The nonaxisymmetric elastoplastic stress–strain state of bodies of revolution under nonisothermal combined loading is analyzed with allowance for secondary plastic strains. The study is based on the use of the constitutive equations of the theory of small-curvature processes and finite-element method. The model of elastic unloading of a material with perfect Bauschinger effect and isotropic hardening is employed. Numerical examples illustrate how the choice of an unloading model affects the results obtained.
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N. I. Bezukhov, V. L. Bazhanov, I. I. Gol’denblat, et al., Design for Strength, Stability, and Vibrations at High Temperatures [in Russian], Mashinostroenie, Moscow (1965).
I. A. Birger, B. F. Shorr, I. V. Dem’yanushko, et al., Thermal Strength of Machine Parts [in Russian], Mashinostroenie, Moscow (1975).
Ya. M. Grigorenko, Yu. N. Shevchenko, et al., Numerical Methods, Vol. 11 of the 12-volume series Composite Mechanics [in Russian], “A.S.K”, Kyiv (2002).
Yu. N. Shevchenko, M. E. Babeshko, V. V. Piskun, and V. G. Savchenko, Spatial Thermoplasticity Problems [in Russian], Naukova Dumka, Kyiv (1980).
Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, Thermoviscoplastic Processes of Combined Deformation of Structural Members [in Russian], Naukova Dumka, Kyiv (1992).
Yu. N. Shevchenko and V. G. Savchenko, Thermoviscoplasticity, Vol. 2 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1987).
Yu. N. Shevchenko, V. G. Savchenko, and D. A. Ishchenko, Method and Software for Analysis of the Nonstationary Heat Conduction in and the Elastoplastic Stress–Strain State of Structural Members such as Solids of Revolution under Axisymmetric Mechanical and Thermal Loads [in Russian], Guidelines, Inst. Mekh. AN USSR, Kyiv (1988).
Yu. N. Shevchenko, V. G. Savchenko, D. A. Ishchenko, and V. M. Pavlychko, Method and Applied Software for Analysis of the Nonstationary Heat Conduction in and the Elastoplastic Stress–Strain State of Structural Members such as Solids of Revolution under Axisymmetric Mechanical and Thermal Loads [in Russian], Recommendations R 54-284-90, VNIINMASh, Moscow (1990).
M. E. Babeshko and V. G. Savchenko, “Axisymmetric elastoplastic state of compound shells subject to thermal and mechanical loading and radiation exposure,” Int. Appl. Mech., 53, No. 4, 368–373 (2017).
M. E. Babeshko and V. G. Savchenko, “Analyzing processes of nonisothermal loading of shells of revolution with allowance for repeated plastic strains,” Int. Appl. Mech., 53, No. 6, 639–646 (2017).
M. E. Babeshko and V. G. Savchenko, “On allowance for the third invariant of stress deviator in analysis of processes of deformation of thin shells,” Int. Appl. Mech., 54, No. 2, 163–171 (2018).
M. E. Babeshko and V. K. Stryuk, “Calculating the stress state of a solid cylinder on the basis of the theory of flow with isotropic hardening,” Sov. Appl. Mech., 10, No. 6, 587–591 (1974).
V. A. Bazhenov, M. O. Vabishchevich, I. I. Solodei, and E. A. Chepurnaya, “Semianalytic finite-element method in dynamic problems of linear fracture mechanics,” Int. Appl. Mech., 54, No. 5, 519–530 (2018).
H. Hencky, “Zur theorie der plastischer deformationen und der hierdurch im material hervorgerufenen nachspannungen,” ZAMM, 4, No. 4, 323–334 (1924).
D. A. Ishchenko and V. G. Savchenko, “Influence of taking account of secondary plastic deformations on the solution of the axisymmetric thermoplasticty problem,” Sov. Appl. Mech., 24, No. 3, 229–233 (1988).
L. Prandtl, “Anwendungsbeispile zu einem Henckyschen satz uber das platische gleichgewicht,” ZAMM, 3, No. 6, 401–406 (1923).
A. Reuss, “Berucksichtigung der elastischen formanderung in der plastizitatstheorie,” ZAMM, 10, No. 3, 266–274 (1930).
V. G. Savchenko and M. E. Babeshko, “Thermostressed state of layered bodies of revolution damaging under deformation,” Int. Appl. Mech., 54, No. 3, 287–305 (2018).
Yu. N. Shevchenko and V. G. Savchenko, “Three-dimensional problems of thremoviscoplasticity: focus on Ukrainian research (Review),” Int. Appl. Mech., 52, No. 3, 217–271 (2016).
E. A. Storozhuk, I. S. Chernyshenko, and O. V. Pigol’, “Elastoplastic state of an elliptical cylindrical shell with a circular hole,” Int. Appl. Mech., 53, No. 6, 647–654 (2017).
M. Zyczkowskii, Combined Loadings in the Theory of Plasticity, PWN, Polish Scientific Publishers, Warsaw (1981).
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Translated from Prikladnaya Mekhanika, Vol. 55, No. 4, pp. 101–112, July–August 2019.
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Savchenko, V.G., Babeshko, M.E. Technique of Allowing for Plastic Strains Under Unloading in Thermoplasticity Problems for Axisymmetric Bodies. Int Appl Mech 55, 416–425 (2019). https://doi.org/10.1007/s10778-019-00961-3
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DOI: https://doi.org/10.1007/s10778-019-00961-3