Under the elastic-plastic condition, the J-integral of helical gear crack describes the stress and stress field at the crack front from the angle of power. The J-integral of helical gear crack has an important characteristic: the value of J-integral has nothing to do with the integral circuit. Its advantage is that it can avoid the rigorous analysis of the crack tip directly. Because of this characteristic, it is widely used in two-dimensional and three-dimensional crack bodies, and solves many fracture problems of non-linear elastic bodies in real life.

At the tip of the three-dimensional crack, the J integral of the helical gear crack is uniquely determined and has a corresponding critical value JC. The J integral value of helical gear crack is easy to be measured in the experiment. If the measured data in the experiment is the crack initiation point, JC represents the critical value of the crack initiation point; if the measured data in the experiment is the crack initiation point, JC represents the instability point.