A unified atomic energy release rate criterion for nonlinear brittle fracture in graphene nanoribbons

The existence of a notch in a single-atom-thick graphene nanoribbon brings about significant nonlinearity in deformation within the extremely confined stress concentration field of only a few nanometers near the notch root. However, whether the continuum-based mechanics theory is still valid for fracture due to such stronglynonlinear and extremely small stress concentration is questionable. Here, we demonstrate that stress-based criterion with linear-media assumption breaks down at a critical size of ACS = 19.7 nm, and moreover the one based on nonlinear-media assumption also fails to describe the nonlinear brittle fracture in a notched graphene nanoribbon below a lower dimensional limit of ACNL = 2.4 nm because of the atomic discreteness. By fully considering the nonlinearity and atomic discreteness, an atomic energy release rate (ERR) theory is proposed, and it is found that the atomic ERR criterion works well for a notch in nonlinear graphene nanoribbon even below the lower limit of continuum-based mechanics. It finally brings about an ultimate unification in describing nonlinear brittle fracture in both notched and cracked systems. These results demonstrate that the proposed atomic ERR criterion is not only size-independent but also shape-independent for all scales.