Multiferroic response of nanocrystalline lithium niobate J. Appl. Phys. 111, 07D907 (2012) Non-radiative complete surface acoustic wave bandgap for finite-depth holey phononic crystal in lithium niobate This paper presents research results on the electro-thermomechanical behavior of piezoelectric ceramics for use in actuator applications with an emphasis on ferroelectric fatigue. The material being investigated is a lead zirconate titanate piezoelectric ceramic with the composition PbZr 0.53 Ti 0.47 O 3 ͑PZT-5H͒. Results presented in this paper include an augmented constitutive model that accounts for the temperature-dependent piezoelectric properties. Using this model, nonlinear effects measured at one temperature can be extrapolated to other temperatures with good accuracy. Experimental studies into 180°and 90°polarization switching of PZT-5H indicate that the dielectric flux to dipole the material appears to be an adequate criterion for predicting this nonlinear switching behavior. Fatigue studies show that material degradation is strongly influenced by temperature and by the magnitude of the applied electric field. Above a critical temperature, PZT-5H no longer fatigues in the presence of large electric fields due to changes in the electromechanical properties such as the depolarization strain. Using a finite element model incorporating the proposed constitutive relations along with a domain switching criterion, this paper suggests that fatigue degradation is primarily caused by mechanical stresses in the material resulting from spatially variant electric fields causing preferential domain wall motion. The large stress mismatches induce mechanical damage in the form of cracks.

Piezoelectric materials exhibit nonlinear behavior when subjected to large electrical or mechanical loads. This strong nonlinear material behavior is induced by localized polarization switching (i.e., change of the polarization direction) at the subgrain level. In this article, a nonlinear finite element code is described to model polarization switchings in piezoceramics subjected to large electromechanical loads. The local polarization switching criterion is based on electric displacement combined with stability arguments. To evaluate the model, three cases are studied in this article: a partially electroded specimen simulating 180° polarization switching, a fully electroded specimen simulating 90° switching and a plate containing a void. The analytical results are compared with experimental data obtained from Moiré interferometer with reasonable agreement. Stresses in the vicinity of the voids are computed and the results are used to explain fatigue behavior observed in piezoceramics. It has been determined that, for a material undergoing full polarization switching, compressive stress along the polarization direction reduces internal stresses and extends fatigue life. If the applied electric field value is below the coercive field limit, the compressive prestress can increase the stresses thus reducing fatigue life.

In this paper a fmite element model of polarization switching in piezoelectric ceramics is presented. A plane strain four-node element with nodal displacements and voltage degrees of freedom is used. The element incorporates two types of polarization switching: 900 and 1800 switching with electric flux as a switching criterion and with piezoelectric coefficients dependent upon electric field values. The model is used to compute strains for a partially electroded rectangular plate and a hole in a square plate simulating a void in a material. In both ofthese simulations sufficiently large electric fields are applied to cause domains to rotate 1800 with calculation of strains along the boundary between dissimilarly poled regions being investigated. In addition to this study, 900domain wall motion is studied on a fully electroded rectangular plate with domains along the diagonal rotated 900 ddomains in the corners retaining their original polarization. For each ofthese three cases:partially electroded specimen, void in plate, and full 900 switching, the analytical results are compared with experimental data obtained from a Moire interferometer. Comparison between experimental data and theoretical results indicates reasonable agreement between the two suggesting the correct physics is incorporated in the analytical model. In a separate analytical study, stress concentrations near both holes and cracks in the presence of an electric field are calculated. For the linear problem or low electric field values the crack geometry generates significantly larger stresses than a circular hole. For the nonlinear problem, where domain wall motion occurs, the hole and the crack have stress intensity factors of similar magnitude. Finally, reducing the peak stress with implication to extending fatigue life ofthe piezoceramics is suggested. Nomenclature oj -Mechanical stress cii -Mechanical strain D, -Electric flux E, -Electric field i -Electric potential (Di-Weight function in Galerkin method ni -Normal vector N1 -Shape functions ux, Ui -Displacement in x-direction uy, U2 -Displacement in y-direction CjjkE Stiffness measured at constant electric field -Piezoelectric stress coefficients d, -Piezoelectric strain coefficients CnmC Dielectric permittivity measured at constant strain L -Rotation matrix for a tensor in engineering notation R -Rotation matrix in conventional notation 9O Permanent strain associated with 900 switching

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