In this article, an experimental investigation to study the effect of residual stresses on the nonlinear behavior of ferroelectric ceramic material is reported. The effect of residual stresses on the behavior at low electric field and mechanical stress is demonstrated first by showing the large difference in the linear properties measured from strain behavior under mechanical and electrical loading, and resonance method. This is followed by an investigation on the mechanism of polarization reversal due to cyclic electric field. Based on the observed large magnitude of strain and the comparison of the magnitude of the sum of transverse strains with the magnitude of strain in the poling direction it is concluded that polarization reversal due to cyclic electric field in the ferroelectric material at morphotropic phase boundary is the result of two successive 90o domain switchings. Finally, two types of combined loading experiments were conducted to investigate the residual stress and electric field effect on the mechanism of domain switching. The behavior under combined loading showed many new interesting characteristics, and possible mechanisms for such behavior is discussed. While most of the characteristics of the ferroelectric behavior observed in the present experimental study could be explained based on the residual stress state, the understanding of others need further studies.
KEYWORDS: Switching, Crystals, Finite element methods, Chemical elements, Polarization, Switches, Ferroelectric materials, Mathematical modeling, Data modeling, Sun
A finite element model for the nonlinear behavior of piezoelectric material is developed. Important issues in modeling the nonlinear behavior of piezoelectric material at micro-scale is discussed and methods to solve such issues are proposed. A procedure is developed to obtain RVE from the simplified microstructure of the material. The RVE is obtained based on a statistical parameter, which is a measure of the degree of heterogeneity at a point. The material properties at the micro-scale are obtained from the macro-scale properties by rule of mixture approach. A finite element iterative solution procedure is then used to model the material behavior by averaging the local response over the entire RVE. Nonlinear behavior of the material is due to the domain switching phenomenon and is simulated based on internal energy density based switching criterion. A numerical example is given for PZT-4 material and the results agree qualitatively with the experimental results.
Experimental results reported by many researchers showed that the coercive electric field for ferroelectric switching depends on mechanical stresses present in the material. Similarly, the coercive stress for ferroelastic switching depends on the electric field. To model these dependences, several domain switching criteria based on different considerations have been proposed in earlier studies. In this paper, these domain switching criteria are briefly reviewed and the predictions based on these domain switching criteria are compared with the available experimental data for 180 degree(s) domain switching in PZT. It is found that the predictions do not match the experimental results. Motivated by this observation, a new domain switching criterion based on internal energy density is proposed. This new criterion is found to yield very good predictions compared with the existing experimental results for 180 degree(s) domain switching in PZT. To verify the new domain switching criterion for 90 degree(s) switching, experiments were conducted using PZT-5H. The new experimental result indicates that the new domain switching criterion gives a much better prediction than other existing criteria.
Recently, there have been extensive investigations on the shape control of beams using piezoelectric actuators. Most studies, however, assumed linear piezoelectric constitutive equations, which are not valid for actuations involving high electric fields. This paper examines the effect of nonlinear behavior of the piezoelectric materials in the shape control of piezoelectric beams. The governing coupled electromechanical equations for nonlinear material behavior is developed for a general three-dimensional structural element using the Gibbs free energy formulation. Nonlinearity is accounted in the analysis by incorporating an adequate number of nonlinear terms in the Gibbs free energy expression. Since many of the higher order material properties are not available for most of the piezoelectric materials, experimental data that are available for the nonlinear relationship between the electric field and the electric displacement are used. A finite element model is developed for the beam with piezoelectric actuators using a modified bilinear four-node quadratic element. The expression for the actuation voltages required for shape control is then obtained by minimizing an error function, defined as the area between the achieved and desired shape. The final system of coupled equations is solved by an iterative finite element procedure. Comparison of numerical results obtained for both linear and nonlinear piezoelectric behaviors showed the importance of incorporating nonlinear effects in the shape control of piezoelectric beams.
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