Abstract

In this paper we set out to present the constitutive equations of the work hardening single crystal or polycrystalline solid from the knowledge of the atomistic processes, i.e. dislocation behaviour. An important role is played by the plastic Gibbs equation, which is a differential relation between the parameters which define a plastic state. The physical meaning of the state parameters, intensive and extensive ones, entering this equation is discussed. As the derivation of the Gibbs equation is difficult in concept we suspend it to later work. This is in accordance with the postulatory approach to thermodynamics followed by authors as Callen[47]. The attention in this paper is focused on the information attainable hereof. Equilibrium and stability conditions related to the dislocation state are discussed. Explicit constitutive equations relating such variables, as stress, strain, temperature and dislocation state are presented for a single crystal and a somewhat idealized polycrystalline material. Its derivation demands however validity of the principle of superposition.

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