Method of elastic solutions to the tasks of irradiation creep considering the effect of stresses and accumulated irreversible strain on the material irradiation swelling
Keywords:inelastic deformation, irradiation swelling, irradiation creep, method of elastic solutions, iteration process, convergence and accuracy of successive approximations
The method of elastic solutions for the irradiation creep nonlinear boundary values, which allows one to describe non-isothermal processes of inelastic deformation considering the irradiation swelling and creep of the irradiated material, is considered. To model the processes of irradiation swelling and creep, modern approaches are used considering the damaging dose, irradiation temperature, the influence of the stress state, and the accumulated irreversible strain. A modified method of elastic solutions for solving the boundary problems of irradiation creep is investigated. It is considered that the development and investigation of the iterative method properties within the tasks of radiation creep are complicated by the fact that it is necessary to account for a rather strict restriction associated with the asymmetry of the operator relating the errors of the iterative process for two successive approximations to verify their convergence and accuracy. Under such conditions, the standard approach of investigating the convergence of an iterative process concerning the properties of self-corrected operators is unacceptable. Moreover, the standard procedure of symmetrization of the equation for successive approximations leads to excessively conservative estimates of the convergence of the iterative method. Therefore, the optimization of its convergence rate has a rather approximate character. This problem is solved using a special regulatory requirement to analyze the convergence of successive approximations, which made it possible to develop a modified iterative process and to bring its local convergence to the general case of the equations of radiation creep. The modified process properties have been studied in detail. Based on the obtained results, the prior estimation of the asymptotic convergence rate of successive approximates has been obtained. The approaches to the optimization of the method of elastic solution regarding the tasks of irradiation creep are obtained.
Chirkov, O. Yu. (2021). Analysis of Models of Radiation Swelling and Radiation Creep, which take into account the Influence of Stresses, in the Problems of Mechanics of Inelastic Deformation. Part 1. Formulation of Defining Equations, Strength of Materials. 53, pp. 199-212. https://doi.org /10.1007/s11223-021-00276-0
Chirkov, O. Yu. (2021). Analysis of the Correctness of Problems in the Mechanics of Inelastic Deformation with the Influence of Stress State on the Processes of Radiation Swelling and Radiation Creep of the Material. Dopov. Nac. akad. nauk Ukr. 2021, 2, pp. 29-37 (in Ukrainian). https://doi.org/10/15407/dopovidi2021.02.029
Chirkov, O. Yu. (2021). The Correctness of the Radiation Creep Equations that Take into Account Stress and Accumulated Irreversible Deformation in the Radiation Model Swelling of the Irradiated Material. Dopov. Nac. akad. nauk Ukr. 2021, 4, pp. 36-45 (in Ukrainian). https://doi.org/10.15407/dopovidi2021.04.036
Sorokin, A., Margolin, B. & Kursevich, I. (2011). Effect of Neutron irradiation on mechanical properties of materials of WWER reactor internals. Iss. Mater. Sci., 2(66), pp. 131-151 (in Russian).
Margolin, B., Murashova, A. & Neustroiev, V. (2012). Analysis of the Influence of Type Stress State on Radiation Swelling and Radiation Creep of Austenitic Steels, Strength of Materials, 44, pp. 227-240. https://doi.org/10.1007/s11223-012-9376-3
Ortega, J. M. & Rheinboldt, W. C. (1970). Iterative Solution if Nonlinear Equations in Several Variables. New York; London: Academic Press.
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