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0902-T03-07.1

Cohesive Model of Electromechanical Fatigue for Ferroelectric Materials and Structures Santiago A. Serebrinsky, Irene Arias1 and Michael Ortiz Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, U.S.A. 1 Dep. de Matem`atica Aplicada III, Universitat Polit`ecnica de Catalunya, Barcelona 08034, Spain ABSTRACT We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density. The ferroelectric cohesive law exhibits a monotonic envelope and loading-unloading hysteresis. The model is applicable whenever the changes in properties leading to fatigue are localized in one or more planar-like regions, modelled by the cohesive surfaces. We validate the model against experimental data for a simple test configuration consisting of an infinite slab acted upon by an oscillatory voltage differential across the slab and otherwise stress free. The model captures salient features of the experimental record including: the existence of a threshold nominal field for the onset of fatigue; the dependence of the threshold on the applied-field frequency; the dependence of fatigue life on the amplitude of the nominal field; and the size effect on the coercive field. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT. A particularly appealing feature of the model is that it can be incorporated in a very natural and convenient way into a general finite element analysis of structures and devices for fatigue life assessment. INTRODUCTION Ferroelectric materials are extensively used in a variety of sensor and actuator applications, where the coupling between mechanical and electrical fields are of primary interest. They are also a promising set of materials for improved dynamic as well as non-volatile memory devices, where only the electrical properties are directly exploited. However, ferroelectrics are brittle, and their low fracture toughness (in the order of 1 MPa m1/2 ) makes them susceptible to cracking. In addition, ferroelectric materials exhibit electrical fatigue (loss of switchable polarization) under cyclic electrical loading and, due to the strong electro-mechanical coupling, sometimes mechanical fatigue as well. Conversely, the propagation of fatigue cracks hinders the performance of the devices and raises serious reliability concerns. Ferroelectric fatigue is caused by a combination of electrical, mechanical and electrochemical processes, each of which has been claimed to be responsible for fatigue [1]. Several electrochemical mechanisms have been posited as the likely cause of polarization fatigue [2, e.g.], but no general consensus appears to have emerged as yet. Fatigue mechanisms variously include processes of distributed damage over the bulk and processes

0902-T03-07.2

of localized damage, including microcrac