Scale effects in convoluted thermal/spatial statistics of plasticity initiation in small stressed volumes during nanoindentation

Abstract

The elastic–plastic transition of crystals at small length scales can be quantitatively evaluated by sudden discontinuities (pop-ins) on nanoindentation load–displacement curves. For defect free crystals under nanocontacts, pop-in stress fluctuations result purely from the thermally activated process of homogeneous dislocation nucleation, while at intermediate contact sizes, fluctuations can arise from the spatial statistics of pre-existing defects. Here, we find that the convolution of the above thermal and spatial effects exhibits a distinct dependence on the stressed volume size, dislocation density and geometric factors that describe crystallography and slip anisotropy. These essential features are captured in a unified model that includes both homogeneous dislocation nucleation and heterogeneous activation of pre-existing dislocations. Our theoretical predictions compare remarkably well with experimental findings. In particular, the model describes the observed strong and complex dependence of pop-in probability on indentation direction in NiAl. Implications for other small scale mechanical tests such as micropillar compression are discussed.