Behavior Of Piezoelectric Materials Research Articles

Exact solutions of the 2‐D frictional sliding contact problem of electrically insulated triangular and cylindrical punches on piezoelectric materials

AbstractThe present paper performs an exact electro‐mechanical contact analysis for piezoelectric materials under a frictional sliding triangular or cylindrical punch. The Coulomb frictional law is used inside the contact region. Appropriate fundamental solutions that can lead to real solutions of electro‐mechanical quantities are derived for real and complex eigenvalues. A second kind singular integral equation of Cauchy type is obtained for the stated problem, whose exact solution can be found by using the excellent properties of Jacobi Polynomials. Closed‐form expressions of stress components and electrical displacement are obtained, which provide benchmark solutions for examining the frictional contact behaviors of piezoelectric materials. Numeric results are presented. The influences of the friction coefficient on the contact region, stress components and electric displacement are detailed.

A doubly nonlinear problem associated with a mathematical model for piezoelectric material behavior

AbstractWe consider a mathematical model, which describes piezoelectric material behavior. This model is similar to models of plasticity theory. However, piezoelectric models describe coupled mechanical and electrical material behavior. Therefore they contain additional nonlinearities in the piezoelectric tensor and in the enthalpy function, which is non quadratic. These nonlinearities cause difficulties in the proof of existence theorems. Under the assumption that the piezoelectric tensor is constant (i.e. independent of P), we show how the system of model equations can be reduced to a doubly nonlinear evolution equation of the form zt ∈ G(‐Mz‐Φ (z) + f), which contains a composition of two monotone operators. The monotone mapping G is a subdifferential of the indicator function of some convex set while the second monotone mapping Φ is the Nemyckii operator of a monotone function. We prove existence of strong solutions, if Φ is replaced by a regularization. If in addition Φ is Lipschitz continuous we can show that the solution is unique.

Study on the Mechanical Characteristics of Multilayer Piezoelectric Stack Actuator

This paper presents results on mechanical behavior of multilayer piezoelectric stack actuators for use in active member under combined electro-mechanical Loadings. The objective of this study is to investigate the behavior of piezoelectric materials and to determine the properties necessary for design of such actuator systems. Two types of experiments are performed: influences of the preload on characteristics of the stack and dynamic test. The measurements indicate strong dependence of the actuator piezoelectric properties on the electro-mechanical loading conditions. The displacement output is initially enhanced with an increase of the mechanical preload, and the maximum value is obtained at the preload of about 0.4 KN. But much higher preload will cause the decrease of the displacement output. Within low frequency band of about 400 Hz, the displacement magnitude of the stack is nearly constant, and the phase lag increases with the increase of the driving frequency at the applied sine sweep voltage with the amplitude of 150V.

Existence results for a nonlinear evolution equation containing a composition of two monotone operators

AbstractWe present an existence result for an evolution equation with a nonlinear operator, which is a composition of two monotone mappings. The first monotone mapping is a subdifferential of the indicator function of some convex set while the other is constructed as the Nemyckii operator of a monotone function. Such equations arise from the mathematical models, which describe piezoelectric material behavior. Under some additional assumptions we prove the existence and uniqueness of the strong solution for the case, when the operator generated by the monotone function is a Lipschitz continuous mapping. In the case of a nonlinear growth of the monotone function we prove the existence of the strong solution (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental Analysis of Electro-Mechanical Characterization of Piezoelectric Stack Actuators

This paper presents the results of experimental analysis and theoretical research of piezoelectric stack actuators. The key is to understand the behavior of piezoelectric materials mechanical loads in this paper, and to determine optimum working conditions. Based on analysis of some parameters and driven model, which are necessary to performing design optimization to achieve maximum energy transfer and minimum power consume, provide relevant evidence For the subsequent theoretical research.

A study of the effect of the electro-mechanical loading history on the fracture strength of piezoelectric material

Many studies to grasp and describe the fracture behavior of piezoelectric materials under electro-mechanical loading have been done. Although the crack energy density (CED) theory predicts that the mechanical and electrical CEDs can depend on the loading history, the effect of electro-mechanical loading history on the fracture strength of piezoelectric materials has not been studied. Therefore, in this paper, a fracture criterion based on the mechanical contribution of CED (CEDM) is introduced. Its applicability is studied by analyzing the results of three-point bending test regarding the loading path dependence of the fracture strength of piezoelectric ceramic. From the results of ( E → M) and ( M → E) tests for a C-21 piezoelectric ceramic specimen, it was found that the fracture behavior of piezoelectric ceramics depend on the loading history. The results further showed that the effect of the electric field on the fracture strength of piezoelectric ceramic in the ( M → E) test was larger than that in the ( E → M) test. Results from linear FE analyses, which assumed that the fracture-initiating load was the same, indicated that the CEDM values increased linearly from negative to positive, and the slopes of CEDM in descending order were: linear ( M → E) analysis > linear ( M, E) analysis > linear ( E → M) analysis.

