Continuum descriptions of dislocations under stress reversals

A general continuum theory of dislocation motion is used to investigate the response of crystalline solids to cyclic straining in uniaxial tension and compression. For macroscopically homogeneous deformation under uniaxial stress a simple one-dimensional equation suffices to relate the plastic strain rate to dislocation flux. The material is characterized by evolutionary equations for multiplication of dislocations and for immobilization of moving dislocations. Some simple example materials are considered and it is shown by numerical calculation that these exhibit respectively a Bauschinger effect, isotropic hardening, and isotropic softening when subjected to a program of alternating strains at a constant rate.