Investigations on Multi-axial Domain Switching Criteria for Piezoceramics
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Investigations on Multi-axial Domain Switching Criteria for Piezoceramics Bernd Laskewitz, Dayu Zhou and Marc Kamlah Forschungszentrum Karlsruhe GmbH Institute for Materials Research II D-76021 Karlsruhe, Germany ABSTRACT Initially unpoled soft PZT was subjected to a proportional, coaxial electromechanical loading. The ratio of compressive stress to electric field was changed between the experiments. From this series of nonlinear polarization and strain responses were obtained. Based on an offset method, initial domain switching states in the two-dimensional stress-electric field space were determined. In continuum mechanics, thin walled tubes are used to investigate multi-axial stress states. In this context, thin walled means a ratio of wall thickness to radius of 1:10 or thinner. However, simple linear dielectric analysis indicates an inhomogeneous electric field distribution in such geometries. Therefore, the suitability of hollow cylinders (in the range from thick to thin walled tubes) for multi-axial electromechanical experiments has to be investigated. Simulations with a finite element tool based on a phenomenological constitutive model for ferroelectric and ferroelastic hysteresis behavior were performed. The results confirm inhomogeneous distributions of electric fields and stresses after poling. A geometry variation is discussed to minimize these effects. INTRODUCTION The investigation of the multi-axial behavior of piezoceramics and the determination of the distributions of the electrical and mechanical quantities, e.g. electric field or stress, is important regarding the different kinds of applications of piezoceramics. These multi-axial loading conditions require appropriate constitutive models which have to be developed on the basis of phenomenology and micromechanics. In this work, we report systematic experimental results for a commercial soft PZT material under coaxial, proportional electromechanical loading. In addition to polarization, strain measurements were performed simultaneously, from which closed switching surfaces were obtained in the biaxial stress-electric field space. The experimental data were compared with several switching criteria existing in the literature. Especially, the determination of switching criteria for the onset of electrically and mechanically induced domain switching processes is necessary as an input to constitutive models predicting the large signal hysteresis behaviour of piezoceramics. In this paper, we investigate the suitability of piezoceramic hollow cylinders (in the range from thick to thin walled tubes) for the exploration of electromechanical loading histories with multi-axial stress states. In practice, piezoceramic tubes are used in a wide range of applications from microdispensing to scanning microscopy. CO-AXIAL PROPORTIONAL ELECTROMECHANICAL EXPERIMENTAL RESULTS Measurements were performed on the initially unpoled PIC151 piezoceramic (PI Ceramic, Lederhose, Germany). From previous measurements [1,2], the following parameters are known (listed in
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