A two-parameter description of heterogeneous dislocation distributions in deformed metal crystals

Abstract

A two-parameter model of heterogeneous dislocation distributions (cell structures) in deformed metals has been developed. The model permits a description of the effective mechanical and energetic properties of (one-dimensional) cell structures in terms of the local properties (dislocation densities and volume fractions) of cell walls and cell interiors and includes the limiting case of the homogeneous dislocation distribution. Long-range internal stresses that arise unavoidably in heterogeneous dislocation distributions during deformation are an important feature of the model. The model is consistent with the well-established empirical relationships between the macroscopic flow stress, the mean dislocation density and the cell wall spacing. It is shown that, for a given mean dislocation density, the macroscopic flow stress is always lower for a heterogeneous than for a homogeneous dislocation distribution. This result and the fact that the total elastic strain energy in the stress-applied state (with contributions from the dislocations, the long-range internal and the applied stress) decreases progressively with increasing heterogeneity of the dislocation distribution are considered to be the major reasons for dislocation cell formation.