SELF-SIMILAR CRACK EXPANSION METHOD FOR THE STRESS INTENSITY FACTOR ANALYSIS

The Self-Similar Crack Expansion (SSCE) method is proposed to evaluate stress intensi-ty factors at crack tips, whereby stress intensity factors of a crack can be determined by the crackopening displacement over the crack, not just by the local displacement around the crack tip. The crackexpansion rate is estimated by taking advantage of the crack self-similarity. Therefore, the accuracy ofthe calculation is improved. The singular integrals on crack tip elements are also analyzed and are pre-cisely evaluated in terms of a special integral analysis. Combination of these two techniques greatly in-creases the accuracy in estimating the stress distribution around the crack tip. A variety of two-dimen-sional cracks, such as subsurface cracks, edge cracks, and their interactions are calculated in terms ofthe self-similar expansion rate. Solutions are satisfied with errors less than 0.5% as compared with theanalytical solutions. Based on the calculations of the crack interactions, a theory for crack interactionsis proposed such that for a group of aligned cracks the summation of the square of SIFs at the right tipsof cracks is always equal to that at the left tips of cracks. This theory was proved by the mehtod ofSelf-Similar Crack Expansion in this paper.