Abstract
Based on the Williams' method of the eigenfunction expansions, the singular stress distribution near a mode I crack tip yielding on two inclined slip-planes is obtained in the form with an undetermined constant. It is found that stresses have the singularity of the form r λ-1, where r is the distance from the crack tip, and the exponent λ-1 lies between-0.5 and 0, depending on the inclination angle of the slip-planes. The undetermined constant is then estimated by combining our result with an approximate solution obtained by J.R. Rice. The case of a mode III crack is also analyzed and the results are compared with a known closed-form solution and discussed.
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