New integration scheme for the branch crack problem

Chen, Y.Z.; Hasebe, Norio

doi:10.1016/0013-7944(95)00052-w

Cited by 59 publications

(50 citation statements)

References 9 publications

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“…By substituting (20) and (21) into (14), letting the point z approach a point t o j ∈ L j on the j-th branch (see Figure 4b), and using the Plemelj formula for the Cauchy-type integral [Muskhelishvili 1953], one will find the following singular integral equation [Chen and Hasebe 1995]:…”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

“…In addition, the dislocation distribution g k (t) should satisfy the following single-valued condition of displacements [Chen and Hasebe 1995]:…”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

“…Once the solution for the function g j (t) is obtained from (22) and (26), the SIFs at the branch tip A j can be evaluated by [Savruk 1981;Chen and Hasebe 1995] …”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

“…Although, this assertion is not easy to prove theoretically. In the literature, many researchers use this assumption in the branch or kinked crack problems [Theocaris 1977;Savruk 1981;Chen and Hasebe 1995].…”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

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A singular integral equation method for examining asymptotic solutions of a kinked crack with infinitesimal kink length

Chen

Lin

Wang

2010

JOMMS

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This paper investigates the singular integral equation method for examining the stress intensity factor and the T-stress in the asymptotic solution of a kinked crack with an infinitesimal kink length. A numerical technique for the branch crack problem is introduced, which depends upon distribution of dislocation along the crack face. The technique reduces the branch crack problem to the solution of a singular integral equation. The kinked cracked problem can be considered as a particular case of the branch crack, and this problem can be solved by using the suggested technique. It is found from the computed results that the available asymptotic solution can give qualitatively correct results for stress intensity factors and the T-stress. In addition, the available asymptotic solution can only give sufficiently accurate results in a narrow range of the length of the kinked portion and the inclined kink angle.

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Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

“…In addition, the dislocation distribution g k (t) should satisfy the following single-valued condition of displacements [Chen and Hasebe 1995]:…”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

“…Once the solution for the function g j (t) is obtained from (22) and (26), the SIFs at the branch tip A j can be evaluated by [Savruk 1981;Chen and Hasebe 1995] …”

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

Section: Formulation For the Solution Of The Branch Crack Problemmentioning

confidence: 99%

See 2 more Smart Citations

A singular integral equation method for examining asymptotic solutions of a kinked crack with infinitesimal kink length

Chen

Lin

Wang

2010

JOMMS

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“…For example, there have been methods based on the quarter-point finite element (Barsoum 1974), the enriched finite element method (Gifford and Hilton 1978), the boundary collocation method (Newman 1971), the integral equation method (Sneddon 1973), the body force method (Nisitani 1985), the boundary elements method (Cruse 1988), and the dislocation method (Chen and Hasebe 1995), plus mesh-free methods such as the element-free Galerkin method (Fleming et al 1997). To avoid remeshing in modeling crack problems, diverse techniques were proposed, including the incorporation of a discontinuous mode on an element level (Oliver 1995), a moving mesh technique (Rashid 1998), and an enrichment technique based on a partition-of-unity X-FEM (Belytschko and Black1999).…”

Section: Introductionmentioning

confidence: 99%

A New Scheme for Crack Growth Modeling by Coupling Modified Quarter Point Crack-Tip Element and the Level Set Method

Abdelaziz

2013

Jou. Eng. Res.

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Abstract:In this paper, an efficient, numerical procedure is presented to track crack growth modeling without remeshing. The method's key feature is the coupling of a modified quarter-point crack tip element (MQPE) with the level set method (LSM) for crack growth problems. The LSM was used to represent the crack location, including the location of crack tips. The MQPE was used to compute the stress and displacement fields necessary for determining the rate of crack growth. Numerical test cases including various geometrical exceptions (the center-crack plate specimen, the single edge-crack plate specimen, and the double-edge crack plate) demonstrate the accuracy, robustness, and efficiency of the MQPE/LSM coupling. The extrapolation technique was used to estimate numerically the calibration factor for various specimens. This work confirms the feasibility of the MQPE/LSM to model accurately the singularity existing in the vicinity of the cracks. It allows an economic and adequate calculation of the stress intensity factors, which can be introduced into the various criteria of fracture or laws of propagation of the crack. The new method reduces the need for remeshing, and results agree well with reference data.

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Multiple branch crack problem for circular torsion cylinder

Chen

1999

Commun. Numer. Meth. Engng.

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SUMMARYA multiple branch crack problem for a circular torsion cylinder is studied in this paper. All branches emanate from the centre of the section. The relevant boundary problem belongs to the modi®ed Dirichlet problem. The modi®ed Dirichlet problem is converted into the solution of two Dirichlet problems of the Laplace equation for the doubly connected region. The ®nite dierence method is suggested to solve the problem. Finally, the torsion rigidity coecient can be evaluated. Numerical examples are given to demonstrate the use of the proposed method.

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New integration scheme for the branch crack problem

Cited by 59 publications

References 9 publications

A singular integral equation method for examining asymptotic solutions of a kinked crack with infinitesimal kink length

A singular integral equation method for examining asymptotic solutions of a kinked crack with infinitesimal kink length

A New Scheme for Crack Growth Modeling by Coupling Modified Quarter Point Crack-Tip Element and the Level Set Method

Multiple branch crack problem for circular torsion cylinder

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