoceramics under uniaxial loading

摘要

Our aim is the motivation of a macroscopic constitutive model for engineering reliability analysis of piezoceramic components designed for so-called "smart" electromechanical sensor and actuator applications. Typically, such components are made of ferroelectric ceramics, mostly PZT or modified PZT ceramics, which exhibit significant history-dependent nonlinearities such as the well known dielectric, butterfly, and ferroelastic hystereses due to domain switching processes. Following an approach proposed previously by the authors1 (Smart. Mater. Struct. 9(1999), 441 - 459), we first propose a constitutive framework capable of representing general thermo-electromechanical processes. This framework makes use of internal variables and is thermodynamically consistent with the Clausius-Duhem inequality for all admissible processes. Next, we focus on uni-axial electromechanical loadings and introduce microscopically motivated internal variables and their evolution equations. In order to verify the underlying assumptions, we discuss the numerically calculated model response to standard electromechanical loading paths. This model is capable of reproducing the aforementioned typical hysteresys phenomena and mechanical depolarization as well as other nonlinear electromechanical coupling phenomena. Furthermore, the model response exhibits rate-dependence, which is typical in the response of ferroelectric ceramics.