A computational investigation of length-scale effects in the fracture behaviour of a graphene sheet using the atomistic J-integral

The overarching objective of this paper is to investigate the validity of application of continuum-based linear elastic fracture mechanics (LEFM) methodology, which is often employed by researchers to model fracture processes at the "discrete" atomic scale. The potential sources of error in the application of LEFM at the nanoscale are: (a) Length-scale effects, (b) non-local effects due to long range inter-atomic forces, and (c) entropic effects due to random thermal motion of atoms. The material selected for this study is monolayer graphene, primarily because extensive data, both experimental and analytical, already exist for this material in the literature for model validation. Further, an atomistic J-integral is implemented as a nano-scale fracture metric to investigate flaw-tolerance at the nanoscale reported by many researchers, and to develop a methodology to predict the initiation fracture toughness of the material. For this purpose, a bond-order based potential (ReaxFF) available in LAMMPS molecular dynamics (MD) software is utilized to accurately pinpoint bond separation. Predictions obtained using the atomistic J are compared with LEFM predictions for the case of a single (zig-zag) graphene sheet with a center-crack under tensile loading at room temperature, and show significant deviation from LEFM for crack lengths below a certain threshold.