Fracture and mechanical properties of graphene-like two-dimensional materials using molecular dynamics (MD) simulations

Graphene is a monoatomic thick sheet of sp2-hybridized carbon atoms tightly packed in a honeycomb lattice structure. Since its discovery, it has drawn extensive attention to the science community for its unique 2D structure and has been studied for both basic science and commercial applications due to its extraordinary thermal, optical, and mechanical properties. In this research, we employed molecular dynamics simulations and machine learning methods to study mechanical and fracture properties of graphene-like two-dimensional materials (i.e.; C3N, bicrystalline graphene, and polycrystalline graphene). Molecular dynamics (MD) simulations are used to extract the traction-separation laws (TSLs) of symmetric grain boundaries of bicrystalline graphene. Grain boundaries with realistic atomic structures are constructed using different types of dislocations. The TSLs of grain boundaries are extracted by using cohesive zone volume elements (CZVEs) ahead of the crack tip. The areas under the traction-separation curves are used to calculate the separation energy of the grain boundaries. The results show that as the grain boundary misorientation angle increases the separation energy of the grain boundaries decreases. The impact of temperature on the traction separation laws is studied. The results show that, with an increase of the temperature from 0.1 K to 300 K, the separation energy first increases to reach its peak at around 25 K and then slightly decreases. Finally, a deep convolutional neural network model has been developed to predict the mechanical and grain properties of polycrystalline graphene. The data required for training our machine learning model is generated using molecular dynamics simulations by modeling the behavior of polycrystalline graphene under uniaxial tensile loading. More than 2000 data points are generated for graphene sheets of different grain sizes and grain orientations. The goal is to train the network such that it can predict the Young's modulus and fracture stress of graphene sheets by analyzing an image of the polycrystalline sheet.
Molecular dynamics simulations are also used to study the mechanical and fracture properties of C3N, a graphene-like two-dimensional material. The impact of initial crack orientation on the crack path is studied by applying tensile strain to C3N sheets containing initial cracks in the armchair and zigzag directions. The results show that the cracks grow by creating new surfaces in the zigzag direction. The impact of temperature and strain rate on Young's modulus and fracture stress of C3N are studied. The capability of Griffith theory, and quantized fracture mechanics (QFM) in predicting the fracture strength of C3N is studied. The molecular dynamic results indicate that Griffith theory cannot predict the fracture strength of C3N if the crack length is shorter than 9 nm. The notch effects on the fracture strength of C3N is studied and it is shown that notch effects are important in predicting the fracture strength of C3N. Using the Rivling-Thomas method, the molecular dynamics simulations predict a critical energy release rate of 10.982 Jm-2 for C3N.