Kseniia A. Kurmoiartseva

This article describes a modified multiscale constitutive model for analyzing the stress-strain behavior of polycrystalline materials, which explicitly accounts for the influence of grain boundary misorientation on the mechanical response. The model was implemented as a user subroutine and added to the SIMULIA Abaqus FEA software suite. A slip system compatibility factor was introduced into the hardening law via a relation for critical shear stresses, enabling the capture of interactions between dislocations and grain boundaries. The model was used in a numerical study of a generated polycrystalline structure of 308LSi austenitic stainless steel. The results of the study reveal the localization of stresses and plastic strains near high-angle grain boundaries, demonstrating the significant influence of crystallo-geometric factors on material hardening.

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.

The creation of materials with optimal properties is possible when studying the polycrystalline materials behavior during both the manufacturing and operation processes. The brief review of existing approaches to solving these problems and justification of the proposed approach is given. Models based on the introduction of internal variables, multi-level approach and crystal plasticity are prospective tool for solving such problems. The internal variables are responsible for the material meso- and microstructure and the underpinning mechanisms of deformation. The internal variables allow to explicitly describe changes in a material structure and therefore in physical and mechanical properties. The structure of the mathematical model is presented. The fatigue crack nucleation mechanism in titanium alloys is described. The subtask results of the critical dislocation density determination and the influence of misorientation for the crack nucleation are given.

Titanium alloys have found wide application in the aircraft industry. They are in use as materials for products for which the period of safe operation is very significant. The internal structure and service life of components heavily depends on their manufacture and operation processes. Besides, it is important to take into account damage accumulation processes and the evolution of material properties during deformation. The purpose of the present research is to develop a direct multilevel mathematical model based on crystal plasticity. This model must be able to allow the analysis of the behavior of titanium alloy materials and to describe the processes of damage accumulation. Crystal plasticity is a promising framework for solving such problems since it is able to describe the evolution of the internal material structure and the accumulation of defects of various nature. In this paper, the structure of the mathematical constitutive model, its evolutionary equations for dislocation densities and dislocation-based submodels of crack nucleation are given.

To predict the behavior of components and constructions it is necessary to develop the methods and mathematical models which take into account the self-organization of microstructural processes and the strain localization. The damage accumulation processes and the evolution of material properties during deformation are important to take into account. The heterogeneity of the process of damage accumulation is due to the appropriate physical mechanisms at the scale levels, which are lower than the macro-level. The purpose of this work is to develop a mathematical model for analyzing the behavior of polycrystalline materials that allows describing the damage accumulation processes. Fracture is the multistage and multiscale process of the build-up of micro- and mesodefects over the wide range of loading rates. The formation of microcracks by mechanisms is caused by the interactions of the dislocations of different slip systems, barriers, boundaries and the inclusions of the secondary phase. This paper provides the description of some of the most well-known models of crack nucleation and also suggests the structure of a mathematical model based on crystal plasticity and dislocation models of crack nucleation.