Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis

 doi:10.1016/j.jmps.2007.03.009

Mechanism-based discrete dislocation
plasticity is used to investigate the effect of size on micron scale
crystal plasticity under conditions of macroscopically homogeneous
deformation. Long-range interactions among dislocations are naturally
incorporated through elasticity. Constitutive rules are used which
account for key short-range dislocation interactions. These include
junction formation and dynamic source and obstacle creation.
Two-dimensional calculations are carried out which can handle high
dislocation densities and large strains up to 0.1. The focus is laid on
the effect of dimensional constraints on plastic flow and hardening
processes. Specimen dimensions ranging from hundreds of nanometers to
tens of microns are considered. Our findings show a strong
size-dependence of flow strength and work-hardening rate at the micron
scale. Taylor-like hardening is shown to be insufficient as a rationale
for the flow stress scaling with specimen dimensions. The predicted
size effect is associated with the emergence, at sufficient resolution,
of a signed dislocation density. Heuristic correlations between
macroscopic flow stress and macroscopic measures of dislocation density
are sought. Most accurate among those is a correlation based on two
state variables: the total dislocation density and an effective,
scale-dependent measure of signed density.

Published in J Mech Phys Solids Vol 56, Issue 1, January 2008, pages 132--156.