The effect of replacing non-analytic trajectories with break points on smooth paths to the complexity of deformation and loading processes of materials

This article is devoted to an experimental study of the effect of rounding off corner points of two-link strain trajectories on complex loading processes during elastoplastic deformation of materials. Replacing corner points in their vicinity with local sections of circles allows a nonanalytic trajectory to be replaced with a smooth trajectory. Experimental studies were performed on thin-walled tubular specimens of the low-carbon steel St3 on an SN-EVM automated testing system. The loading programs for tubular specimens were set in the Ilyushin's deviatoric strain space. The rounding of the corner point of a two-link strain trajectory with an angle of 90° between the branches by arcs of circles with curvatures of 200, 400, as well as the rounding of the corner point of a two-link strain trajectory with an angle of 135° between the branches by arcs with curvatures of 400, 800 are considered. The experimental data characterizing the vector and scalar properties of the material are presented. The experimental data show that the effect of complex loading on the relationship between stresses and strains in a curved section is not immediately apparent. In the curved section, the magnitude of the stress vector modulus first increases, and then decreases with the formation of stress dives. The minimum point of the stress dive is located on the next straight branch of the strain trajectory. In the curvilinear section, the angle of delay increases, and in the next straight branch it decreases, and with the increase of the strain it tends to be zero. The rate of decrease of the angle of delay depends little on the differences in the geometry of the previous history of strain trajectory. In the second straight branch, the experimental results for a smooth and original two-link strain trajectories become little distinguishable from each other. Thus, replacing the original non-analytical strain trajectory to a smooth trajectory affects the complexity of the process of deformation and loading of the materials only in the vicinity of the corner point. This circumstance can be taken into account when numerically modeling the processes of elastoplastic deformation of materials and integrating the defining relations, replacing nonanalytic trajectories with smooth ones. This can be taken into account in the numerical calculation of elastic-plastic deformation and integration of constitutive relations, replacing non-analytical strain trajectories by smooth ones.