ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity. The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure. The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage,which is related to the piezoelectric properties.     

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer (PMUT) actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezoelectric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deformation, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.     

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.     

Piezoelectric generator based on torsional modes for power harvesting from angular vibrations

Torsional vibration of a circular piezoelectric shell of polarized ceramics mounted on a rotationally vibrating base is analyzed. The shell is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy from angular vibrations to electrical energy. Analytical expressions and numerical results for the output voltage, current, power, efficiency and power density are given.     

DAMAGE DETECTION STRATEGY FOR RETICULATED STRUCTURES BASED ON INCOMPLETE STRAIN MODE

Damage detection based on strain responses of vibration is highly attractive for monitoring long-span reticulated structures.However,there are a lot of structure members in reticulated structures and it is impossible to install strain sensors in each member.Therefore,how to locate and quantify damages with the incomplete mode shapes obtained from few strain sensors is a challenge topic.A new strategy,named incomplete strain mode damage detection(ISMDD) strategy,is proposed in this paper.In the strategy,the distribution of the strain sensors in the reticulated structures can be optimized through sensitive analysis on strain mode perturbation matrix,which can be obtained by perturbation theory.Mode assurance criterion(MAC) value is applied in damage location,and the members with relative large MAC values are defined as damage members.In addition,damage index obtained by solving the perturbation equation is used for damage quantification.Numerical analysis on a long-span reticulated structure,including damage location and quantification for single-and multi-member damages,detection for different damage quantity,the effect analysis of sensor quantity,are performed to verify the effectiveness of the proposed ISMDD strategy.It can be shown from the analysis that the ISMDD strategy is effective in damage location and quantification for both single-and multi-member damages.And the quantity of strain sensors has effect on damage location,but has no obvious influence on damage quantification.Additionally,the anti-noise pollution ability analysis of the ISMDD strategy is carried out,which shows that the ISMDD strategy has excellent anti-noise pollution ability for both single-and multi-damaged members.     

TRANSIENT RESPONSE OF COPLANAR INTERFACIAL CRACKS BETWEEN TWO DISSIMILAR PIEZOELECTRIC STRIPS UNDER ANTI-PLANE MECHANICAL AND IN-PLANE ELECTRICAL IMPACTS

The dynamic response of multiple coplanar interface cracks between two dissimilar piezoelectric strips subjected to mechanical and electrical impacts is investigated. Solutions to two kinds of electric boundary conditions on crack surfaces, i.e. electric impermeable and electric permeable, are obtained. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations,which can be solved numerically. The effects of electrical load, geometry criterion of piezoelectric strips, relative location of cracks and material properties on the dynamic energy release rate are examined.     

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI－PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation. The crack face is partly conductive and partly impermeable. The results show that the stress intensity factor is identical with the mode III stress intensity factor independent of the conducting length. But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.     

RESPONSE ANALYSIS OF PIEZOELECTRIC SHELLS IN PLANE STRAIN UNDER RANDOM EXCITATIONS

The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.     

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique,the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface.Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable.The results can be reduced to the well-known solutio...     

New discrete element models for elastoplastic problems

The discrete element method （DEM） has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the interelement parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method （FEM） and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.     

Damage analysis and fracture criteria for piezoelectric ceramics

Both the mechanical and the electrical damages are introduced to study fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are proposed by using the damage theory combined with the well-known piezoelectric fracture experiments of Park and Sun [Fracture criteria of piezoelectric ceramics, J. Am. Ceram. Soc. 78 (1995) 1475-1480]. One is based on a critical state of the mechanical damage and the other on a critical value of a proper linear combination of both the mechanical and the electrical damage variables. It is found that the fracture load predicted, which takes the mechanical damage into account only (mode 1), has greater deviation than predicted result by considering a proper linear combination of the mechanical and the electrical damages (mode 2). And the fracture criterion corresponding to mode 2 presented is shown to be superior to mode 1. It is also demonstrated that the mechanical damage has greater effect on fracture than the electrical damage.     

Analysis of the Dynamic Stability of Electrical Graded Piezoelectric Circular Cylindrical Shells

I. INTRODUCTION In recent years, piezoelectric materials have been widely used as sensors and actuators in the areaof smart structures, and shell-type piezoelectric smart structures have become the focus of research.Various analytical and ?nite element models for piezoelectric shells have been developed[1??3]. Inaddition, a series of exact studies on the bending and buckling of piezoelectric circular cylindrical shellhave been presented by Chen et al.[4??7]. Recently, the use of functi…     

Fracture behaviors of piezoelectric materials

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.     