Active Control of Crack Propagation in Laminated Composite Plate Embedded with Piezoelectric Material

The concept of using piezoelectric materials with structural elements is to monitor the behavior of the structure when it is subjected to a load. This paper describes a kind of self repairing structures by integrating the piezoelectric patch with laminated composite plate. The coupled character of mechanical and electrical behavior of piezoelectric material will be used to sense the deformation in the material and actuate it to resist the deformation when subjected to a load. The fatigue behavior of the laminated composite plate is studied for the cyclic bending load by experiment. Mathematical simulation is carried out using finite element method. The test specimen is prepared from a glass/epoxy laminated composite plate. The laminate is constructed as cross-ply with 50:50 fiber/matrix. The alternating stresses are derived from the tensile and three point flexure tests. The fatigue behavior is studied for the constant amplitude displacement at three different stress levels. Based on the fatigue characteristics observed from the experiments, the laminate without and with piezoelectric patch are simulated using finite element method. The simulation results for laminated composite plate with piezoelectric patch has shown a considerable increase in the fatigue life cycles.

Experimental Analysis of Electro-Mechanical Characterization of Piezoelectric Stack Actuators

This paper presents the results of experimental analysis and theoretical modeling of piezoelectric stack actuators. The focus of this paper is to understand the behavior of piezoelectric materials under the combined electro-mechanical loadings scenario, and to determine fundamental properties and optimum working conditions. Some parameters, including output displacement, hysteresis, output force and mechanical stiffness, are evaluated under varied pre-stress level and driven voltage values representative of in-service conditions. The measurements indicate strong dependence of the actuator piezoelectric properties and stiffness on the electro-mechanical loading conditions. This research also identified and calculated some parameters of the induced strain actuators electro-mechanical model, which are necessary to performing design optimization to achieve maximum energy transfer and minimum power consume.

Tracking control of piezoelectric actuator system using inverse hysteresis model

The intrinsic hysteresis behavior of piezoelectric material limits the tracking control accuracy of the actuators. This paper describes a tracking control method for piezoelectric actuators based on the combination of feedforward and feedback loops. The hysteresis of piezoelectric actuators is linearized in feedforward loop with an inverse hysteresis model based on a neural network. The number of parameters in the neural network based inverse model is relatively small and the parameters are easy to identify. The feedback loop is used to reduce the accumulated error produced by the inverse hysteresis model. The experimental results show that the accuracy is significantly improved in tracking control by using the combination of feedback and feedforward control.

Effect of finite cracking on the electromechanical coupling properties of piezoelectric materials

Cracks and porosities inside the piezoelectric materials can weaken the electromechanical coupling effect, and hence influence the electromechanical coupling behavior of piezoelectric materials considerably. This paper studies the effect of internal cracking on the effective properties of piezoelectric media. It focuses on the piezoelectric medium of finite size with finite crack. The mechanical and electric fields in the piezoelectric material and the crack are formulated by singular integral method. Effects of crack size, medium border, and electric permeability of the crack on the overall electromechanical properties of the piezoelectric material are obtained and displayed graphically. In addition, the crack tip coupling electromechanical field intensity factors are also presented as they are not available in open literature for a finite crack in a finite piezoelectric media.

Finite Element Formulation for Ferroelectric Hysteresis of Piezoelectric Materials

For the numerical simulation of non-linear piezoelectric material behavior, we use a constitutive relation that is based on a decomposition of the physical quantities dielectric displacement and mechanical strain into a reversible and an irreversible part. Therein, we set the irreversible part of the dielectric displacement equal to the irreversible electric polarization and express the irreversible mechanical strain by a polynomial ansatz of the irreversible electric polarization. The reversible parts of mechanical strain and dielectric displacement are further described by the linear piezoelectric constitutive law. We apply a Preisach hysteresis operator to compute the irreversible polarization from the history of the driving electric field. Furthermore, the entries of the piezoelectric modulus tensor are assumed to be functions of the electric polarization. To efficiently solve the non-linear system of partial differential equations, we have developed a quasi-Newton scheme and use the finite element (FE) method for the numerical solution. This FE scheme has been applied to numerically calculate the dynamic behavior of a piezoelectric disc and a stack actuator. The obtained results compare well to measured data.

