Theories of plasticity under complex loading along flat trajectories of deformations

The paper considers variants of theories of plastic flow with combined hardening, which are widely used in applied calculations of structures. A comparative analysis of the theories under complex loading along flat strain trajectories is carried out and covers the entire range of strain paths from multilink polylines to curved trajectories of constant and variable curvatures. The strain path from medium to large curvatures are considered. The analysis of the research results is carried out in the vector space of A.A. Il’yushin. We consider plane trajectories of deformations in the form of a square, three circles passing the origin of coordinates, and trajectories in an asteroid-like form. The results of the calculations are compared with the results of the experimental studies of the response stress trajectories, scalar and vector properties. Variants of theories are considered: isotropic hardening model; Ishlinsky-Prager-Kadashevich-Novozhilov model (linear kinematic and isotropic hardening); model similar to Ono-Wang's model; the Armstrong-Frederick-Kadashevich model (the Korotkikh model is based on this model); the Shabosh model with three evolutionary Armstrong-Frederick-Kadashevich equations; Themis model based on the invariant theory of plasticity; Bondar model with a three-term structure of the evolutionary equation for kinematic hardening. We give the material parameters (functions) that close the variants of plasticity theories. A satisfactory agreement with the experiment for all deformation trajectories is achieved in calculations based on the models of Ishlinsky-Prager-Kadashevich-Novozhilov, Shabosh and Temis. The difference between the results of calculations and experiments does not exceed 30 %. The best agreement with the experiment is achieved on the basis of the Bondar model with the difference between the results of the calculations and experiments for all trajectories less than 10 %.