Jan Kratochvil

Abstract:

Deformation bands are the basic microstructural elements in metal single crystals and polycrystals where the dominating deformation mechanism is a dislocation glide. The deformation bands are detected in a form of elongated misoriented domains separated by roughly parallel families of geometrically necessary boundaries. From the continuum mechanics point of view the deformation bands are spontaneous deformation instabilities, Biot (1965). The deformation bands are a consequence of anisotropy of hardening. The anisotropy causes that it is energetically less costly to flow the material through the crystal lattice buckled by the deformation bands with a decreased number of the active slip systems than to flow it through a lattice deformed homogeneously by multislip. In our approach a symmetric double slip model of a plane strain compression, a spontaneous formation of the deformation bands is presented in a variational form suitable for an energetic consideration. We adopt the rigid-plastic, rate-independent approximation, which turns out to be the optimal viewpoint pointing to the essential features of the formation of the deformation bands. A simple version of the model based on the standard hardening rule reveals the conditions for the formation of the deformation bands. It is shown that in the simplified case the predicted bands have extreme properties: the band orientation is perpendicular to the direction of the compression and their width tends to zero. Except for a modification of the hardening rule of the advanced model, which incorporates additionally the higher plastic strain gradients, we follow the classical crystal plasticity framework. The gradients represent hardening caused by the incremental work needed to build-up the boundaries and to overcome the dislocation bowing (Orowan) stress. The proposed model provides a unified interpretation of the band orientation, their width, the misorientation across the band boundaries, their dislocation composition, and the band reorientation occurring at large strains in agreement with observations.