This paper develops a macroscopic polarization switching model which characterizes the ferroelastic switching mechanisms inherent to lead zirconate-titanate (PZT) in a manner suitable for subsequent transducer and control design. We construct Helmholtz and Gibbs energy relations at the lattice level which quantify the internal and electrostatic energy associated with 90 and 180 degree dipole orientations. Equilibrium relations appropriate for homogeneous materials in the presence of thermal relaxation are determined by balancing the Gibbs and relative thermal energies using Boltzmann principles. Macroscopic models suitable for nonhomogeneous, polycrystalline compounds are constructed through stochastic homogenization techniques. Attributes and limitations of the model are illustrated through comparison with experimental PLZT data.
A ferroelastic switching model for single crystal piezoceramic compounds is developed. The model is based on a phenomenological Landau-Devonshire type thermodynamic theory for the materials.
The model incorporates externally applied electric fields and compressive stress inputs to the crystals and models the 90° and 180° ferroelastic and ferroelectric switching induced by the inputs. Properties of the ferroelastic model are qualitatively similar to experimental PLZT data.
Pre-stressed curved actuators consist of a piezoelectric ceramic (lead zirconate titanate or PZT) sandwiched between various substrates and other top layers. In one configuration, the substrates are stainless steel with a top layer made with aluminum (THUNDER). In another configuration, the substrates and top are based on fiberglass and carbon composite layers (Lipca-C2). Due to their enhanced strain capabilities, these pre-stressed piezoelectric devices are of interest in a variety of aerospace applications. Their performance as a function of electric field, temperature and frequency is needed in order to optimize their operation. During the processing steps, a mismatch between the properties of the various layers leads to pre-stressing of the PZT layer. These internal stresses, combined with restricted lateral motion, are shown to enhance the axial displacement. The goal is to gain an understanding of the resulting piezoelectric behavior over a range of voltages, and frequencies. A nonlinear model, which quantifies the displacements generated in THUNDER actuators in response to applied voltages for a variety of boundary conditions, is developed. The model utilizes a hysteretic electric field-polarization relationship and predicts displacements based on the geometry and physical characteristics of the actuator components. The accuracy of the model and associated numerical method is demonstrated through comparison with experimental data.
This paper summarizes a nonlinear technique for quantifying the displacements generated in THUNDER actuators in response to applied voltages for a variety of boundary conditions and exogenous loads. A PDE model is constructed using Newtonian principles to quantify the displacements in the actuator due to field inputs to the piezoceramic patch. A free energy based hysteretic stress-strain relation is employed to model the electromechanical coupling in the PZT. A finite element method and Crank-Nicholson scheme are developed to discretize the model; properties of the model are illustrated through comparison with experimental data.