A preliminary investigation of dislocation cell structure formation in metals using continuum dislocation dynamics

Abstract

A continuum dislocation dynamics model capable of capturing the cellular arrangements of dislocations in deformed crystals is presented. A small strain formulation of the model is given, followed by sample results of stress-strain behaviour, dislocation density evolution, dislocation cell pattern, lattice rotation, and geometrically necessary dislocation density and strain energy density distributions. An important finding of the current work is that dislocations form patterns under all circumstances due to their long range interactions. It is found, however, that the famous cell structure pattern forms when cross slip is activated. It is also found that cells are 3D sub-regions surrounded by dislocations walls in all directions, and they form, disappear, and reappear as a result of the motion of cell walls and formation of new walls by cross slip. It is further found that the average cell size is connected with the applied resolved shear stress according to the similitude principle observed in related experiments. The importance of these results is briefly discussed in the context of recrystallization.