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Abstract

Unlike macroscopic indentation experiments, nanoindentation exhibits two additional phenomena: size- and pop-in effects. A number of publications has been devoted to the description of the former effect with the help of continuum and strain gradient approaches, whereas it is the goal of this work to consider the pop-in phenomenon. Here we present a simple, non-local crystal plasticity model based on dislocation densities, which again are grouped in statistically stored and geometrically necessary dislocation densities. To capture the homogeneous dislocation nucleation the model is extended by a stress dependent nucleation criterion.

The results of nanoindentation simulations in a two dimensional model mimicking an aluminum single crystal with different initial dislocation density configurations are presented. They reveal two types of pop-in behavior: first, the well-known pop-in due to homogeneous dislocation nucleation in dislocation-free single crystals, which shows the ability to capture these characteristic load-indentation behaviour within a continuum framework. In addition, recent experimental findings [1] have described a different type of pop-in phenomenon at comparably lower load levels, that is observed in pre-strained materials. By mimicking a pre-existing heterogeneous dislocation distribution, our model is able to qualitatively reproduce this second type pop-in. For both cases the dislocation density evolution during the indentation is critically discussed.

[1] Lodes, M., Hartmaier, A., Göken, M., Durst, K., 2011. Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: Experiments and molecular dynamics simulations. Acta Materialia 59, 4264-4273.