Application of the Hypersingular Boundary Integral Equation in Evaluating Stress Intensity Factors for 2D Elastostatic Fracture Mechanics Problems
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 (SIF) 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. Knowing the value of the SIF, one can predict if the crack will propagate or not. As the conventional boundary integral equation (CBIE) degenerates when a mathematical crack is modeled, dual boundary integral equation approach developed earlier has been adopted in the current work. It utilizes the hypersingular boundary integral equation (HBIE) along with the CBIE. Weakly singular form of HBIE is utilized in the current work to eliminate the hypersingularity analytically. SIFs are evaluated using the crack opening displacement (COD), displacement extrapolation (DE) and the J-integral approaches. A stand-alone code has been developed in C++ for calculating the SIFs of general 2D domains with cracks. The code has been validated by evaluating the SIFs for the standard components, for which the SIF 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 significant (87% - 97%) 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. To the best of author’s knowledge this approach has not been reported in the literature for elastostatic crack problems.
School:University of Cincinnati
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:boundary element method hypersingular bie fracture mechanics stress intensity factor
Date of Publication:01/01/2006