Statistical analysis of the size- and rate-dependence of yield and plastic flow in nanocrystalline copper pillars

Abstract

The effects of specimen size and strain rate on the plastic deformation response of sub-mu m-sized nanocrystalline Cu pillars were examined through a series of micro-compression experiments, with particular emphasis on the stochastic nature of the measured responses. A large number of micropillars two different diameters, both with an average grain size of 6 nm, were prepared by employing the single batch process of e-beam lithography and electroplating and tested. By recourse to statistical analysis, it was recognized the yield strength and flow stress increase with pillar size and strain rate. Further, the rate sensitivity in smaller pillars was more pronounced, implying synergetic interactions between the deformed volume and the strain rate imposed. The coupling influence of size and rate on yield was analyzed by estimating the parameters in a statistical distribution having Weibull-like formula, revealing that the enhanced role of free surface in smaller pillar may make it easy to trigger yielding. The size dependence of rate-sensitive plastic flow was also statistically examined in detail and discussed in terms of strain-rate sensitivity, activation volume, and the combined roles of free surfaces and grain boundaries.