Application of nonlinear continuum dislocation theory to antiplane shear

Abstract

We apply the nonlinear dislocation theory to the problem of antiplane constrained shear in a single crystal with one slip system. By taking dissipation into account, the relaxed energy functional has to be minimized. We show that, up to a threshold strain, no dislocations are nucleated and therefore the plastic slip is zero. Since this threshold value depends on the width of the specimen, a size effect takes place. The stress strain curve turns out to be a hysteresis loop exhibiting the work hardening due to the dislocation pile-up. It is shown that the Bauschinger effect holds true.