Microplasticity and yielding in crystals with heterogeneous dislocation distribution

In this study, we use discrete dislocation dynamics simulation to investigate the effect of heterogeneous dislocation density on the transition between quasi-elastic deformation and plastic flow in face-centered cubic single crystals. By analyzing the stress-strain curves of samples with an initial, axial dislocation density gradient, we arrive at the following conclusions: (i) in the regime of quasi-elastic deformation before the onset of plastic flow, the effective elastic modulus of the simulated samples falls significantly below the value for a dislocation-free crystal. This modulus reduction increases with decreasing dislocation density gradient: crystals with homogeneous dislocation distribution are thus weakest in the quasi-elastic regime; (ii) the transition towards plastic flow occurs first in regions of reduced dislocation density. Therefore, the overall yield stress decreases with increasing dislocation density gradient; (iii) crystals with dislocation density gradient exhibit a more pronounced hardening stage during which stress is re-distributed onto stronger regions with higher dislocation density until the sample flows at a constant flow stress that is approximately independent of dislocation density gradient. We interpret these findings in terms of a continuum dislocation dynamics inspired model of dislocation density evolution that accounts for geometrically reversible ('inversive') dislocation motions. The transition between quasi-elastic and plastic deformation is interpreted as a transition from inversive to non-inversive dislocation motion, and the initial differences in elastic modulus are related to a density dependent polarizability of the dislocation system. The subsequent plastic flow behavior is analyzed in terms of a modified version of Mughrabi's composite model.