A Piezoelectric Screw Dislocation Interacting with a Dielectric Crack in a Hexagonal Piezoelectric Material

2005 ◽  
Vol 9 ◽  
pp. 183-190
Author(s):  
Jin Xi Liu ◽  
X.L. Liu
Keyword(s):  
Electric Field ◽  
Screw Dislocation ◽  
Electric Displacement ◽  
Image Force ◽  
Mapping Method ◽  
Piezoelectric Medium ◽  
Intensity Factors ◽  
Potential Jump ◽  
Piezoelectric Screw Dislocation ◽  
Dielectric Crack

This paper is concerned with the interaction of a piezoelectric screw dislocation with a semi-infinite dielectric crack in a piezoelectric medium with hexagonal symmetry. The solution of the considered problem is obtained from the dislocation solution of a piezoelectric half-plane adjoining a gas medium of dielectric constant ε0 by using the conformal mapping method. The intensity factors of stress, electric displacement and electric field and the image force on the dislocation are given explicitly. The effect of electric boundary conditions on the dislocation-crack interaction is analyzed and discussed in detail. The results show that ε0 only influences the electric displacement and electric field intensity factors and the image force produced by the electric potential jump.

scholarly journals Interaction of a Screw Dislocation with Interface and Wedge-Shaped Cracks in One-Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Lian he Li ◽  
Yue Zhao
Keyword(s):  
Screw Dislocation ◽  
Electric Fields ◽  
Electric Displacement ◽  
Image Force ◽  
Coupling Constants ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

Interaction of a screw dislocation with wedge-shaped cracks in one-dimensional hexagonal piezoelectric quasicrystals bimaterial is considered. The general solutions of the elastic and electric fields are derived by complex variable method. Then the analytical expressions for the phonon stresses, phason stresses, and electric displacements are given. The stresses and electric displacement intensity factors of the cracks are also calculated, as well as the force on dislocation. The effects of the coupling constants, the geometrical parameters of cracks, and the dislocation location on stresses intensity factors and image force are shown graphically. The distribution characteristics with regard to the phonon stresses, phason stresses, and electric displacements are discussed in detail. The solutions of several special cases are obtained as the results of the present conclusion.

A Magnetoelectric Screw Dislocation Interacting with an Elliptical Inhomogeneity Containing a Confocal Rigid Line

2011 ◽  
Vol 239-242 ◽  
pp. 2195-2200 ◽  
Author(s):  
Chun Zhi Jiang ◽  
You Wen Liu ◽  
Chao Xie
Keyword(s):  
Screw Dislocation ◽  
Electric Displacement ◽  
Image Force ◽  
Material Behavior ◽  
Shear Stresses ◽  
Displacement Fields ◽  
Plane Shear ◽  
Elliptical Inhomogeneity ◽  
Rigid Line ◽  
The Matrix

Based on the complex variable method, the magnetoelectroelastic interaction of a generalized screw dislocation with an elliptical inhomogeneity containing a electrically conductive confocal rigid line under remote anti-plane shear stresses, in-plane electric and magnetic loads is dealt with. The generalized screw dislocation is located inside either the inhomogeneity or the matrix. The analytical-functions of complex potentials for stresses, electric displacement fields and magnetic induction fields in both the inhomogeneity and the matrix are derived. The image force acting on the dislocation are also calculated explicitly. The results show that the influence of the rigid line on the interaction effect between a generalized screw dislocation and an elliptical inhomogeneity is significant. In addition, the material behavior also plays an important role on the image force.

Interaction of a Screw Dislocation with an Interfacial Crack in Two Dissimilar Piezoelectric Layers

2004 ◽  
Vol 261-263 ◽  
pp. 141-146
Author(s):  
Jin Xi Liu ◽  
Ai Ping Liu ◽  
Z.Q. Jiang ◽  
Ai Kah Soh
Keyword(s):  
Conformal Mapping ◽  
Screw Dislocation ◽  
Complex Variable ◽  
Piezoelectric Effect ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Mapping Technique ◽  
Intensity Factors ◽  
Piezoelectric Layers ◽  
Crack Tip Shielding

A screw dislocation interacting with a semi-infinite interfacial crack in two dissimilar piezoelectric layers is studied. The complex variable method and the conformal mapping technique are employed to obtain the solution of the problem. The stress and electric displacement intensity factors are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electro-elastic material constants. Numerical example shows that the influence of piezoelectric effect on the crack tip shielding is significant.

Magnetoelectroelastic Interaction between a Generalized Screw Dislocation and Multiple Circular Inclusions

2010 ◽  
Vol 26 (3) ◽  
pp. 309-316
Author(s):  
M. H. Shen ◽  
F.M. Chen ◽  
S. Y. Hung ◽  
S.N. Chen
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Screw Dislocation ◽  
Analytical Solutions ◽  
Displacement Field ◽  
Complex Variable ◽  
Crack Problem ◽  
Image Force ◽  
Variable Method ◽  
The Matrix

AbstractIn this paper, the interaction of a generalized screw dislocation with multiple circular inclusions perfectly bonded to an unbounded matrix under remote magnetoelectromechanical loadings is dealt with. The analytical solutions of electric field, magnetic field and displacement field either in the inclusions or the matrix are obtained by use of the complex variable method. The image force acting on the magnetoelectric screw dislocation is calculated by using the generalized Peach-Koehler formula. Finally, the influence of material combinations on the image force is examined for several practical examples. The obtained solutions can be used as Green's functions for the analysis of the corresponding magnetoelectric crack problem.

