A Phenomenological Cohesive Model of Ferroelectric Fatigue

Laboratori de Cà lcul Numèric, Departament de Matemà tica Aplicada III, Universitat Politècnica de Catalunya, E-08034, Barcelona, Spain
Acta Materialia (Impact Factor: 4.47). 02/2006; 54(4). DOI: 10.1016/j.actamat.2005.10.035
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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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Available from: Irene Arias, Jan 08, 2014
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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. [8] 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. [9] and Verhoosel and Gutiérrez [10]. "
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    ABSTRACT: The reliability of smart structures and in particular of ferroelectric multilayer actuators (MLA) is essentially reduced by accumulation of damage and crack formation. Such failure processes are numerically simulated in the current research by finite element method (FEM) employing coupled electro-mechanical analyses. At first, the poling process during manufacturing of the actuator is simulated. Next, an alternating electric voltage with a constant amplitude is applied to mimic in-service conditions. In order to model the bulk material, ferroelectric user elements are implemented into the commercial software ABAQUS © , thus allowing to simulate domain switching processes. Material damage is considered by means of a cyclic cohesive zone model (CCZM). The traction-separation law (TSL) accounts for electro-mechanical interaction. It was found that the poling process of the actuator may induce crack initiation at an electrode surface, which is driven further by the cyclic electric loading. Damage accumulation is observed due to mechanical and electrical field concentrations near the electrode tip. To the best of our knowledge, it is the first coupled ferroelectromechanical modeling combined with gradual damage accumulation in smart structures which is an important step towards future optimizations of the actuator design.
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    • "The fracture criterion of Park and Sun [30] agreed well with experimental results. Fulton and Gao [14] and Gao et al. [16] extended this criterion to non-linear effects and in [3] to fatigue cracks. The extended finite element (XFEM) method was originally developed to model arbitrary crack growth without remeshing [5] [25]. "
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    • "The choice of crack boundary condition becomes relevant when modeling the failure in such materials through the discrete account of the strong discontinuities. Constitutive models allowing for discontinuities in the displacement field as well as in the electric potential along the finite element boundaries are developed in Arias et al. [1] and Verhoosel and Gutiérrez [66]. Simulations of cohesive fatigue effects in grain boundaries of a piezoelectric mesostructure are performed in Utzinger et al. [65]. "
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    ABSTRACT: This paper presents new finite elements with embedded strong discontinuities in the form of jumps in the mechanical displacement field as well as jumps in the electric potential for the modeling of failure in electromechanical coupled solids. Such materials which are commonly used in smart systems in the form of actuators or sensors are prone to defects in the form of cracks represented by such strong discon-tinuities. In this work a discrete account of the individual jumps is made with the possibility of their propagation through the individual finite elements without the need of remeshing or refinement strate-gies. Originated for purely mechanical based materials and commonly referred as the strong discontinu-ity approach an extension to account for the electromechanical coupling and the additional jumps in the electric potential is made in this work. The decomposition of that methodology into a global problem, representing here the electromechanical boundary value problem, and a local problem through which the strong discontinuities are introduced, serves convenient when developing the corresponding finite elements based on the requirement to avoid stress locking phenomena. This idea is extended in this work to develop new finite elements based on the incorporation of electrical separation modes directly into the discrete formulation, keeping its local and computational efficient property with regard to the storage and possible static condensation of the parameters used to describe the mechanical and electrical discon-tinuities. On a constitutive level, the mechanical traction separation law is extended to account for a soft-ening type behavior in the relation between the normal component of the electric displacement field and the surface charge density. This is accomplished through the derivation of a localized electromechanical damage model based on the principle of maximum damage dissipation. The performance of the resulting new finite elements is illustrated with several numerical simulations including a compact tension test and a three point bending test of piezoelectric ceramics and compared with experimental results avail-able in the literature.
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