Berlin 2018 – scientific programme
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MM: Fachverband Metall- und Materialphysik
MM 36: Topical Session (Symposium MM): Fundamentals of Fracture
MM 36.5: Talk
Wednesday, March 14, 2018, 12:45–13:00, TC 006
Atomistic-based fracture criteria for continuum models — Johannes Möller1,3, Hamad ul-Hassan2, Erik Bitzek1, Alexander Hartmaier2, and •Rebecca Janisch2 — 1Friedrich-Alexander Universität Erlangen-Nürnberg — 2ICAMS, Ruhr-Universität Bochum — 3Fraunhofer Institut für Werkstoffmechanik, Freiburg
Continuum mechanics provides an efficient way to model fracture at the engineering scale, based on stresses, stress intensity factors, and energy release rates. Additionally, material-specific information and failure criteria are required to describe fracture at this scale. At the atomic scale, in contrast, the breaking of atomic bonds is caused by critical forces acting on individual atoms. Here, we present a systematic, mesh-independent approach that directly connects the interatomic forces to stress-based failure criteria for finite element implementations of continuum models. We base our approach 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, the latter being the common approach, e.g., for ab-initio density functional theory calculations of cohesive properties. 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. The implementation in a finite element scheme will be demonstrated.