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 macroscale. 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.

Two‐level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations

“…In the absence of experimentally created loading process images under large displacement gradients, it is impossible to state that the method proposed by the authors of this article is the most correct method for creating the loading process images under large deformation. But, as it was shown in paper [52], the process image created by method 1 is dependent on rigid motion applied to the representative volume, which definitely breaks the basic postulates of elastoplastic process theory by A.A. Ilyushin and the theory of constitutive relations in general.…”

“…One of the main postulates of elastoplastic process theory of Ilyushin is isotropy postulate in its specific form [2,52]: for initially isotropic material the loading process image in combined five-dimensional space ℵ (5) (of stresses and strains) Fig. 1 Process image (method PI1) for different deformation breaking paths (13) and (14); (a) numerical simulation, (b) experiment [51].…”

“…As it is shown in [52], the process image depends on rigid motion applied to the representative volume (in general) for the PI1 decomposition method. The process image created in coordinate systems determined by the other two methods does not depend on the selected reference system.…”

“…The independence of loading process image from application of quasi-rigid motion (or selection of frame) [1] in terms of different hypothesis for motion decomposition into quasi-rigid and deformational motions is an important problem arising in the course of creating a loading process image of the representative macrovolume. As it is shown in [52], the process image depends on rigid motion applied to the representative volume (in general) for the PI1 decomposition method. The process image created in coordinate systems determined by the other two methods does not depend on the selected reference system.…”