Modeling the fracture behavior of piezoelectric materials using a gradual polarization switching model

Polarization switching experiments conducted on polycrystal piezoelectric materials indicate that the polarization switching is gradual (occurs over a range of applied electrical and mechanical loads). An empirical model that considers the gradual change in the polarization direction is proposed to capture the polarization switching phenomena and apply it to modeling the fracture behavior of piezoelectric materials. Changes in the dielectric constants (measured from a 90° polarization switching experiment) and the polarization direction are used to estimate the amount of domain switching for an applied electric field. To model polarization switching in a generalized state of stresses and electric fields, the applied electric field (during the experiment) is converted to the corresponding value of internal energy density causing polarization switching. Internal energy density is used as the parameter to estimate the amount of domain switching and the resulting gradual change in the polarization direction. The gradual polarization switching model computes changes in the material properties and spontaneous strain contributions (arising from crystal shape change in the switching domains) based on the current polarization direction. A finite element solution procedure that incorporates the gradual polarization switching model is developed and interfaced with ABAQUS. Stress–strain variations obtained from the compression experiments and FEA are compared for PZT-4 (Zr/Ti = 52/48) and PZT-5H (Zr/Ti = 53/47). The C(T) specimen that was used in Mode-I fracture experiments is analyzed with a slit crack assumption. Microscopic observations of the region near the crack tip of a C(T) fracture specimen is used to capture the actual crack geometry generated by the machining process. A finite element model with the actual crack geometry is used to investigate the influence of finite dimensions of the crack cavity on the size of the polarization switching zones in the vicinity of the crack tip and its effects on the opening stress and the stress intensity ahead of the crack tip.

Crack driving force and energy-momentum tensor in electroelastodynamic fracture

The energy flux integral and the energy-momentum tensor for studying the crack driving force in electroelastodynamic fracture are formulated within the framework of the nonlinear theory of coupled electric, thermal and mechanical fields based on fundamental principles of thermodynamics. This formulation lays a foundation for in-depth understanding of the fracture behavior of piezoelectric materials. Remarkably, the dynamic energy release rate thus obtained has an odd dependence on the electric displacement intensity factor for steady-state propagation of a conventional (unelectroded) crack with exact, electrically permeable, semi-permeable, or impermeable crack surface condition, which is in agreement with experimental evidence.

A differential effective medium model for piezoelectret foams

Polymer foams with piezoelectric properties, called piezoelectrets, have recently gained interest in the acoustics and scientific community. These foams are heterogeneous materials consisting of a continuous polymer containing electrically polarized elliptical voids. The macroscopically observable piezoelectric behavior results from the unique combination of the high void-polymer elastic contrast and the void polarization. Existing modeling methods to approximate the macroscopic piezoelectric properties of these foams are elementary one-dimensional noncoupled electrostatic models. In this study, a coupled mean field microelectromechanical model has been developed as a predictive tool of the macroscopically observed piezoelectric material behavior. This technique employs Green’s function solutions of the three-dimensional (3D) stress equilibrium equations and Gauss’ Law. The result is a multiscale differential effective medium model approximating the 3D effective stiffness, dielectric permittivity, and piezoelectric coupling coefficients as a function of the constituent material properties, void shape and orientation, and deposited charge density. The model is employed to study the sensitivity of macroscopic foam behavior to various constituent material and void variables. This approach improves the approximation of the true piezoelectret behavior by capturing the influence of microscopic material structure and properties on macroscopic piezoelectric performance.

Grain Orientation Scattering in Nonlinear Constitutive Modeling of Piezoelectric-ferroelectric Materials

The ability to enhance and to improve the efficiency of micromechanical models for the coupled electromechanical constitutive behavior of piezoelectric materials in the nonlinear regime is investigated. Motivated by the limited strain actuation capabilities of the existing piezoelectric materials and structures, it is recognized that the nonlinear regime has to be explored. However, due to the complex, strongly coupled, and hysteretic behavior of the material, the quantitative prediction of its nonlinear response requires complex and time-consuming algorithms. In this study, the ability to improve the efficiency of the micromechanical algorithm by using a deterministic set of directions as a representative of the scattering of grain's orientation within the piezoelectric polycrystal is investigated. Various types of deterministic grain sets that include an equal area, a spiral, and Fekete grain sets are examined. The constitutive micromechanical model for the piezoelectric material and the algorithms for the generation of the various grain sets are presented and discussed. Numerical results that compare the capabilities of the model that uses the deterministic scattering approach and those that adopt a random scattering, which is commonly used today, are presented and discussed. Emphasis is placed on the ability to predict the complex nonlinear material response and on the computational efficiency. The article closes with a summary and conclusions.

