For citation:
Radchenko V. P., Glebov V. E. A method for calculating the relaxation of residual stresses in surface-hardened cylinders with incisions under combined torque and tensile force loading under conditions of high-temperature creep. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 2, pp. 265-279. DOI: 10.18500/1816-9791-2026-26-2-265-279, EDN: QTCUOJ
A method for calculating the relaxation of residual stresses in surface-hardened cylinders with incisions under combined torque and tensile force loading under conditions of high-temperature creep
Based on the finite element method, a method is proposed for solving the problem of residual stress relaxation in surface-hardened cylinders with incisions of various profiles: semicircular, square, V-shaped, and in cylinders with a series of periodically arranged semicircular incisions. In accordance with the method of advanced surface plastic deformation the incisions were applied to a pre-hardened smooth sample. The proposed technique consists in the sequential application of an analytical mathematical model for reconstructing the residual stress-strain state in a smooth cylinder, a method for calculating initial deformations for cylinders with incisions, and a time step method for solving the problem of relaxation of residual stresses under creep conditions. The correctness of applying the calculation based on initial deformations is illustrated in the special case of a smooth sample by comparing solutions for reconstructing the stress-strain state using an analytical mathematical model and the finite element method, which practically coincide. Similarly, when solving the problem of relaxation of residual stresses under creep conditions, a complete correspondence was established between the calculation data using the finite element method and the grid method from independent sources for a smooth hardened sample. It is established that for incisions with a high stress concentration (V-shaped incision and incision with a square profile), the task of reconstructing the initial stress-strain state must be solved in an elastoplastic formulation. Based on the developed numerical method, a number of residual stress relaxation problems have been solved for cylinders with a wide range of geometric parameters of the incisions. The effect of concentrators on the kinetics of residual stresses is analyzed. The results of numerous variable calculations are presented.
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