An atomistic methodology of energy release rate for graphene at nanoscale

Graphene is a single layer of carbon atoms packed into a honeycomb architecture, serving as a fundamental building block for electric devices. Understanding the fracture mechanism of graphene under various conditions is crucial for tailoring the electrical and mechanical properties of graphene-based devices at atomic scale. Although most of the fracture mechanics concepts, such as stress intensity factors, are not applicable in molecular dynamics simulation, energy release rate still remains to be a feasible and crucial physical quantity to characterize the fracture mechanical property of materials at nanoscale. This work introduces an atomistic simulation methodology, based on the energy release rate, as a tool to unveil the fracture mechanism of graphene at nanoscale. This methodology can be easily extended to any atomistic material system. We have investigated both opening mode and mixed mode at different temperatures. Simulation results show that the critical energy release rate of graphene is independent of initial crack length at low temperature. Graphene with inclined pre-crack possesses higher fracture strength and fracture deformation but smaller critical energy release rate compared with the graphene with vertical pre-crack. Owing to its anisotropy, graphene with armchair chirality always has greater critical energy release rate than graphene with zigzag chirality. The increase of temperature leads to the reduction of fracture strength, fracture deformation, and the critical energy release rate of graphene. Also, higher temperature brings higher randomness of energy release rate of graphene under a variety of predefined crack lengths. The energy release rate is independent of the strain rate as long as the strain rate is small enough