Tensile strength of graphene versus temperature and crack size: Analytical expressions from molecular dynamics simulation data

Graphene, the strongest known material, is significantly influenced by the loading conditions, the environmental temperature and the existence of internal imperfections and discontinuities such as cracks. Higher temperatures lead to higher atomic kinetic energies and easier failure of graphene while even a one atom vacancy may cause a dramatic reduction in its strength. The aim of the present study is to describe analytical expressions which associate the tensile strength of the monolayer graphene with the temperature and the length of a possible centrally positioned, straight crack. For this reason, molecular dynamics simulations are conducted to compute all the necessary numerical data. Then special equations are developed by fitting the computed data into appropriate non-linear regression surfaces. The proposed non-linear analytical equations are capable of straightforwardly predicting the strength of graphene given the chirality, the temperature and the size of the center crack under investigation.