ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


From inter-atomic forces to stress fields at a crack tip - incorporating the results of atomistic calculations into continuum models

Date: 14.03.2018
Place: DPG Spring Meeting, Berlin, Germany

Johannes Möller
Hamad Hassan
Erik Bitzek, Department of Materials Science and Engineering, Department of Materials Science and Engineering Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
Alexander Hartmaier
Rebecca Janisch

Continuum mechanics describes deformation and failure of a material in an effective manner, and the material-specific information is provided via constitutive models. A persisting challenge in multiscale modelling is to construct realistic, transferrable, and tractable constitutive laws. We present a scale-jumping concept, which directly connects the interatomic forces to the continuum stress field around a crack tip. We investigated the forces acting at a cleavage plane in tungsten in two scenarios, using different empirical potentials. The decohesion was modelled by a rigid displacement of two semi-infinite half-crystals, and as well by imposing boundary conditions of a mode-I stress intensity field, which lead to a realistic crack-opening. The comparison shows, that the restoring tractions at a crack tip can be decomposed into pairwise interatomic forces, in spite of these forces be¬ing environment-dependent. Thus, they can be obtained from molecular statics with the simple loading geometry. Furthermore, the concept leads to an unambiguous scaling of the critical stresses and displace¬ments, from GPa / Å on the atomic level, to the order of MPa and hundreds of nm on the mesoscale. This ensures its applicability within a finite element scheme, as will be demonstrated.

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