Abstract

This research supports recent eAorts to provide an energetic approach to the prediction of stress‐strain relations for single crystals undergoing single slip and to give precise formulations of experimentally observed connections between hardening of single crystals and separation of active slip-bands. Non‐classical, structured deformations in the form of twolevel shears permit the formulation of new measures of the active slip-band separation and of the number of lattice cells traversed during slip. A formula is obtained for the Helmholtz free energy per unit volume as a function of the shear without slip, the shear due to slip, and the relative separation of active slip-bands in a single crystal. This formula is the basis for a model, under preparation by the authors, of hardening of single crystals in single slip that is consistent with the Portevin-Le Chatelier eAect and the existence of a critical resolved shear stress. # 2000 Elsevier Science Ltd. All rights reserved.

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