Two collinear mode-III cracks in one-dimensional hexagonal piezoelectric quasicrystal strip

Zhou, Yan‐Bin; Li, Xian-Fang

doi:10.1016/j.engfracmech.2017.10.030

Cited by 33 publications

(10 citation statements)

References 26 publications

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“…A non-uniformly generally loaded anti-plane crack in a half-space of a one-dimensional piezoelectric quasicrystal was studied by using an extension of the classical continuous dislocation layer method [25]. By using the integral transform technique, the problem of two collinear mode-III cracks in 1D hexagonal piezoelectric quasicrystal strip has been reduced to solving a standard singular integral equation, and exact closed-form solutions have been obtained for the cracks either parallel or perpendicular to the strip boundaries [26,27]. Li et al [28] performed the fracture analysis of a transversely isotropic piezoelectric quasicrystal cylinder under axial shear, and found that the quasicrystal fracture is governed by the phonon or phason field, depending on the phonon-phason loading ratio.…”

Section: Using Complex Variable Function Methods and Conformal Mappin...mentioning

confidence: 99%

Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect

Jin

Yang

et al. 2019

Acta Mech

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Section: Using Complex Variable Function Methods and Conformal Mappin...mentioning

confidence: 99%

Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect

Jin

Yang

et al. 2019

Acta Mech

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“…A non-uniformly, generally loaded anti-plane crack in a half-space of a 1D piezoelectric quasicrystal was studied by using an extension of the classical continuous dislocation method [23]. By using the integral transform technique, the problem of two collinear mode-III cracks in a 1D, hexagonal piezoelectric quasicrystal strip has been reduced to solving a standard singular integral equation, and exact closed-form solutions have been obtained for the cracks parallel to the strip boundaries [24]. Li et al [25] performed the fracture analysis of a transversely isotropic, piezoelectric quasicrystal cylinder under axial shear, and found that the quasicrystal fracture is governed by the phonon or phason field, depending on the phonon-phason loading ratio.…”

Section: Introductionmentioning

confidence: 99%

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

Gao

Zhong

et al. 2021

Z Angew Math Mech

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In this paper, the interaction of collinear interface cracks between dissimilar onedimensional (1D) hexagonal quasicrystals with piezoelectric effect under antiplane shear and in-plane electric loading has been studied. By using complex variable method the mixed boundary value problem for the interface cracks was reduced to the solution of Riemann-Hilbert problem. Analytic full-field solution for phonon and phason stresses, electric fields, electric displacement in the cracked bi-materials has been obtained based on the electrically permeable crack model. The electric field and electric displacement inside the interface cracks are found to be nonlinearly distributed under line loadings. The field intensity factors of the interface cracks depend on both the mechanical and electric load for the line loading case, but the field intensity factors depend only on mechanical loading when the uniform loadings are applied at infinity. The investigation of the SIFs of neighboring interface cracks has been used to predict possible crack propagation. It is found that when the neighboring cracks are close enough, the inner crack tips are more likely to propagate and when the neighboring cracks are far away from each other, the outer crack tip of the bigger crack has more possibility to propagate.

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“…Zhang et al [21] addressed the static bending deformation of a functionally graded multilayered 1D hexagonal piezoelectric QC simply supported nanoplate. Zhou and Li [22] dealt with the problem of two collinear cracks in a one-dimensional hexagonal piezoelectric QC strip under mode III far-field loading, while they analyzed the electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a 1D hexagonal piezoelectric quasicrystal layer with the aid of a singular integral equation in ref. [23].…”

Section: Introductionmentioning

confidence: 99%

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

Liu

2020

Mathematical Problems in Engineering

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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.

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Two collinear mode-III cracks in one-dimensional hexagonal piezoelectric quasicrystal strip

Cited by 33 publications

References 26 publications

Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect

Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

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

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