Fundamentals of brittle failure at the atomic scale

. In this work, we investigate the elementary processes of brittle failure initiation with molecular simulation techniques. Failure initiation theories aim at bridging the gap between energy-driven failure at high stress concentrations and stress-driven failure in absence of stress concentration, and thus capturing the transition at moderate stress concentrations and associated scale effects. We study graphene, which is one of the few materials with a sufficiently small characteristic length (ratio between toughness and strength) to be addressed by molecular simulations. We also consider a toy model that proves helpful for physical interpretations. Performing molecular simulations of pre-cracked graphene, we found that its failure behavior can overcome both strength and toughness in situations of very high or low stress concentrations, respectively; which is consistent with one particular theory, namely Finite Fracture Mechanics (FFM), which considers failure initiation as the nucleation of a crack over a finite length. Details of the atomic mechanisms of failure are investigated in the athermal limit (0K). In this limit, failure initiates as an instability (negative eigenvalue of the Hessian matrix), irrespective of the stress concentration. However, the atomic mechanisms of failure and their degeneracy (eigenvector of the negative eigenvalue) strongly depend on stress concentration and points to the nucleation of a deformation band whose length decreases with stress concentration. This atomic description is quite similar to FFM theory. At finite temperature, failure is no more deterministic because of thermal agitation. An extensive study to characterize the effects of temperature,