A simplified crystallographic approach of bifurcation for single crystals and polycrystals

Localization of the plastic deformation such as necking, kink and shear ban ds in polycrystal and single crystals leads to inhomogeneous strain field a nd 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 sca le for different steps of the plastic deformation, using simultaneously mic roextensometry (microgrids) and electronic diffraction (EBSD) within the SE M. Three components of the Green Lagrange tensor, of the strain rate and la ttice spin were obtained within the band and the matrix before and during b ifurcation. Localization in cfc single crystal and steel (bcc) polycrystals , presented similarities concerning the activation of two shear planes in t he necking area and the evolution of the inhomogeneous strain field and lat tice rotation. These phenomena can be correlated to the activation of two c rystallographic slip systems for the single crystal and two families of par allel slip planes within the grains for the polycrystals. The gradients wer e analyzed by Cosserat theory: a constitutive law taking into account the l attice 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 app lied to the polycrystal assumed to a "super single crystal".