Electro-elastic Fields of Piezoelectric Materials with An Elliptic Hole under Uniform Internal Shearing Forces

The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields inside and outside the elliptic hole are considered.

Compensation of stress intensity factors in hollow cylinders containing several cracks under torsion by electro-elastic coating

In this article, a formulation for a hollow cylinder reinforced with an electroelastic layer is investigated. The hollow cylinder and its electro-elastic coating are under the Saint-Venant torsional loading. First, the solution to the problem containing a Volterra-type screw dislocation is obtained by using the Fourier transform. The problem is then reduced to a set of Cauchy singular integral equations by the distributed dislocation method. Finally, several examples are presented to show the effect of the electro-elastic coating on the reduction of the stress intensity factors at the crack tips.

THE ELECTRO-ELASTIC FIELD OF THE INFINITE PIEZOELECTRIC MEDIUM WITH TWO PIEZOELECTRIC CIRCULAR CYLINDRICAL INCLUSIONS

The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields.The analytical solution is obtained.The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation.From the results obtained,it can be found that the electro-elastic field depends on the material constants of individual phases,the geometric parameters of the system and the applied antiplane shear stresses and electric fields at infinity.In addition,the specific cases when two circular cylindrical inclusions are tangent to each other and they are holes and/or rigid ones,are also studied in this paper.

Exact Solutions for Piezoelectric Materials with an Elliptic Hole or a Crack under Uniform Internal Pressure

The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.

Analysis and Numerical Approximation of an Electro-Elastic Frictional Contact Problem

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.

Electro-elastic features of YBa3(PO_(4))3 and YbBa3(PO_(4))3 crystals with pure face-shear mode for acoustic wave sensor applications

The fundamental shear horizontal(SH0)waves have been proved to be a very useful method for nondestructive testing due to their non-dispersive characteristics.Currently,although several methods have been proposed to generate SH0 waves,it is still a challenge to obtain pure SH0 wave mode efficiently.Herein,in this study,non-centrosymmetric YBa3(PO_(4))3(YBP)and YbBa3(PO_(4))3(YbBP)crystals with pure face-shear mode were grown via the traditional Czochralski pulling method at temperatures above 1800℃.High resolution X-ray diffraction was carried out to evaluate the crystalline quality.Results showed that the YBP and YbBP crystals were of good quality,with the full width at half-maxima being on the order of 42.500 and 52.300,respectively.Moreover,the full set of electro-elastic constants for the YBP and YbBP crystals were determined and collated using a combination of impedance and pulse-echo methods.The piezoelectric coefficient(d14)of the YBP and YbBP crystals were determined to be 10.6 pC/N and 11.4 pC/N,respectively,corresponding to the electromechanical coupling coefficient(k14)equal to 15.4%and 15.9%,exhibiting large and pure face-shear vibration mode.Collectively,these results indicate that the YBP and YbBP crystals are promising for acoustic wave sensing application.

Measurement of all electro-elastic constants of lithium tetraborate(Li_2B_4O_7)crystal

A new approach to determine all the electro-elastic constants of the piezoelectric crystals in class 4mm has been put forward. As an example, all the constants of Lithium Tetraborate (Li2B4O7) crystal have been measured by means of the approach.The outstanding advantage of the approach is that it only needs to employ in measurement three crystal plates differently oriented.

Temperature dependent behaviors of electro-elastic properties of NdCa_(4)O(BO_(3))_(3)crystal with monoclinic symmetry

Rare-earth calcium oxyborate crystals(RECa_(4)O(BO_(3))_(3),RECOB,RE:rare-earth elements)are a kind of multifunctional crystal materials.In this work,the temperature dependent behaviors of the electroelastic constants of NdCOB crystal were investigated over the temperature range of-80-200℃,and their temperature coefficients were evaluated.It is found that NdCOB crystal possesses minimal variation of relative dielectric permittivities(<3%).The temperature coefficient of frequency for ZY cut with width shear vibration mode is in the order of 0.07×10^(-4)/℃.The temperature coefficients of the elastic compliances are obtained to be in the range of-33.0×10^(-4)/℃-32.2×10^(-4)/℃.Particularly,the sand swere found to show low temperature coefficients of the elastic compliances,i.e.1.0×10^(-4)/℃and-0.4×10^(-4)/℃,respectively,indicating the existence of zero temperature coefficient of frequency crystal cut.Furthermore,the electromechanical coupling factors and piezoelectric coefficients as a function of temperature were studied.The electromechanical coupling factor kand piezoelectric coefficient dare determined to be~30.8%and~15.2 pC/N at room temperature,respectively.The large piezoelectric response and zero temperature coefficient of frequency indicate the potential usage of NdCOB crystal for piezoelectric frequency devices over a wide temperature range.

Higher-order electroelastic modelling of piezoelectric cylindrical nanoshell on elastic matrix

This paper develops electro-elastic relations of functionally graded cylindrical nanoshell integrated with intelligent layers subjected to multi-physics loads resting on elastic foundation.The piezoelectric layers are actuated with external applied voltage.The nanocore is assumed in-homogeneous in which the material properties are changed continuously and gradually along radial direction.Third-order shear deformation theory is used for the description of kinematic relations and electric potential distribution is assumed as combination of a linear function along thickness direction to show applied voltage and a longitudinal distribution.Electro-elastic size-dependent constitutive relations are developed based on nonlocal elasticity theory and generalized Hooke’s law.The principle of virtual work is used to derive governing equations in terms of four functions along the axial and the radial directions and longitudinal electric potential function.The numerical results including radial and longitudinal displacements are presented in terms of basic input parameters of the integrated cylindrical nanoshell such as initial electric potential,small scale parameter,length to radius ratio and two parameters of foundation.It is concluded that both displacements are increased with an increase in small-scale parameter and a decrease in applied electric potential.

新型压电晶体Ga_(0.12)Al_(0.88)PO_4电弹常数的测量

采用两类切型的晶片,利用动态法对用缓慢升温法生长的新型非铁电性二元系压电晶体Ga_(0.12)Al_(0.88)PO_4电弹常数进行了测量。