Modeling the effect of dislocation density on the strength statistics in nanoindentation

High variability in material strength is observed when the characteristic length scale of the specimen or stressed region approaches the mean dislocation spacing. However, few efforts have been made, either through experimentation or simulation, to quantify the distributions of material strength in this regime. In the present work, we investigate the effect of dislocation density on the statistical distribution of the critical indenter force required to initiate plasticity in nanoindentation. By coupling discrete dislocation dynamics with the finite element method, we are able to quantify the effect of initial dislocation density, rho(o), on both the mean and standard deviation of the critical force. Our results suggest a rho(-1/2)(o) power law scaling for both the mean and standard deviation.