Strain softening, slip localization and propagation: From simulations to continuum modelling

A continuum model is proposed for the Luders-like behaviour of single-crystals of dilute alloys undergoing strain softening. A constitutive form is established which incorporates a spatial coupling in the form of a second gradient. The latter takes into account the elastic interactions of dislocations of like sign, as suggested by earlier results obtained with the help of a numerical simulation. An approximate one-dimensional solution is proposed which yields three possible types of behaviour. uniform deformation, static and propagative strain localizations. The main properties of the Luders-like deformation, in particular the band velocity, are calculated and discussed as a function of the characteristic features of strain softening. Although this model is elaborated at a mesoscopic scale and does not take into account possible geometrical couplings, its results agree numerically with the existing data on the dynamics of band propagation. Copyright (C) 1996 Acta Metallurgica Inc.