A theoretical note on mode-I crack branching and kinking

An energy-based fracture mode has been derived for the mode-I crack branching and kinking. The classic JiJi-integral has been further explored by a new partial integral path and the analytical solution of the energy release rate for crack branching and kinking from a mode-I crack tip has been established. The crack branching/kinking angle has also been analytically derived. It shows that the Griffith’s theorem and conservation law can be applied to both mode-I crack extension and mode-I crack branching and kinking. The branching mechanism for quasi-static mode-I crack has been theoretically investigated. The branching toughness and the K-based criterion for crack branching have been defined. The crack branching phenomena predicted by the present model are in well agreement with the experimental observations reported in the literatures.