Labibov R. Characteristics of plastic deformation of one- and two-dimensional structural elements with yielding plateau

Labibov R. R. Characteristics of plastic deformation of one- and two-dimensional structural elements with yielding plateau. – Qualifying scientific work on manuscript rights. Thesis for the degree of Candidate of Technical Sciences in the 05.23.17 “Structural Mechanics” (19 – Architecture and construction). – Oles Honchar Dnipro National University, Ukrainian State University of Science and Technologies, ESI “PDABA” of the Ministry of Education and Science of Ukraine, Dnipro, 2026. The research is devoted to the development of mathematical methods and numerical models of materials with yield plateau. Correct description of physical processes occurring in them allows determining the limits of mechanical usage and evaluation of structural stability in the scenarios where such materials are used in practice. Generalized variant of plastic flow theory with combined hardening was proposed for description of a material with yielding plateau on its stress-strain diagram during soft loading and tooth-peak during hard loading. Theory is built on the assumption that rapid drop of stresses after tooth-peak is caused by strain-softening connected with the release of dislocations. Cases of cyclic loading with tension-compression cycles was considered with the main accent of the plastic deformation that is connected to propagation of Lüders bands and slow plasticity wave that divides a specimen into plastic domain with Lüders stresses and elastic domain. The case of alternating load is analyzed, in which the material is loaded periodically with a force of alternating sign. The solution of the problem of accumulation of plastic deformation shows total amount of cycles required to reach the limit when fracture occurs. It was determined that plastic deformation during cyclic loading occurs at lesser stresses than the state of plasticity on the yielding plateau. Using the proposed model problems of development of slow plasticity waves during a strip tension, pure bending, etc. were considered. Solution of a problem of slip lines development during complex shear is proposed. Employing known description of crystalline lattice processes during plastic slip the analytical model describes plastic localization during emergence of discrete structures in the material on macro-scale due to loss of homogeneity along one of the axes. Conditions of development of shear bends through time are investigated and mathematically described. During continuous accumulation of deformations on the yield plateau the shear process between crystallic layers on the grain scale is connected to split of the material into two phases with specific arrangement that can be observed visually (Lüders bands). The solution was found by introduction of special functions into stationary problem equations that bring time parameter into consideration. Proposed approach may be applied to a variety of problems of slip line development under an influence of arbitrary loading.