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

Abstract

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.