scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Thermodynamic Modeling of Hysteresis Effects in Piezoceramics for Application to Smart Structures

01 Jan 2008-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 46, Iss: 1, pp 280-284
TL;DR: In this paper, the effect of the amplitude of the electric field on the hysteresis loop has been studied experimentally by Nalwa et al. under cyclic variation of the applied electric field, which leads to an interesting variation of strain with respect to electric field (E), and it is denoted as butterfly loop.
Abstract: W ITH the development of piezoceramic sensors and actuators of varying shapes and sizes for use in structural applications, the field of smart structures has emerged as an area of research of great importance [1]. The mechanical, thermal, and electrical behavior of piezoceramics has been studied extensively by physicists and material scientists [2–9]. The introduction of these materials in structural applications has created a necessity to review the traditional structural modeling and analysis. Under cyclic variation of the applied electric field, piezomaterials exhibit polarization-electric (P-E) field hysteretic losses, as shown in Fig. 1. The points indicated by the symbols Ps, Pr, and EC represent saturation polarization, remnant polarization, and the coercive electric field, respectively. The saturation polarization Ps corresponds to the value of maximum polarization, which shows negligible change with further increase in electric field. Remnant polarization Pr is the value of polarization when the electric field becomes zero. Coercive electric fieldEC corresponds to the points of zero polarization. The observed phenomenon is due to the delay in polarization switching with variation in electric field. P-E hysteresis effect leads to an interesting variation of strainwith respect to electric field ( E), and it is denoted as butterfly loop. The hysteresiswill be affected by various parameters such as temperature, amplitude of oscillating electric field, frequency of oscillation, and external mechanical preloading. The effect of the amplitude of the electric field on the hysteresis loop has been studied experimentally by Nalwa [2]. It is observed that the remnant polarization and coercive electric field are functions of amplitude of the electric field. With a decrease in amplitude of the electric field, there is a reduction in the values of maximum polarization, remnant polarization, and coercive electric field. Viehland and Chen [3] experimentally studied the effects of frequency of oscillation of the electric field on the hysteresis loop. From the experiments, it was observed that if the amplitude of the electric field is above the coercive electric field ECmax corresponding to the case with saturation polarization, then the dissipation energy increases with an increase in frequency, whereas if the amplitude of the electric field is belowECmax, then the dissipation energy increases with a decrease in frequency. The effect of mechanical preloading on hysteresis has been studied experimentally by Arndt et al. [4]. It is observed that when a compressive mechanical preloading is applied parallel to the electric field, the reduction in polarization is found to be higher than that corresponding to the case with mechanical loading applied perpendicular to the electrical field. With the application of compressive mechanical preloading, the remnant polarization and coercive field show a reduction in magnitude. Mathematical modeling of hysteresis was approached at two different levels: 1) at the microscopic level and 2) at the macroscopic level of the piezomaterial. The microscopic models of hysteresis can be categorized as 1) polarization switching based on the Eshelby inclusion model [10], 2) crystal-plasticity-based nonlinear switching models [11], 3) free-energy-based domain-switching model [12], and 4) dipole–dipole interaction models with threshold-switching energy given by the time-dependent Ginzburg–Landau model [13,14] or the Landau–Devonshire model [15,16]. Macroscopic models can be categorized as either empirical models or thermodynamically consistent models. Empirical models are based on either introducing an additional variable in the constitutive relations [17], by representing the P-E curve by a tanhyperbolic function [18], or by using the Presaich model [19,20]. Bassiouny et al. [21–24] developed a thermodynamic phenomenological model for capturing the electromechanical hysteresis effects based on the work-hardening plasticity model. A similar approach was followed by McMeeking and Landis [25] in modeling domain switching in ferroelectric materials. A model based on extended irreversible thermodynamics was proposed by Lu and Hanagud [26]. Presented as Paper 1743 at the 15-th AIAA/ASME/AHS Adaptive Structures Conference, Honolulu, HI, 23–26 April 2007; received 1 May 2007; accepted for publication 25 August 2007. Copyright © 2007 by V. L. Sateesh, C. S. Upadhyay, and C. Venkatesan. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/08 $10.00 in correspondence with the CCC. ∗Graduate Student, Department of Aerospace Engineering. Student Member AIAA. Associate Professor, Department of Aerospace Engineering. Pandit Ramachandra Dwivedi Chair Professor, Department of Aerospace Engineering. Senior Member AIAA. AIAA JOURNAL Vol. 46, No. 1, January 2008
Citations
More filters
Journal ArticleDOI

[...]

