Keywords: piezoelectric transducer, finite element method, design optimization, crack initiation, ANSYS.

Piezoelectric transducers have been used in wide applications range from aircraft and automotive to printers and textile machinery. The transducers frequently fracture under high electric fields. The most efficient geometry for some transducers has the disadvantage of electrodes ending inside the ceramic (wrapped electrodes). There are maximum magnitudes of the electric field on the electrode boundaries. A stress concentration along the boundary is the consequence. High mechanical stresses at these regions lead to crack initiation and crack propagation and finally to the faulure of the transducer.

An initiation of cracks by stress concentration during the first poling cycle in partially electroded PZT's is investigated. A circular partially electrode specimen was chosen. The focus is on the influence of the electrode shape and the placement with respect to crack initiation. The most interesting part is the optimization of the electrode shape to minimize a stress concentration. This work is based on the finite element method, where the ANSYS package was used.

All computations were performed on a model of a commercially available transducer produced by Piezoceram s.r.o., Czech Republic. A bottom electrode covers the whole botom side and it is wrapped on the upper side. Material properties of the transducer are defined by tensors of elastic coefficients, piezoelectric moduli and relative permitivity. The model is based on the modelling of the spatial distribution of electric and elastic fields, where theSOLID5 element is used. The element has four degrees of freedom at each node for piezoelectric analysis: voltage and three components of displacements. The electrodes were implemented by coupling the voltage degree of freedom of the surface nodes of the electrodes. The electrodes of the real specimen are very thin, it is not necessary to model them.

Our main task is to minimize the extreme magnitudes of the von Mises stress along the bounding line. In the ANSYS program, several different optimization tools and methods are available. Our optimization procedure contained two optimization steps. The first step is performed by the random design generation method and the second step is performed by the first order method.

We can compare maximum magnitudes of the von Mises stress field before and after optimization. The difference between these values is approximately 30%. Lower values of stress reduce the risk of crack initiation during the first poling cycle in partially electroded PZT transducers. Our results show, that the proportions of electrodes are very important parameters of partially electroded transducers. The proportions are represented by the placement and the wrapping radius. These results accord with results described in [1], which are based only on the electric field analysis. The effect of spontaneous deformation on crack initiation is described in references [2,3], but these papers do not include an optimization procedure.

1

J. Novak, R. Dolezal, "Finite Element Analysis of Crack Initiation in Partially Electroded PZT Transducers", Proceedings of EUROSIM 2007, ISBN 978-3-90 1608-32-2, 2007.

2

J. Novak, J. Maryska, "Modelling of Electric and Elastic Fields in Piezoelectric Transducers", Proceedings of ASM 2006, Rhodos, Greece, 2006.

3

J. Novak, "Application of FEM in Problems of Piezoelectric and Ferroelectric Structures", Ph.D. thesis, Technical University of Liberec, 2004.

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