Electromechanical Effects of a Screw Dislocation Around a Finite Crack in a Piezoelectric Material

2001 ◽  
Vol 69 (1) ◽  
pp. 55-62 ◽  
Author(s):  
J. H. Kwon ◽  
K. Y. Lee
Keyword(s):  
Screw Dislocation ◽  
Electric Displacement ◽  
Piezoelectric Medium ◽  
Electromechanical Effects ◽  
Out Of Plane ◽  
Finite Crack ◽  
Line Force ◽  
Field Intensity Factors ◽  
Electrical Loads ◽  
As Stress

The interaction between a screw dislocation and a finite crack in an unbounded piezoelectric medium is studied in the framework of linear piezoelectric theory. A straight screw dislocation with the Burgers vector, which is normal to the isotropic basal plane, positioned around the tip of a finite crack is considered. In addition to having a discontinuous electric potential across the slip plane, the dislocation is assumed to be subjected to a line force and a line charge at the core. The explicit solution is derived by means of complex variable and conformal mapping methods. All field variables such as stress, strain, electric field, electric displacement near the crack tip, and the forces on a screw dislocation, the field intensity factors, and the energy release rate are determined under the combined out-of-plane mechanical and in-plane electrical loads. Also, the effects of screw dislocation and electrical loads are numerically analyzed.

Dynamic Anti-Plane Characteristic of an Infinite Piezoelectric Medium With a Non-Circular Cavity

2005 ◽  
Author(s):  
Tianshu Song ◽  
Lili Sun ◽  
Diankui Liu
Keyword(s):  
Electric Field ◽  
Dynamic Stress ◽  
Mapping Method ◽  
Piezoelectric Medium ◽  
Circular Cavity ◽  
Characteristic Parameters ◽  
Stress Concentrations ◽  
Plane Shear ◽  
Concentration Factors ◽  
Piezoelectric Characteristic

In this paper, dynamic stress concentrations are studied in an infinite piezoelectric medium with a non-circular cavity under time harmonic incident anti-plane shear wave and inplane electric field. Based on complex variable and conformal mapping method, the dynamic stress concentration factors and the electric field concentration factors at the boundary of the non-circular cavity are obtained by applying the orthogonal function expansion technique. Numerical examples about an infinite piezoelectric medium with an elliptic cavity are provided with different elliptic axial length ratios, different wave numbers and different piezoelectric characteristic parameters. The calculating results show that dynamic analyses are very important to an infinite piezoelectric medium with a non-circular cavity at lower frequencies and larger piezoelectric characteristic parameters.

Size Effect of a Crack in a Micropolar Piezoelectric Medium

2009 ◽  
Vol 417-418 ◽  
pp. 525-528
Author(s):  
Gan Yun Huang ◽  
Shou Wen Yu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Constitutive Relations ◽  
Electric Displacement ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Piezoelectric Medium ◽  
Intensity Factors

A crack problem in a micropolar piezoelectric solid is considered. By using simplified constitutive relations, the problem can be reduced to the solution of a set of Cauchy singular integral equations with the help of Fourier integral transform technique. Numerical results for stress intensity factors, couple stress intensity factors and electric displacement intensity factors show that micropolar theory can be expected to explain certain size effects in piezoelectric solids.

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.

Force on a Piezoelectric Screw Dislocation

1990 ◽  
Vol 57 (4) ◽  
pp. 863-869 ◽  
Author(s):  
Y. E. Pak
Keyword(s):  
Screw Dislocation ◽  
Image Force ◽  
Linear Elasticity Theory ◽  
Line Force ◽  
Internal Stress Field ◽  
Piezoelectric Screw Dislocation ◽  
Electrical Loads ◽  
Discontinuous Displacement ◽  
Piezoelectric Behavior ◽  
Independent Integral

A screw dislocation in a hexagonal crystal exhibiting piezoelectric behavior is analyzed in the framework of linear elasticity theory. Considered is a straight dislocation with the Burgers vector normal to the isotropic basal plane. In addition to having a discontinuous displacement and a discontinuous electric potential across the slip plane, the dislocation is subjected to a line force and a line charge at the core. The solution is obtained in a closed form by means of a semi-inverse method. The electric enthalpy which takes the place of the internal energy is calculated for the screw dislocation considered in the analysis. The interaction energy for two different internal stress-field systems is derived to calculate the force acting on an electroelastic singularity. Both the standard method and a generalized path-independent integral is used to calculate the force on a piezoelectric screw dislocation subjected to external mechanical and electrical loads. Also calculated are the force between two parallel screw dislocations and the image force due to a free surface.

Sign in / Sign up

Export Citation Format

Share Document