THEORY OF SOLITARY PLASTIC WAVES .1. LUDERS BANDS IN POLYCRYSTALS

A dislocation dynamical model of the reaction-diffusion type is used to describe the spatio-temporal dynamics of Luders band propagation in polycrystals. The diffusive nature of dislocation glide is traced back to the random crystallographic orientation of the active slip systems. The role of pile-ups in dislocation multiplication is accounted, for by a dynamical generalization of the Hall-Petch law. It is argued that Luders bands in polycrystals are related to a bistable dynamics of mobile dislocations. Further results obtained cover the dependences on material parameters and deformation conditions of (1) the occurrence, (2) the strain, propagation velocity and width of Luders bands, and (3) the upper and lower yield stresses. These results are in good agreement with experimental findings.