Energetics of two-level shears and hardening of single crystals

An energetic description of the hardening behavior of single crystals undergoing slip is analyzed. Simultaneous macroscopic simple shear and mesoscopic slips are described by means of a class of structured deformations called "two-level shears," along with recently proposed measures of separation of active slip-bands and the number of lattice cells traversed during slip. The energetics of two-level shears gives rise to a response consistent with the experimentally observed loading and unloading behavior of a single crystal in G. I. Taylor's soft device, as well as with the Portevin-le Chatelier effect. The initial critical resolved shear stress, the flow stress, and the hardening response are obtained, and an application to aluminum single crystals is discussed.