Statistically based continuum model of misoriented dislocation cell structure formation

Abstract

The formation of misoriented dislocation cells in the course of plastic deformation is explained within the framework of continuum mechanics as a result of the trend to reduce the energetically costly hardening in multislip by locally decreasing the number of active slip systems by local lattice rotations. A model of an infinite crystal deformed in plane strain by symmetric double slip, where the plastic strain is carried by straight, parallel, edge dislocations, is considered. The nonlocal constitutive equations of the model are derived from statistical mechanics description of the collective behavior of dislocations. The finite cell size as well as the orientation of the cell boundaries result from the competition between two tendencies: the internal and dissipative energy tend to decrease the cell size, whereas the short-range dislocation interactions oppose this tendency.