Crystal-plasticity based modeling and simulation of geometrically-necessary dislocations at a crack front in ductile single crystals

Abstract
This work is concerned with the formulation and numerical implementation of a constitutive model for ductile single crystals containing cracks or other geometric imperfections. In particular, attention is focused here on the modeling of the emergence of geometrically-necessary dislocations (GNDs) at such imperfections due to inhomogeneous deformation there. To this end, we formulate a glide-system model for GND density consistent with the model of Ashby and use it to extend the Cailletaud model for single crystal plasticity to include the effects of GNDs on the material behaviour of such crystals. This extended model is then implemented in an FE-based 3D-simulation of the material behaviour at a crack front in round bars consisting of single crystals of the nickel superalloy SC16. In particular, preliminary simulation results are presented and discussed for GND development at the crack front for two crystalcrack orientations. In these, the GND density is maximal generally at the crack front in the middle and decreases toward its edges.