Weight Functions for Stress Intensity Factors and T-Stress for Oblique Cracks in A Half-Space

Fett, T.; Rizzi, G.

doi:10.1007/s10704-005-0024-9

Cited by 42 publications

(46 citation statements)

References 5 publications

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“…It must be underlined that, for these more complex cases, the WFs have been reported rather recently in the literature and only for few geometries, as a cracked half-plane [18,19].…”

Section: The Weight Functions Methodmentioning

confidence: 99%

“…For an oblique edge crack in a halfplane, two sources for the WFs can be found: [18,19]. In the first study, a solution is provided for 20 ∘ ≤ ≤ 90 ∘ through 80 coefficients of power series expansions, while in the second case 8 coefficients are given, but only for some discrete values of (15 ∘ , 30 ∘ , 45 ∘ , 60 ∘ , and 90 ∘ ) (see Appendix for complete details).…”

Section: Weight Functionsmentioning

confidence: 99%

“…At this point, the SIFs can be calculated by means of (4), changing the sign of if the WFs from [19] are chosen, that is, as anticipated in Section 3.2 and detailed in the Appendix.…”

Section: Model Implementationmentioning

confidence: 99%

“…The general expressions of the WFs in [18,19] are similar and can be written as functions of the coordinate along the crack (with origin at the crack mouth), of the crack length , and of the angle : in both [18,19], while , = 0 for > 2 in [19].…”

Section: Appendix Weight Function For An Oblique Crack In a Half-planementioning

confidence: 99%

“…As already stated, the coefficients , are provided as functions of the angle = /2 − in [18] and for some discrete values of it in [19]. They are plotted in Figure 10(a).…”

Section: Appendix Weight Function For An Oblique Crack In a Half-planementioning

confidence: 99%

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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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“…It must be underlined that, for these more complex cases, the WFs have been reported rather recently in the literature and only for few geometries, as a cracked half-plane [18,19].…”

Section: The Weight Functions Methodmentioning

confidence: 99%

Section: Weight Functionsmentioning

confidence: 99%

“…At this point, the SIFs can be calculated by means of (4), changing the sign of if the WFs from [19] are chosen, that is, as anticipated in Section 3.2 and detailed in the Appendix.…”

Section: Model Implementationmentioning

confidence: 99%

Section: Appendix Weight Function For An Oblique Crack In a Half-planementioning

confidence: 99%

“…As already stated, the coefficients , are provided as functions of the angle = /2 − in [18] and for some discrete values of it in [19]. They are plotted in Figure 10(a).…”

Section: Appendix Weight Function For An Oblique Crack In a Half-planementioning

confidence: 99%

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Analytical Modeling of an Oblique Edge Crack in Rolling Contact Fatigue

Puccio

2018

Mathematical Problems in Engineering

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A Trefftz method for evaluating the T‐stress for cracks emanating from a hole in a rectangular plate

Chen

Wang

Lin

2007

Commun. Numer. Meth. Engng.

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SUMMARYThis paper proposes a Trefftz method for evaluating the T -stress for cracks emanating from a hole in a rectangular plate. In this method, the displacement and the stress field are an elasticity solution, which is derived from complex potentials. The complex potentials are assumed in a series form with undetermined coefficients. After using the minimum potential energy principle, an algebraic equation for the undetermined coefficients can be formulated. The coefficients can be obtained from the equation, and the whole stress field is determined. Stress intensity factor and T -stress can be evaluated immediately from the known solution. Merit of the suggested method is addressed. For three particular cases, R = 0, R/w = 0.25 and R/w = 0.5, the computed results are tabulated.

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Crack paths and the problem of global directional stability

Pham

Bahr

et al. 2006

Int J Fract

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Crack paths of original Griffith crack and edge crack under biaxial remote mode-I loading after different local disturbances are calculated by using integro-differential equations of first-order perturbation and numerical simulation with FEM respectively.Considering the asymptotic behaviour for large crack lengths the problem of global directional stability is reinvestigated extending the work by Melin. For the Griffith crack, correct power functions for the asymptotic path with one or both crack tips growing have been determined. The wellknown critical stress biaxiality ratio R c = 1 for the global directional stability has been obtained independently whether the crack is disturbed by local imperfections in geometry or in loading. For an edge crack the calculated critical stress biaxiality ratio for the global directional stability R c = 0.616, also irrespective of the local disturbances, corresponds to a positive T-stress and is considerably smaller than the value R > 0.95 estimated by Melin (2002). In general, cracks need not propagate asymptotically in the direction perpendicular to the largest principal stress (without crack). This is found to be due to the effect of the boundaries.Considering the initial crack growth exclusively, it is shown that the solution for crack path prediction in series expansion form as derived by Cotterell and Rice (1980) for traction-free crack faces (after correction of a misprint) is exact in the two first terms in all cases. Thus, for small crack growth the Cotterell and Rice solution is universal with respect to all loading and geometrical situations.

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Weight Functions for Stress Intensity Factors and T-Stress for Oblique Cracks in A Half-Space

Cited by 42 publications

References 5 publications

Analytical Modeling of an Oblique Edge Crack in Rolling Contact Fatigue

Analytical Modeling of an Oblique Edge Crack in Rolling Contact Fatigue

A Trefftz method for evaluating the T‐stress for cracks emanating from a hole in a rectangular plate

Crack paths and the problem of global directional stability

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