The applicability and the low limit of the classical fracture theory at nanoscale: The fracture of graphene

Abstract

Miniaturization of mechanical structures offers excellent performances of the device while has brought problems of fracture at nanoscale. However, whether the classical fracture theory is applicable at such a small scale and what is its low limit are still challenging problems. In this paper, by conducting atomistic simulation of graphene and compared with the reported in-situ experiments, the applicable range of distance from crack tip for crack-tip stress distribution models and the low limit of crack length for fracture criterion are investigated. It is found that all crack-tip stress models are invalid within fracture process zone whose dimension is 2.5 Å away from crack tip. The energy-based fracture criteria are not applicable when the crack length is less than 8 nm due to the nonlinear stress–strain relationship, while the modified Griffith criterion can be applied to low limit of crack length 5 Å. For the stress-based fracture criterion, the stress intensity factor criterion fails when the crack length is less than 8 nm due to the decreasing size of critical K-dominant zone ΛK, while the theory of critical distances and quantized fracture mechanics can accurately predict the critical fracture stress regardless of the crack length, which can be unified by a non-local stress criterion. This work will provide a mechanical basis for the reliable application of the microelectronic devices at nanoscale.