Stress intensity factor evaluation using singular finite elements

The classical theory of linear elastic fracture mechanics proposes that the stress and energy field near a crack tip can be accurately evaluated by determining the stress intensity factors. Several recent investigations, however, have demonstrated the previously unrecognized importance of the higher-order terms also present in the series eigenfunction representation of the near-tip crack environment. The finite element method has been shown to quite effectively yield these higher-order coefficients, with the method previously utilized only to determine the first term of the series expansion (the stress intensity factor). By numerically evaluating the higher-order coefficients for several finite geometries, the near-tip environment has been shown to be much more sensitive to variations in these terms, than previously believed. This is a phenomenon that no accurate crack propagation study, regardless of specific propagation theory, should disregard without careful consideration, particularly because of the inherent accumulated error in any incremental propagation study.