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.

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.

Non-uniformly loaded row of moving shear cracks in magnetoelectroelastic media

2019 ◽  
Vol 25 (2) ◽  
pp. 374-388
Author(s):  
GE Tupholme
Keyword(s):  
Magnetic Induction ◽  
Electric Displacement ◽  
Numerical Data ◽  
General Point ◽  
Shear Cracks ◽  
Intensity Factors ◽  
Graphical Displays ◽  
Layer Method ◽  
Dislocation Layer ◽  
Magnetic Induction Intensity

Derivations and discussions are obtained in detail of the closed-form representations of the components of the deformation fields at a general point created by a moving row of smart magnetoelectroelastic shear cracks that are subjected to non-uniform mechanical, electric, and magnetic loadings. The creative analysis exploits a generalization of the basic dislocation layer method. Near a crack tip, their angular variations and the corresponding stress, electric displacement and magnetic induction intensity factors are deduced. Graphical displays of some illustrative numerical data are presented. As a particular case, the results for an analogous stationary row of non-constantly loaded magnetoelectroelastic cracks are derived. The correctness and validity of the results of this novel analysis are examined by the verification of their agreement with those previously presented for various limiting particular cases.

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.

Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane

2017 ◽  
Vol 28 (19) ◽  
pp. 2823-2834 ◽  
Author(s):  
Mojtaba Ayatollahi ◽  
Mojtaba Mahmoudi Monfared ◽  
Mahsa Nourazar
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Field Intensity ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Mode Iii ◽  
Singular Stress ◽  
Field Intensity Factors

This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velocity has great effect on the field intensity factors.

Anti-Plane Interface Edge Crack between Two Dissimilar Piezoelectric Blocks

2004 ◽  
Vol 261-263 ◽  
pp. 471-476
Author(s):  
Shu Hong Liu ◽  
Z.Z. Zou ◽  
B.Q. Xu ◽  
Z.G. Zhang
Keyword(s):  
Edge Crack ◽  
Piezoelectric Materials ◽  
Normal Component ◽  
Electric Displacement ◽  
Intensity Factors ◽  
Plane Shear ◽  
Boundary Collocation Method ◽  
Field Intensity Factors ◽  
Strain Stress ◽  
Interface Edge

The problem of an interface edge crack between two dissimilar piezoelectric materials is analyzed under the conditions of anti-plane shear and in-plane electrical loading. The crack is considered to be traction-free, but electric permeable one across which the normal component of the electric displacement are continuous. A series form of electromechanical solution and field intensity factors are obtained. The results show that all fields including strain, stress, electric field strength and electric displacement are singular in the front of crack tip. At last, the stress intensity factor is solved by the boundary collocation method (BCM), numerical results are given and discussed.

scholarly journals Analysis of Mode I Conducting Crack in Piezo-Electro-Magneto-Elastic Layer

2013 ◽  
Vol 18 (1) ◽  
pp. 153-176
Author(s):  
B. Rogowski
Keyword(s):  
Boundary Conditions ◽  
Electric Displacement ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Intensity Factors ◽  
Permeable Crack ◽  
Crack Face ◽  
Field Intensity Factors ◽  
Dielectric Crack ◽  
Thickness Field

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

Investigation of a Mode III Crack in Functionally Graded Magnetoelectroelastic Materials

2007 ◽  
Vol 348-349 ◽  
pp. 713-716
Author(s):  
Bao Lin Wang ◽  
H.Y. Zhang
Keyword(s):  
Electric Displacement ◽  
Elastic Stiffness ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Mode Iii ◽  
Material Inhomogeneity ◽  
Magnetoelectroelastic Materials ◽  
Field Intensity Factors ◽  
Magnetic Induction Intensity ◽  
Series Of Functions

In this study, an anti-plane crack in a functionally graded magnetoelectroelastic materials is investigated. It is assumed that the material properties such as elastic stiffness c44(y), piezoelectric coefficient e15(y), dielectric constant ε11(y), piezomagnetic coefficient α15(y), magnetoelectric coupling coefficient μ11(y) and magnetic permeability υ11(y) vary one-dimensionally on the ycoordinate with a series of functions f(y).An asymptotic analysis is done and the problem is solved by means of singular integral equation technique. The influence of the material inhomogeneity on crack tip stress, electric displacement and magnetic induction intensity factors are studied. The results are considered to reveal the effect of material inhomogeneity and geometry of the crack on the field intensity factors.

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