Toughening and weakening in ferroelectric ceramics by domain-switching process under mixed electric and mechanical loadi
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I. INTRODUCTION
FERROELECTRIC ceramics, for their excellent electric-mechanical properties, are increasingly used in smart structures, such as sensors, actuators, and memory devices. However, ferroelectric ceramics are brittle and susceptible to cracking, and because all these smart structures and devices are usually used under both electric and mechanical loading, a better understanding of their fracture mechanism is needed. In the absence of an external electric field, a ferroelectric material exhibits a spontaneous polarization. The direction of polarization can be changed under high electric or mechanical loadings. A switching of 180 deg is activated primarily by the electric field and causes little strain. A switching of 90 deg results from the electric or stress fields and causes an incompatible strain of fixed amount and orientation that contracts along the previous poling direction and elongates along the current one. Figure 1 illustrates the typical crystal structure of the ferroelectric materials (the crystal structure of BaTiO3) and all the switching possibilities when under an electric field or stress.[1] The fracture-toughness character of ferroelectric ceramics motivates a link between the toughening mechanism and the polarization switch assisted by the crack-tip electromechanical field. It has been shown by experiments based on the Viker’s indentation technique,[4] that the measured fracture toughness for a crack propagating along the poling direction has a shorter crack length than the ones normal to it. Consequently, the former has a higher fracture toughness, and the latter a lower one.[2–10] Recent consensus attributes the XUELI HAN, Postdoctoral Student, and XUEJUN LI, Graduate Student, are with the Department of Mechanical Engineering, The University of Calgary, Calgary, AB T2N 11V4 Canada. SCOTT X. MAO, Professor, is with the Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261. Contact e-mail: [email protected] Manuscript submitted July 5, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
fracture-toughness variation of ferroelectrics to polarization switching, and some mechanical models have been proposed to establish a link between the toughness mechanism and the polarization switching.[11–15] A crack concentrates the mechanical field, and, usually, also the electric field at the crack tip.[16–19] In this article, an attempt is made to model the mechanism of fracture induced by progressive polarization switching in poled ferroelectric ceramics, produced by the intensified stress and electric fields near the crack tip. The analysis is based on the change of crack-tip stress intensities provided by the polarization switching-induced stresses, following the spirit of transformation toughening in ceramics.[20,21,22] An analysis for an initially poled ferroelectric ceramic in a remote uniform electric field and under either a remote mode I or mode II loading is given. The geometry of the switched zones are given in Section II. The switch-induced toughening is
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