Origin of the size dependence of micropillar strength
In plain words
Metal pillars a few hundredths of a millimeter wide or smaller are many times stronger than large crystals, with strength rising as the diameter shrinks by a power law. Several mechanisms are proposed, but none predicts the exponent and its variation between metals.
Precise statement
Flow stress of FCC micropillars scales as $\tau \sim D^{-n}$ with $n \sim 0.6 \text{ to } 0.7$ for diameters D from about $1e-5 \text{ to } 1e-3\,\mathrm{cm}$ (Uchic et al. 2004), while BCC metals show smaller n correlated with the temperature dependence of screw dislocation mobility. Determine which mechanism (truncation of single-arm sources, dislocation starvation, exhaustion hardening) controls n, and whether n is universal for FCC, via 3D dislocation dynamics compared with experimental statistics. An answer is the mechanism with predicted n versus material, D and initial dislocation density.
What would settle it
Dislocation dynamics simulations with measured initial microstructures reproducing n for FCC and BCC pillars, tested on pillars of controlled initial dislocation density.
Status in the literature
Source-truncation models reproduce $n \sim 0.6$ for FCC; the BCC trend and the role of initial dislocation density remain unresolved.