Application of the invariant plastic flow theory for mathematical modeling of the processes of testing specimens under complex elastic-plastic deformation


The invariant plastic flow theory is applied for modeling the processes of testing thin-walled tubular steel specimens under complex elastic-plastic deformation. A software package for calculating simple and complex paths of deformation of thin-walled tubular specimens and analyzing the results obtained was developed for a model with translation and isotropic hardening, a combination of Kadashevich-Novozhilov and Arutyunyan-Vakulenko models. The errors arising in the course of numerical modeling of the deformation process beyond the elastic area are compensated by the correction algorithm that makes it possible to return to the loading hypersurface at each stage of calculation. A number of numerical experiments dealing with testing tubular steel 40Х16Н9Г2С specimens were conducted. The model parameters were chosen according to the data of repeated loading. The results of numerical stimulation of the processes of cyclical twist of the specimens, proportional loading, complex two-section and multi-section deformation paths, as well as the process of curvilinear deformation path in the form of concentric circles are presented. The observance of the principle of delay of vector and scalar properties is demonstrated, two-section deformation paths with different angles of fracture taken as an example. The numerical results are compared with the experimental data.

About the authors

Yu. M. Temis

Central Institute of Aviation Motors named after P.I. Baranov, Moscow

Author for correspondence.

Russian Federation

Doctor of Science (Engineering), Professor

Head of the Department

D. A. Alkhimov

Moscow State University of Mechanical Engineering (MAMI)


Russian Federation

Postgraduate student

A. D. Martynova

Central Institute of Aviation Motors named after P.I. Baranov, Moscow


Russian Federation



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