Dissipative driving force in ductile crystals and the strain localization phenomenon

This paper is concerned with crystals undergoing large plastic deformations. The free energy per unit volume of the reference crystal is supposed to depend on the elastic distortion as well as on constant tensors characterizing the crystal symmetry. The dissipative driving force is shown to be equal to the Eshelby stress tensor relative to the reference crystal. For single crystals obeying Taylor's equation the driving force reduces to the Eshelby resolved shear stress, which is power-conjungate to the slip rate. The Schmid law formulated with respect to the latter is used to determine the critical hardening rate at the onset of the shear band formation. (C) 1998 Elsevier Science Ltd. All rights reserved.