Interaction between a screw dislocation and an oblique edge crack in a half-infinite MEE solid

Liu, Xin; Guo, Junhong

doi:10.1016/j.tafmec.2016.07.008

Cited by 15 publications

(8 citation statements)

References 27 publications

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“…Complex potential function (CPF) method introduced by Muskhelishvili [1] is the simplest and most rigorous method to investigate the behavior of SIFs, measured at the tip of cracks to determine the stability behavior of bodies or materials containing cracks or flaws. Many researchers used CPF methods to investigate the crack problems in an infinite plane [2][3][4], finite plane [5,6] and half plane [7][8][9]. Gray et al [2] and Nik Long et al [3] established the relevant hypersingular integral equations (HSIEs) using CPF method in calculating the SIFs with Green's function, and crack opening displacement (COD) function as the unknown, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Legros et al [7] performed the analysis of multiple circular inclusions in an elastic half plane based on complex singular integral equation with the unknown tractions at each circular boundary approximated by a truncated complex Fourier series. Liu and Guo [8] used the CPF method to calculate the SIFs for the interaction between a screw dislocation and an oblique edge crack in a half plane with the help of Cauchy integral formula. Elfakhakhre et al [9] investigated the behavior of the SIFs at the crack tips in half plane elasticity using the modified complex potentials (MCPs) with the distribution dislocation as the unknown function.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

et al. 2021

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A new mathematical model is developed for the analytical study of two cracks in the upper plane of dissimilar materials under various mechanical loadings, i.e., shear, normal, tearing and mixed stresses with different geometry conditions. This problem is developed into a new mathematical model of hypersingular integral equations (HSIEs) by using the modified complex potentials (MCPs) function and the continuity conditions of the resultant force and displacement with the crack opening displacement (COD) function as the unknown. The newly obtained mathematical model of HSIEs are solved numerically by utilizing the appropriate quadrature formulas. Numerical computations and graphical demonstrations are carried out to observe the profound effect of the elastic constants ratio, mode of stresses and geometry conditions on the dimensionless stress intensity factors (SIFs) at the crack tips.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

et al. 2021

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“…Hu and Chen [26,27] reduced the mixed boundary value problem of crack in the MEE material to the dual integral equation by means of the integral transformation method and discussed the impact of electric, magnetic and force loads on the crack tip field. Liu and Guo [28] studied the effect of geometrical parameters and dislocation locations on field intensity factors and energy release rate in a semi-infinite MEE solid by using the complex variable function method. Gao et al [29,30] gave exact solution to the problem of elliptic holes or cracks in an MEE material subjected to farfield loading and general solution of the cosine cracks by using the Stroh formulism.…”

Section: Introductionmentioning

confidence: 99%

Surface effect on a nano‐elliptical hole or nano‐crack in magnetoelectroelastic materials under antiplane shear

2019

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Based on the Gurtin‐Murdoch surface/interface model, an antiplane shear problem of a magnetically and electrically impermeable nano‐elliptical hole in magnetoelectroelastic (MEE) materials with surface effect is presented subjected to far‐field anti‐plane mechanical and in‐plane electrical and magnetic loadings. By using the complex function method and conformal mapping technique, exact closed‐form solutions of the stress, electric displacement and magnetic induction intensity factors near the crack tip are obtained when the nano‐elliptical hole is reduced to a nano‐crack. Numerical examples are provided to show the effects of size of nano‐crack on the field intensity factors near the crack tip induced by mechanical, electrical and magnetic loadings for the piezoelectric (PE), piezomagnetic (PM) and MEE materials with surface effect. The interaction between the stress field, electric field and magnetic field around the nano‐hole is analyzed. The results show that the obtained solution is close to the classical elasticity solution with increasing size of the nano‐crack.

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“…Li and Pan (2016) studied the response of a layered anisotropic MEE half-space to internal static forces and dislocations applied over a horizontal circle, using the Fourier transform and Stroh formalism. Liu and Guo (2016) investigated the interaction between a static screw dislocation and an oblique crack in an MEE half-plane via the complex variable function method. Again, while these static deformations or simplified (2D) dynamic models are very useful, the important time-harmonic dislocation problem in multilayered MEE solids has not been attacked so far, which motivates the present study.…”

Section: Introductionmentioning

confidence: 99%

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

Moshtagh

Eskandari‐Ghadi

Pan

2019

Journal of Intelligent Material Systems and Structures

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Modeling layered systems with dislocations is very challenging; yet, it is important since most smart structures are made of multilayers to make best use of the combined effective property. As such, during the manufactures, defects, such as dislocations, could be introduced in the multilayers. In this article, we analytically find, for the first time, the response of three-dimensional multilayered magneto-electro-elastic systems due to time-harmonic dislocations. The dislocations are the most general, containing the elastic dislocations and discontinuity of the electric potential and/or magnetic potential over a circular region in any layer in the medium. The fully coupled partial differential equations of motion and the Gauss law for the magneto-electro-elastic materials are solved in terms of cylindrical system of vector functions, and the dual variable and position method is further introduced to treat the multilayers. Numerical examples are carried out based on the derived analytical solution to demonstrate the effects of the time-harmonic dislocations on the induced magneto-electro-elastic fields. This analytical solution is important in both electrodynamics and elastodynamics, with possible applications in material sciences and physics. The numerical results are useful in design process of smart devices made of magneto-electro-elastic solids applicable to other engineering fields like renewable energy.

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Interaction between a screw dislocation and an oblique edge crack in a half-infinite MEE solid

Cited by 15 publications

References 27 publications

Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

Surface effect on a nano‐elliptical hole or nano‐crack in magnetoelectroelastic materials under antiplane shear

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

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