The finite difference technique for solving crack problems

Abstract

A detailed examination of the Finite Difference method for solving crack problems is presented and discussed. The three classical mode I configurations (i.e. Centered Crack Plate, Double Edge Notch and Single Edge Notch) as well as an uncommon case (A Penny Shape Crack embedded in a circular plate in bending) are solved and discussed. The Stress Intensity Factors are computed by taking more than one (first) term in William's Series, using two or three points near the tip. This technique improves the accuracy and frees one from relying on the very first point near the tip as a measure base. In most cases, the accuracy was found to be between 1–3% for uniform mesh size in the order of 5% from the half crack length. No special imposed functions were used near the tip, which makes the technique competitive to the Finite Element method, especially for 3-D problems or cases where the degree of singularity is not known. The solution is found iteratively (a two step SOR method) and some techniques for quick convergence are discussed.