Elementary observations on the averaging of dislocation mechanics: Dislocation origin of aspects of anisotropic yield and plastic spin

With a view towards utilization in macroscopic continuum models, an approximation to the root-mean-square of the driving force field on individual dislocations within a “representative volume element” is derived. The plastic flow field of individual dislocations is also similarly averaged. Even under strong simplifying assumptions, non-trivial results on the origin and nature of anisotropic macroscopic yielding, plastic spin, and the plastic flow rule (for single and polycrystalline bodies) are obtained. A particular result is the explicit dependence of the plastic response of a material point of the averaged model on the presence of dislocations within it, an effect absent in conventional theories of plastic response (e.g. J2 plasticity). Also noteworthy is the explicit geometric accounting of the indeterminacy of the slip-plane identity of the screw dislocation that appears to lead to some differences with conventional ideas.