Self-similar crack expansion method for two-dimensional cracks under mixed mode loading conditions

Abstract

The self-similar crack expansion (SSCE) method is proposed to evaluate stress intensity factors of two-dimensional cracks under mixed-mode loading conditions. With this method, stress intensity factors for the crack in an infinite medium or semi-infinite medium can be determined by calculating the crack-opening displacements over the crack surface. The energy release rate of an extending crack is precisely estimated by taking advantage of the crack self-similarity. In the boundary integral equation technique, the singular integrals near crack tips are evaluated based on closed form expressions. Combination of these two techniques significantly increases the accuracy in the stress intensity factor (SIF) calculations. A variety of SIFs for cracks, such as subsurface cracks, edge cracks and the interactions among them are calculated using various types of crack expansions in the SSCE method. Results show good accuracy for crack analysis, with errors in SIFs of two-dimensional cracks less than 0.5%. This provides an analytical tool for predicting fatigue life of materials. An interesting finding in the relationship between SIFs is presented for a group of aligned cracks under tensile loading.