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 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 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.

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.

The Higher Order Mechanical and Electric Fields for Arbitrarily Oriented Crack with the Physical Weak-Discontinuity

2014 ◽  
Vol 602-605 ◽  
pp. 283-286
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Electric Fields ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for anti-plane crack oblique to the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The crack is oriented in arbitrary direction. The crack surfaces are assumed to be electrically impermeable. The material properties of FGPMs are assumed to be linear functions with their gradient direction perpendicular to the interface. By using the eigen-expansion method, the high order crack tip stress and electric displacement fields are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

scholarly journals Mixed Electrical Conditions on Interface Inclusion in a Piezoelectric Bimaterial under Antiplane Mechanical and Inplane Electric Loadings

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
A. Sheveleva ◽  
V. Loboda ◽  
A. Kryvoruchko
Keyword(s):  
Exact Analytical Solution ◽  
Electric Displacement ◽  
Engineering Application ◽  
Intensity Factors ◽  
Riemann Boundary Value Problem ◽  
Material Interface ◽  
Riemann Boundary ◽  
Piezoelectric Bimaterial ◽  
Analytical Expressions ◽  
Rigid Interface

An absolutely rigid interface inclusion in a bimaterial piezoelectric space under the action of antiplane mechanical and in-plane electric loadings is analyzed. One zone of the inclusion is electrically insulated while the other part is electrically permeable. This problem is important for engineering application, but it has not been solved earlier in an analytical way. Presenting all electromechanical quantities via sectionally analytic vector functions, the combined Dirichlet-Riemann boundary value problem is formulated. An exact analytical solution of this problem is obtained. Closed form analytical expressions for electromechanical quantities at the interface are derived. Some of these values are also presented graphically along the corresponding parts of the material interface. Singular points of the shear strain and the electric displacement are found and the corresponding intensity factors are determined as well.

scholarly journals Static component of photothermal response in non-transparent samples

2012 ◽  
Vol 25 (3) ◽  
pp. 213-224 ◽  
Author(s):  
Zlatan Soskic ◽  
Slobodanka Galovic ◽  
Nebojsa Bogojevic ◽  
Slobodan Todosijevic
Keyword(s):  
Temperature Distribution ◽  
Mean Value ◽  
Optical Absorption Coefficient ◽  
Back Side ◽  
One Dimensional ◽  
Static Component ◽  
Special Cases ◽  
Static Part ◽  
The Mean ◽  
Analytical Expressions

The paper presents the analysis of the static component of temperature distribution in non-transparent samples during photothermal measurements. Analytical expressions for static part of temperature distribution in the irradiated sample and in its surroundings are determined using one dimensional model of heat transfer in a typical photothermal environment. It is established that the dominant factors that influence the shape and the mean value of the temperature distribution are optical absorption coefficient and thermal conductances of the sample and the surroundings. Important special cases are described and analytical expressions for temperatures of the front and the back side of the sample are derived.

Interaction of a Screw Dislocation with an Interfacial Crack in Two Dissimilar Piezoelectric Layers

2004 ◽  
Vol 261-263 ◽  
pp. 141-146
Author(s):  
Jin Xi Liu ◽  
Ai Ping Liu ◽  
Z.Q. Jiang ◽  
Ai Kah Soh
Keyword(s):  
Conformal Mapping ◽  
Screw Dislocation ◽  
Complex Variable ◽  
Piezoelectric Effect ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Mapping Technique ◽  
Intensity Factors ◽  
Piezoelectric Layers ◽  
Crack Tip Shielding

A screw dislocation interacting with a semi-infinite interfacial crack in two dissimilar piezoelectric layers is studied. The complex variable method and the conformal mapping technique are employed to obtain the solution of the problem. The stress and electric displacement intensity factors are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electro-elastic material constants. Numerical example shows that the influence of piezoelectric effect on the crack tip shielding is significant.

Longitudinal Shear of a Compound Elastic Half-Space Weakened by Cracks

2014 ◽  
Vol 1020 ◽  
pp. 286-290 ◽  
Author(s):  
Karo L. Aghayan ◽  
Edvard Kh. Grigoryan ◽  
Vahan G. Zakaryan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Infinite Plate ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Antiplane Deformation ◽  
Intensity Factors ◽  
Special Cases ◽  
Deformation State

The problem of fracture mechanics concerning contact interaction between elastic infinite plate and elastic compound semi–space is investigated. Plate and semi–space are weakened by finite through cracks, which are perpendicular to surface of heterogeneity in the same plane. Assuming that structure is deformed in antiplane deformation state it is required to determine the contact stress distribution and fracture stress intensity factors dependence of structure heterogeneity and geometrical parameters. Using the Fourier integral transform the problem is reduced to find the solutions of system of two singular integral equations. System solutions behavior at integration domain endpoints is investigated for all cases. In some special cases of cracks location, equations kernels can also contain fixed singularities. An efficient numerical method to solve such equations is suggested. Numerical calculations are done and results are shown in tables and graphs, which express contact stresses and stress intensity factors dependence on problem parameters and simultaneously reveal dangerous cases of fracture of the structure.

scholarly journals Effective elastic properties of one-dimensional hexagonal quasicrystal composites

2021 ◽  
Vol 42 (10) ◽  
pp. 1439-1448
Author(s):  
Shuang Li ◽  
Lianhe Li
Keyword(s):  
Composite Materials ◽  
Explicit Expression ◽  
Elastic Properties ◽  
Function Method ◽  
Volume Fraction ◽  
Effective Properties ◽  
Elliptic Cylinder ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

AbstractThe explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

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