MULTILEVEL MODELS OF POLYCRYSTALLINE METALS: COMPARISON OF CONSTITUTIVE RELATIONS FOR CRYSTALLITES

Abstract

Different formulations of geometrically nonlinear elasticviscoplastic constitutive relations for the mesolevel (the level of an individual crystallite), which are a key element of multilevel models of polycrystalline met als and alloys, are given and compared; various elastic relationships are used to determine the stresses. The most popular relations in finite form in the unloaded configuration, the relations in finite form using the motion decomposition with an explicit separation of the moving coordinate system motion, equivalent to the last constitutive relations in the rate form, as well as their linear approximation, and the relations in the rate form in the current configuration are considered. The estimations are given showing the equivalence or proximity of the stresses determined in the considered formulations with the same kinematic impacts. The results of numerical calculations carried out for randomly chosen kinematic impacts confirm the above conclusions about the similarity of mesolevel model formulations. It is noted that the formulation using the motion decomposition with an explicit separation of the moving coordinate system motion allows theoretically justified to go to the close formulation in the rate form in the current configuration, which is preferable for the numerical solution of boundary value problems with varying contact conditions (necessary for modeling of thermomechanical processing technological processes).

Keywords: multilevel models of polycrystals, large deformations, constitutive relations, internal variables, elastoviscoplasticity.