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 Rietveld refinement, microstructure, conductivity and impedance properties of Ba[Zr0.25Ti0.75]O3 ceramic synthesized by solid state reaction were reported.
95 citations
TL;DR: In this paper, a thermodynamically consistent framework combining the phenomenological and micromechanical models was developed to predict the coupled behavior of 1-3 piezocomposites with different volume fractions and bulk piezoceramics.
Abstract: A study is carried out to compare the non-linear behaviour of 1-3 piezocomposites with different volume fractions and bulk piezoceramics. Experiments are conducted to measure the electrical displacement and strain on piezocomposites and ceramics under high cyclic electrical loading. A thermodynamically consistent framework, combining the phenomenological and micromechanical models, is developed to predict the coupled behavior. Volume fractions of three distinct uni-axial variants (instead of six variants) are used as internal variables to describe the microscopic state of the material. In this model, the grain boundary effects are taken into account by introducing the back fields (electric field and stress) as non-linear kinematic hardening functions. In order to calculate the effective properties (elastic, piezoelectric, and dielectric constants) of piezocomposites for different volume fractions, an analytical model based on equivalent layered approach is proposed. The predicted effective properties are incorporated in the proposed model, and the classical hysteresis (electrical displacement versus electric field) as well as butterfly curves (strain versus electric field) is simulated. Comparison between the experiments and the simulations shows that this model can reproduce the characteristics of non-linear coupled response. It is observed that the variation in fiber volume fraction has a significant influence on the response of the 1-3 piezocomposites.
25 citations
TL;DR: In this paper, a thermodynamically consistent uni-axial framework is developed to predict the nonlinear behavior of 1-3 piezocomposites with different volume fractions and bulk piezoceramics.
16 citations
TL;DR: In this paper, a simplified macroscopic uni-axial model based on physical mechanisms of domain switching and continuum damage mechanics has been developed to predict the nonlinear fatigue behavior of 1-3 piezocomposites for temperature dependent electrical fatigue loading conditions.
Abstract: 1-3 type piezocomposites are very attractive materials for transducers and biomedical application, due to its high electromechanical coupling effects. Reliability study on 1-3 piezocomposites subjected to cyclic loading condition in transducer application is one of the primary concern. Hence, this study focuses on 1-3 piezocomposites for various PZT5A1 fiber volume fraction subjected to electrical fatigue loading up-to 106 cycles and at various elevated temperature. Initially experiments are performed on 1-3 piezocomposites, in order to understand the degradation phenomena due to various range in amplitude of electric fields (unipolar & bipolar), frequency of applied electric field and for various ambient temperature. Performing experiments for high cycle fatigue and for different fiber volume fraction of PZT5A1 is a time consuming process. Hence, a simplified macroscopic uni-axial model based on physical mechanisms of domain switching and continuum damage mechanics has been developed to predict the non-linear fatigue behaviour of 1-3 piezocomposites for temperature dependent electrical fatigue loading conditions. In this model, damage effects namely domain pinning, frozen domains and micro cracks, are considered as a damage variable (ω). Remnant variables and material properties are considered as a function of internal damage variable and the growth of the damage is derived empirically based on the experimental observation to predict the macroscopic changes in the properties. The measured material properties and dielectric hysteresis (electric displacement vs. electric field) as well as butterfly curves (longitudinal strain vs. electric field) are compared with the simulated results. It is observed that variation in amplitude of bipolar electric field and temperature has a strong influence on the response of 1-3 piezocomposites.
11 citations
TL;DR: In this article, a simplified macroscopic model based on physical mechanisms of domain switching is developed to predict the nonlinear behavior of electrical fatigue in lead zirconate titanate (PZT) for different loading frequencies.
Abstract: A systematic investigation on electrical fatigue in lead zirconate titanate (PZT) is carried out for different loading frequencies. Experiments are conducted up to 106 cycles to measure the electrical displacement and longitudinal strain on bulk ceramics in the bipolar mode with large electrical loading conditions. A simplified macroscopic model based on physical mechanisms of domain switching is developed to predict the non-linear behaviour. In this model, the volume fraction of a domain is used as the internal variable by considering the mechanisms of domain nucleation and propagation (domain wall movement). The measured material properties at different fatigue cycles are incorporated into the switching model as damage parameters and the classical strain versus electric field and electric displacement versus electric field curves are simulated. Comparison between the experiments and simulations shows that the proposed model can reproduce the characteristics of non-linear as well as fatigue responses.
11 citations
Cites methods from "A thermodynamically motivated model..."
...These models are based on the description of the material at the domain or single crystal length scale, and they make use of homogenization theory to reproduce polycrystalline behaviour [22–27]....
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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