A constitutive model for ferroelectric PZT ceramics under uniaxial loading

Our aim is the presentation of a macroscopic constitutive model for the purpose of engineering reliability analysis of piezoceramic components designed for so-called 'smart' electromechanical sensor and actuator applications. Typically, such components are made of materials like ferroelectric lead zirconate titanate ceramics which exhibit significant history-dependent nonlinearities such as the well known dielectric, butterfly and ferroelastic hystereses due to switching processes. Furthermore, phase transitions lead to distinct thermo-electromechanical coupling properties and rate effects are present. In a first step, we 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 uniaxial electromechanical loadings and introduce microscopically motivated internal variables and their evolution equations. In order to verify the underlying a priori assumptions, we discuss extensively the numerically calculated model response to standard electromechanical loading paths. It turns out that the model represents the typical hystereses mentioned above as well as mechanical depolarization and other nonlinear electromechanical coupling phenomena. Furthermore, the model response exhibits rate effects.