A method of determining the components of the strain rate tensor based on the method of current functions is developed. It is assumed that, with an axisymmetric plastic deformation of the metal in a channel with curvilinear borders, the kinematics of the process are similar to a flat flow. Using the incompressibility equation and the differential equation of the current lines, it is established that the current function maintains a constant value along the current lines. Two infinitely close current lines are considered in the flow plane to explain the kinematic content of the current function. The expression for flow through the finite transverse-sized tube was obtained. In the absence of radial velocity components at the boundaries, we obtain the restrictions imposed on derivatives of the current functions at these boundaries. The method of calculation of kinematic deformation characteristics for established axisymmetric processes will allow to simplify the mathematical processing of the obtained results. Real processes of metal processing are always accompanied by uneven plastic molding, which affects the power and kinematic parameters, the quality of finished products. The main technological factors affecting the appearance of the inhomogeneity and the nature of its distribution are the form factor (geometric parameters of the original workpiece) and the coefficient of contact friction. The study of technological parameters affecting the distribution of non-uniformity of plastic molding will allow to create practical recommendations for reducing the influence of the above mentioned parameters to ensure more uniform plastic deformation. Due to elastic-plastic deformation and local heating, which occur during surface-plastic deformation processing, the stress-strain and physical state of the surface layer is formed. This changes the microgeometry of the surface, the physical and mechanical properties of the surface layer of the workpiece. The surface treated by methods of surface-plastic deformation, has high hardness, residual compression stresses in the surface layer, smoothed out the micro-roughness. Accordingly, increases wear resistance, fatigue strength, resistance to corrosion and more.

In this paper we consider two-legged trajectories in the space of the deformation vector. Trajectories were obtained in tensile experiments with subsequent torsion and tensile experiments with subsequent joint tension and stretching of standard solid cylindrical samples from steel 10. Deformation was carried out according to programs that ensure the linearity of trajectories in the deformation space. The components of the stress deviator were determined using an anisotropically strengthened body model. In this experiment, a function characterizing the Bauschinger effect and a function characterizing the hereditary influence of the load history on the current state of the metal during plastic deformation was experimentally determined. It is shown that in the case of nonmonotonic loading, which is characterized by trajectories of large curvature, it is necessary to use O. A. Ilyushin's theory of plasticity, and the model G. Bachhaus yields satisfactory results only for trajectories of medium and low curvature. In general, the suitability of a particular plasticity theory needs to be verified experimentally.