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

Оrynyak, І. V.; Oryniak, Andrii

doi:10.1016/j.engfracmech.2016.04.018

Cited by 1 publication

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…Murakami 8 suggested a shape factor, referred to as the square root of the area, about 0.5 for an engineering estimation of the maximum SIF for an arbitrarily 3D internal crack or 0.65 for an arbitrarily 3D surface crack. 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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%