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.

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.

Interaction between a screw dislocation and a bridged crack with surface elasticity

2016 ◽  
Vol 22 (12) ◽  
pp. 2217-2239 ◽  
Author(s):  
Moxuan Yang ◽  
Xu Wang
Keyword(s):  
Screw Dislocation ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Surface Elasticity ◽  
Image Force ◽  
Opening Displacement ◽  
Crack Bridging ◽  
Line Force ◽  
Crack Tips ◽  
Crack Faces

We examine the contribution of crack bridging and surface elasticity to the elastic interaction between a mode III finite crack and a screw dislocation. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The crack faces are subjected to a bridging force which is assumed to be proportional to the crack opening displacement, whereas the bridging stiffness is allowed to vary arbitrarily along the crack. By considering a continuous distribution of both screw dislocations and line forces on the crack, the boundary value problem is reduced to two decoupled first-order Cauchy singular integro-differential equations. After the expansion of the unknown line dislocation and line force densities and the known variable bridging stiffness into Chebyshev polynomials, these singular integro-differential equations are solved numerically using the collocation method. Owing to the incorporation of surface elasticity, the stresses at the crack tips only exhibit the weak logarithmic singularity when the dislocation is located on the real axis where the crack is located, whereas in the case when the dislocation is not on the real axis, the stresses at the crack tips exhibit both the weak logarithmic and the strong square-root singularities. The two densities, the crack opening displacement across the crack faces and the image force acting on the screw dislocation are specifically calculated. We note that crack bridging only exerts an effect on the line dislocation density but has no influence on the line force density. In addition, we demonstrate that both surface elasticity and crack bridging can reduce the strengths of the logarithmic stress singularity at the crack tips and the magnitude of the crack opening displacement across the crack faces. Our results also clearly show that both crack bridging and surface elasticity exert a significant influence on the magnitude and direction of the image force acting on the screw dislocation.

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]

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.

The coupling interaction of a piezoelectric screw dislocation with a bimaterial containing a circular inclusion

2016 ◽  
Vol 22 (3) ◽  
pp. 538-556
Author(s):  
Hui Chai ◽  
Chiping Jiang ◽  
Fan Song ◽  
Peng Yan
Keyword(s):  
Screw Dislocation ◽  
Order Approximation ◽  
Equilibrium Points ◽  
Image Force ◽  
Potential Method ◽  
Circular Inclusion ◽  
Mapping Technique ◽  
Coupling Interaction ◽  
Piezoelectric Screw Dislocation ◽  
Complex Potential Method

The coupling interaction of a piezoelectric screw dislocation with a bimaterial containing a circular inclusion is investigated by the complex potential method and conformal mapping technique. Explicit series solutions are obtained and then cast into new expressions with the coupling interaction effects separated. The new expressions converge much more rapidly and their one-order approximation formulae have satisfactory accuracy in many cases. According to the generalized Peach–Koehler formula, the image force acting on the screw dislocation is explicitly obtained and numerically studied to reveal the coupling interaction arising from multiple material properties as well as the geometry of inhomogeneous phases. In all regions, the coupling interaction has a significant influence on the number, location and stability of dislocation equilibrium points. In particular, the inclusion can reverse the image force within a region in the material on the other side of the interface.

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.

scholarly journals Interaction of Screw Dislocation with Edge Interfacial Crack on Fine-Grained Piezoelectric Coating/Substrate

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Shuaishuai Hu ◽  
Jiansheng Liu ◽  
Junlin Li ◽  
Xiufeng Xie
Keyword(s):  
Screw Dislocation ◽  
Interfacial Crack ◽  
Mapping Function ◽  
Image Force ◽  
Infinite Plane ◽  
Principle Of Superposition ◽  
Fine Grained ◽  
Substrate Structure ◽  
Piezoelectric Bimaterial ◽  
The Right

The interaction between micro- and macrocracks in a fine-grained piezoelectric coating/substrate under remote antiplane mechanical and in-plane electrical loadings was studied. The principle of superposition and a mapping function method was used to transform the fine-grained coating/substrate structure containing the screw dislocation and the edge interfacial crack into the right semi-infinite plane piezoelectric bimaterial with screw dislocation to simplify the problem. Furthermore, the electric field, displacement field, intensity factors, and image force of these two problems were established. In addition, numerical calculations were then given graphically to study the effects of the elastic modulus of the material, the size of the crack, the thickness of the coating, and the screw dislocation angle on the edge interface crack and dislocation.

scholarly journals Elastodynamic image forces on screw dislocations in the presence of phase boundaries

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170484 ◽  
Author(s):  
Beñat Gurrutxaga-Lerma
Keyword(s):  
Screw Dislocation ◽  
Image Force ◽  
Planar Interface ◽  
Rigid Surface ◽  
Phase Boundaries ◽  
Unit Force ◽  
Screw Dislocations ◽  
Planar Phase ◽  
Explicit Formulae ◽  
Rigid Interface

The elastodynamic image forces acting on straight screw dislocations in the presence of planar phase boundaries are derived. Two separate dislocations are studied: (i) the injected, non-moving screw dislocation and (ii) the injected (or pre-existing), generally non-uniformly moving screw dislocation. The image forces are derived for both the case of a rigid surface and of a planar interface between two homogeneous, isotropic phases. The case of a rigid interface is shown to be solvable employing Head's image dislocation construction. The case of the elastodynamic image force due to an interface is solved by deriving the reflected wave's contribution to the global solution across the interface. This entails obtaining the fundamental solution (Green's function) for a point unit force via Cagniard's method, and then applying the convolution theorem for a screw dislocation modelled as a force distribution. Complete, explicit formulae are provided when available. It is shown that the elastodynamic image forces are generally affected by retardation effects, and that those acting on the moving dislocations display a dynamic magnification that exceed the attraction (or repulsion) predicted in classical elastostatic calculations.

Interaction of a piezoelectric screw dislocation with an insulating crack

2002 ◽  
Vol 82 (15) ◽  
pp. 2805-2824 ◽  
Author(s):  
Tong-Yi Zhang ◽  
Tian-Hong Wang ◽  
Ming-Hao Zhao
Keyword(s):  
Screw Dislocation ◽  
Piezoelectric Screw Dislocation
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