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.

Interaction Between a Semi-Infinite Crack and a Screw Dislocation in a Piezoelectric Material

1999 ◽  
Vol 67 (1) ◽  
pp. 165-170 ◽  
Author(s):  
Kang Yong Lee ◽  
Won Gyu Lee ◽  
Y. Eugene Pak
Keyword(s):  
Screw Dislocation ◽  
Piezoelectric Material ◽  
Electric Displacement ◽  
Crack Tip ◽  
Linear Elasticity Theory ◽  
The Core ◽  
Line Charge ◽  
Extension Force ◽  
Line Force ◽  
Field Intensity Factors

The interaction between a semi-infinite crack and a screw dislocation under antiplane mechanical and in-plane electrical loading in a linear piezoelectric material is studied in the framework of linear elasticity theory. A straight dislocation with the Burgers vector normal to the isotropic basal plane near a semi-infinite crack tip is considered. In addition to having a discontinuous electric potential across the slip plane, the dislocation is subjected to a line-force and a line-charge at the core. The explicit solution for the model is derived by means of complex variable and conformal mapping methods. The classical 1/r singularity is observed for the stress, electric displacement, and electric field at the crack tip. The force on a screw dislocation due to the existence of a semi-infinite crack subjected to external electromechanical loads is calculated. Also, the effect of the screw dislocation with the line-force and line-charge at the core on the crack-tip fields is observed through the field intensity factors and the crack extension force. [S0021-8936(00)01501-4]

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.

Mode III Interfacial Edge Crack in a Magnetoelectroelastic Bimaterial

2004 ◽  
Vol 261-263 ◽  
pp. 393-398 ◽  
Author(s):  
Ai Kah Soh ◽  
Jin Xi Liu
Keyword(s):  
Edge Crack ◽  
Electric Displacement ◽  
Mapping Technique ◽  
Mode Iii ◽  
Variable Approach ◽  
Out Of Plane ◽  
Line Force ◽  
Closed Form Analytical Solution ◽  
Line Singularities ◽  
Magnetoelectroelastic Bimaterial

This paper deals with a Mode III interfacial edge crack in a magnetoelectroelastic bimaterial subjected to line singularities such as an out-of-plane line force, a line electric charge, a line magnetic charge and a straight screw dislocation. The surfaces (including crack surfaces) of the bimateral are assumed to be electrically open and magnetically closed. The closed-form analytical solution to the problem is obtained by employing the complex variable approach in conjunction with the conformal mapping technique. The intensity factors of stress, electric displacement and magnetic induction are given explicitly. The obtained results can be used as the Green's function to solve more complicated problems.

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.

scholarly journals Nonuniformly Loaded Stack of Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
G. E. Tupholme
Keyword(s):  
Electric Displacement ◽  
Polar Angle ◽  
Antiplane Shear ◽  
Shear Cracks ◽  
Intensity Factors ◽  
One Dimensional ◽  
Isotropic Solid ◽  
Special Cases ◽  
Field Intensity Factors ◽  
Explicit Representations

Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

Wave Propagation in a Piezoelectric Coupled Solid Medium

2002 ◽  
Vol 69 (6) ◽  
pp. 819-824 ◽  
Author(s):  
Q. Wang
Keyword(s):  
Wave Propagation ◽  
Wave Velocity ◽  
Electric Potential ◽  
Solid Medium ◽  
Electric Displacement ◽  
Piezoelectric Medium ◽  
Wave Number ◽  
Mode Shapes ◽  
Coupled Structures ◽  
Shear Horizontal

Shear horizontal (SH) wave propagation in a semi-infinite solid medium surface bonded by a layer of piezoelectric material abutting the vacuum is investigated in this paper. The dispersive characteristics and the mode shapes of the deflection, the electric potential, and the electric displacements in the thickness direction of the piezoelectric layer are obtained theoretically. Numerical simulations show that the asymptotic phase velocities for different modes are the Bleustein surface wave velocity or the shear horizontal wave velocity of the pure piezoelectric medium. Besides, the mode shapes of the deflection, electric potential, and electric displacement show different distributions for different modes and different wave number. These results can be served as a benchmark for further analyses and are significant in the modeling of wave propagation in the piezoelectric coupled structures.

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.

Ripples in Graphene Sheets and Nanoribbons

2016 ◽  
Vol 100 ◽  
pp. 87-92
Author(s):  
Sanjay Prabhakar ◽  
Roderick Melnik
Keyword(s):  
Graphene Nanoribbons ◽  
Displacement Vector ◽  
Graphene Sheets ◽  
Spontaneous Generation ◽  
Intrinsic Properties ◽  
Band Engineering ◽  
Electromechanical Effects ◽  
Out Of Plane ◽  
Plane Displacement ◽  
Graphene Structures

We study the influence of ripple waves on graphene sheets and graphene nanoribbons. Such waves are originating from the electromechanical effects, among other possible mechanisms. By considering variations in the in-plane and out-of-plane displacement vector, we show that the spontaneous generation of ripple waves has no preferred orientation. Intrinsic properties of ripple waves induce a large pseudopotential that in its turn is to induce large pseudomagentic fields that can be implemented into the band engineering of graphene structures.

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