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.

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]

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.

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.

Interaction between an edge dislocation near a circular void within the framework of the theory of strain gradient elasticity

2018 ◽  
Vol 27 (3-4) ◽  
Author(s):  
Kamyar Davoudi
Keyword(s):  
Edge Dislocation ◽  
Function Method ◽  
Dislocation Line ◽  
Gradient Elasticity ◽  
Image Force ◽  
Strain Gradient Elasticity ◽  
Gradient Solution ◽  
Stress Function Method ◽  
Classical Size ◽  
Isotropic Theory

AbstractThe purpose of this paper was to consider an edge dislocation near a circular hole within the isotropic theory of gradient elasticity. The stress field is derived with the help of a stress function method. The gradient stresses possess no singularity at the dislocation line. As a result, the image force exerted on the dislocation due to the presence of the hole remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size effect.

Interaction of a screw dislocation with a crack in an anisotropic body

1991 ◽  
Vol 6 (12) ◽  
pp. 2578-2584 ◽  
Author(s):  
Tong-Yi Zhang ◽  
J.E. Hack
Keyword(s):  
Screw Dislocation ◽  
Stress Component ◽  
Anisotropic Body ◽  
Image Force ◽  
Shielding Effect ◽  
Crack Plane ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Isotropic Media ◽  
Shielding Effects

The stress field, image force, and shielding effect of a screw dislocation in the vicinity of a Mode III crack were formulated for both semi-infinite and finite length cracks. The results show that there is an abnormal stress component, ŝ31, on the crack plane. This leads to a nonzero image force along the axis perpendicular to the crack plane when the dislocation is located on the crack plane. However, the abnormal stress component and image force disappear for orthotropic and isotropic media. The image force along a slip plane has the same expression as in isotropic media with an effective shear modulus. Generally the shielding effects are the same as in isotropic media. The anisotropy changes only the magnitude of the shielding effects. The case of multiple dislocations is also discussed.

scholarly journals Exact Solutions for Interaction of Parallel Screw Dislocations with a Wedge Crack in One-Dimensional Hexagonal Quasicrystal with Piezoelectric Effects

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xin Lv ◽  
Guan-Ting Liu
Keyword(s):  
Crack Propagation ◽  
Field Line ◽  
Field Intensity ◽  
Wedge Angle ◽  
Image Force ◽  
Intensity Factors ◽  
One Dimensional ◽  
Line Force ◽  
Shaped Crack ◽  
Field Intensity Factors

The purpose of this paper is to consider the interaction between many parallel dislocations and a wedge-shaped crack and their collective response to the external applied generalized stress in one-dimensional hexagonal piezoelectric quasicrystal, employing the complex variable function theory and the conformal transformation method; the problem for the crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann–Hilbert boundary value problems. The analytical solutions of the generalized stress field are obtained. The dislocations are subjected to the phonon field line force, phason field line force, and line charge at the core. The positions of the dislocations are arbitrary, but the dislocation distribution is additive. The dislocation is not only subjected to the external stress and the internal stress generated by the crack, but also to the force exerted on it by other dislocations. The closed-form solutions are obtained for field intensity factors and the image force on a screw dislocation in the presence of a wedge-shaped crack and a collection of other dislocations. Numerical examples are provided to show the effects of wedge angle, dislocation position, dislocation distribution containing symmetric configurations and dislocation quantities on the field intensity factors, energy release rate, and image force acting on the dislocation. The principal new physical results obtained here are (1) the phonon stress, phason stress, and electric displacement singularity occur at the crack tip and dislocations cores, (2) the increasing number of dislocations always accelerates the crack propagation, (3) the effect of wedge angle on crack propagation is related to the distribution of dislocations, and (4) the results of the image force on the dislocation indicate that the dislocations can either be attracted or rejected and reach stable positions eventually.

Stress Fields and Energy Analysis during the Fracture of Composite Materials

2014 ◽  
Vol 532 ◽  
pp. 524-533 ◽  
Author(s):  
Hamid Hamli Benzahar ◽  
Mohamed Chabaat
Keyword(s):  
Stress Intensity Factor ◽  
Composite Material ◽  
Energy Release ◽  
Main Crack ◽  
Energy Analysis ◽  
Damage Zone ◽  
Stress Fields ◽  
Shielding Effect ◽  
Release Rates ◽  
Energy Release Rates

The present study evaluates stress fields, the stress intensity factor and energy release rates at the time of the cracking in a composite material. Our problems are formulated using two materials having different parameters such as the shearing modulus and the Poissons ratio. After having determined the displacement and stress fields, one homogenized the latter in order to allow comparing the results with those of other researchers. During the propagation of the main crack, the surrounding dislocation induces two effects: amplification effect which increases the stress at the main crack-tip and a shielding effect which reduces the propagation of the main crack. Finally, Energy Release Rates (ERR) associated to the different transformation inside the damage zone is evaluated on the basis of the superposition of all energies: the energy due to the main crack, the energy due to the existing dislocation and the energy due to the interaction.

The Analysis of Plane Flat Lap Interface End of Orthotropic Bi-Material

2011 ◽  
Vol 233-235 ◽  
pp. 1950-1953
Author(s):  
Cai Xia Ren ◽  
Jun Lin Li
Keyword(s):  
Stress Intensity Factor ◽  
Function Method ◽  
Complex Function ◽  
Stress Fields ◽  
Stress Singularities ◽  
Displacement Fields ◽  
Multiple Stress ◽  
Stress Functions ◽  
Material Fracture ◽  
Material Plane

The orthotropic bi-material plane interface end of a flat lap is studied by constructing new stress functions and using the composite complex function method of material fracture. When the characteristic equations’ discriminates and, the theoretical formulas of stress fields, displacement fields and the stress intensity factor around the flat lap interface end are derived, indicating that there is no oscillatory singularity. There are multiple stress singularities of the orthotropic bi-material plane flat lap interface end.

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