The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Jiang, Lijuan; Liu, Guanting

doi:10.1088/1674-1056/26/4/044601

Cited by 18 publications

(15 citation statements)

References 27 publications

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“…Equation 29represents the case of the interaction of a screw dislocation with a wedge-shaped crack. If (1) = (2) , the result is in excellent agreement with the result in [17].…”

Section: Stress Intensity Factors and Image Force On The Dislocationsupporting

confidence: 81%

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Zhao

2019

Mathematical Problems in Engineering

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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.

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“…Equation 29represents the case of the interaction of a screw dislocation with a wedge-shaped crack. If (1) = (2) , the result is in excellent agreement with the result in [17].…”

Section: Stress Intensity Factors and Image Force On The Dislocationsupporting

confidence: 81%

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Zhao

2019

Mathematical Problems in Engineering

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“…We remark that when x 2 in Equations (13) and (14) approaches zero from either side of the interface, we derive the corresponding solutions on the interface. Following Nakahara and Willis [25], we define…”

Section: Fundamental Solutions Of Phonon and Phason Dislocations Alonmentioning

confidence: 99%

“…For soft matter 2D QCs, Li and Fan [13] obtained dislocations and solutions of the second kind for 2D QCs. Recently, the interaction between a screw dislocation and a wedge-shaped crack was investigated by Jiang and Liu [14] in the piezoelectricity of 1D hexagonal QCs. Li and Liu [15] performed an electro-elastic analysis on an icosahedral QC containing a straight dislocation with piezoelectric effects.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions and analysis of an interfacial crack in a one-dimensional hexagonal quasicrystal bi-material

Fan

Chen

Zhang

et al. 2020

Mathematics and Mechanics of Solids

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Using the Stroh formalism, Green’s functions are obtained for phonon and phason dislocations and opening displacements on the interface of a one-dimensional hexagonal quasicrystal bi-material. The integro-differential equations governing the interfacial crack are then established, and the singularities of the phonon and phason displacements at the crack tip on the interface are analyzed. To eliminate the oscillating singularities, we represent the delta function in terms of the Gaussian distribution function in the Green’s functions and the integro-differential equations, which helps reduce these equations to the standard integral equations. Finally, a boundary element numerical approach is also proposed to solve the integral equation for the crack opening displacements, the asymptotic expressions of the extended intensity factors, and the energy release rate in terms of the crack opening displacements near the crack tip. In numerical examples, the effect of the Gaussian parameter on the numerical results is discussed, COMSOL software is used to validate the analytical solution, and the influence of the different phonon and phason loadings on the interfacial crack behaviors is further investigated.

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“…Li and Fan [20] investigated the dislocations and solutions for the second kind of 2D quasicrystals of soft matter. Recently, Jiang and Liu [21] investigated the effect of the interaction between a screw dislocation and wedge-shaped crack on the piezoelectricity of a 1D hexagonal quasicrystal. Li and Liu [22] performed an electroelastic analysis on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

Fan

Chen

et al. 2019

Z Angew Math Mech

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In this paper, we derive a fundamental solution for extended dislocations of onedimensional (1D) hexagonal piezoelectric quasicrystals. Based on the Stroh formalism, the fundamental solutions for 1D hexagonal piezoelectric quasicrystals expressing by extended dislocations, including phonon, electric, and phason dislocations, are obtained. Then, by considering the continuously distributed dislocations to be a crack, the crack opening displacement, intensity factor, and energy release rate of the extended dislocation are expressed. Numerical calculations are used to confirm the validity of the theory and to investigate the effect of different parameters on the energy release rate. K E Y W O R D S crack, energy release rate, extended dislocation, fundamental solutions, one-dimensional piezoelectric quasicrystals Z Angew Math Mech. 2019;99:e201800232.

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The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Cited by 18 publications

References 27 publications

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Fundamental solutions and analysis of an interfacial crack in a one-dimensional hexagonal quasicrystal bi-material

Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

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