VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University277110.18287/2412-7329-2015-14-3-24-36UnknownApplication of the invariant plastic flow theory for mathematical modeling of the processes of testing specimens under complex elastic-plastic deformationTemisYu. M.<p>Doctor of Science (Engineering), Professor</p>
<p>Head of the Department</p>tejoum@ciam.ruAlkhimovD. A.<p>Postgraduate student</p>alhdmitrii@gmail.comMartynovaA. D.<p>Engineer</p>martynasty@yandex.ruCentral Institute of Aviation Motors named after P.I. Baranov, MoscowMoscow State University of Mechanical Engineering (MAMI)19112015143-124360112201501122015Copyright © 2015, VESTNIK of the Samara State Aerospace University2015<p>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.</p>Plasticityplastic flowcomplex deformationstress-strain statemechanical teststubular specimenПластичностьпластическое течениесложное деформированиенапряжённо-деформированное состояниеиспытаниятрубчатый образец[1. Temis Y.M. Teoriya neizotermiches-kogo plasticheskogo techeniya s izotropnym i anizotropnym uprochneniem. V kn.: Mashinostroenie. Entsiklopediya. Dinamika i prochnost' mashin. Teoriya mekhanizmov i mashin. T. I-3. V 2-kh kn. Kn. 2 [Theory of non-isothermal plastic flow with isotropic and non-isotropic hardening. In the book: Mechanical engineering. Encyclopedia. Dynamics and strength of machines and mechanisms. V.1-3. In 2 books. Book 2. Moscow: Mashinostroenie Publ., 1994. P. 227-231. (In Russ.)][2. Dem’yanushko I.V., Temis Y.M. To build theories of plastic flow with non-isotropic hardening for materials under the influence of physical fields. Izvestiya Akademii Nauk SSSR. Mekhanika Tverdogo Tela. 1975. No. 5. P. 111-119. (In Russ.)][3. Malinin N.N. Prikladnaya teoria plastichnosti i polzuchesti [Applied theory of plasticity and creep]. Moscow: Mashinostroenie Publ., 1975. 400 p. (In Russ.)][4. Temis Y.M. Self-corrected proceedings method for solving non-linear problems of elasticity and plasticity. Trudi CIAM. 1980. No. 918. 24 p. (In Russ.)][5. Zhubchaninov V.G., Okhlopkov N.L., Garanikov V.V. Experimental’naya plastichnost’. Kniga 1. Processi slozhnogo deformirovania [Experimental plastisity. Book 1. Processes of the complex deformation]. Tver: Tver State Technical University Publ., 2003. 172 p. (In Russ.)][6. Bondar V.S., Danshin V.V. Plastichnost’. Proporcional’nye i neproporcional’nye nagruzhenija [Plasticity. Proportional and disproportionate loading]. Moscow: Fizmatlit Publ., 2008. 176 p. (In Russ.)]