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 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. Peer Reviewed Postprint (author's final draft)
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"For simulation of damage initiation and evolution the concept of cohesive zone models is quite efficient, when one or several possible damage paths with embedded cohesive elements can be introduced a priori. Arias et al.  made first adaptation of the classical exponential cohesive zone model to ferroelectric materials to simulate electric fatigue, whereby some physical simplifications were made. Consecutive simulations with cohesive zone elements but with piezoelectric bulk behavior were performed by Utzinger et al.  and Verhoosel and Gutiérrez . "
"A constitutive cohesive zone model for piezoelectric bulk behavior under mechanical loading allowing for discontinuities both in the elastic displacements and the electric potential along the element boundaries was developed in . In the above mentioned papers8910 only two-dimensional cracked bodies and cohesive elements are considered besides that most of the cohesive zone models do not take into account a progressive damage during subcritical electromechanical loading. The present paper attempts to overcome the aforementioned limitations, combining all the required demands in a single approach by using a non-linear ferroelectric bulk behavior (domain switching) and an enhanced electromechanical cyclic cohesive law for threedimensional analyses of the electromechanical fracture. "
[Show abstract][Hide abstract]ABSTRACT: Fracture of ferroelectric materials is studied numerically using an advanced exponential cyclic cohesive zone model. The implemented irreversible cohesive law allows damage accumulation during (re)loading. Change in polarization direction (as a result of possible switching of ferroelectric domains) around cracks due to applied electromechanical loading is considered. In order to represent the permittivity of the grain boundaries or the crack faces a parallel plate capacitor model is implemented into the cohesive law. Numerical simulations are performed for the basic test model as well as for a crack in ferroelectric bulk material. The results show realistic electric field influence on the fracture toughness of the specimen as well as crack initiation and growth pattern. Mechanisms of the crack initiation and propagation in the ferroelectric medium under cyclic electric loading of constant amplitude are illustrated.
"The fracture criterion of Park and Sun  agreed well with experimental results. Fulton and Gao  and Gao et al.  extended this criterion to non-linear effects and in  to fatigue cracks. The extended finite element (XFEM) method was originally developed to model arbitrary crack growth without remeshing  . "
[Show abstract][Hide abstract]ABSTRACT: We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.