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Abstract

Cohesive properties of grain boundaries from ab initio density functional theory calculations are valuable input for multi-scale models of fracture. 3D traction separation laws can be derived from the results of so-called “ab initio tensile and shear tests”. It will be shown that they are valid for the complete parameter space of grain boundary geometry and chemistry, and furthermore allow a unified treatment of single crystals and grain boundaries. The use of this rather schematic approach is justified by demonstrating the equivalence of forces that occur during the process of bond breaking in front of a sharp crack tip and during rigid body separation of half crystals. Furthermore, a fracture mechanics model is developed to scale the critical atomic forces for bond breaking into meaningful continuum mechanical quantities in form of a scale-sensitive traction separation law.