Two-scale models of polycrystals: Independence of the loading process image of a representative macrovolume

Abstract

The paper considers variants of constructing the process image introduced by A.A. Ilyushin for loading of a representative macrovolume of polycrystalline metal with high displacement gradients. Analysis is performed to clarify whether the loading process image in the variants under study depends on the rigid rotation imposed on the entire representative volume (or on the choice of a reference frame). It is found that with high displacement gradients, the loading process image is rather difficult to construct. Possible ways of decomposing the motion into quasi-rigid and strain-induced motions are investigated. The behavior of the representative macrovolume is described using a two-scale model based on the physical theory of elasto-viscoplasticity. The motion of rigid coordinate systems descriptive of quasi-rigid motion is defined by a specific hypothesis of motion decomposition on the macro-scale. The hypotheses under consideration are the following: (i) the whole motion of the representative volume is strain-induced motion; (ii) the motion is decomposed into strain-induced motion and quasi-rigid motion whose spin is determined by averaging mesoscale spins calculated from a certain general lattice rotation model; and (iii) the quasi-rigid and strain-induced motions are defined respectively by the antisymmetric and symmetric parts of the macroscale displacement velocity gradient. It is shown that with the first hypothesis, the loading process image depends on the rigid rotation imposed on the representative volume as a whole; with the other two hypotheses, the process image does not depend on the choice of the reference frame. At the same time, the third hypothesis makes it impossible to determine the lattice rotations independently of macroscale kinematic relations which, in fact, are determined by micro- and mesoscale physical interactions.