Fracture ab initio: A force-based scaling law for atomistically informed continuum models

In fracture mechanics, established methods exist to model the stability of a crack tip or the kinetics of crack growth on both the atomic and the macroscopic scale. However, approaches to bridge the two scales still face the challenge in terms of directly converting the atomic forces at which bonds break into meaningful continuum mechanical failure stresses. Here we use two atomistic methods to investigate cleavage fracture of brittle materials: (i) we analyze the forces in front of a sharp crack and (ii) we study the bond breaking process during rigid body separation of half crystals without elastic relaxation. The comparison demonstrates the ability of the latter scheme, which is often used in ab initio density functional theory calculations, to model the bonding situation at a crack tip. Furthermore, we confirm the applicability of linear elastic fracture mechanics in the nanometer range close to crack tips in brittle materials. Based on these observations, a fracture mechanics model is developed to scale the critical atomic forces for bond breaking into relevant continuum mechanical quantities in the form of an atomistically informed scale-sensitive traction separation law. Such failure criteria can then be applied to describe fracture processes on larger length scales, e.g., in cohesive zone models or extended finite element models.