Size dependence of yield strength simulated by a dislocation-density function dynamics approach

The size dependence of the strength of nano- and micron-sized crystals is studied using a new simulation approach in which the dynamics of the density functions of dislocations are modeled. Since any quantity of dislocations can be represented by a density, this approach can handle large systems containing large quantities of dislocations, which may handicap discrete dislocation dynamics schemes due to the excessive computation time involved. For this reason, pillar sizes spanning a large range, from the sub-micron to micron regimes, can be simulated. The simulation results reveal the power-law relationship between strength and specimen size up to a certain size, beyond which the strength varies much more slowly with size. For specimens smaller than ~4000b, their strength is found to be controlled by the dislocation depletion condition, in which the total dislocation density remains almost constant throughout the loading process. In specimens larger than ~4000b, the initial dislocation distribution is of critical importance since the presence of dislocation entanglements is found to obstruct deformation in the neighboring regions within a distance of ~2000b. This length scale suggests that the effects of dense dislocation clusters are greater in intermediate-sized specimens (e.g. 4000b and 8000b) than in larger specimens (e.g. 16 000b), according to the weakest-link concept.