Online Phase Tracking of Interferometric Optical Fiber Sensors for Vibration Control

Online phase tracking of an extrinsic Fabry—Perot interferometer (EFPI) and experimental vibration control of a composite beam with a sensing patch are investigated. EFPI sensors have nonlinearity due to their interferometric characteristics. We propose a new sensing patch for compensation of this interferometric nonlinearity. This newly developed sensing patch consists of an EFPI sensor and another sensor that can produce directional information. Therefore, it uses the advantages of their components used in conjuction in order to overcome the disadvantages of the components used separately. A sensing patch that comprises an EFPI sensor and a piezoceramic is fabricated, and the characteristics are experimentally investigated. A simple and practical logic is applied to real-time tracking of the optical phase of an interferometer. The experimental results show that the proposed sensing patch does not suffer from the nonlinear behavior of conventional EFPI sensors and the hysteretic behavior of piezoelectric materials. Moreover, it has excellent strain resolution and a wide dynamic sensing range. The application of a sensing patch has been also investigated: vibration control with this sensing patch has been performed using a fuzzy logic controller (FLC), and the possibility of using a sensing patch as a sensoriactuator is considered.

Durability properties of piezoelectric stack actuators under combined electromechanical loading

This paper presents results on the electro-thermo-mechanical behavior of piezoelectric materials for use in actuator applications with an emphasis on durability performance. The objective of this study was to compare the performance of different commercially available actuator systems and to determine the properties necessary for the design of such actuator systems. Basic piezoelectric properties of five stack actuators were determined as a function of mechanical preload and temperature. Changes in these properties during ferroelectric fatigue up to 107cycles were determined from strain-field relations after a specified number of fatigue cycles. Experimental results indicate a strong dependence of piezoelectric properties and power requirements on mechanical loading conditions. Results indicate that the optimum operating conditions (i.e., mechanical preload) that will improve actuation capabilities of piezoelectric stack actuators can be determined. That is, strain output was found to increase by 60% for some actuators upon the application of certain compressive prestress. Results of fatigue tests indicate negligible degradation in strain output for some stack actuators even when operated under mechanical preload that causes large displacements through domain wall motion. Similar trends in strain output and current degradation curves (as a function of fatigue cycles) suggest that material degradation can be indirectly inferred from simply measuring the current being dissipated by the material and the fatigue predicted by measuring the strain output (quantity related to domain motion). Finally, temperature rise of lead zirconate titanate stacks due to self-heating should be taken into account when designing actuator systems, since temperature changes were found to significantly influence both strain output and power required to drive piezoelectric stack actuators. Physical mechanisms of ferroelectric fatigue are explored.

Applicability of crack energy density to fracture strength evaluation of piezoelectric ceramics

A lot of studies have been made to grasp and describe fracture behavior of piezoelectric material under electromechanical loadings. However, even the criterion to describe the dependence of static fracture strength on electric field has not been established yet. In this paper, a fracture criterion based on mechanical contribution of crack energy density is proposed and its applicability is studied by analyzing not only the three-point bending fracture test results by the authors on piezoelectric ceramics called C-2 but also the compact tension fracture tests by Park and Sun on piezoelectric ceramics called PZT-4, based on the criterion.

Underlying memory-dominant nature of hysteresis in piezoelectric materials

Although the existence of nonlocal memories in hysteresis behavior of piezoelectric materials has been demonstrated, their detailed and thorough properties have yet to be revealed. Along this line, we disclose and demonstrate the underlying memory-dominant nature of hysteresis, and characterize its important properties that must be considered for the accurate prediction of hysteresis trajectory in piezoelectric materials. More specifically, the concept of recording the turning points, targeting the previously recorded turning points, curve alignment, and wiping-out effects at these points are introduced as the basic intellectual properties of hysteresis nonlinearity. A constitutive memory-based mathematical modeling framework is then developed and trained for the precise prediction of a hysteresis path for arbitrarily assigned input profiles. Utilizing a piezoelectric-driven actuator, it is experimentally demonstrated that if the number of memory units is sufficiently selected, model response in the prediction of a hysteresis track is significantly improved.

Thermal Effects of Cracked Piezoelectric Materials under Cycling Electric-Loading

It is still an open problem how the thermal effect influences the fracture behavior of piezoelectric materials especially under cycling electrical loading. Experimental observations have found that the fracture toughness of piezoelectric solids under electric loading may be greatly different from that under mechanical loading. A pronounced rise of temperature may be caused either by mechanical or by electric loading. In this paper, the thermal effects and energy dissipation mechanism in cracked piezoelectric materials under cyclic-electric-loading have been studied. The temperature rise is derived under the assumption of decoupling between thermal and electromechanical fields and the influences of frequency and the shape of electric wave on the temperature rise are quantitatively analyzed.