A simplified crystallographic approach of bifurcation for single crystals and polycrystals

Abstract

Localization of the plastic deformation such as necking, kink and shear bands in polycrystal and single crystals leads to inhomogeneous strain field and lattice rotation field. In order to study at microscopic and macroscopic scales the formation and propagation of such instabilities, single copper crystals and steel polycrystals were deformed in tension within a SEM. The strain field and lattice rotation field were analyzed at the micrometer scale for different steps of the plastic deformation, using simultaneously microextensometry (microgrids) and electronic diffraction (EBSD) within the SEM. Three components of the Green Lagrange tensor, of the strain rate and lattice spin were obtained within the band and the matrix before and during bifurcation. Localization in cfc single crystal and steel (bcc) polycrystals, presented similarities conceming the activation of two shear planes in the necking area and the evolution of the inhomogeneous strain field and lattice rotation. These phenomena can be correlated to the activation of two crystallographic slip systems for the single crystal and two families of parallel slip planes within the grains for the polycrystals. The gradients were analyzed by Cosserat theory: a constitutive law taking into account the lattice curvature (through couple stress tensor) and hardening law dependent on a density of geometrically necessary dislocations within the band. Such analysis previously developed for a two dimensional single crystal, is applied to the polycrystal assumed to a super single crystal.