Abstract: The system of singular integral equations are obtained in this paper by considering the boundary conditions of a crack, with the solution of the singular integral equations, the stress intensity factors of a crack tip are calculated. By means of using the current theories about crack spread, the direction of a crack propagation is determined. i.e. the vertical surface crack propagates into the thin surface layer in the direction which is opposite from the surface friction and has an angle of about 20 degrees with the surface; The tip of the branched crack spreads to the surface to the surface in the direction of about 60 degrees with the declined crack.

Key words: 齿轮, 裂纹扩展, 应力强度因子