Deformation Behavior of Tungsten Single Crystals During Wedge Nanoindentation - a Numerical Study

Abstract

The present work aims at the numerical investigations on the plastic deformation behavior of tungsten single crystals on the microscale, based on finite-element (FE) wedge nanoindentation simulations. These numerical studies on plasticity of body-centered cubic materials in the range of nanometers to few micrometers require not only an incorporation of a crystal plasticity model to describe slip dominated plastic deformation in the FE-simulations but moreover, the consideration of geometrically necessary dislocations (GND) and non-Schmid effects. Thus, an existing crystal plasticity model was extended to determine gradients of plastic shear and non-Schmid effects for the implementation of enhanced FE-simulations of wedge nanoindentation. A comprehensive evaluation of the influence of GNDs and non-Schmid effects on the plastic deformation response of the single crystal was performed under plane strain conditions. Dependent on the applied model, a significant difference in the stress state, the plastic shear on active slip systems and material pile-up around the indenter was observed. In contrast, solely slight deviations in the density of GNDs and crystal lattice rotation under the residual imprint were found. With the gradient-based crystal plasticity model, a size dependency of the plastic deformation could be described in addition. Further, a comparison between numerical and experimental results regarding GNDs, crystal lattice rotation and the residual geometry of the indent was performed. A very good agreement between the experimental and simulated deformed geometry of the specimen was found in the crystal plasticity simulation. The comparison of the GND density and lattice rotation in the region under the indenter flanks showed a good agreement as well. However, all numerical simulations overestimate both, the crystal lattice rotation and density of GNDs that occur in the region under the indenter tip.