Calculation of mixed mode stress intensity factors for an elliptical subsurface crack under arbitrary normal loading

K., J. Alizadeh; Ghajar, Rahmatollah

doi:10.1111/ffe.12271

Cited by 10 publications

(4 citation statements)

References 25 publications

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“…The modeling and calculation are more troublesome when applying error ellipse to determine the coordinates of the point. To improve the shortcomings of the bootstrap method, based on calculation and modeling (Liu et al, 2019;Prabhu et al, 2017;Shu et al, 2017;Wu et al, 2016;Wu et al, 2018) and considering the characteristics of two-dimensional (2D) normal distribution (Alizadeh and Ghajar, 2015), the error ellipse method is proposed. The fatigue measure data (Li and Lu, 2007;Wormsen et al, 2015) of AISI 8630 M (5) steel and LY12CZ aluminum alloy sheets are analyzed by the error ellipse model; it can reduce sampling errors and obtain reasonable S-N curves.…”

Section: Introductionmentioning

confidence: 99%

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

Liu

Fang

et al. 2020

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Purpose The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve. Design/methodology/approach Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution. Findings By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method. Originality/value The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

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Section: Introductionmentioning

confidence: 99%

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

Liu

Fang

et al. 2020

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“…A number of two‐dimensional WFs were derived including two‐dimensional point load WF for semielliptical cracks in thin plates . Moreover, Ghajar and Alizadeh Kaklar utilized two‐dimensional WF as the components of a 3 × 3 matrix in order to determine the SIFs for the elliptical subsurface cracks under arbitrary normal and shear loadings. Each WF is applicable for an individual geometry of cracked body.…”

Section: Introductionmentioning

confidence: 99%

A new weight function for one‐dimensional subsurface cracks under general loading

Abdoli

Khezri

Kaklar

2019

Fatigue Fract Eng Mat Struct

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In the present study, weight functions (WFs) of a subsurface crack were derived by proposing a new general form for approximate one‐dimensional WF. The WFs coefficients were considered as a function of crack length to depth ratio and were obtained using reference stress intensity factors (SIFs) of 16 cracks under uniform, linear, and parabolic normal and shearing loadings. The verification was performed by comparison of the straight and coupled SIFs calculated by WF and finite element modelling under some complicated loadings. In conclusion, the WFs can be simply and effectively employed for evaluating the cracks under any complex stress distributions.

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“…Some analytical weight functions available in the literature are able to relate the SIF at each point of an embedded planar two‐dimensional crack subjected to mode I loading or under mixed mode loading . The Oore‐Burns weight function displays a simple analytic form and gives an exact result in the special cases of penny‐shaped cracks or tunnel cracks.…”

Section: Introductionmentioning

confidence: 99%

“…9 Some analytical weight functions available in the literature are able to relate the SIF at each point of an embedded planar two-dimensional crack subjected to mode I loading [10][11][12][13][14] or under mixed mode loading. 15,16 The Oore-Burns 12 weight function displays a simple analytic form and gives an exact result in the special cases of penny-shaped cracks or tunnel cracks. Furthermore, this weight function can be used for surface cracks after the introduction of proper coefficients inferred from classical analysis of a surface elliptical crack such as Normal-Rauj equations (see for instance refinements).…”

Section: Introductionmentioning

confidence: 99%

An approximation in closed form for the integral of Oore–Burns for cracks similar to a star domain

Livieri

Segàla

2017

Fatigue Fract Eng Mat Struct

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A B S T R A C T In this paper, we give an explicit new formulation for the three-dimensional mode I weight function of Oore-Burns in the case where the crack border agrees with a star domain. Analysis in the complex field allows us to establish the asymptotic behaviour of the Riemann sums of the Oore-Burns integral in terms of the Fourier expansion of the crack border. The new approach gives remarkable accuracy in the computation of the Oore-Burns integral with the advantage of reducing the size of the mesh. Furthermore, the asymptotic behaviour of the stress intensity factor at the tip of an elliptical crack subjected to uniform tensile stress is carefully evaluated. The obtained analytical equation shows that the error of the Oore-Burns integral tends to zero when the ratio between the ellipse axes tends to zero as further confirmation of its goodness of fit.Keywords 3D weigh function; fracture mechanics; stress intensity factor. N O M E N C L A T U R Ea,b = dimensionless semi-axis of an elliptical crack a; b = actual semi-axis of an elliptical crack e = eccentricity of ellipse k I = mode I stress intensity factor for a dimensionless domain u , v = auxiliary dimensionless coordinate system x , y = dimensionless Cartesian coordinate system x; y = actual Cartesian coordinate system E(e) = elliptical integral of second kind K I2 = Taylor expansion up to second order of K I for an ellipse K(e) = elliptical integral of first kind K I = mode I stress intensity factor K Irw = mode I stress intensity factor from Irwin's equation Q = point of Ω Q ' = point of crack border δ = size of mesh over crack Δ = distance between Q and ∂Ω σ n = nominal tensile stress in x; y actual Cartesian coordinate system σ = nominal tensile stress in x; y dimensionless Cartesian coordinate system Ω = crack shape ∂Ω = crack border I N T R O D U C T I O NThe advantages of the use of weight functions for the assessment of stress intensity factors (SIFs) are well known in the literature, especially when many loads act on the component. For each geometry, we have to estimate the correct weight function related to the location where the crack nucleates and then propagates under fatigue loading. For a correct evaluation of the SIF, the proper weight function should be calculated;Correspondence: P. Livieri.

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Calculation of mixed mode stress intensity factors for an elliptical subsurface crack under arbitrary normal loading

Cited by 10 publications

References 25 publications

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

A new weight function for one‐dimensional subsurface cracks under general loading

An approximation in closed form for the integral of Oore–Burns for cracks similar to a star domain

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