Cohesive Model of Electromechanical Fatigue for Ferroelectric Materials and Structures
Ferroelectric materials are extensively used in a variety of sensor and actuator applications, where the non-linear 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 1MPam1/2) 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. Despite recent experimental and modelling advances, the precise nature of the interactions between fracture, deformation and defect structures underlying ferroelectric fatigue is in need of further elucidation, and a physics-based multiscale model enabling the prediction of the fatigue life of ferroelectric devices is yet to emerge. Therefore, there remains a need for phenomenological and empirical models that can be experimentally validated and used in engineering design. We present a model of electro-mechanical ferroelectric fatigue based on the postulate of a ferroelectric cohesive law that: couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density; and 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 dependence of the coercive field on the size of the component, or size effect. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT.
© 2006 Springer.