A practical method to estimate the stress concentration of notches

Shin, C.S.; Man, Ke; Wang, C.M.

doi:10.1016/0142-1123(94)90338-7

Cited by 58 publications

(28 citation statements)

References 8 publications

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“…Problems of stress concentration and notch tip stress distribution are also dealt with in two recent and important contributions [14,15]. Approximate expressions and close-form solutions, based essentially on Neuber, Creager-Paris, Shin and Glinka's formulas (sometimes modified by means of geometry correction factors), are reported.…”

Section: Introductionmentioning

confidence: 99%

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

1996

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The problem of evaluating linear elastic stress fields in the neighborhood of cracks and notches is considered. An analytical solution valid for cracked and notched components is given in general terms, according to Muskhelishvili's method based on complex stress functions. The solution is particularly useful for V-shape notches in wide and finite plates under uniform tensile loading. It will be demonstrated that some remarkable solutions of fracture mechanics and notch analysis already reported in the literature can be considered special cases of this general solution, as soon as appropriate values of the free parameters are adopted.

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Section: Introductionmentioning

confidence: 99%

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

1996

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“…Since the theoretical 2D solutions for the stress concentrations regarding holes in infinite bodies have been obtained based on the classical complex variables (Muskhelishvili 1963;Savin 1961), many efforts have been made to achieve planar solutions for holes and notches in infinite plates (Sadowsky and Sternberg 1947;Shin et al 1994;Moftahar et al 1995;Singh et al 1996;Wang et al 1999). However, these planar solutions can not describe the effects of thickness and material properties on the stress fields.…”

Section: Three-dimensional Effects On the Stress Concentrations At Nomentioning

confidence: 98%

Three-dimensional stress fields near notches and cracks

2008

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Structures with notches have a tendency to develop critical crack growth because of the stress concentration. The strength of the structures with stress gradient usually shows strong three-dimensional (3D) effects even under in-plane loading. The commonly twodimensional (2D) models for fracture assessments of bodies with notches and cracks may lead to inaccurate predictions when in-plane loading is applied to certain 3D geometries. In the paper, the recent researches on the 3D effects of stress concentrations at notches and 3D stress fields of cracks are summarized. A new concept of equivalent thickness of the point on the crack front line is proposed based on the detailed analyses of the 3D out-ofplane stress fields of cracks, and then new empirical formulae of the 3D out-of-plane stress constraint factor T z of I-II mixed-mode cracks are obtained by use of the equivalent thickness. Combining the T z with the in-plane constraint parameters T or Q, the 3D multi-parameter descriptions of the stress field in front of various types of cracks using K -T z , J -T z , K -T -T z and J -Q-T z combination can be formulated.

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“…where w is the correction function obtained from the former case of an ellipse in an infinite plate under tensile stress: Table 6 Comparison between the predicted and FEA peak stresses obtained by Shin et al (1994) for two identical collinear ellipses in an infinite plate aligned perpendicular to the axial loading direction (e percent error) Murakami (1987) reported in Shin et al (1994) The correction function (64) is valid when the stress over the area covered by the notch is principally subjected to tensile loading. If we insert the linear simplification (25) of J Vρ in Eq.…”

Section: J Vρ For Peak Stress Evaluation From Sif Under Mode I Loadingmentioning

confidence: 98%

“…(63). All numerical data are taken from the work of Shin et al (1994) where the difference from FEA and the Inglis' exact solution was found to be around 1-2% when the a/b ratio ranges from 0.107 to 2.979. Tables 6 and 7 show a sound agreement between the FE results and the analytical ones.…”

Section: J Vρ For Peak Stress Evaluation From Sif Under Mode I Loadingmentioning

confidence: 99%

Analytical evaluation of J-integral for elliptical and parabolic notches under mode I and mode II loading

Livieri

Segàla

2007

Int J Fract

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In the present work the J-integral (indicated here as J Vρ because two parallel flanks are not present) was calculated by using, along the free border, the exact analytical stress distribution for the ellipse and the asymptotic one for parabolic notches. The material was assumed as homogeneous isotropic and linear elastic. First, for an ellipse under remote tensile loading, the expression of J Vρ has been analytically calculated on the basis of Inglis' equations. The equations have been used to prove that, in terms of J-integral, the crack is the limit case of an equivalent elliptic notch. Furthermore, by distinguishing the symmetric and skew-symmetric terms, the well-known Stress Intensity Factors (SIF) of mode I and II for a crack in a wide plate under tension are obtained by adding a limiting condition. Second, by means of Creager-Paris' equations, J Vρ has been analytically calculated for a parabolic notch of assigned tip notch radius ρ. The asymptotic value of J Vρ and the relationship between the peak stress and the relative SIF are the same as the ellipse. Finally, as an engineering application, we provide an accurate formula for the evaluation of the Notch Stress Intensity Factors of a crack, mainly subjected to tensile stress, from the peak stress of the equivalent ellipse under the same loading.

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A practical method to estimate the stress concentration of notches

Cited by 58 publications

References 8 publications

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

Three-dimensional stress fields near notches and cracks

Analytical evaluation of J-integral for elliptical and parabolic notches under mode I and mode II loading

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