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.

15 citations

Journal ArticleDOI

[...]

TL;DR: In this paper, the second-order nonlinear constitutive equations are used in the variational principle approach to develop a nonlinear finite element (FE) model for piezoelectric laminated composite plates and shells.
Abstract: In this article, we focus on static finite element (FE) simulation of piezoelectric laminated composite plates and shells, considering the nonlinear constitutive behavior of piezoelectric materials under large applied electric fields. Under the assumptions of small strains and large electric fields, the second-order nonlinear constitutive equations are used in the variational principle approach, to develop a nonlinear FE model. Numerical simulations are performed to study the effect of material nonlinearity for piezoelectric bimorph and laminated composite plates as well as cylindrical shells. In comparison to the experimental investigations existing in the literature, the results predicted by the present model agree very well. The importance of the present nonlinear model is highlighted especially in large applied electric fields, and it is shown that the difference between the results simulated by linear and nonlinear constitutive FE models cannot be omitted.

15 citations

Journal ArticleDOI

[...]

TL;DR: In this article, an attempt is made to study these (P-E) nonlinear effects on the static response of laminated composite plates with piezo actuators and to find the most effective piezo lay-up and ply orientation which gives the maximum deflections.
Abstract: Polarization–electric-field (P–E) interaction results in rendering the stress tensor non-symmetric and in a nonlinear force term in the equilibrium equation. In this paper, an attempt is made to study these (P–E) nonlinear effects on the static response of laminated composite plates with piezo actuators. Further, this paper also focuses on finding the most effective piezo lay-up and ply orientation which gives the maximum deflections. Four different piezo lay-up configurations and three ply orientations are considered. It has been observed from the study that width-wise strips show more transverse bending and twisting. However, full length piezo layers show maximum longitudinal bending. The results of nonlinear analysis show a more considerable softening trend in deformations than that of the linear analysis in the case of longitudinal bending and twisting. In the case of transverse bending this nonlinear effect shows a hardening trend. Further, it has been observed that the influence of P–E nonlinearity depends on the stiffness of the core material, the geometric arrangement of piezo patches, the boundary conditions and the actuation voltage.

6 citations

Journal ArticleDOI

[...]

TL;DR: In this paper, a higher order finite element model has been developed for the analysis of debonding in a smart cantilever beam, where the debonding has been incorporated at the interfaces between piezo patches and the core.
Abstract: Using basic electro-elastic formulation and variational formulation, a higher order finite element model has been developed for the analysis of debonding in a smart cantilever beam. Full length piezo patch embedded at the top and bottom of the aluminium core has been assumed to be de-bonded. The debonding has been incorporated at the interfaces between piezo patches and the core, at the mid span of the beam for one third length of the beam. The effect of debonding in sensing mode has been analysed by presenting the induced potential, axial displacement, axial/transverse electric field and stresses for fully bonded and de-bonded smart cantilever beam. The variation in electric potential, electric field, axial displacement/strain/stress and shear strain/stress observed in case of debonding demonstrates that the mechanics of debonding is complex coupled electro-mechanical behaviour. In the de-bonded beam, the induced potential at the free piezo surface and at the interfaces shows a sinusoidal variation from root to the tip as compared to the linear variation in bonded beam. This is attributed to the non-linear bending moment variation from root to the tip in case of de-bonded beam. The maximum stress in debonding increases nearly 1.5 times to that of bonded beam sensing at various locations.

2 citations

Journal ArticleDOI

[...]

TL;DR: In this article, a layer-by-layer finite element formulation is developed for both static and dynamic analyses of smart plates including hysteresis effects, and linear and nonlinear analyses are carried out to study the effect of nonlinearity due to polarization-electric field interaction on the response of the smart plates.
Abstract: The coupled electrothermoelastic constitutive relations, representing the behavior of piezo materials, are shown to be nonlinear when the polarization―electric field interaction effects are properly accounted for. Under static condition, the polarization―electric field nonlinearities correspond to a distributed body force and body moment. For time varying situations, polarization―electric field interaction exhibits a hysteresis effect. Using the nonlinear constitutive relations, a layer-by-layer finite element formulation is developed for both static and dynamic analyses of smart plates including hysteresis effects. Linear and nonlinear analyses are carried out to study the effect of nonlinearity due to polarization―electric field interaction on the response of the smart plates. To validate the present formulation, the results of static analysis of a smart plate are compared with experimental data available in literature. It is observed that the P-E hysteresis effects show a friction-type damping in the dynamic response of the smart plate.

