Surface effects and the size-dependent hardening and strengthening of nickel micropillars

We evaluate the extent to which two mechanisms contribute to the observed size effect of the ultimate yield strength of micropillars of diameters in the range of 1–30μm: dislocation pile-ups, modeled by means of a physically based non-local single-crystal plasticity model; and the short-range interaction of dislocations with the free surface of the micropillars, e.g., through the formation of surface steps. To this end, we formulate a crystal-plasticity model that accounts for the self-energy of geometrically necessary dislocations and the formation energy of dislocation steps at the boundary of the solid. These two additional sources of energy have the effect of rendering the internal energy of the solid non-local, thereby introducing the possibility of size effects. By way of validation of the model, we simulate the uniaxial compression tests on [269] nickel micropillars of Dimiduk et al. (2005). The calculated dependence of the ultimate strength of the micropillars exhibits strong power-law behavior, and is in good agreement with observation. Our analysis suggests that non-local hardening due to the self-energy of geometrically necessary dislocations does not suffice to account for the observed size effect of the ultimate yield strength of micropillars, and that surface effects, such as resulting from the formation energy of dislocation steps, contribute significantly to that size effect.