Method of elastic solutions to the tasks of irradiation creep considering the effect of stresses and accumulated irreversible strain on the material irradiation swelling

Abstract

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.