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.

Line Force, Charge, and Dislocation in Anisotropic Piezoelectric Composite Wedges and Spaces

1995 ◽  
Vol 62 (2) ◽  
pp. 423-428 ◽  
Author(s):  
M. Y. Chung ◽  
T. C. T. Ting
Keyword(s):  
Electric Displacement ◽  
Form Solution ◽  
Piezoelectric Composite ◽  
Real Form ◽  
Line Charge ◽  
Radial Plane ◽  
Line Force ◽  
Line Dislocation ◽  
Charge Line ◽  
Composite Wedge

Two-dimensional problems of anisotropic piezoelectric composite wedges and spaces are studied. The Stroh formalism is employed to obtain the basic real-form solution in terms of two arbitrary constant vectors for a particular wedge. Explicit real-form solutions are then obtained for (i) a composite wedge subjected to a line force and a line charge at the apex of the wedge and (ii) a composite space subjected to a line force, line charge, line dislocation, and an electric dipole at the center of the composite space. For the composite wedge the surface traction on any radial plane θ = constant and the electric displacement Dθ normal to the radial plane θ = constant vanish everywhere. For the composite space these quantities may not vanish but they are invariant with the choice of the radial plane.

Interaction Between A Permeable Crack And Piezoelectric Screw Dislocations, Line Forces And Line Charges In A Finite Piezoelectric Cylinder

2014 ◽  
Vol 44 (4) ◽  
pp. 51-68 ◽  
Author(s):  
H. P. Song ◽  
C. F. Gao
Keyword(s):  
Dislocation Line ◽  
Electric Displacement ◽  
Complex Function ◽  
Image Force ◽  
Stress Fields ◽  
Shielding Effect ◽  
Permeable Crack ◽  
Piezoelectric Cylinder ◽  
Line Charge ◽  
Line Force

Abstract The problem of a piezoelectric screw dislocation, line force and line charge around a permeable crack in a finite piezoelectric cylinder is dealt with in this paper. Utilizing the complex function and conformal mapping methods, the closed form solutions of the stress fields and the electric displacement fields are derived. The stress intensity factor and the image force are discussed in detail. The results show that the stress fields are in direct proportion to the line force, but independent of the line charge. The shielding effect produced by the dislocation increases with the increasing of the radius of the piezoelectric cylinder. Moreover, the unstable equilibrium point and the image force are also severely affected by the radius of the piezoelectric cylinder.

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.

The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 1015 ◽  
pp. 97-100
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Ying Chen
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

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.

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.

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.

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