Viscoplasticity of metals: Comments on statistical approaches to dislocation reactions

Dislocations, i.e., line defects in the crystal structure, are at the origin of viscoplastic deformation in metals. In the literature, the statistical approaches to the dislocation dynamics in terms of dislocation densities are often used. There, the key ingredient for modeling the ubiquitous strain hardening is the interplay between the mobile and forest (i.e., immobile) dislocations, which is captured in terms of reaction-type contributions in the evolution of the dislocation densities. In this paper, we demonstrate that a certain class of such models is in conflict with thermodynamic principles. The origin of this conflict is identified. Specifically, the absence of the reversal processes for any of the reactions is problematic and sharply contrasts to usual chemical reactions. Possible solutions for restoring the thermodynamic admissibility are discussed.