Stress intensity factors calculation for surface crack in cylinders under longitudinal gradient pressure using general point load weight function

Googarchin, Hamed Saeidi; Ghajar, Rahmatollah

doi:10.1111/ffe.12101

Cited by 18 publications

(9 citation statements)

References 20 publications

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“…A careful analysis of our technique allows us to amend Eq. (14). Let α be the coordinate of the pole Q 0 .…”

Section: S T a R D O M A I N Smentioning

confidence: 99%

“…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%

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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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“…A careful analysis of our technique allows us to amend Eq. (14). Let α be the coordinate of the pole Q 0 .…”

Section: S T a R D O M A I N Smentioning

confidence: 99%

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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“…14 Ghajar and Saeidi Googarchin showed that this general form of WF can be used for surface cracks. 24,25 M…”

Section: W E I G H T F U N C T I O N M E T H O Dmentioning

confidence: 99%

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

Ghajar

2014

Fatigue Fract Eng Mat Struct

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A B S T R A C T Normal loading causes mixed fracture modes in an elliptical subsurface crack because of the nonsymmetrical geometry with respect to the crack face. In this paper, mixed mode weight functions (MMWFs) for elliptical subsurface cracks in an elastic semi-infinite space under normal loading are derived. Reference mixed mode stress intensity factors (MMSIFs), calculated by finite element analysis, under uniform normal loading are used to derive MMWFs. The cracks have aspect ratios and crack depth to crack length ratios of 0.2-1.0 and 0.05 to infinity, respectively. MMWFs are used to calculate MMSIFs for any point of the crack front under linear and nonlinear two-dimensional (2D) loadings. So, in order to evaluate the fatigue crack growth phenomenon under complicated 2D stress distributions, MMWFs can be easily used. The comparison between the MMSIFs obtained from the MMWFs and finite element analysis indicates high accuracy.Keywords elliptical subsurface cracks; mixed mode weight functions; semi-infinite space; two-dimensional stress distribution. N O M E N C L A T U R EA = crack face area A im = constant coefficients AE max = maximum absolute error a = semi-major axis of ellipse, crack length a ij = coefficients B nim = constant coefficients b ij = coefficients c = semi-minor axis of ellipse c ij = coefficients D I = weight function coefficient, mode I D II = weight function coefficient, mode II D III = weight function coefficient, mode III D i = weight function coefficients d i = coefficients E(α) second kind of the elliptical integral E′ = material constant h = depth of the crack K I = mode I stress intensity factor K In = normalized mode I stress intensity factor K II = mode II stress intensity factor K IIn = normalized mode II stress intensity factor K III = mode III stress intensity factor K IIIn = normalized mode III stress intensity factor K r = reference stress intensity factor L = point of loading MRE(%) = mean relative error Correspondence: R. Ghajar.

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“…Hence the instability extension of a hydraulic fracture can be analysed based on linear elastic fracture mechanics (LEFM) 17 . Stress intensity factor is not only an important parameter to express the crack-tip stress, but an important index to judge the crack instability state in LEFM 18 . Therefore, it is of great significance to analyse the distribution characteristics of the crack-tip stress field in an anisotropic material, understand the anisotropy of coal rock fracture toughness, and further study the complex extension rule of a hydraulic fracture.…”

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confidence: 99%

Effects of Bedding on Hydraulic Fracturing in Coalbed Methane Reservoirs

et al. 2017

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Bedding is a special structure of coal, which has notable effects on the mechanical parameters of coal and on the hydraulic fracture propagating in coalbed methane reservoirs. To study the effects of bedding on anisotropic characteristics of coal fracture toughness, three-point bending tests have been carried out on raw coal specimens. The results indicate that fracture toughness and failure modes of the specimens both have strong anisotropy due to bedding. A geological geomechanical model of a coalbed methane (CBM) reservoir is built taking into account the effect of bedding to study the hydraulic fracture propagation and the influence of bedding on the fracture network. The hydraulic fracture initiates at the end of the perforation and tends to bifurcate and swerve at the bedding to produce induced fractures. Ultimately, these fractures form a complicated fracture network. The fracture toughness of bedding has great influence on hydraulic fracture geometry. The fracture is likely to bifurcate and swerve at the bedding to form multiple secondary fractures with larger bedding fracture toughness.

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Stress intensity factors calculation for surface crack in cylinders under longitudinal gradient pressure using general point load weight function

Cited by 18 publications

References 20 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

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

Effects of Bedding on Hydraulic Fracturing in Coalbed Methane Reservoirs

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