Interpretation of the size effects in micropillar compression by a strain gradient crystal plasticity theory

Abstract

This work presents a study of the behavior of micropillars compressed with a flat punch, considering a continuum model based on a higher-order strain gradient crystal plasticity theory. Hardening models are associated with the density of geometrically necessary dislocations. Size effects observed in the present calculations are governed by the development of slip-bands in the micropillar and the geometrically necessary dislocations that build up around them. Two critical factors are identified as defining the slip-band behavior. One is the aspect ratio considered for the micropillar. Shorter micropillars introduce geometrical restrictions to the free path for dislocations in the slip-band, which may result in the development of a substantial amount of geometrically necessary dislocations and size dependent hardening (strain hardening and strengthening). In longer micropillars the effect is not observed and then the proposed model is incapable of capturing size effects in these cases. The other factor is the hardening model used. Two possible models are considered: a dissipative model directly related to slip rate gradients and an energetic model derived from a defect energy. Qualitative comparisons with experiments indicate that dissipative hardening is a more adequate representation of micropillar compression than the energetic model used. Finally, it is shown that a large friction between punch and crystal may inhibit strengthening converting it into strain hardening. Low friction coefficients also tend to promote the concentration of plastic strains in one slip system.