Interpretation of Plastic Deformation by Means of a Dislocation-Disclination Reaction Kinetics

The microstructure development under plastic deformation up to large strains is modelled by means of a four-component reaction kinetics for the densities of mobile and immobile dislocations and disclinations. The resulting system of nonlinear differential equations is able to describe the transition from a dislocation-dominated to a disclination-controlled kinetics running into a (quasi-)stationary state and, nally, into an instability. For an estimation of the resulting ow stress three contributions are taken into account: a redundant dislocation one governed by a Taylor law, a subgrain size one governed by a Hall-Petch relationship, and a misorientation one. To connect the density of sessile disclinations to the mean subgrain size and the mean misorientation new relationships based on stochastic geometry are used.