Cites background or methods from "Thermodynamic Modeling of Hysteresi..."

  • [...]

  • [...]

  • [...]

  • [...]

References
More filters
Book

[...]

28 Sep 1990
TL;DR: In this article, the physical mechanisms of deformation and fracture are discussed, including linear elasticity, thermo-elasticity, and viscoelastic properties of real solids.
Abstract: 1. Elements of the physical mechanisms of deformation and fracture 2. Elements of continuum mechanics and thermodynamics 3. Identification and theological classification of real solids 4. Linear elasticity, thermoelasticity and viscoelasticity 5. Plasticity 6. Viscoplasticity 7. Damage mechanics 8. Crack mechanics.

3,630 citations


"Thermodynamic Modeling of Hysteresi..." refers methods in this paper

  • [...]

Journal ArticleDOI

[...]

TL;DR: In this paper, the authors present an overview and assessment of the technology leading to the development of intelligent structures, which are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning and power amplification electronics.
Abstract: HIS article presents an overview and assessment of the technology leading to the development of intelligent structures. Intelligent structures are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning, and power amplification electronics. Such actuating, sensing, and signal processing elements are incorporated into a structure for the purpose of influencing its states or characteristics, be they mechanical, thermal, optical, chemical, electrical, or magnetic. For example, a mechanically intelligent structure is capable of altering both its mechanical states (its position or velocity) or its mechanical characteristics (its stiffness or damping). An optically intelligent structure could, for example, change color to match its background.17 Definition of Intelligent Structures Intelligent structures are a subset of a much larger field of research, as shown in Fig. I.123 Those structures which have actuators distributed throughout are defined as adaptive or, alternatively, actuated. Classical examples of such mechanically adaptive structures are conventional aircraft wings with articulated leading- and trailing-edge control surfaces and robotic systems with articulated manipulators and end effectors. More advanced examples currently in research include highly articulated adaptive space cranes. Structures which have sensors distributed throughout are a subset referred to as sensory. These structures have sensors which might detect displacements, strains or other mechanical states or properties, electromagnetic states or properties, temperature or heat flow, or the presence or accumulation of damage. Applications of this technology might include damage detection in long life structures, or embedded or conformal RF antennas within a structure. The overlap structures which contain both actuators and sensors (implicitly linked by closed-loop control) are referred to as controlled structures. Any structure whose properties or states can be influenced by the presence of a closed-loop control system is included in this category. A subset of controlled structures are active structures, distinguished from controlled structures by highly distributed actuators which have structural functionality and are part of the load bearing system.

455 citations

Journal ArticleDOI

[...]

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.

373 citations


"Thermodynamic Modeling of Hysteresi..." refers methods in this paper

  • [...]

Journal ArticleDOI

[...]

368 citations


"Thermodynamic Modeling of Hysteresi..." refers result in this paper

  • [...]

  • [...]

Journal ArticleDOI

[...]

TL;DR: In this article, the authors derived the differential equations and boundary conditions describing the behavior of an electrically polarizable, finitely deformable, heat conducting continuum in interaction with the electric field.
Abstract: The differential equations and boundary conditions describing the behavior of an electrically polarizable, finitely deformable, heat conducting continuum in interaction with the electric field are derived by means of a systematic application of the laws of continuum physics to a macroscopic model consisting of an electronic charge continuum coupled to a lattice continuum. The resulting rotationally invariant description of thermoelectroelasticity consists of five differential equations in five dependent variables and, when thermal considerations are omitted, reduces to four differential equations in four dependent variables. These same four differential equations of electroelasticity in the same four dependent variables along with the associated boundary conditions can readily be obtained, by means of a Legendre transformation, from existing consistent variational treatments of electroelasticity, which yield a system of seven equations in seven dependent variables.

342 citations