Continuum simulation of the evolution of dislocation densities during nanoindentation
P. S. Engels, A. Ma, A. Hartmaier.
International Journal of Plasticity, 38, 159-169, (2012)
When nanoindenting dislocation-free regions of single crystals a so-called pop-in phenomenon is commonly observed. Molecular dynamics (MD) studies have revealed homogeneous nucleation of dislocations in a perfect crystal as a mechanism causing such pop-in behavior. In this work we transfer this knowledge gained on the atomic scale into a dislocation nucleation model that is applied within a dislocation density based crystal plasticity description. Furthermore, we develop a non-local formulation of a crystal plasticity model that is devised to yield a valid description of plasticity also in situations where the dislocation density is small or even vanishing and where conventional plasticity models fail. This is accomplished by studying the evolution of statistically stored and geometrically necessary dislocation densities separately. We apply this non-local crystal plasticity model to investigate the evolution of dislocation densities in the early stages of nanoindentation. The results of our continuum model show good agreement with MD simulations for cases where nanoindentation into an initially dislocation-free crystal is studied, i.e. where a popin occurs when the critical stress underneath the indenter reaches the critical value for homogeneous dislocation nucleation. After thus validating our model we study the influence of pre-existing homogeneous and local dislocation densities. Both cases show a good qualitative agreement with recent experimental findings and it is concluded that pre-existing local dislocations densities reduce the load at which a pop-in occurs and - more importantly - change the mechanism from homogeneous dislocation nucleation to rapid dislocation multiplication. In general, our results show that continuum plasticity formulations can be extended such that applications to nanoscale volumes become possible.
Keyword(s): dislocations; crystal plasticity; elastic–viscoplastic material; finite differences; nanoindentation