Analysis of the non-singular stress terms for the sharp notches under anti-plane loading

Yang, Yongyu; Pan, Wei; Yao, Shanlong; Chen, Cheng; Wu, Qiaoguo

doi:10.1016/j.engfracmech.2021.107583

Cited by 8 publications

(6 citation statements)

References 33 publications

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“…In a recent work, Yang et al 33 employed a determined system of equations ( N = 3 in Figure 11) to calculate the unknown coefficients of sharp notches under antiplane loading conditions. It is seen in Figure 11 that this determined approach (i.e., three equations for three coefficients) leads to significant error even for the coefficient of the first term, especially when the angle of notch is small.…”

Section: Resultsmentioning

confidence: 99%

“…It is seen in Figure 11 that this determined approach (i.e., three equations for three coefficients) leads to significant error even for the coefficient of the first term, especially when the angle of notch is small. On the other hand, the approach used by Yang et al 33 is highly sensitive to the selection of nodes such that the values calculated as the coefficients will be changed as the input nodes change. These limitations do not exist in the method adopted in this paper.…”

Section: Resultsmentioning

confidence: 99%

“…As seen, under tractionfree boundary conditions, the first eigenvalue is always less than one, which causes stress singularity at the notch tip. Noteworthy to mention that Yang et al 33 have used another method for obtaining the eigenvalues of this problem. They used an unknown angular function instead of using definite relations to describe stress and displacement fields.…”

Section: Analytical Framework 21 | Displacement and Stress Fieldsmentioning

confidence: 99%

“…Fractal-like finite element method (FFEM) and strain energy approach (SEA) were used by Treifi and his coworkers 31,32 to compute SIFs of homogeneous and bi-material sharp Vnotches subjected to modes I, II, and III loadings. In the most recent work, Yang et al 33 utilized FEM and derived a series expansion similar to the Williams series and attempted to evaluate SIF and HOT coefficients for a sharp notched plate under antiplane loading.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Mehraban

Ayatollahi

Bahrami

et al. 2021

Fatigue Fract Eng Mat Struct

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Current paper studies the effects of higher order terms (HOTs) on the stress and displacement fields around sharp V-notched components under pure antiplane shear (mode III) loading. For this aim, two V-notched test samples each containing four different notch angles are simulated in a finite element (FE) commercial software. Subsequently, the over-deterministic technique is used as an approach to calculate the coefficients of singular and nonsingular terms out of the nodal displacement values. To verify the accuracy of the values calculated as the coefficients, the stress field reconstructed from the truncated series expansions is compared with the direct nodal outputs of FE analysis. The results demonstrate that the use of nonsingular terms of the asymptotic series expansion is necessary only in the case that the distribution of stress at far distances from the notch tip is sought and the notch angle is small. To check the stability of the results, some of the parameters which affect accurate determination of unknown coefficients and convergence of the numerical results are studied.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Analytical Framework 21 | Displacement and Stress Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Mehraban

Ayatollahi

Bahrami

et al. 2021

Fatigue Fract Eng Mat Struct

View full text Add to dashboard Cite

show abstract

“…Strain energy approach (SEA) and fractal-like finite element method (FFEM) were developed by Treifi and Oyadiji 22,23 for calculation of the generalized stress intensity factors (SIFs) of bi-material notches. In a recent study, Yang et al 24 assumed that the displacement field at the vicinity of notch tip can be described by a series expansion which is consisted of two separate functions. The first function is based on the radial distance from the notch tip and the second function is an angular function dependent on the angle of each point relative to the notch bisector line.…”

Section: Introductionmentioning

confidence: 99%

On the effects of higher order stress terms in pure mode III loading of bi‐material notches

Bahrami

Ayatollahi

Mehraban

et al. 2022

Fatigue Fract Eng Mat Struct

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The effects of higher order terms (HOTs) on the stress distribution at the vicinity of the sharp corner of two bonded dissimilar materials were investigated under pure out‐of‐plane (mode III) loading. To achieve this aim, finite element (FE) analysis in conjunction with the over‐deterministic technique were performed for two specimens, each containing four different notch opening angles. The coefficients of singular and non‐singular stress terms were then computed from the displacement field determined from the FE analysis. The elastic stresses obtained directly from the FE analysis were compared with those reconstructed from the truncated series expansions, in order to validate the accuracy of the calculated coefficients. The numerical results show that although the contribution of HOTs in the out‐of‐plane stress field is less than that of the in‐plane notch problems, ignoring their effects can lead to considerable errors in the stress field estimation. The magnitude of numerical error depends on the geometry and loading conditions of the bi‐material notch.

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Stress and strain fields near cracks in solids with stress state-dependent elastic properties under conditions of anti-plane shear

Lomakin,

Korolkova

2024

Acta Mech

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Analysis of the non-singular stress terms for the sharp notches under anti-plane loading

Cited by 8 publications

References 33 publications

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

On the effects of higher order stress terms in pure mode III loading of bi‐material notches

Stress and strain fields near cracks in solids with stress state-dependent elastic properties under conditions of anti-plane shear

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