Interaction of an edge dislocation with a coated elliptic inclusion

Chen, Fu Mo; Chao, Ching‐Kong; Chen, Chin Kun

doi:10.1016/j.ijsolstr.2011.01.027

Cited by 23 publications

(2 citation statements)

References 26 publications

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“…In the same year, the interaction between an edge dislocation and bimetallic elastic solid was reduced to two standard problems in potential theory by him [4]. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, Chen et al [5] derived the analytical solution for plane elasticity problems of an elliptically cylindrical layered media subject to an arbitrary edge dislocation. Zhou et al [6] reviewed recent works about inclusions well.…”

Section: Introductionmentioning

confidence: 99%

Interaction between a screw dislocation and an elastic elliptical inhomogeneity by using the angular basis function

Chen

Lee

Kao

2022

Z. Angew. Math. Phys.

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The behavior of displacement field due to a screw dislocation is similar to the angular basis function (ABF) Arg(z). It is different from the radial basis function (RBF) ln(r) that is used to describe the velocity potential of a sink or source. Nevertheless, the complex-valued fundamental solution ln(z) contains the two parts of RBF ln(r) and ABF Arg(z). In this paper, not only the RBF in the null-field boundary integral equation (BIE) but also the ABF for the screw dislocation are employed to study the interaction between a screw dislocation and an elastic elliptical inhomogeneity. This problem is decomposed into a free field with a screw dislocation and a boundary value problem containing an elliptical inhomogeneity. The boundary value problem is solved by using the RBF and the null-field BIE. Since the geometric shape is an ellipse, the degenerate kernel is expanded to a series form under the elliptical coordinates, while the unknown boundary densities are expanded to eigenfunctions. By combining the degenerate kernel and the null-field BIE, the boundary value problem can be easily solved. The inconsistency between Sendeckyj [1] and Gong & Meguid [2] for the problem was also found by using the present approach. The error in [2] was also printed out. Finally, some examples are demonstrated to verify the validity of the present approach.

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Section: Introductionmentioning

confidence: 99%

Interaction between a screw dislocation and an elastic elliptical inhomogeneity by using the angular basis function

Chen

Lee

Kao

2022

Z. Angew. Math. Phys.

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“…Those include a dislocation embedded in any shapes of multilayered composite, such as: circular media [2], elliptic media [3], and plane layered media [4]. A fracture mechanics problems also can be solved using complex potential methods together with logarithmic singular integral equations [5].…”

Section: Introductionmentioning

confidence: 99%

Complex Potential Methods for a Crack and Three-phase Circular Composite in Anti-plane Elasticity

Wikarta¹,

Wasiwitono²,

Sidharta³

2017

Int. Journal of Mech. Eng. Sc.

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Interaction between an anti-plane crack with a three-phase circular composite by using complex potential methods is considered in this paper. The solution procedures for solving this problem consist of two parts. In the first part, based on complex potential methods in conjunction with analytical continuation theorem and alternating technique, the complex potential functions of a screw dislocation interacting with three-phase circular composites are obtained. The second part consists of the derivation of logarithmic singular integral equations by introducing the complex potential functions of screw dislocation along the crack border together with superposition technique. The logarithmic singular integral equations is then solved numerically by modeling a crack in place of several segments. Linear interpolation formulae with undetermined coefficients are applied to approximate the dislocation distribution along the elements, except at vicinity of crack tip where the dislocation distribution preserves a square-root singularity. The mode-III stress intensity factors are then obtained numerically in terms of the values of the dislocation density functions of the logarithmic singular integral equations.

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A Numerical Determination of the Interactions Between Dislocations and Multiple Inhomogeneities

Jiang

Liu

Zhu

et al. 2023

Advanced Structured Materials

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Interaction of an edge dislocation with a coated elliptic inclusion

Cited by 23 publications

References 26 publications

Interaction between a screw dislocation and an elastic elliptical inhomogeneity by using the angular basis function

Interaction between a screw dislocation and an elastic elliptical inhomogeneity by using the angular basis function

Complex Potential Methods for a Crack and Three-phase Circular Composite in Anti-plane Elasticity

A Numerical Determination of the Interactions Between Dislocations and Multiple Inhomogeneities

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