Numerical methods for determination of stress intensity factors of singular stress field

Liu, Yihua; Wu, Zhaoxing; Yong-cheng, Liang; Liu, Xiaomei

doi:10.1016/j.engfracmech.2008.06.007

Cited by 41 publications

(27 citation statements)

References 34 publications

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“…On the other hand, almost all of the previous studies [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] are focused on the methods for determining NSIFs and not the coefficients of the higher order terms. Hence, the determination of the coefficients of higher order terms in notched components can be of great importance.…”

Section: Introductionmentioning

confidence: 99%

“…Noda and Takase [43] calculated the 3D NSIFs for a V-shaped notch in a round bar using the singular integral equation of the body force method. Liu et al [44] proposed a numerical approach for calculating the NSIFs as well as the orders of stress singularity by using the stresses obtained from finite element analysis. Treifi et al [45] extended the Fractallike Finite Element Method (FFEM) to model the singularity conditions resulting at a notch tip.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method

Ayatollahi

Nejati

2011

International Journal of Mechanical Sciences

102

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method

Ayatollahi

Nejati

2011

International Journal of Mechanical Sciences

102

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“…4. Applying the numerical method developed by Liu et al (2008), from these distributions the values of the order of the stress singularity λ I − 1 for the aforementioned stress components σ r , σ θ , τ r θ are calculated numerically as −0.2355, −0.2409, −0.2265, respectively. These numerical results are in good agreement with the theoretical value, −0.2324, obtained from the eigenequation (23), the maximum of the relative error being 3.66%.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Asymptotic fields near an interface corner in orthotropic bi-materials

Liu

2009

Int J Fract

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Based on the existing asymptotic solutions of the displacement and singular stress fields in the vicinity of a singular point in 2D orthotropic elastic materials, the two simple eigenequations are explicitly given for the symmetric and anti-symmetric deformation modes to determine the orders of the stress singularity at the interface corner in orthotropic bi-materials, respectively. The related displacement and singular stress fields near the interface corner are also explicitly established. The relevant stress intensity factors are defined as in the case of crack problems. The theoretical results have been confirmed by numerical, finite-element-based results in a special bi-material case. The solution obtained in this paper may be applied to the interface corner in the orthotropic/orthotropic, orthotropic/isotropic, and isotropic/isotropic bi-materials, and it will be very useful to evaluate the strength of the bonded orthotropic bi-materials with interface corners.

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“…As a result of the above procedure, the displacement and singular stress fields near the interface edge are derived in the completely explicit expressions. Although the path independent H-integral, which was employed by many authors Dunn, 1999, 2002;Shin et al, 2007), is one of the most powerful method, we here use a simpler and very effective numerical method proposed by Liu et al (2008) to determinate stress intensity factors. According to this method, the orders of the stress singularity as well as the related stress intensity factors can be numerically calculated simultaneously by applying the asymptotic solution of the singular stress field and FEM results.…”

Section: Introductionmentioning

confidence: 99%

Singular stress field near interface edge in orthotropic/isotropic bi-materials

Liu

2010

International Journal of Solids and Structures

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a b s t r a c tBased on the asymptotic fields near the singular points in two-dimensional isotropic and orthotropic elastic materials, the eigenequation as well as the displacement and singular stress fields near the interface edge, with an arbitrary wedge angle for the orthotropic material, in orthotropic/isotropic bi-materials are formulated explicitly. The advantages of the developed approach are that not only the eigenequation is directly given in a simple form, but also the eigenvector is no longer needed for the determination of the asymptotic fields near the interface edge. This approach differs from the known methods where the eigenequation is constantly expressed in terms of a determinant of matrix, and the eigenvector is required for the determination of the asymptotic fields. Therefore, the solution proposed in this paper is more convenient and effective for the analysis of the singular stresses near the interface edge in the orthotropic/isotropic bi-material. To demonstrate the validity of the presented formulae, an example is selected for the comparison of analytical and FEM results. According to the theoretical analyses, the influences of the wedge angle and material constant of the orthotropic material on the singular stresses near the interface edge are discovered clearly. The results obtained may give some references to certain engineering designs such as the structural repair or strengthening.

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Numerical methods for determination of stress intensity factors of singular stress field

Cited by 41 publications

References 34 publications

Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method

Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method

Asymptotic fields near an interface corner in orthotropic bi-materials

Singular stress field near interface edge in orthotropic/isotropic bi-materials

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