Impact of grain size distribution on the multiscale mechanical behavior of nanocrystalline materials

A macro–micro scale transition model based on self-consistent approximation is proposed to explore the effect of grain size and grain size distribution, along with the strain rate, on the mechanical response of nanocrystalline (nc) materials. The representative volume element (RVE) is composed of grains supposed to follow an elastic–viscoplastic behavior, and randomly distributed with a grain size distribution following a log-normal statistical function. The grain interior and grain boundary are not taken as two independent phases with different volume fractions, but as an integral object to sustain deformation mechanisms of grain-boundary sliding, grain-boundary diffusion and grain-interior plasticity. Numerical results for the case of nc copper are shown to be in good agreement with available experimental data. The predictions firstly display that not only the mean grain size plays an important role but also the grain size dispersion has a slight impact on the flow stress. A decrease of the yield stress with an increasing of the grain size dispersion occurs. Secondly, the strain rate sensitivity has strong effect on the mechanical behavior of nc materials and the effect increases with decreasing the grain size. Lastly, deviations of the internal stress and local strain from the overall stress and macroscopical strain occur, respectively. Local plastic strains and internal stresses, developing within the RVE, have been recorded and discussed. Using the present model, we have also studied the failure behavior of nc materials.