Fracture strength and fracture toughness of graphene: MD simulations

An attempt is made here to address the fundamental issues on the validity of Griffith’s theory to estimate the fracture strength at nano-scales and valid a/W ratios to predict the fracture strength and fracture toughness of graphene, through molecular dynamics simulations. The influence of a/W ratio on the fracture toughness of graphene is systematically investigated through molecular dynamics simulations by adopting the hexagonal lattice structure of a mono-layer graphene sheet.  Two different square domains with ten different lattice orientations and thirteen different initial crack lengths are considered in the analysis. Based on the results, the lower bound of the a/W ratio is defined as the value beyond which Young’s Modulus starts to decrease with increase in a/W. On the other hand, fracture toughness is observed to increase with increase in a/W ratio until reaching the peak value, followed by a decreasing trend with further increase in a/W ratios. Therefore, the upper bound of a/W ratio is recommended as the value beyond which fracture toughness starts to decrease. Accordingly, a range of 0.15<a/W<0.45 is recommended to predict the fracture toughness of graphene.