Stress intensity factors for an edge cracked circular bar in tension and bending

Ng, C.K.; Fenner, D. N.

doi:10.1007/bf00017205

Cited by 25 publications

(10 citation statements)

References 10 publications

(19 reference statements)

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“…A comparative evaluation of the SIF results is performed for validation purposes with some results from the literature. The main results based on the Ng and Fenner model, are first given in Table for cracked beams subjected to a combined axial and bending force, and some additional expressions of dimensionless SIF are listed in the following Valiente model

\frac{K_{I_{N}} ((), η)}{σ_{N} \sqrt{π a}} = 1.4408 - 3.6364 η + 19.35 η^{2} - 34.7849 η^{3} + 36.8446 η^{4}

James and Mills model

\frac{K_{I_{N}} ((), η)}{σ_{N} \sqrt{π a}} = 0.926 - 1.771 η + 26.421 η^{2} - 78.481 η^{3} + 87.911 η^{4}

\frac{K_{I_{M}} ((), η)}{σ_{M} \sqrt{π a}} = 0.63 + 0.035 η - 3.336 η^{2} + 13.406 η^{3} - 6.002 η^{4}

with a crack depth 0.01 ≤ η ≤ 0.65 for a straight‐edged crack subjected to axial and bending loading. Daoud et al :

\frac{K_{I_{N}} ((), η)}{σ_{N} \sqrt{π a}} = 1.11 - 3.59 η + 24.87 η^{2} - 53.39 η^{3} + 57.23 η^{4}, 0.06 \leq η \leq 0.7

\frac{K_{I_{M}} ((), η)}{σ_{M} \sqrt{π a}} = 1.04 - 3.64 η + 16.86 η^{2} - 32.59 η

…”

Section: Numerical Results and Comparisonssupporting

confidence: 81%

“…Qizhi investigated the problem of three‐points bending of circular cracked beams with the synthesis method. Ng and Fenner built a 3D FEM with both straight and circular‐arc crack fronts in an edge‐cracked circular bar to compute SIFs in tension and bending. Shin and Cai applied experimental results and FEM to define the SIF of an elliptical surface crack in a circular shaft under tension and bending.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Cao

Dimitri

et al. 2016

Fatigue Fract Eng Mat Struct

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This paper examines two engineering methods of evaluating the stress intensity factors for cracked beams and bars subjected to a combined loading and proposes innovative formulations, as far as the circular cross section is concerned. Based on the definition of the stress intensity factors, the compliance matrix is determined as the inverse of the stiffness matrix, modelling the cracked section of a beam through a line‐spring approximation with interactive forces computed within fracture mechanics. A comparative evaluation of numerical predictions based on the proposed methods is also performed with methods available from the literature. Results for free vibration analyses of beams with transverse non‐propagating open cracks are presented and compared in order to estimate the accuracy and efficiency of the proposed methods, where a good agreement is generally found. More specifically, two different coupling effects are herein analysed for circular beams subjected to a combined bending, axial and shear loading, first, and a combined bending, shear and torsion loading, subsequently.

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\frac{K_{I_{N}} ((), η)}{σ_{N} \sqrt{π a}} = 1.4408 - 3.6364 η + 19.35 η^{2} - 34.7849 η^{3} + 36.8446 η^{4}

James and Mills model

\frac{K_{I_{N}} ((), η)}{σ_{N} \sqrt{π a}} = 0.926 - 1.771 η + 26.421 η^{2} - 78.481 η^{3} + 87.911 η^{4}

\frac{K_{I_{M}} ((), η)}{σ_{M} \sqrt{π a}} = 0.63 + 0.035 η - 3.336 η^{2} + 13.406 η^{3} - 6.002 η^{4}

with a crack depth 0.01 ≤ η ≤ 0.65 for a straight‐edged crack subjected to axial and bending loading. Daoud et al :

\frac{K_{I_{N}} ((), η)}{σ_{N} \sqrt{π a}} = 1.11 - 3.59 η + 24.87 η^{2} - 53.39 η^{3} + 57.23 η^{4}, 0.06 \leq η \leq 0.7

\frac{K_{I_{M}} ((), η)}{σ_{M} \sqrt{π a}} = 1.04 - 3.64 η + 16.86 η^{2} - 32.59 η

…”

Section: Numerical Results and Comparisonssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Cao

Dimitri

et al. 2016

Fatigue Fract Eng Mat Struct

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“…Under cyclic or repeated loadings, the fatigue failure of a round bar often develops. Many analyses have been carried out to determine the SIFs along the front of an edge flaw 1–5 . An actual surface crack is usually be replaced by an equivalent circular arc or an elliptical‐arc edge flaw.…”

Section: Introductionmentioning

confidence: 99%

Stress intensity factors for surface fatigue crack in a round bar under cyclic axial loading

Feng

Kuang

2007

Fatigue Fract Eng Mat Struct

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A B S T R A C T In this paper, the surface fatigue crack growth shape for an initial straight-fronted edge crack in an elastic bar of circular cross-section is determined through experiments under pure fatigue axial loading. Three different initial notch depths are discussed. The relations of the aspect ratio (b/c) and relative crack depth (b/D) are obtained, and it is shown that there is a great difference in the growth of cracks with different initial front shapes and crack depths. Further, using the three-dimensional finite element method, the stress intensity factors (SIFs) are determined under remote uniform tension loading. Since the relationship of b/c and b/D changes during the fatigue crack growth, the SIFs are determined for different surface crack configurations.

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“…Papers [11] and [12] deal with K-solutions for a cracked cylinder obtained by means of 3D finite element analysis, and [13] and [14] present results for the same body using the boundary integral equation method. In paper [15] the free surface effect is discussed, and [16] offers some K-solutions for a cracked cylinder in tension and bending. References [17][18][19][20][21] are devoted to fatigue crack growth in round bars.…”

Section: Introductionmentioning

confidence: 99%

Stress intensity factor solutions for a cracked bolt loaded by a nut

Toribio

1992

Int J Fract

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This paper presents the calculation of stress intensity factor (K) solutions for surface cracks in the thread ground of bolts subjected to axial loading directly applied by the nut. The stress-strain computations have been done by means of the finite element method with quarter-point singular isoparametric elements along the crack front. The stress intensity factor is calculated through the stiffness derivative method, by using a virtual crack extension technique to compute the energy release rate. Two modifications are made to improve the accuracy of the results: the displacement not only of the main node, but also of the quarter-point nodes located in the normal plane and the adjacent nodes in the crack line, avoiding both the change of the singularity and the crack curving. The results show that direct loading on the thread flank by a nut increases the stress intensity factor. This effect decreases with the crack length. For the deepest circular cracks, however, nut loading relaxes the K-value, mainly at the crack surface.

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Stress intensity factors for an edge cracked circular bar in tension and bending

Cited by 25 publications

References 10 publications

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Stress intensity factors for surface fatigue crack in a round bar under cyclic axial loading

Stress intensity factor solutions for a cracked bolt loaded by a nut

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