Abstract
Based on experimental studies, a model of the control effect on the plastic deformation process under boundary asymmetric loading conditions has been developed. The regulating factor of plastic deformation unevenness δ, which determines the stress–strain state of the entire deformation zone and the boundary conditions, is presented. The boundary conditions, determined by additional compressive and tensile stresses along the height, generate shear stresses and specific loading regimes at the edges and within the deformation zone itself. The confirmed reduction in interaction, which coincides with the effect of plastic deformation occurring under conditions of force unevenness, is one of the criteria for the controlling effect. A distinctive feature of this approach is the recognition and proof of the existence of a controlling additional effect under conditions of complex force and deformation loading. Theoretical and experimental studies have revealed such effects under various loading conditions. Based on a closed-form problem in plasticity theory and the method of argument functions of a complex variable, a mathematical model of the control process exerted by the metal’s plastic flow zone has been developed. A key feature of the solution to this theoretical problem was the consideration of the interaction between zones under different force loads, represented by a finite-difference scheme in the mathematical model. The decisive influence of deformation unevenness from the working rolls on the force and deformation parameters of the process was demonstrated, with the deformation unevenness factor δ serving as a quantitative measure of this influence. The result obtained through theoretical justification was confirmed by numerical simulation and a comparison of calculated data with experimental data, ensuring the reliability of the result.