Atomic-scale mutual integrals for mixed-mode fracture: Abnormal fracture toughness of grain boundaries in graphene

In this study, we developed a computational scheme based on the atomic-level J-based mutual integral (or two-state conservation integral) to analyze the mixed-mode fracture along grain boundaries (GB) in polycrystalline solids. Discrete atomic information, obtained from molecular dynamics simulation of crack propagation along GBs in polycrystalline solids, is incorporated with asymptotic singular fields near an interfacial crack tip between dissimilar materials in the atomic-level J-based mutual integral, to extract the individual stress intensity factors of modes I and II. As a model problem, crack propagation along GBs in polycrystalline graphene, an ordered array of non-hexagonal defects, is analyzed. In the model, GBs are considered to be the most favorable paths for crack propagation, as the carbon atoms along the GBs experience less-ordered interatomic interactions than those in pristine graphene. When a mixed-mode loading is applied to a crack running along a graphene GB, as the mode mixity increases, the fracture toughness of GBs in graphene gradually increases. However, if the mode mixity is greater than 8°, the fracture toughness gradually decreases, which can be considered a unique characteristic of GBs in graphene. This abnormally-low fracture toughness of GBs in graphene for high mode mixity, may be interpreted as the competition between bond-rotation and bond-breaking mechanisms of carbon atoms, in conjunction with the Stone-Wales transformation and nonagon structures at the crack tip along GBs in graphene.