The paper provides results of the study of correctness of the mathematical model that includes the influence of stresses on irradiation-induced swelling of metal in the problems of elastic-plastic deformation mechanics. The present-day approaches to modeling irradiation-induced swelling, which take into account a damaging dose, irradiation temperature, and the effect of the stress state on the swelling deformation, are discussed. The constitutive equations that describe the elasticplastic deformation processes allowing for the influence of a stress mode on the irradiation-induced swelling in metal are put forward. Analysis of these equations has made it possible to find the conditions that ensure correctness of the plasticity equations considered and to make a lower-bound estimate of the maximum permissible value of free swelling and irradiation dose. A priori estimates of the maximum permissible value of free swelling and damaging dose are given for 08Kh18N10T steel under various irradiation temperatures. In the practice of strength design such estimates are needed at the stage of problem formulation in order to analyze adequacy of input data, for they enable one to assess a prior the possibility of solving the problem for a given temperature and irradiation dose. The boundary-value problem that describes non-isothermal processes of elasticplastic deformation including swelling strains has been defined in the form of a nonlinear operator equation. Based on the findings regarding the correctness of the constitutive equations, we have established the existence and uniqueness of the generalized solution and its continuous dependence on applied loads, thermal strains and swelling strains. The convergence of the method of elasticity solutions and the method of variable elasticity parameters has been studied as applied to a thermoplasticity problem including irradiation-induced swelling strains.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. N. Kisilevskii, Changes in the Mechanical Properties of Steels and Alloys during Radiation Exposure [in Russian], Naukova Dumka, Kiev (1977).
G. S. Pisarenko and V. N. Kisilevskii, Strength and Plasticity of Materials in Radiation Flows [in Russian], Naukova Dumka, Kiev (1979).
V. N. Kisilevskii, Strength of Structural Materials of Nuclear Reactors [in Russian], Naukova Dumka, Kiev (1990).
S. N. Votinov, V. I. Prokhorov, and Z. E. Ostrovskii, Irradiated Stainless Steels [in Russian], Nauka, Moscow (1987).
N. V. Sharyi, V. P. Semishkin, V. A. Piminov, and Yu. G. Dragunov, Strength of Main Equipment and Piping of WWER Reactor Units [in Russian], IzdAT, Moscow (2004).
Yu. Konobeev, A. V. Subbotin, and S. I. Golubov, “The theory of void and interstitial dislocation loop growth in irradiated metals,” Radiat. Eff. Defect. S., 20, No. 4, 265–271 (1973).
Yu. V. Konobeev and V. A. Pechenkin, “On the mechanism of nucleation of vacancy voids in metals and under irradiation,” Vopr. Atom. Nauk. Tekhn. Ser. Fiz. Radiats. Materialoved., No. 1, 3–7 (1978).
Yu. V. Konobeev and V. A. Pechenkin, “State-of-the-art of the theory of irradiation-induced porosity in metals,” in: Irradiation-Induced Defects in Metallic Crystals [in Russian], Nauka, Alma-Ata (1978), pp. 187–210.
V. N. Bykov and Yu. V. Konobeev, “Irradiation damage of structural materials of fast neutron reactors,” Atom. Énerg., 43, No. 1, 20–27 (1977).
A. A. Sorokin, B. Z. Margolin, I. P. Kursevich, et al., “The influence of neutron irradiation on mechanical properties of materials of internals of WWER reactor pressure vessels,” Vopr. Materialoved., No. 2 (66), 131–151 (2011).
B. Z. Margolin, I. P. Kursevich, A. A. Sorokin, et al., “Embrittlement and fracture toughness of highly irradiated austenitic steels for vessel internals of WWER type reactors. Part 2. Relation between irradiation swelling and irradiation embrittlement. Physical and mechanical behavior,” Strength Mater., 42, No. 2, 144–153 (2010).
N. K. Vasina, B. Z. Margolin, A. G. Gulenko, and I. P. Kursevich, “Irradiation-induced swelling of stainsell steels. The influence of various factors. Processing of experimental data and definition of constitutive equations,” Vopr. Materialoved., No. 4 (48), 69–88 (2006).
B. Z. Margolin, A. I. Murashova, and V. S. Neustroev, “The influence of stresses on irradiation-inducedswelling of austenitic steels,” Vopr. Materialoved., No. 4 (68), 124–139 (2011).
B. Z. Margolin, A. I. Murashova, and V. S. Neustroev, “Analysis of the influence of type of stress state on radiation swelling and radiation creep of austenitic steels,” Strength Mater., 44, No. 3, 227–240 (2012).
L. M. Kachanov, Fundamentals of the Plasticity Theory [in Russian], Nauka, Moscow (1969).
A. Yu. Chirkov, “Construction of two-level integration schemes for the equations of plasticity in the theory of deformation along the paths of small curvature,” Strength Mater., 44, No. 6, 645–667 (2012).
M. M. Vainberg, Variational Method and Method of Monotone Operators [in Russian], Nauka, Moscow (1972).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1981).
S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Moscow (1988).
I. I. Vorovich and Yu. P. Krasovskii, “On the method of elastic solutions,” Dokl. AN SSSR, 126, No. 4, 118–121 (1959).
V. S. Lenskii and G. L. Brovko, “Method of homogeneous linear approximations in uncoupled problems of thermo-irradiation elasticity and plasticity,” in: Thermal Stresses in Structural Elements [in Russian], Issue 11, Naukova Dumka, Kiev (1971), pp. 100–103.
D. L. Bykov, “On some methods of solving problems of the plasticity theory,” in: Elasticity and Inelasticity [in Russian], Issue 4, MGU, Moscow (1975), pp. 119–149.
Yu. M. Temis, “Convergence of the method of variable parameters of elasticity in numerical solution of plasticity problems by the finite element method,” in: Applied Problems of Strength and Plasticity. Statics and Dynamics of Deformable Systems [in Russian], Moscow (1982), pp. 21–34.
S. É. Umanskii, “On convergence of the method of variable parameters of elasticity,” Prikl. Matem. Mekhan., No. 3, 577–581 (1980).
A. Yu. Chirkov, “Analysis of boundary-value problems describing the non-isothermal processes of elastoplastic deformation taking into account the loading history,” Strength Mater., 38, No. 1, 48–71 (2006).
J. M. Ortega and W. C. Rheinboldt, Iterative Solution if Nonlinear Equations in Several Variables, Academic Press, New York–London (1970).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Prochnosti, No. 1, pp. 5 – 22, March – April, 2020.
Rights and permissions
About this article
Cite this article
Chirkov, A.Y. On the Correctness of the Well-Known Mathematical Model of Irradiation-Induced Swelling with the Influence of Stresses in the Problems of Elastic-Plastic Deformation Mechanics. Strength Mater 52, 183–198 (2020). https://doi.org/10.1007/s11223-020-00165-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11223-020-00165-y