Ferroelectric and ferroelastic piezoceramics – modeling of electromechanical hysteresis phenomena
About: This article is published in Continuum Mechanics and Thermodynamics.The article was published on 2001-08-01. It has received 388 citations till now. The article focuses on the topics: Hysteresis & Ferroelectricity.
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TL;DR: In this article, a model for studying the domain pattern of ferroelectric materials and its evolution is developed, and the electrostatic potential is made explicit, and consequently the model is able to predict the micro-structural evolution and the macro-scopic behavior of Ferroelectrics subjected to realistic electro-mechanical boundary conditions.
Abstract: A model for studying the domain pattern of ferroelectric materials and its evolution is developed. In a departure from prior work, the electrostatic potential is made explicit, and consequently the model is able to predict the microstructural evolution and the macroscopic behavior of ferroelectrics subjected to realistic electro-mechanical boundary conditions. Nucleation of domains and propagation of domain walls are investigated under combined electro-mechanical loading and compared to recent experiments. The correlation between the microstructural change and macroscopic response provides evidence that the recently observed large strain actuation of ferroelectric materials is due to 90° domain switching.
290 citations
TL;DR: Theoretical analyses and experimental observations of the failure and fracture behaviors of piezoelectric materials are presented in this paper, where the theoretical analyses are based on the Stroh formalism.
Abstract: Theoretical analyses and experimental observations of the failure and fracture behaviors of piezoelectric materials are presented. The theoretical analyses are based on the Stroh formalism. A strip dielectric breakdown model is proposed to estimate the effect of electrical non-linearity on the piezoelectric fracture of electrically insulated cracks. The reviewed experiments include the indentation fracture test, the bending test on smooth samples, the fracture test on pre-notched or pre-cracked samples, the environment-assisted fracture test, etc. For electrically insulated cracks, the experimental results show a complicated fracture behavior under combined electrical and mechanical loading. Fracture data are greatly scattered when a static electric field is applied. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate (PZT) ceramics. A charge-free zone model is introduced to understand the failure behavior of conducting cracks in the depoled lead zirconate titanate ceramics under electrical and/or mechanical loading. These theoretical and experimental results indicate that fracture mechanics concepts are useful in the study of the failure behaviors of piezoelectric materials.
284 citations
TL;DR: In this paper, the authors give a short overview and a critical discussion about the present state in the field of piezoelectric fracture mechanics, with emphasis on special features like anisotropy, mode mixture and electric properties of cracks.
Abstract: Piezoelectric and ferroelectric materials have gained extensive applications in electromechanical devices, microelectromechanical systems and smart composite materials. In order to assess the strength and durability of those materials and components, exhaustive theoretical and experimental investigations have been performed over the past three decades. The aim of the paper is to give a short overview and a critical discussion about the present state in the field of piezoelectric fracture mechanics. After an introduction, linear piezoelectric fracture theory is explained with emphasis to special features like anisotropy, mode mixture and electric properties of cracks. Next, suggested fracture criteria are presented and contrasted with experimental observations in fracture testing. Cracks under static, cyclic and dynamic loading by electrical and mechanical fields are taken into account. A great challenge is to tackle the non-linear phenomena and ferroelectric domain switching in the fracture process zone. Finally, conclusions are drawn with respect to open problems and desirable future research areas. To limit the scope of the paper, fracture behavior of interface cracks will not be addressed.
223 citations
TL;DR: In this paper, the influence of preload stress on the ferroelectric hysteretic behavior of piezoelectric ceramics was investigated for soft lead zirconate titanate (PZT) material under various uniaxial compressive stress preloads.
Abstract: This paper deals with the influence of preload stress on the ferroelectric hysteretic behavior of piezoelectric ceramics. The polarization and strain versus electric field hysteresis loops were measured for soft lead zirconate titanate (PZT) piezoceramic material under various uniaxial compressive stress preloads of up to −400 MPa. The investigation revealed that the superimposed compression load reduced the remnant polarization, decreased the coercive field, and also had a significant impact on the dielectric and piezoelectric properties. With increasing mechanical load, dielectric hysteresis and butterfly hysteresis became less and less pronounced, as the compressive stress prevented full alignment of the domains and induced mechanical depolarization. The slopes of the polarization and strain curves at zero electric field were measured to evaluate the dependence of permittivity and piezoelectric coefficients on the prestress. The experimental results were interpreted in terms of the non-180° domain switching process under combined electromechanical loading.
