Windows to trigger crack branching for cracked solids under mixed Mode-I/II loading

For a cracked solid under mixed Mode-I/II loading, the present investigation shows that six energy-based driving forces act respectively on the six subintervals around a crack tip, which controls the underlying fracture configurations, including complex crack branching. Using the geometrical modelling that describes multiple cracks initiation from a crack tip and a mixity parameter φn, subinterval division for crack tip boundary to maximized the energy release rate has been proposed. This is an efficient way to reveal theoretically energy-based driving forces acting on the local boundaries around a crack tip, and to show that the number of the subintervals is no greater than six. Three windows are suggested, within which the crack multiple-branching is more likely to be triggered. Compact tension shear (CTS) specimens made from general-purpose Polystyrenes (GPPS) under mixed Mode-I/II loading for a given φn are considered to investigate fracture behaviors. The typical experimental findings are consistent with some typical fracture behaviors predicted by the present modelling. The current theoretical and experimental investigations could be helpful to refresh the understanding of crack branching under quasi-static or dynamic mixed Mode-I/II loading.