Workhardening and substructural geometry of metals

Abstract

In this paper a model describing workhardening at ambient temperature for moderate to large strains is presented. The model is based on a differential equation describing the evolution of dislocation density, which is complemented by a formula for computing dislocation cell size, and a qualitative relationship for the evolution of cell shape as caused by cell wall sliding or annihilation. Cell deformation is taken to be proportional to macroscopic deformation. It is assumed that a single proportionality parameter applies for all strains. No distinction is being made between cell multiplication and cell wall sliding. Both phenomena are assumed to be operative at constant rates for all strains. The resulting differential equation for the dislocation density can be analytically integrated, and a formula for workhardening results in the usual way. The persistence of a nonzero workhardening rate at large strains is shown to be related to the geometrical evolution of the dislocation substructure. The model was validated by fitting it to experimental stress- strain data, and comparing the computed substructural parameters to experimental values found in literature.