Effects of static electric field on the fracture behavior of piezoelectric ceramics

The paper gives an overview on experimental observations of the failure behavior of electrically insulating and conducting cracks in piezoelectric ceramics. The experiments include the indentation fracture test, the bending test on smooth samples, and the fracture test on pre-notched (or pre-cracked) compact tension samples. For electrically insulating cracks, the experimental results show a complicated fracture behavior under electrical and mechanical loading. Fracture data are much scattered when a static electric field is applied. A statistically based fracture criterion is required. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate ceramics and that the concepts of fracture mechanics can be used to measure the electrical fracture toughness. Furthermore, the electrical fracture toughness is much higher than the mechanical fracture toughness. The highly electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under purely electric loading, which is impossible under mechanical loading in the brittle ceramics. The project supported by an RGC grant from the Research Grant Council of the Hong Kong Special Administrative Region, China     

Stress Analysis And Geometrical Configuration Selection for Multilayer Piezoelectric Displacement Actuator

Multilayer piezoelectric ceramic displacement actuators are susceptible to cracking in the region near the edge of the internal electrode, which may cause system damage or failure. In this paper, the stress distribution of a multilayer piezoelectric composite is investigated in a working environment and the optimized geometrical con?guration of the piezoelectric layer is obtained. The stress distribution in the structure and the stress concentration near the edge of th…     

压电介质损伤、断裂力学研究的现状

压电介质的损伤与断裂力学是现代固体力学的重要课题．本文简要地综述了压电介质损伤与断裂力学研究的现状,集中讨论了：（１）裂纹面电边界条件的不同模型及其求解的结果;（２）宏观连续力学与细观力学用于压电介质的损伤与断裂的静力学分析;（３）压电介质动态断裂分析的某些新结果．文末,指出了今后在压电介质损伤与断裂研究的某些有吸引力的研究方向     

Theoretical model of piezoelectric fibre pull-out

A theoretical model of a single piezoelectric fibre pull-out is developed to study the interaction between fibre deformation, pull-out stress and corresponding electrical field. Computer simulation of the stress–displacement curve of the fibre pull-out process is presented. Numerical examples show that the piezoelectric fibre pull-out behaviour can be both described and affected by its electrical field. Therefore, the interactions between the mechanical and electric fields of the fibre/matrix system can be employed to monitor and control the fracture behaviour of active fibre composites.     

Fracture prediction for piezoelectric ceramics based on the electric field saturation concept

The electrical field saturation model is applied to the fracture prediction of piezoelectric materials containing electrically impermeable cracks. This model is analogously similar to the electric displacement saturation model that available in the literature. An electrical field saturation strip near the crack front is introduced in the analytical model. The stress intensity factor K and the energy release rate G are obtained in closed-form. It is found that fracture predictions based on K and G criteria are identical. Fracture predictions based on the electric field saturation model and the electric displacement model are also found to be the same.     

压电薄板切口尖端前沿力电损伤场分析

基于Yang等建立的三维各向异性压电损伤本构模型,给出了广义平面应力压电损伤问题的本构方程和有限元平衡方程,运用有限元方法分析了张开角和深度对切口前沿力电损伤分布的影响规律。结果表明,张开角对力损伤的影响较小,并且几乎不改变力电损伤的区域尺寸,但是深度对力电损伤的大小和区域尺寸都有很大的影响。     

Crack energy density of a piezoelectric material under general electromechanical loading

Crack energy density is considered and used as a possible fracture parameter in piezoelectricity under arbitrary electromechanical remote loads. The closed-form solution of a crack in a piezoelectric infinite plate subjected to general static electromechanical loading is obtained through a method alternative to the more common Stroh’s formalism. This analytical method, which is based on the spectral theorem of linear algebra, involves a transformation of similarity induced by the fundamental matrix in order to express the equations governing the problem in terms of complex potentials. The application of the mechanical boundary condition of stress-free crack and of one of the three considered electric boundary conditions (impermeable, permeable or semipermeable) leads then to the formulation of a Hilbert problem whose solution yields the stress and displacement fields. The crack energy density factors for mixed mode are then calculated under different mechanical and electrical loadings, as well as under different electric boundary conditions. The non-singular terms of the stress expressions are retained as well. The definition of the minimum energy density fracture criterion, as proposed by Sih, is given, and the influence of load biaxiality and positive or negative applied electric field on the criterion results is analyzed. The prediction of the incipient branching angle as from the energy density approach is also compared to that arising from the maximum circumferential stress theory for a mixed mode loading condition. Numerical results and graphs are presented and discussed for a PZT-4 piezoelectric ceramic.