Theories of plasticity under complex loading along spatial trajectories of deformations

Abstract

Variants of theories of plastic flow with combined hardening, which are widely used in practical calculations of structures, are considered. A comparative analysis of variants of the theory under complex loading along the spatial trajectories of deformations of constant and variable curvature and torsion is carried out. The trajectories of large curvature and from medium to large torsion are considered. The analysis of the research results is carried out in the vector space of A.A. Il’yushin. The spatial trajectories of deformations in the form of helical lines of constant and variable curvature are considered. The calculation results are compared with the results of experimental studies on the response components of the stress vector and scalar properties along the deformation trajectory. Variants of the theory are considered: the Ishlinsky - Prager - Kadashevich - Novozhilov model (linear kinematic hardening and isotropic hardening); 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 transformation of the evolutionary equation for kinematic hardening. Material parameters (functions) that close versions of the theory of plasticity are given. Satisfactory agreement with the experiment for all trajectories of deformations is achived when calculating on the basis of the Shabosh model - 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 - the difference between the results of calculations and experiments for all trajectories does not exceed 10 %. The Bondar Model is closed by three material parameters and one material function which are determined from simple experiments on uniaxial tension after preliminary compression (kink of the deformation trajectory by 180°). Bondar plasticity model has a generalization for non-isothermal loading, many features of cyclic disproportionate and proportional loading and describes the processes of damage accumulation (resource).