A thermodynamically motivated model for ferroelectric ceramics with grain boundary effects
TL;DR: In this paper, a micromechanically motivated model is embedded into an electromechanical coupled finite element formulation in which each grain is represented by a single finite element and the initial dipole directions are assumed to be randomly oriented to mimic the virgin state of the unpoled ferroelectric polycrystal.
Abstract: The aim of this paper is to capture the grain boundary effects taking into consideration the nonlinear dissipative effects of ferroelectric polycrystals based on firm thermodynamic principles. The developed micromechanically motivated model is embedded into an electromechanically coupled finite element formulation in which each grain is represented by a single finite element. Initial dipole directions are assumed to be randomly oriented to mimic the virgin state of the unpoled ferroelectric polycrystal. An energy-based criterion using Gibbs free energy is adopted for the initiation of the domain switching process. The key aspect of the proposed model is the incorporation of effects of the constraint imposed by the surrounding grains on a switching grain. This is accomplished by the inclusion of an additional term in the domain switching criterion that is related to the gradient of the driving forces at the boundary of the grains. To study the overall bulk ceramics behavior, a simple volume-averaging technique is adopted. It turns out that the simulations based on the developed finite element formulation with grain boundary effects are consistent with the experimental data reported in the literature.
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TL;DR: In this paper, the performance of 1-3 piezocomposites with different volume fractions and bulk piezoceramics was compared with experimental measurements, and the predicted effective properties were incorporated in the proposed model and the dielectric hysteresis (electric displacement versus electric field) as well as butterfly curves (strain versus electric fields) were simulated.
5 citations
TL;DR: An energy-based model of the ferroelectric polarization process is presented, and numerical examples gained in the open source software package Netgen/NGSolve are presented.
Abstract: An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the pr...
4 citations
DOI•
01 Jan 2017
TL;DR: In this paper, a thermodynamically consistent material model was developed to describe the macroscopic non-linear hysteretic behavior of ferroelectric single and polycrystalline materials.
Abstract: The present thesis deals with the development of thermodynamically consistent material models to describe the macroscopic non-linear hysteretic behaviour of ferroelectric single and polycrystalline materials. At first, a phenomenological material model is discussed in order to gain an understanding of the overall electromechanical coupling behaviour as well as to study the rate-dependent macroscopic polarisation evolution in crystalline ferroelectric solids. Following the phenomenological framework, laminate-based models are developed by treating the volume fraction of the tetragonal ferroelectric variants as internal state variables in their thermodynamic potentials. By considering different averaging principles, distinct thermodynamic potentials are postulated for the individual laminate-based material models. The influence of both the loading rate and the magnitude of the external compressive stress on the domain evolution and polarisation switching in tetragonal ferroelectric single crystals under combined electromechanical loading is simulated with help of the developed laminate-based models. Finally, a homogenisation-type strategy based on random orientations of the individual single crystal grains in a polycrystalline aggregate is detailed. The properties of the randomly oriented grains are averaged within a finite element framework to simulate the polarisation switching response and the macroscopic hysteresis curves for a bulk tetragonal ferroelectric ceramic.
1 citations
Cites background from "A thermodynamically motivated model..."
...However, a gradient term at the boundary of the switching domain was considered in [7] to avoid the sharp change in the Gibbs energy between any two neighbouring grains....
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...[3, 7] aimed at incorporating the interaction between the neighbouring ferroelectric grains in their micromechanical model formulations....
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TL;DR: In this paper , a simple phase-field model based on the anisotropy of the grain boundary energy was developed to simulate the microstructure evolution of ferroelectric ceramics.
1 citations
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TL;DR: In this paper, an energy-based model of the ferroelectric polarization process is presented, which is governed by two constitutive functions: the free energy function and the dissipation function.
Abstract: An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the primary independent unknowns. As an internal variable, the remanent polarization vector is chosen. The model is then governed by two constitutive functions: the free energy function and the dissipation function. Choices for both functions are given. As the dissipation function for rate-independent response is non-differentiable, it is proposed to regularize the problem. Then, a variational equation can be posed, which is subsequently discretized using conforming finite elements for each quantity. We point out which kind of continuity is needed for each field (displacement, dielectric displacement and remanent polarization) is necessary to obtain a conforming method, and provide corresponding finite elements. The elements are chosen such that Gauss' law of zero charges is satisfied exactly. The discretized variational equations are solved for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve.
1 citations
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TL;DR: In this paper, a finite element formulation which includes the piezoelectric or electroelastic effect is given, a strong analogy is exhibited between electric and elastic variables, and a stiffness finite element method is deduced.
Abstract: A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.
972 citations
TL;DR: In this article, lead lanthanum zirconate titanate (PLZT) was loaded with compressive stress parallel to the polarization and the stress vs strain curve was recorded.
Abstract: Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs electric field curves and the corresponding electric displacement vs electric field loops [1]. It is also the source of a stress—strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress [2, 3]. In this work, ceramic lead lanthanum zirconate titanate (PLZT) is polarized by loading with a strong electric field. The resulting strain and polarization hysteresis loops are recorded. The polarized sample is then loaded with compressive stress parallel to the polarization and the stress vs strain curve is recorded. The experimental results are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The observed strain and electric displacement hysteresis loops and the nonlinear stress—strain curve for the polycrystalline ceramic are reproduced by the simulation.
651 citations
TL;DR: In this article, the limitations of linear constitutive modeling and limitations of this composition of PLZT as an actuator material are examined, and the "yield" or ferroelastic switching stress is suggested as a good criteria for assessing the capability of actuator ceramics.
448 citations
388 citations
TL;DR: In this paper, a constitutive model for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field is developed for nonlinear switching, where the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation.
Abstract: A constitutive model is developed for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field. It is envisaged that the polycrystal consists of a set of bonded crystals and that each crystal comprises a set of distinct crystal variants. Within each crystal the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation and to a change in the average linear electromechanical properties. It is further assumed that switching is resisted by the dissipative motion of domain walls. The constitutive model for the progressive switching of each crystal draws upon elastic–plastic crystal plasticity theory, and a prescription is given for the tangent moduli of the crystal, for any assumed set of potentially active transformation systems. A self-consistent analysis is used to estimate the macroscopic response of tetragonal crystals (representative of lead titanate) under a variety of loading paths. Also, the evolution of the switching surface in stress-electric field space is calculated. Many of the qualitative features of ferroelectric switching, such as butterfly hysteresis loops, are predicted by the analysis.
388 citations