Prediction of Crystallographic Texture Formation in Polycrystalline Samples under Severe Plastic Deformation Based on a Two-Level Statistical Elasto-Viscoplastic Model

A multilevel mathematical model is proposed for studying the technological processing of metals and alloys by severe plastic deformation. The model is based on crystal elasto-viscoplasticity and can describe the evolving structure as well as predict crystallographic texture formation. A geometrically nonlinear nonstationary boundary value problem of quasi-static elasto-viscoplastic deformation of macroscopic polycrystalline samples is formulated in rate form, including systems of equations describing physical mechanisms at various structural scale levels. A distinctive feature of the proposed formulation is that it takes into account variable contact conditions on the material surface specified for each moment of the loading process. As a basic constitutive model, a two-level model of a polycrystal is used in which the characteristics of a macroscopic representative volume are calculated by consistent statistical averaging over the values of similar quantities for the contained mesoscopic elements (crystallites). Within the approach used, information on crystallographic textures in different parts of the workpiece is provided in the form of samples of crystal lattice orientations. The associated output data of numerical calculations are reproduced in a reduced form using cluster analysis methods. The developed apparatus is applied to study the drawing of a solid copper cylinder.