ATOMISTIC AND CONTINUUM MODELLING OF FRACTURE OF

The extraordinary mechanical and electronic properties of graphene have been used to fabricate revolutionary nanomechanical devices [1]. Graphene reinforcement remarkably improves the fracture toughness and fatigue crack propagation resistance of composite materials [2]. A thorough understanding of fracture properties of graphene is necessary in designing advance devices and composite materials. Experimental studies on the fracture properties of graphene are very difficult due to practical problems involved with experiments at the nanoscale [3]. Therefore atomistic methods such as molecular dynamics (MD) simulations play a key role in studying the fracture properties of graphene. In this work we use a novel approach to calculate the J integral using MD simulations, performed in LAMMPS MD package with AIREBO potential. Fig. 1(a) shows the changes in potential energy with crack propagation in an armchair graphene sheet with a size of 7.6 nm × 7.6 nm. A crack, length of ~0.7 nm, is placed in the centre of the sheet. Periodic boundary conditions are used along in plane directions. Simulation temperature is 1 K. Strain rate and time step are 0.001 ps-1 and 0.5 fs, respectively. Slopes of the piecewise continuous curve in Fig. 1(a), indicated as θi and θi+1, are proportional to the J integral [4]. The critical value of