Anisotropic toughness and strength in graphene and its atomistic origin

This paper presents the implication of crystallographic orientation on toughness and ideal strength in graphene under lattice symmetry-preserving and symmetry-breaking deformations. In symmetry-preserving deformation, both toughness and strength are isotropic, regardless of the chirality of the lattice; whereas, in symmetry-breaking deformation they are strongly anisotropic, even in the presence of vacancy defects. The maximum and minimum of toughness or strength occur for loading along the zigzag direction and the armchair direction, respectively. The anisotropic behavior is governed by a complex interplay among bond-stretching deformation, bond-bending deformation, and the chirality of the lattice. Nevertheless, the condition for crack-nucleation is dictated by the maximum bond-force required for bond rupture, and it is independent of the chiral angle of the lattice or loading direction. At the onset of crack-nucleation a localized nucleation zone is formed, wherein the bonds rupture locally satisfying the maximum bond-force criterion. The nucleation zone acts as the physical origin in triggering the fracture nucleation process, but its presence is undetectable from the macroscopic stress-strain data.