Effects of dislocation density and sample-size on plastic yielding at the nanoscale: a Weibull-like framework

Micro-compression tests have demonstrated that plastic yielding in nanoscale pillars is the result of the fine interplay between the sample-size (chiefly the diameter D) and the density of bulk dislocations ρ. The power-law scaling typical of the nanoscale stems from a source-limited regime, which depends on both these sample parameters. Based on the experimental and theoretical results available in the literature, this paper offers a perspective about the joint effect of D and ρ on the yield stress in any plastic regime, promoting also a schematic graphical map of it. In the sample-size dependent regime, such dependence is cast mathematically into a first order Weibull-type theory, where the power-law scaling the power exponent β and the modulus m of an approximate (unimodal) Weibull distribution of source-strengths can be related by a simple inverse proportionality. As a corollary, the scaling exponent β may not be a universal number, as speculated in the literature. In this context, the discussion opens the alternative possibility of more general (multimodal) source-strength distributions, which could produce more complex and realistic strengthening patterns than the single power-law usually assumed. The paper re-examines our own experimental data, as well as results of Bei et al. (2008) on Mo-alloy pillars, especially for the sake of emphasizing the significance of a sudden increase in sample response scatter as a warning signal of an incipient source-limited regime.