Single versus successive pop-in modes in nanoindentation tests of single crystals

From recent nanoindentation experiments, two types of pop-in modes have been identified: a single pop-in with a large displacement excursion and a number of pop-ins with comparable and small displacement excursions. Theoretical analyses are developed here to study the roles played by indenter tip radius, pre-existing defect density, heterogeneous nucleation source type, and lattice resistance on the pop-in modes. The evolution of dislocation structures in earlier pop-ins provides input to modeling a stochastic, heterogeneous mechanism that may be responsible for the subsequent pop-ins. It is found that when the first pop-in occurs near theoretical shear stress, the pop-in mode is determined by the lattice resistance and tip radius. When the first pop-in occurs at low shear stress, whether the successive pop-in mode occurs depends on how the heterogeneous dislocation nucleation source density increases as compared to the increase of the total dislocation density. The above transitions are found to correlate well with the ratio of indenter tip radius to the mean spacing of dislocation nucleation sources.