Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

Stress intensity factor solutions for two-dimensional elastostatic problems by the hypersingular boundary integral equation

2009 ◽  
Vol 44 (4) ◽  
pp. 235-247 ◽  
Author(s):  
A Sahli ◽  
O Rahmani
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Hypersingular Boundary Integral Equation

The boundary element method is a numerical method that can be advantageously used for a wide range of engineering problems, including the stress concentration problems encountered in fracture mechanics. In linear elastic fracture mechanics (LEFM), the stress intensity factor is an important parameter. Cracks, if present in the region experiencing the modes of deformation, increase the stress amplitude significantly and this high stress may lead to premature failure of the engineering components. If the value of the SIF is known, it is possible to predict whether the crack will propagate or not. As the conventional boundary integral equation (CBIE) degenerates when a mathematical crack is modelled, a previously developed dual boundary integral equation approach has been adopted in the current work. It utilizes the hypersingular boundary integral equation (HBIE) along with the CBIE. A weakly singular form of HBIE is utilized in the current work to eliminate the hypersingularity analytically. Stress intensity factors are evaluated using the crack opening displacement (COD), displacement extrapolation (DE), and the J-integral approaches. A stand-alone code has been developed for calculating the stress intensity factors of general two-dimensional domains with cracks. The code has been validated by evaluating the stress intensity factors for the standard components, for which the stress intensity factor values are available in the literature. Accurate and well-converged results are obtained proving the robustness of the code. A linear combination of the CBIE and HBIE was applied at the crack and a significant (87–97 per cent) reduction in the condition numbers for the system of equations was observed for the examples studied. Again, the results obtained are accurate and well converged.

Analysis of Slant Surface Cracks with Step Notches Subject to Contact Loadings by a Variational Boundary Integral Method

2007 ◽  
Vol 353-358 ◽  
pp. 1125-1128
Author(s):  
He Hui Wang ◽  
Meng Xi Hu ◽  
Yi Fan Chen ◽  
Dong Liang Wang ◽  
Ke Di Xie
Keyword(s):  
Stress Intensity ◽  
Half Plane ◽  
Stress Intensity Factors ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Symmetric System ◽  
Dislocation Loops ◽  
Intensity Factors ◽  
Slant Surface

Modes I and II stress intensity factors are analyzed by means of a variational boundary integral method (VBIM) for slant surface-breaking cracks in a half-plane with surface steps subject to contact loadings. This method represents the crack as a continuous distribution of dislocation loops. The crack opening displacements, which are related to the geometry of loops and their Burgers vectors, can be determined by minimizing the elastic potential energy, obtained from the known expressions of the interaction energy of a pair of dislocation loops, of the solid. In contrast to other methods, this approach finally reduces to a symmetric system of equations with milder singularities of the type 1/R, which facilitate the numerical treatments. By modeling the surface boundary of the half-plane as half part of an infinite crack breaking through an infinite solid, this paper demonstrates that the VBIM can be well extended to solve the fracture problems of inclined surface-breaking cracks in a half-plane with curve or step notches subject to combined contact loadings, and presents results of stress intensity factors for a variety of loadings, cracks and step surface configurations. Numerical results of test examples are in good agreement with the existing results in the literature.

Benchmark Results for the Problem of Interaction Between a Crack and a Circular Inclusion

2003 ◽  
Vol 70 (4) ◽  
pp. 619-621 ◽  
Author(s):  
J. Wang, ◽  
S. G. Mogilevskaya, and ◽  
S. L. Crouch
Keyword(s):  
Stress Intensity ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Stress Intensity Factors ◽  
Integral Method ◽  
Circular Inclusion ◽  
Complex Variables ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

This paper is a reply to the challenge by Helsing and Jonsson (2002, ASME J. Appl. Mech., 69, pp. 88–90) for other investigators to confirm or disprove their new numerical results for the stress intensity factors for a crack in the neighborhood of a circular inclusion. We examined the same problem as Helsing and Jonsson using two different approaches—a Galerkin boundary integral method (Wang et al., 2001, in Rock Mechanics in the National Interest, pp. 1453–1460) (Mogilevskaya and Crouch, 2001, Int. J. Numer. Meth. Eng., 52, pp. 1069–1106) and a complex variables boundary element method (Mogilevskaya, 1996, Comput. Mech., 18, pp. 127–138). Our results agree with Helsing and Jonsson’s in all cases considered.

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