Compound crack fracture theory of spur gear

The cracks in practical components are often composite cracks composed of two or more cracks. Considering the random combination of component materials, loads, geometric structure of parts and other factors in the actual situation, there may be two or three crack forms of type I, type II and type III near the crack tip (leading edge). Because the propagation behavior of composite crack is very different from that of single type crack, it is imperative to study the propagation behavior of composite crack.

Through observation, it is found that there is a great difference between the propagation direction of composite crack and that of mode I crack. The main difference is that the crack propagation direction of the former is not along the direction of the original crack surface, but along an angle with the original crack. Therefore, two key problems must be solved for composite crack:

(1) In what direction does the crack begin to grow? That is, the cracking angle needs to be determined.

(2) Under what conditions does the crack begin to grow? That is, the critical conditions need to be determined.

For these two problems, scholars have put forward three main composite mode crack fracture theories, which are introduced as follows.

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