The green's function for a slant edge crack

Hills, D.A.; Sackfield, A.; Uzel, Almıla

doi:10.1016/0013-7944(84)90130-9

Cited by 11 publications

(4 citation statements)

References 9 publications

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“…Green's function technique can also be used for fast calculation of stress intensity factors. In this method, Green's function is the stress intensity factor, which is calculated for a point load.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

Rad

Forouzan

Dolatabadi

2014

Fatigue Fract Eng Mat Struct

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In this paper, the fatigue crack growth in helical gear tooth root has been simulated using linear elastic fracture mechanics. The extended finite element method has been used to simulate 3D fatigue crack growth and obtain growth path. Paris equation has been used to calculate the fatigue life of the gear. The modelling time has reduced considerably compared to previous works carried out on 3D crack growth in gears. Some verifications have been carried out to ensure the reliability of the results.

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Section: Introductionmentioning

confidence: 99%

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

Rad

Forouzan

Dolatabadi

2014

Fatigue Fract Eng Mat Struct

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“…Some crack-line Green's functions have already been determined: Hartranft and Sih [4] determined them for the special case of a normal edge crack, and Hills et al [5] for a slant crack.…”

Section: Introductionmentioning

confidence: 99%

Crack‐line and Edge Green's Functions for Stress Intensity Factors of Inclined Edge Cracks

Rooke¹,

Rayaprolu²,

Aliabadi

1992

Fatigue Fract Eng Mat Struct

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Fretting loads on the surfaces of structural components can cause accelerated growth of short cracks. The rate of growth will depend on the combined stress intensity factor resulting from both remote and local loading. Many stress intensity factor solutions are available for remote loading, but solutions for arbitrary fretting loads are not readily accessible. In this paper accurate crack-line Green's functions are obtained from a boundary element analysis and then used to develop the Green's functions for loads on the edge of a half-plane containing a slant crack at various angles to the edge. These latter Green's functions can be used to obtain stress intensity factors for arbitrary stresses (normal or shear) on the edge of the half-plane without further stress analysis; simple integration procedures are all that is required. NOMENCLATURE= boundaries of applied edge stress B, = coefficient defined in equation (30) 0, = coefficient defined in equation (33) E(t, I) = integral defined in equation (D7) Eo(r, I) =integral defined in equation (D12) f = force on crack (p or q ) F = force on sheet edge (P or Q) g = general crack-line Green's function gf, = specific crack-line Green's function G = general edge Green's function G$ = specific edge Green's function Z(m, I) = integral defined in equation (D5) Zk = integral defined in equation (C4) J,,, = integral defined in equation (19) J, = J, -J,,,,, (m = 0, 1 . . . No + 2) K; = stress intensity factor due to force on edge i = summation variable in equation (25), i = 0, 1,. . . , I K, KN = general stress intensity factor K;, K:, = stress intensity factors due to stress (n or T ) on edge I = summation variable in equation (27), 1 = 0,1, . . . , L L,, = integral defined in equation (A5) rn = summation variable in equation (30), m = 0, 1, . . . , M n = summation variable in equation (13), n = 0, 1, . . . , No N = I, opening mode; N = 11, sliding mode p f = coefficients of normal-force crack-line Green's function q: = coefficients of shear-force crack-line Green's function p , q = normal and shear forces on crack faces P, Q = normal and shear forces on edge of sheet 441 442 D. P. ROOICE et al. r = radial distance (r2 = x 2 + y 2 ) s,'= non-dimensional stress defined in equation (7) S l = integral defined by equation (1 7) Kf = integral defined by equation (1 7) x, = position of force on crack x, y = global Cartesian co-ordinates X = q / a y = lbll(lbl + a ) z = JI -zux sin 9 + U'X* 3%=s!-s!+2TL= T,F-T;,, 11, < = local Cartesian coordinates 9 = angle between crack and normal to edge p = Jb2 -2bq sin 9 + q 2 u = applied stress uo = normal stress constant u,= general stress at crack site a , = general stress on edge of half-plane u{ = stress at crack site in direction off due to force F on edge T = applied shear stress q, = shear stress constant

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“…Damage processes as pitting, spalling, fretting [2], or even catastrophic failures [3] are frequently attributed to fatigue phenomena. This topic has attracted many researchers since the 1980s, for example, [4][5][6][7], but a renewed interest has characterized the last decade, for example, [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of an Oblique Edge Crack in Rolling Contact Fatigue

Puccio

2018

Mathematical Problems in Engineering

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Surface cracks represent a frequent cause of damage and even failure in rolling contacts, observed in gears, cams, rails, and so on. In the literature, different approaches have been applied to describe the crack behaviour by means of Fracture Mechanics parameters, such as the stress intensity factors (SIFs) and the -integral. In this paper, a general procedure for dealing with plane problems is presented, which is based on Linear Elastic Fracture Mechanics hypotheses. It combines the Weight Function Method for evaluating the SIFs in a loading cycle with the Kolosov-Muskhelishvili complex variable approach for estimating the nominal stress field. In this way, a completely analytical procedure can be applied for a general loading condition, assuming that the real geometry can be simplified in a half-plane with an oblique edge crack. As test case, a travelling load has been considered representing a combination of three contributions: Hertzian pressure distribution, traction force due to friction, and pressurization of the crack faces. A comparison with literature results proved that the proposed approach can be an efficient tool for SIFs estimation and crack growth description.

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The green's function for a slant edge crack

Cited by 11 publications

References 9 publications

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

Crack‐line and Edge Green's Functions for Stress Intensity Factors of Inclined Edge Cracks

Analytical Modeling of an Oblique Edge Crack in Rolling Contact Fatigue

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