Abstract
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.
Highlights
Resistance to crack propagation is undoubtedly one of the most important properties of structural materials
The strength of interatomic bonds is reflected in the theoretical strength of a material, which can be determined via ab initio density functional theory (DFT) calculations for single crystals[30,31] as well as interfaces with and without impurities.[32,33,34]
The dependence of the binding energy per unit area, i.e., the energy difference of a configuration with respect to the fully separated crystal halves, on the separation distance is shown in Fig. 2 for the two interatomic potentials in comparison to DFT results
Summary
Resistance to crack propagation is undoubtedly one of the most important properties of structural materials. Following the failure criterion by Griffith, the TS law for the bond-breaking process will have to capture the work of separation of the material, but to predict reliably the trends in cohesive behavior, the strength of the bonds is required as well.[29] The strength of interatomic bonds is reflected in the theoretical strength of a material, which can be determined via ab initio density functional theory (DFT) calculations for single crystals[30,31] as well as interfaces with and without impurities.[32,33,34] this procedure assumes homogeneous expansion perpendicular to, or cleavage along, an infinite crystallographic plane. COMPARISON OF INTERATOMIC FORCES AT CRACK TIPS AND DURING RIGID-BODY SEPARATION
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