197 citations
TL;DR: In this article, a phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed, which is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field.
Abstract: A phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed. The framework of the law is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field that determines when non-linear response is possible. The size and shape of the switching surface in a modified electric field space remains fixed during non-linear behavior but its center moves around and thus is controlled by a kinematical hardening process. In general, the remanent polarization and the remanent strain are used as the internal variables that control how the center of the switching surface moves. However, the form presented in this paper has a one-to-one relationship between the remanent strain and the remanent polarization, simplifying the constitutive law and allowing remanent polarization to be used as the only internal variable controlling the kinematic effects. The constitutive law successfully reproduces hysteresis and butterfly loops for ferroelectric ceramics. The hysteresis and butterfly loops respond appropriately to the application of a fixed compressive stress parallel to the electric field. In addition, the law successfully handles remanent polarization rotation due to the application of electric field at an angle to the polarization direction.
179 citations
Cites background from "Ferroelectric and ferroelastic piez..."
...Comparisons have been made successfully with polarization rotation behavior [25] and investigations of the effect of stress during hysteresis cycling have been made [26]....
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References
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Book•
01 Jan 1960
TL;DR: In this article, the propagation of electromagnetic waves and X-ray diffraction of X rays in crystals are discussed. But they do not consider the effects of superconductivity on superconducting conductors.
Abstract: Electrostatics of conductors Static magnetic field Superconductivity The propagation of electromagnetic waves Spatial dispersion Diffraction of X rays in crystals.
12,543 citations
Book•
06 Oct 1977
TL;DR: In this paper, the theory of ferroelectricity in terms of soft modes and lattice dynamics is developed and modern techniques of measurement, including X-ray, optic, and neutron scattering, infra-red absorption, and magnetic resonance.
Abstract: The book develops the modern theory of ferroelectricity in terms of soft modes and lattice dynamics and also describes modern techniques of measurement, including X-ray, optic, and neutron scattering, infra-red absorption, and magnetic resonance. It includes a discussion of the related phenomena of antiferroelectricity, pyroelectricity, and ferroelasticity and seconds on domains, thin films, ceramics, and polymers, leading on to a comprehensive survey of potential and actual device capabilities for pyroelectric detection, memories, display, and modulation. It should provide an authoritative account for those engaged in research or graduate ferroelectric or pyroelectric devices.
4,931 citations
"Ferroelectric and ferroelastic piez..." refers background in this paper
...It is now the defining property of a ferroelectric material that a domain state can be modified by loadings of sufficient magnitude ([72], p. 37, [ 85 ], p. 9). In particular, an electric field with a magnitude above the coercive field Ec will switch the unit cell such that its spontaneous polarization coincides with that of the field (Fig. 5). In the polycrystal, the switched domain state basically remains unchanged after unloading....
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...Besides electric fields, mechanical stresses of sufficient magnitude may give rise to switching processes as well (Fig. 7). This ferroelastic behavior implies the possibility of mechanically induced irreversible deformations ([ 85 ], pp. 14, 107)....
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...As standard literature on the material science of ferroelectric piezoceramics it is referred to the textbooks [34, 72, 35, 85 , 102], for instance....
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TL;DR: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body as mentioned in this paper, which can be expressed as follows: a body is regarded as a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies.
Abstract: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body. In a formal rational development of the subject, one first tries to state precisely what mathematical entities represent these physical concepts: a body is regarded to be a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies1. Once these concepts are made precise one can proceed to the statement of general principles, such as the principle of objectivity or the law of balance of linear momentum, and to the statement of specific constitutive assumptions, such as the assertion that a force system can be resolved into body forces with a mass density and contact forces with a surface density, or the assertion that the contact forces at a material point depend on certain local properties of the configuration at the point. While the general principles are the same for all work in classical continuum mechanics, the constitutive assumptions vary with the application in mind and serve to define the material under consideration.
1,885 citations
"Ferroelectric and ferroelastic piez..." refers background in this paper
...This inequality has to be satisfied for every admissible thermomechanical process [ 23 , 22]....
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...the standard argument established in [ 23 ] yields that the validity of the potential relations...
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