A mathematical model of steel sample stretching: Establishing a unified nature and mechanism of the relationship between deformation stages

LLC Scientific Production Firm “TEHOSNASTKA-RTD”, 3A Skladskoy Lane, Volzhskiy, 404112, Russia Federation

^* Corresponding author: tehrtd@gmail.com

Published online: 17 February 2025

Abstract

The relevance of creating a mathematical model of deformation of various steels is dictated not only by the fact that it can be used to determine their physical and mechanical data used under certain external loads, but also because the mathematical model itself contributes to understanding the processes that occur in the deformed sample itself, allowing us to reveal the essence of the structure of the metal itself. Moreover, the current studies of this issue, despite the fact that they were carried out on the basis of a physical and mathematical approach, could not model the real process of this mechanism due to the fact that they did not find a single essence of this process. However, these studies have significantly helped in identifying the real mechanism of deformation and creating a new mathematical model. Using the data of existing experimental studies on uniaxial tension of steel rods, establish a single relationship between the stages of their deformation, taking into account the discrete structure of the crystal lattice of the metal, based on elastic and plastic shifts of its kinetic units. Based on the results obtained, develop a mathematical model that allows you to determine the necessary loads when using certain steels in specified conditions of their operation.