Substructure formation during plastic deformation

Abstract

This work addresses cell formation from an initially homogeneous distribution of parallel edge dislocations. We consider an array of interacting, nearly parallel edge dislocations that glide on a single plane, but may also climb. We obtain a set of nonlinear differential equations that describe the evolution of the dislocation distribution, and find the instability conditions that lead toward cells. Three particularly interesting results emerge. First, the distribution of edge dislocations is always at least mathematically unstable with respect to cell formation when dislocations can be created or destroyed. Second, the locus of that instability is very sensitive to the efficiency of the dislocation creation mechanisms. Third, both relatively equiaxed and highly elongated cells may form, depending on the temperature and the ratio of the stresses that drive glide and climb.