Size effects in dislocation depinning models for plastic yield

Typically, the plastic yield stress of a sample is determined from a stress-strain curve by defining a yield strain and reading off the stress required to attain it. However, it is not a priori clear that yield strengths of microscale samples measured this way should display the correct finite size scaling. Here we study plastic yield as a depinning transition of a 1 + 1 dimensional interface, and consider how finite size effects depend on the choice of yield strain, as well as the presence of hardening and the strength of elastic coupling. Our results indicate the existence of a crossover length that depends on the yield strain. It is only above this length scale that standard finite size scaling is expected to hold. These results are also expected to be particularly relevant for simulations of single dislocations, such as those used to study strengthening due to included particles.