New weight functions and second order approximation of the Oore–Burns integral for elliptical cracks subject to arbitrary normal stress field

Livieri, Paolo; Segàla, Fausto

doi:10.1016/j.engfracmech.2015.02.008

Cited by 11 publications

(10 citation statements)

References 26 publications

(30 reference statements)

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“…By calling I 2 , the Taylor expansion of the second order of the Irwin SIF K Irw , and K I2 , the Taylor expansion of the second order of the OB integral K I , from Ref. [26] we obtain the approximation K I ≈ K Irw + K I2 À I 2 precisely up to 10 À3 in the range of 0.5 ≤ b ≤ 1. In Table 4, the agreement among the results obtained with different equation is satisfactory.…”

Section: U N I T a R Y E L L I P T I C A L C R A C K Smentioning

confidence: 94%

“…Furthermore, the same table reports the calculation of the approximation K I 2 of K I obtained by means of a second‐order approximation of the OB integral proposed in explicit form in Ref. []. The conclusion is that Eq.…”

Section: Unitary Elliptical Cracksmentioning

confidence: 97%

“…For the special case of ellipse cracks, the authors obtained a careful closed‐form representation of the OB integral along elliptic cracks under general pressure from previous papers. More precisely, they found a closed expression of the second‐order Taylor expansion of the SIFs with respect to deviation of the ellipse from the disc for a generic tensile stress over the crack . The deviation of an ellipse from the disc is quantitatively described by the parameter ε = 1 − b / a , where a and b are the major and minor semi‐axes respectively.…”

Section: Introductionmentioning

confidence: 99%

“…More precisely, they found a closed expression of the second-order Taylor expansion of the SIFs with respect to deviation of the ellipse from the disc for a generic tensile stress over the crack. 26 The deviation of an ellipse from the disc is quantitatively described by the parameter ε = 1 À b/a, where a and b are the major and minor semi-axes respectively. The exact evaluation of the OB integral by means of an explicit quadrature formula with a polar integration grid was also considered by the authors in Ref.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: U N I T a R Y E L L I P T I C A L C R A C K Smentioning

confidence: 94%

Section: Unitary Elliptical Cracksmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…For example, in flaw characterisation adopted in the fitness-for-service procedure, the flaw is modelled by a simpler geometry such as a trough crack with a straight crack front or with an elliptical or semi-elliptical shape. In this cases, the OB integral should be adopted because the characterisation of a semi-axial ellipse (1, b), when eccentricity e tends to zero, the main contribution of the OB integral T differs from Irwin's analytical solution [11] for a small amount equal to 2 20 e  [12], where e is the eccentricity of the ellipse. The OB integral could also be useful in the fatigue life assessment of materials with small internal defects.…”

Section: Introductionmentioning

confidence: 99%

A closed form for the Stress Intensity Factor of a small embedded square-like flaw

Livieri

Segàla

2020

Frattura Ed Integrità Strutturale

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In the present work, the stress intensity factor (SIF) of a small embedded square-like flaw is calculated by means of a procedure based on the Oore-Burns integral. An explicit equation is given to evaluate the SIF along the two axes of symmetry that correspond to the points where the SIF takes its maximum and minimum value on the contour crack. The SIF is calculated in accordance with FE numerical results.

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Comparison of two numerical procedures for solution of the integro-differential equation of flat crack problem

Оrynyak

Oryniak

2016

Engineering Fracture Mechanics

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New weight functions and second order approximation of the Oore–Burns integral for elliptical cracks subject to arbitrary normal stress field

Cited by 11 publications

References 26 publications

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

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

A closed form for the Stress Intensity Factor of a small embedded square-like flaw

Comparison of two numerical procedures for solution of the integro-differential equation of flat crack problem

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