An energetic description of the hardening behavior of single crystals undergoing single 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.
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