Characterization of the computational accuracy in surface crack problems

The paper focuses on the comparison of di¤erent methods for calculating stress intensity factors (K I ) in surface crack problems based on results of numerical analyses of elastic crack-tip Þelds. The computational accuracy is quantiÞed by means of the so-called Ôaveraged error estimation techniqueÕ which is extended to the evaluation of local errors in the determination of stress intensity factors at characteristic points of the crack front. Numerical data involved in the present study are obtained from boundary-element calculations. Three values of the stress intensity factor, i.e. those deÞned from nodal tractions, displacements and energy-release rate, are provided. The highest error level is found for the displacement-based data, while the energy-release calculations yield the best accuracy. A considerable increase in the error value is noticed near the intersection of the crack front with a body surface where the conventional assumption on the square-root stress singularity is, in general, not applied. It is shown that the accuracy of stress intensity factor analysis can be improved by eliminating uncertainties associated with the local stress state along the crack front.