Shear band development in polycrystals

Abstract

Shear band localizations are studied using a band model involving two polycrystalline aggregates; one representing the material inside the potential band and the other the material outside. Each of these aggregates is assumed to be homogeneously deformed and conditions of compatibility and equilibrium are enforced across the band interfaces. The aggregate constitutive response is obtained from a generalized Taylor polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation, so that no ambiguity arises concerning the choice of active slip systems. Because of the material rate sensitivity a shear band bifurcation is ruled out at achievable strain levels, but localization occurs from the growth of an initial inhomogeneity. Results are presented for imposed loading histories of plane strain tension, biaxial tension and simple shear, both for an initially isotropic aggregate and for an aggregate that has undergone a pre-strain in plane strain compression. Depending on the material properties, the initial conditions and the imposed deformation state, either (i) localization, in the sense of a very high strain rate concentration in the band, takes place; or (ii) the band strain rate increases rapidly for a short interval and then saturates; or (iii) the initial inhomogeneity does not induce a large strain rate concentration in the band. The initial pre-strain promotes earlier localization in plane strain tension and in simple shear. In biaxial tension, localization occurs earlier for the pre-strained material if the initial imperfection is large, but tends to saturate for smaller imperfections. The effects of variations in imperfection amplitude and material strain rate sensitivity are illustrated.