Local strain hardening and nonuniformity of plastic deformation

Local strain hardening in a cross-section of a deforming crystal has been related to the evolutionary behavior of the coupled densities of the mobile and (relatively immobile) forest dislocations. The local mechanical properties thus calculated differ from the bulk properties as obtained by the application of the Orowan relation on the bulk scale or by measuring the overall strain hardening in a macroscopic specimen. This difference is especially pronounced at small strains, and it is attributed to the inherently nonuniform character of plastic deformation by slip. The intrinsic stability of plastic deformation on the local scale has been examined with the help of standard methods of nonlinear analysis. In addition to such nonuniformities as yield points and the occurrence of necking (Considère instability), slip lines and slip bands also appear to be interprétable in terms of local instability of plastic flow.