Unifying the size effect observed in micropillar compression experiments

Abstract

Micropillar compression experiments show size effect, sigma p/mu= A(d/b)(n), where sigma(p), is the flow stress, mu is the resolved shear modulus, d is the pillar diameter and b is Burgers' vector. With fcc metals n -0.67 and A 0.7; however, with bcc metals there is greater variation, with n closer to zero. Here we propose a different but similar empirical relation of sigma(p)/mu = sigma(b)/mu + A'(d/b)(n)', where sigma b is a size independent resistance stress. In which case there must be a strong correlation between the original constants, A and n. This hypothesis is found to be true for the published data from a large number of bcc metals, ionic solids that possess the rock salt crystal structure, and some covalent bonded semiconductors. This correlation is shown to predict a universal power law with the exponent in the range, -1.0 < n' < -0.5, and with A' close to 1. These values are very similar to the empirical relation that can be used to describe the behaviour of fcc metals tested in micropillar compression with sigma b= 0. This universality of the empirical relation provides strong evidence for a common mechanism for the micropillar size effect across a range of materials.