Dynamic aspects of graphene deformation and fracture from approximate density functional theory

Graphene is one of the most intriguing two-dimensional carbon materials. Its mechanical strength and failure are key concerns for materials engineering and applications. Despite the success of fracture mechanics, the mechanism of how pristine materials fail remains an elusive problem. While many theoretical studies based on molecular dynamics using empirical forcefields have tried to address this question, atomic-scale mechanics are not clearly understood. Especially, a widely employed bond-breaking approach based on the critical bond length has not been rigorously tested. Here, utilizing molecular dynamics simulations with density functional based tight binding, we investigate how the failure of the pristine material initiates. The Wiberg bond order (W_BO) to estimate the change of chemical bonds shows a transition from sp² (W_BO ∼ 1.33) to sp³ (W_BO < 1.0) during the deformation. However, it reveals that a single threshold value for either the W_BO or bond length is insufficient to decide failure of pristine material without free edges or defects. Instead, collective behaviors of the local atomic group govern the fracture initiation of pristine graphene. Our study provides dynamic mechanical responses based on quantum mechanics, which have not been captured by empirical forcefields, opening opportunities to design properties by precisely coupling the mechanics and quantum mechanics.