Size dependence of the yield strength of fcc and bcc metallic micropillars with diameters of a few micrometers

Abstract

Recent micropillar compression tests of fcc and bcc single crystals have shown that ‘Smaller is Stronger’ even in the absence of significant strain gradients, an effect that is empirically characterised by a power-law relation. When a micropillar contains a dislocation network, this power-law relation has been explained in terms of the size-dependent operation stress of the weakest single arm dislocation sources. This single arm dislocation source model has successfully captured the power-law relation for the strength of a few fcc micropillars, but a physical interpretation has not been made by comparing different materials. We applied the model, not only to fcc but also to bcc micropillars, to understand quantitatively why different materials have different power-law exponents. Here, the different power-law exponents are interpreted by comparing material parameters that are size-independent properties. Also, by rearranging these parameters such that the formulation becomes independent of material parameters, we found an alternate form of the scaling law that is a unique function of micropillar diameter. Furthermore, recent experimental studies of the effects of increasing the dislocation density, which show hardening for large micropillars and softening for small micropillars, are interpreted in terms of the statistics of dislocation source distribution. The strengths and limitations of this statistical approach are discussed. The effects of temperature on the power-law exponents are also studied.