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Abstract

At the engineering scale, continuum mechanics provides an efficient way to model fracture based on stresses, stress intensity factors, and energy release rates. At the atomic scale, in contrast, the breaking of atomic bonds is caused by critical forces acting on individual atoms. Therefore, a scaling methodology is required to apply information from atomistic scale to the continuum level problems, which are governed by engineering length and time scales. Fracture at the continuum level can be described using state of the art methods such as cohesive zone-based modeling, which requires a material-specific traction-separation law (T-S law). Here, we present a mesh independent approach for atomistic-to-continuum level scaling of the stress and displacement measures, which are used in the T-S law. Our approach is based on a detailed analysis of the forces acting between the atoms in front of a crack tip, as well as between two semi-infinite half-crystals. Such a constellation is used to calculate the properties of cohesive zones based on atomistic simulations. The analysis shows, that the interatomic forces at a crack tip can be directly related to the restoring tractions between the two planar surfaces. This allows for an unambiguous scaling of the critical stresses and displacements, from GPa / Å on the atomic level, to the order of hundreds of MPa and nm on the mesoscale. A series of finite element simulations are performed for KI loading based on the scaled input data for the T-S law and the critical stress intensity factors are calculated and compared with results from the atomistic simulations. We demonstrate and examine the ability of the atomistically informed finite element simulation to directly reproduce results from atomistic simulations.