Size Effects and Stochastic Behavior of Nanoindentation Pop In

A statistical model for pop in initiated at preexisting dislocations during nanoindentation is developed to explain size-dependent pop-in stresses. To verify theoretical predictions of this model, experiments were performed on single-crystal Mo, utilizing indenter radii that vary by over 3 orders of magnitude. The stress where plastic deformation begins ranges from the theoretical strength in small volumes, to 1 order of magnitude lower in larger volumes. An intermediate regime shows wide variability in the stress to initiate plastic deformation. Our theory accurately reproduces the experimental cumulative probability distributions, and predicts a scaling behavior that matches experimental behavior.