Analysis of Radiation Creep Problems Considering Pore Growth Ductile Fracture by Rice–Tracey–Huang Models and Kachanov’s Solution for a Spherical Cavity. Part 2. Validity Check of the Governing Equations

The validity conditions for nonlinear problems of inelastic deformation mechanics, which consider the growth of the volume of nucleated pores in the material exposed to neutron irradiation, are investigated. The porosity analysis of the irradiated material is based on the Rice–Tracey–Huang (RTH) equations and Kachanov’s solution for a spherical cavity. The generalized equation combines the classical RTH equations and includes the modified Huang’s equation, in which an additional continuous function greater than zero is introduced, which depends on the stiffness of the stress state and has a nonnegative derivative. This modification of the classical Huang’s equation improves the properties of the governing equations of the irradiated porous material, which contributes to the weakening of the limitations of the initial data associated with the stiffness of the stress state. The RTH equations are considered to model the growth of the volume concentration of pores in a rigid-plastic material. For the analysis of porosity in an ideal elastic-plastic material, it is proposed to use the solution obtained by Kachanov for a spherical cavity. Applying Kachanov’s solution to the simulation of the pore concentration growth allows one to consider the radiation creep in the elastic region of the deformation diagram of the irradiated material in contrast to the classical RTH equations, in which the elastic region is not considered. Modern models of radiation swelling and radiation creep are used, considering the damaging dose, irradiation temperature, and the effect of stress state and accumulated irreversible deformation on the processes of swelling and creep of irradiated material. To analyze the behavior of irradiated porous material, radiation creep equations are used, in which irreversible deformations include instantaneous plastic, radiation swelling, radiation creep, and structural volume deformations that consider the concentration of pores in the material. The analysis of the properties of the governing equations allowed us to establish the conditions under which the dissipation power and the power developed by the additional stresses on the additional deformations caused by them do not decrease during the loading of the irradiated porous material. Based on the obtained energy inequalities that generalize Drucker’s postulate, the conditions are established that ensure the correctness of the governing equations of radiation creep, which consider the growth of the pore volume according to the generalized RTH equation and Kachanov’s solution for a spherical cavity. According to the results of the analysis, irradiation contributes to the growth of the pore volume in the material, and the limitation of the maximum values of the stiffness parameter of the stress state, taking into account the obtained a priori estimates, contributes to the stability and convergence of the computational processes for solving the boundary value problem.