New aspects of a single-crystal gradient plasticity model: Rate-dependency of size-dependent response

Abstract

Gradient crystal plasticity and rate-dependent plasticity models have been widely developed. However, describing the rate-dependency of the size-dependent behavior remains a long-term challenge and is of great interest in the field. This study investigates the interaction between the rate and size dependency of single crystals. The main contribution is to determine whether the size dependency of the stress–strain responses increases or decreases with increasing deformation rates. A thermodynamically consistent model based on the finite-deformation single-crystal gradient plasticity framework proposed by Gurtin is presented. In the current formulation, the particular features are a rate-dependent function and a rate-sensitivity parameter incorporated into the dissipative gradient strengthening term. These features allowed us to observe the disparate rate-dependencies induced by the dissipative conventional and dissipative gradient terms. From an experimental perspective, few studies have investigated the interaction between the size- and rate-dependence of single crystals. Interestingly, these studies reported different modes of interaction. Here, we categorize existing experimental stress–strain data into two distinct groups: first, the stress data obtained at fixed overall strains, and second, those captured at offset strains, that is, at the yield or post-yield strains. The numerical results obtained through a two-dimensional framework and based on a common set of material and modeling parameters were qualitatively compared with existing experimental data reported for different materials. Trends in the interactions were numerically captured and discussed. The results indicate the promising potential of the model for describing the rate-dependency of the size-dependent yield stress and subsequent behaviors.