An analytical model of fracture process zone to explain why crack-tip opening angle works

An analytical model of fracture process zone (FPZ) was proposed to explore the intrinsic meaning of the constant crack-tip opening angle (CTOA) fracture criterion. A relationship between critical CTOA and the essential work of fracture (EWF) was then established. According to above relationship, critical CTOA is found to represent the critical state of FPZ. During stable crack growth, FPZ is fixed since stress state and material properties are changeless, and this is why constant CTOA works. In the case external boundary far from the FPZ, the FPZ will only depend on thickness and material properties, and then critical CTOA will own in-plane geometry transferability. In addition, the linear relationship between critical CTOA and local fracture strain is also explained.