Dislocation Patterns and Deformation Bands

Abstract

The methods of stability theory and nonlinear analysis are employed in order to explain the origin and evolution of dislocation patterns as well as the related phenomena of persistent slip bands, shear bands, and Portevin-Le Chatelier bands. A framework is developed for classifying and properly interpreting the hierarchy of plastic instabilities and their manifestations in the description of the macroscopic stress-strain curve. Preliminary results have been obtained which, among other things, provide the range and temperature dependence of the wavelength of the ladder structure of the persistent slip bands, in agreement with experimental observations. Moreover, they suggest the structure and thickness of shear bands, as well as the periodicity and velocity of Portevin-Le Chatelier bands.