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Cohesive laws for grain boundaries from ab initio calculations
- Date: 07.09.2009
- Place: Euromat 2009, Glasgow, UK
Continuum modelling of crack propagation along interfaces is often performed by applying the so-called cohesive-zone (CZ) model. In such a cohesive model of fracture a traction-separation (TS) law describes the mechanical response of an interface to an applied load. At the same time crack propagation can be regarded as a bond-breaking process on the atomic scale. To fully capture the physics of this process with a TS law, this should be derived from atomistic calculations. Especially if the influence of segregated impurities, which can alter the bond character, shall also be described, a quantum mechanical treatment is necessary. However, the implementation of TS laws derived from ab initio calculations into mesoscopic simulation schemes is not straight forward. The separation of interatomic bonds is characterized by peak stresses of the order of magnitude of the theoretical strength (~ 10 GPa) and critical separations of only a few Angstrom. Furthermore it has been shown that finite element solutions of cohesive fracture only converge if the mesh size in the cohesive zone is on the order of the critical displacement of the TS law. Thus, FEM calculations based on ab initio TS laws would require full atomic resolution at the crack tip, which is completely undesirable.Recently, several coarse-graining or re-scaling approaches have been suggested in the literature. In this talk we will compare the underlying models and evaluate their predictions by generating TS laws for special grain boundaries in Aluminium from ab initio calculations.