Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

Abstract

It is known that the meso- and microstructures of metals determine the physical, mechanical and operational properties of their final products. Scientific and technological progress of recent decades has given impetus to the elaboration and use of models capable of describing the evolving structure of materials. The most promising are multilevel models that include internal variables and are based on physical theories of elastoplasticity (elastoviscoplasticity). This paper presents the structure and basic relationships of a three-level (macro-, meso-1 and meso-2 levels) elastoviscoplastic model. The developed model operates on such internal variables as dislocation densities on slip systems, barriers on split dislocations and sources of edge dislocations. The model describes the mechanisms of production, annihilation, formation of barriers and sources of dislocations. The law of hardening directly takes into account the densities of dislocations and barriers. The mechanism of inelastic deformation is the gliding of edge dislocations along slip systems. Special emphasis is placed on the influence of split dislocations (prone to forming hard Lomer–Cottrell and Hirth barriers) on the deformation of the material. The model is used to describe the behavior of an elastoviscoplastic polycrystalline aggregate with an FCC lattice. Geometric nonlinearity is taken into account by utilizing decomposition of the crystallite motion into quasi-rigid and deformation components. For this purpose, a rigid moving coordinate system for the crystal lattice is introduced. Examples of the application of the model for analyzing the simple and complex deformation mechanisms of materials with different stacking fault energies and, consequently, with different tendencies toward the decomposition of dislocations and barrier formation are given.