Plastic inclusion with moving boundary. Application to dislocation cell structures

Abstract

Based on the determination of the Helmholtz free energy and the dissipation of an elastoplastic solid containing moving surfaces of plastic strain discontinuity, a micromechanical approach is developed to study the formation of dislocation cell structure and their effects on the mechanical behavior of metals. The results are applied to an evolutive two-phase microstructure representing the dislocation cell structure induced during plastic straining. The internal variables are reduced to the plastic strain of each mechanical phase, the volume fraction and the morphology of the ellipsoidal inclusion describing the cell structure. We obtain the conjugate forces according to the formalism of irreversible thermodynamics. Complementary relations describing the evolution of these internal variables are introduced in order to obtain the constitutive equation for the grain, the evolution of the microstructure as well as the hardening of the two phases. Preliminary results are presented and discussed in the case of a simplified situation.