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.

Keywords:

• Nanoindentation pop-in
• Thermal and spatial statistics
• Scale effects

Acknowledgements

The present work was sponsored by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division (TLL, HB, JRM and EPG) and by the Center for Defect Physics, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science (YFG). The authors are grateful to G. M. Pharr for fruitful discussions.