Fracture analysis of an infinite 1D hexagonal piezoelectric quasicrystal plate with a penny-shaped dielectric crack

Zhou, Yan‐Bin; Li, Xian-Fang

doi:10.1016/j.euromechsol.2019.04.011

Cited by 25 publications

(9 citation statements)

References 42 publications

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“…and we have considered the single-valued condition of generalized displacements, i.e., P(ζ) � 0. e solution of equation ( 20) together with equations ( 23) and (24) gives…”

Section: E Interaction Of N Parallel Screw Dislocations With Crackmentioning

confidence: 99%

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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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“…and we have considered the single-valued condition of generalized displacements, i.e., P(ζ) � 0. e solution of equation ( 20) together with equations ( 23) and (24) gives…”

Section: E Interaction Of N Parallel Screw Dislocations With Crackmentioning

confidence: 99%

“…[23]. Besides, Zhou and Li [24] examined the electroelastic behavior induced by a penny-shaped dielectric crack of a 1D hexagonal piezoelectric quasicrystal plate of finite thickness, and they considered a Yoffe-type moving crack in a 1D hexagonal piezoelectric quasicrystal by using the Fourier transform technique in ref. [25].…”

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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“…QCs are brittle at normal atmospheric temperature [2], so it is prone to produce defects (holes and cracks) in the process of preparation and service. Many scholars have studied the problem of macroscopic defects in one-dimensional hexagonal piezoelectric quasicrystals (1D HPQCs), such as two collinear cracks [3,4], penny-shaped dielectric crack [5] and yoffe-type moving crack [6]. However, when the defects are at nanometer scale, the ratio of surface area to volume of defects is very high [7,8], and the surface properties have a significant influence on the disturbed mesoscale sphere of defects [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

An analytic solution of an arbitrary location through-crack emanating from a nano-circular hole in one-dimensional hexagonal piezoelectric quasicrystals

Xin

Xiao

2023

Mathematics and Mechanics of Solids

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The mode III fracture performance of an arbitrary location through-crack at the edge of a nano-circular hole in one-dimensional hexagonal quasicrystals is studied. Based on the G-M elasticity theory, the piezoelectric quasicrystal theory and the boundary value problems theory, the phonon, phason and electric fields of the nano-defects (nano-hole and nano-cracks) are obtained, and the analytic expressions of the field intensity factors at both ends of through-crack are present. The present solution can be degenerated into the existing results. The relationship between the field intensity factors with the nano-defects related parameters, far-field loads and piezoelectric quasicrystal coupling coefficient are discussed. The field intensity factors have obvious size effects when the defects size is at nanoscale and the surface effect is considered. The field intensity factors tend to be classical theory with the increase in defect size. The field intensity factors show different changes with the increase in crack location angle and relative size between cracks. The size effect of the field intensity factors is significantly affected by the crack location. The far-field mechanical-electric loads and the piezoelectric quasicrystal coupling coefficient have obvious influence on the field intensity factors.

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“…Zhou and Li [13] analyzed a mode‐III crack in one‐dimensional (1D) hexagonal QCs subjected to anti‐plane impact loading. A Yoffe‐type moving crack and a penny‐shaped dielectric crack in one‐dimensional hexagonal piezoelectric QCs have been reported by Zhou and Li [15, 16]. Zhao et al.…”

Section: Introductionmentioning

confidence: 99%

Stress analysis of a mode‐I crack in a 1D hexagonal quasicrystal based on the non‐local theory

Liu

2020

Z Angew Math Mech

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This paper studies the non‐local theory solution of a Mode‐I crack in a 1D hexagonal quasicrystal (QC) by using the generalized Almansi's theorem and the Schmidt method. Based on the Fourier transform, the boundary value problem is reduced to two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. The dual integral equations are derived. Finally, the expression of the phonon stress field and the phason stress field at the crack tip are obtained. Numerical examples are provided to show the effects of the lattice parameter and the crack length on the phonon stress field and the phason stress field near the crack tip. Different from the classical solution, that the present solution exhibits no stress singularity at the crack tips in a 1D hexagonal QC.

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Fracture analysis of an infinite 1D hexagonal piezoelectric quasicrystal plate with a penny-shaped dielectric crack

Cited by 25 publications

References 42 publications

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

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

An analytic solution of an arbitrary location through-crack emanating from a nano-circular hole in one-dimensional hexagonal piezoelectric quasicrystals

Stress analysis of a mode‐I crack in a 1D hexagonal quasicrystal based on the non‐local theory

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