<title>Modeling of polarization switching in piezoceramics</title>

Abstract

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

Nonlinear fracture analysis of piezoelectric ceramics by finite element method

“…Assuming that the criteria for domain switching and electric saturation are functions of the electric displacement only [22,26] and can be expressed in a single function as :…”

“…On the other hand, many researchers have been working on nonlinear constitutive modeling of piezoelectric materials [22][23][24][25][26][27][28][29][30][31][32][33]. At least three categories of models have been proposed.…”

“…At least three categories of models have been proposed. The first category is the micro-mechanics approach in which the domain wall motions of the crystals, 90° or/and 180° switching, are considered but only the macroscopic effect of materials is modelled [22][23][24][25][26]. The second category is the phenomenological hysteresis approach in which the electric displacement-electric field hysteresis loop and the strain-electric field butterfly loop are modelled by various phenomenological parameters [27][28][29][30][31].…”

“…It should be remarked that not many of the above models can be applied to or implemented in finite element analysis. Owing to the practical importance of finite element analysis, ad hoc nonlinear constitutive models have also been proposed recently [25,26,31,35,38].…”

Modeling of piezoelectrically actuated fuel injectors

“…In addition to the linear approaches in [27,11], several more sophisticated actuator models have been described. Among these are polynomial approximations by Croft and Devasia [2] and Heinrich [9], nonlinear differential equations by Dahl and Wilder [3], Coleman and Hodgdon [1] and Smith and Ounaies [26], nonlinear integral equations by Goebel et al [6], operator formulations by Goldfarb and Celanovic [7] and by Mayergoyz [17] and spin models by Fotinich and Carman [4] and by Liu and Liu [14]. Most approaches restrict to either voltage or charge control.…”