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 between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

2019 ◽  
Vol 24 (10) ◽  
pp. 3080-3091
Author(s):  
Xianghua Peng ◽  
Min Yu ◽  
Yuxuan Yang
Keyword(s):  
Composite Materials ◽  
Screw Dislocation ◽  
Coupling Effect ◽  
Elliptic Hole ◽  
Great Influence ◽  
Image Force ◽  
Plane Shear ◽  
Blunt Crack ◽  
The Matrix ◽  
In Series

The paper deals with the interaction of a generalized screw dislocation and an elliptic inhomogeneity containing a confocal elliptic hole in a magneto-electro-elastic composite material. Exact solutions are derived for the case where the generalized screw dislocation is located in the matrix under a remote anti-plane shear stress field, an in-plane electric field, and a magnetic field. Based on the complex variable method, the complex potentials of both the matrix and the inhomogeneity are obtained in series, and analytic expressions for the generalized stress and strain field, the image force, the generalized stress intensity factor of the blunt crack tip, and the energy release rate are derived explicitly. The presented solutions include some previous solutions, such as pure elastic, piezoelectric, piezomagnetic, and circular inclusions. Typical numerical examples are presented and the influences of the dislocation position, the volume of inhomogeneity, and the elliptic hole on these physical quantities are discussed. The results show that the magneto-electro-elastic coupling effect has a great influence on the image force and the equilibrium position of dislocation, especially when the dislocation approaches the interface; the coupling effect makes the image force on the screw dislocation follow different variation laws in piezoelectric–piezomagnetic composite materials compared with elastic materials.

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.

Uniform stress state inside a non-elliptical inhomogeneity near an irregularly shaped hole in antiplane shear

2019 ◽  
Vol 25 (2) ◽  
pp. 362-373 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Antiplane Shear ◽  
Shear Stresses ◽  
Uniform Stress ◽  
Elliptical Inhomogeneity ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Shaped Hole ◽  
Mapping Techniques ◽  
Hole Boundary ◽  
High Level

Analytic continuation and conformal mapping techniques are applied to establish that the state of stress inside a non-elliptical elastic inhomogeneity can remain uniform despite the presence of a nearby irregularly shaped hole when the surrounding matrix is subjected to uniform remote antiplane shear stresses. The hole boundary is assumed to be either traction-free or subjected to antiplane line forces. Detailed numerical results are presented to demonstrate the resulting analytical solutions. Our results indicate that in maintaining a uniform stress distribution inside the inhomogeneity, it is permissible for the stresses in the matrix to exhibit either a square root singularity at sharp corners of a hole boundary or a high level of stress concentration at rounded corners of a hole.

A Screw Dislocation Interacting with a Lip-Shaped Crack Bonded by a Strained Reinforcement Layer under Remote Longitudinal Shear Load

2012 ◽  
Vol 490-495 ◽  
pp. 56-60
Author(s):  
Min Yu ◽  
You Wen Liu
Keyword(s):  
Screw Dislocation ◽  
Complex Function ◽  
Image Force ◽  
Longitudinal Shear ◽  
Singularity Analysis ◽  
Infinite Matrix ◽  
Shear Load ◽  
Riemann Boundary ◽  
The Matrix ◽  
Shaped Crack

The interaction between a screw dislocation and a reinforced lip-shaped crack embedded in an infinite matrix subjected to a remote longitudinal shear load is investigated in this paper. By combining the sectionally holomorphic function theory, Cauchy singular integral, singularity analysis of complex functions and Riemann boundary problem, the problem is reduced to solve an elementary complex potentials equation. The general expressions of complex function in the matrix and the reinforcement layer are derived explicitly in series form for the case when the screw dislocation is located in the matrix. The image force acting on the screw dislocation and the stress intensity factor are also calculated. Some numerical results are provided to discuss the effects of dislocation position, material parameters, geometric configurations and eigenstrain on the image force.

On a Screw Dislocation Interacting With Two Viscous Interfaces

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
X. Wang ◽  
E. Pan
Keyword(s):  
Screw Dislocation ◽  
Equilibrium Position ◽  
Time Moment ◽  
Early Time ◽  
Image Force ◽  
Interface Layer ◽  
Critical Value ◽  
Time Dependent ◽  
Interphase Layer ◽  
The Matrix

We investigate a screw dislocation interacting with two concentric circular linear viscous interfaces. The inner viscous interface is formed by the circular inhomogeneity and the interphase layer, and the outer viscous interface by the interphase layer and the unbounded matrix. The time-dependent stresses in the inhomogeneity, interphase layer, and unbounded matrix induced by the screw dislocation located within the interphase layer are derived. Also obtained is the time-dependent image force on the screw dislocation due to its interaction with the two viscous interfaces. It is found that when the interphase layer is more compliant than both the inhomogeneity and the matrix, three transient equilibrium positions (two are unstable and one is stable) for the dislocation can coexist at a certain early time moment. If the inhomogeneity and matrix possess the same shear modulus, and the characteristic times for the two viscous interfaces are also the same, a fixed equilibrium position always exists for the dislocation. In addition, when the interphase layer is stiffer than the inhomogeneity and matrix, the fixed equilibrium position is always an unstable one; on the other hand, when the interface layer is more compliant than the inhomogeneity and matrix, the nature of the fixed equilibrium position depends on the time: the fixed equilibrium position is a stable one if the time is below a critical value, and it is an unstable one if the time is above the critical value. In addition, a saddle point transient equilibrium position for the dislocation can also be observed under certain conditions.

scholarly journals The interaction between a screw dislocation and a rigid line in a confocal elliptical inhomogeneity

2011 ◽  
Vol 35 (3) ◽  
pp. 985-995 ◽  
Author(s):  
Q.H. Fang ◽  
J.M. Chen ◽  
Z.D. Luo ◽  
H.P. Song ◽  
Y.W. Liu
Keyword(s):  
Screw Dislocation ◽  
Elliptical Inhomogeneity ◽  
Rigid Line

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.

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