Three-level model based on physical theories of plasticity: formulation, implementation algorithms, results of application to the study of cyclic loading

The physical and mechanical properties of metals and alloys, as well as, the operational characteristics of products made of them, are known to be significantly determined by the meso- and microstructure of materials. Therefore, physically oriented models that can be used to analyze the material structure evolution have been intensively developed and widely applied in recent decades for the study of thermomechanical processing of metals and alloys. These models are based on the introduction of internal variables, theories of crystal plasticity (elastoviscous plasticity), and a multilevel approach. In this paper, we consider the structure, mathematical formulation and algorithm for implementing a three-level (macro-, meso-1, and meso-2 levels) dislocation-oriented model designed to study the behavior of a representative macrovolume (macrosample) of mono- and polycrystalline alloys under cyclic deformation paths. The loading is given, and the Voigt (Taylor) hypothesis is used to connect the macro- and mesolevel-1. The mesolevel-2 submodel operates with the densities and velocities of full and split edge dislocations on slip systems. Interactions of dislocations of various systems, such as annihilation, hardening due to forest dislocations, formation of barriers of a dislocation nature (Lomer-Cottrell, Hirt) are taken into account. At mesolevel-1, the description is carried out in terms of shear stresses and shear rates along slip systems, determined by the Orowan equation using the mesolevel-2 data. A rigid moving coordinate system associated with a crystal lattice is introduced to evaluate the rotation of crystallites. The response of the material at the macro level is determined by averaging the stresses in crystallites. The results of applying the model to the study of deformation of alloy macrosamples with different values of stacking fault energy along simple and complex deformation trajectories are presented. It is shown that the materials with low stacking fault energy demonstrate the effect of additional cyclic hardening when loaded along complex deformation trajectories.