Three-Dimensional Electroelastic Analysis of a Piezoelectric Material With a Penny-Shaped Dielectric Crack

2004 ◽  
Vol 71 (6) ◽  
pp. 866-878 ◽  
Author(s):  
Xian-Fang Li ◽  
Kang Yong Lee
Keyword(s):  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Field Intensity ◽  
Three Dimensional ◽  
Intensity Factors ◽  
Elementary Functions ◽  
Dual Integral Equations ◽  
Electroelastic Field ◽  
Field Intensity Factors ◽  
Dielectric Crack

Previous studies assumed that a crack is either impermeable or permeable, which are actually two limiting cases of a dielectric crack. This paper considers the electroelastic problem of a three-dimensional transversely isotropic piezoelectric material with a penny-shaped dielectric crack perpendicular to the poling axis. Using electric boundary conditions controlled by the boundaries of an opening crack, the electric displacements at the crack surfaces are determined. The Hankel transform technique is employed to reduce the considered problem to dual integral equations. By solving resulting equations, the results are presented for the case of remote uniform loading, and explicit expressions for the electroelastic field at any point in the entire piezoelectric body are given in terms of elementary functions. Moreover, the distribution of asymptotic field around the crack front and field intensity factors are determined. Numerical results for a cracked PZT-5H ceramic are evaluated to examine the influence of the dielectric permittivity of the crack interior on the field intensity factors, indicating that the electric boundary conditions at the crack surfaces play an important role in determining electroelastic field induced by a crack, and that the results are overestimated for an impermeable crack, and underestimated for a permeable crack.

scholarly journals Analysis of Mode I Conducting Crack in Piezo-Electro-Magneto-Elastic Layer

2013 ◽  
Vol 18 (1) ◽  
pp. 153-176
Author(s):  
B. Rogowski
Keyword(s):  
Boundary Conditions ◽  
Electric Displacement ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Intensity Factors ◽  
Permeable Crack ◽  
Crack Face ◽  
Field Intensity Factors ◽  
Dielectric Crack ◽  
Thickness Field

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

scholarly journals Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals

2021 ◽  
Vol 42 (5) ◽  
pp. 625-640
Author(s):  
Zhina Zhao ◽  
Junhong Guo
Keyword(s):  
Surface Layer ◽  
Boundary Conditions ◽  
Field Intensity ◽  
Surface Effect ◽  
Crack Tip ◽  
Elliptical Hole ◽  
Engineering Practice ◽  
Intensity Factors ◽  
One Dimensional ◽  
Field Intensity Factors

AbstractTo effectively reduce the field concentration around a hole or crack, an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) is investigated subject to remotely mechanical and electrical loadings. The surface effect and dielectric characteristics inside the hole are considered for actuality. By utilizing the technique of conformal mapping and the complex variable method, the phonon stresses, phason stresses, and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions. Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack. Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer, the aspect ratio of the hole, and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip. The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack, which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

2017 ◽  
Vol 29 (6) ◽  
pp. 1255-1271 ◽  
Author(s):  
MingHao Zhao ◽  
Yuan Li ◽  
CuiYing Fan
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Green Functions ◽  
Intensity Factors

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

scholarly journals Exact Solutions for Interaction of Parallel Screw Dislocations with a Wedge Crack in One-Dimensional Hexagonal Quasicrystal with Piezoelectric Effects

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xin Lv ◽  
Guan-Ting Liu
Keyword(s):  
Crack Propagation ◽  
Field Line ◽  
Field Intensity ◽  
Wedge Angle ◽  
Image Force ◽  
Intensity Factors ◽  
One Dimensional ◽  
Line Force ◽  
Shaped Crack ◽  
Field Intensity Factors

The purpose of this paper is to consider the interaction between many parallel dislocations and a wedge-shaped crack and their collective response to the external applied generalized stress in one-dimensional hexagonal piezoelectric quasicrystal, employing the complex variable function theory and the conformal transformation method; the problem for the crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann–Hilbert boundary value problems. The analytical solutions of the generalized stress field are obtained. The dislocations are subjected to the phonon field line force, phason field line force, and line charge at the core. The positions of the dislocations are arbitrary, but the dislocation distribution is additive. The dislocation is not only subjected to the external stress and the internal stress generated by the crack, but also to the force exerted on it by other dislocations. The closed-form solutions are obtained for field intensity factors and the image force on a screw dislocation in the presence of a wedge-shaped crack and a collection of other dislocations. Numerical examples are provided to show the effects of wedge angle, dislocation position, dislocation distribution containing symmetric configurations and dislocation quantities on the field intensity factors, energy release rate, and image force acting on the dislocation. The principal new physical results obtained here are (1) the phonon stress, phason stress, and electric displacement singularity occur at the crack tip and dislocations cores, (2) the increasing number of dislocations always accelerates the crack propagation, (3) the effect of wedge angle on crack propagation is related to the distribution of dislocations, and (4) the results of the image force on the dislocation indicate that the dislocations can either be attracted or rejected and reach stable positions eventually.

Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane

2017 ◽  
Vol 28 (19) ◽  
pp. 2823-2834 ◽  
Author(s):  
Mojtaba Ayatollahi ◽  
Mojtaba Mahmoudi Monfared ◽  
Mahsa Nourazar
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Field Intensity ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Mode Iii ◽  
Singular Stress ◽  
Field Intensity Factors

This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velocity has great effect on the field intensity factors.

scholarly journals Effect of Couple Stresses on the Stress Intensity Factors for Two Parallel Cracks in an Infinite Elastic Medium under Tension

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shouetsu Itou
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Stress Intensity Factors ◽  
Couple Stress Theory ◽  
Intensity Factors ◽  
Dual Integral Equations ◽  
Couple Stresses ◽  
Parallel Cracks ◽  
Two Parallel Cracks

Stresses around two parallel cracks of equal length in an infinite elastic medium are evaluated based on the linearized couple-stress theory under uniform tension normal to the cracks. Fourier transformations are used to reduce the boundary conditions with respect to the upper crack to dual integral equations. In order to solve these equations, the differences in the displacements and in the rotation at the upper crack are expanded through a series of functions that are zero valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors can be determined using the characteristics of the integrands for an infinite value of the variable of integration. Numerical calculations are carried out for selected crack configurations, and the effect of the couple stresses on the stress intensity factors is revealed.

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