Relationship between the Stress Intensity Factors and Bond σ in Graphene Sheet

摘要

Relationship between the stress intensity factors and the bond σ in the plane of interatomic hexagonal structures within graphite is given numerically. Under the consideration in this plane, the bond π and van der Waals force are ignored, and the plane strain of macroscopical elasticity is considered. The molecular mechanics is used to describe the displacements of atoms in the area near the tip of a crack, and the linear elastic fracture mechanics is used outside this area. Connection between these two theories is based on an assumption that the displacements of atoms along the boundary described by the molecular mechanics are equal to those described by the fracture mechanics. The nonlinear equations of molecular mechanics derived by the modified Morse potential function are solved by using Matlab software. When choosing the maximum stretching force of atomic bond as a failure criterion, the fracture toughness is obtained for Mode I and Mode II problems.