Mechanical properties of materials in calculations of low cycle deformation of structures

It is noted that calculations of the rated strength for bearing elements of extremely loaded structures, including nuclear power plants allow inelastic deformation of the materials of these elements. At the same time calculations of the low cycle fatigue require taking into account factors that are not observed under single loading including, i.e., kinetics of cyclic strains, cyclic creep, change of the mode of inelastic cyclic deformation upon normal operation. Moreover, the materials can be of different types: cyclically hardening, softened or stable. For the first type of materials at a soft loading with constant amplitude of stresses in cycles, the range of strains decreases with an increase in the number of cycles, but increases for the second one. Under a hard mode of loading with constant amplitude of strains the maximum stresses in a cycle for the hardening material increase, and, on the contrary, decrease for softened material. Moreover, the soft loading of softened material results in one-sided accumulation of plastic strains as the number of loading cycles increases. These circumstances must be taken into account both in the analytical description of the kinetics of deformation diagrams and in the corresponding calculation equations used in the strength standards. It is noted that at early stages of forming computation methods developed for these conditions, calculation of stresses was carried out in the assumption of ideal elasticity of the material. The use of such approach was attributed to the lack of available methods for addressing the problem of an inelastic cyclic deformation, complicated on the statement. The subsequent evolution of the theory of cyclic elastoplastic deformation, analytical and numerical solutions of cyclic boundary-value problems, developing of numerical methods of computation and powerful computer packages fundamentally changed the situation providing the possibility of analysis and modeling of physically and geometrically nonlinear deformation processes. It is shown that transition from the elastic adaptability (with an elastic deformation of the structure in a stable cycle) to a sign-variable flow is smooth and continuous, similar to the transition from the elastic to plastic deformation under a single loading. Such a mechanism is similar to conditional boundary of the transition from low cycle to high-cycle fatigue under a cyclic strain. At the same time, we offer to use in calculations the existing rather simple models and experimentally determined parameters of cyclic deformation diagrams of materials. In the modern statement of the problems under consideration, taking into account both the kinetics of cyclic and unilaterally accumulated deformations, with allowance for the manifestation of creep effects in cycles is of fundamental importance. This approach also makes it possible to take into account the acceleration of unsteady cyclic creep due to previous plastic deformation of a different sign, which can be rather significant.

1. Serensen S. V., Makhutov N. A. The Study of patterns of relationship of a deformation and fracture of a soft steel at a low number of cycles / Zavod. Lab. 1964. Vol. 32. N 1. P. 268 – 269 [in Russian].

2. Langer E. F. Design of Pressure Vessels for Low Cycle Fatigue / Transactions of ASME. Ser. D. 1962. Vol. 4. N 3. P. 389 – 402.

3. ASME Boiler and Pressure Vessel Code. Section VIII — Rules for Construction of Pressure Vessels. Division 2-Alternative Rules (BPVC-VIII-2 — 2019) — American Society of Mechanical Engineers. 2019. — 872 p. ISBN 9780791872888.

4. Norms of computation on strength of the equipment and pipelines of nuclear power installations. PNAE G-7-002-86. — Moscow: Énergoatomizdat, 1989. — 525 p. [in Russian]

5. Gokhfeld D. A., Cherniavsky O. F. Limit analysis of structures at thermal cycling. — The Netherlands, Rockville, Maryland, USA: Sijthoff & Noordhoff, Alphen and den Rijn, 1980. — 537 p.

6. Strength at low number of cycles of a loading / Ed. by S. V. Serensen. — Moscow: Nauka, 1969. — 258 p. [in Russian].

7. Makhutov N. A., Frolov K. V., Stekolnikov V. V., et al. Strength and life-time of water-moderated power reactors. — Moscow: Nauka, 1988. — 311 p. [in Russian].

8. Makhutov N. A. Deformation criteria of fracture and computation of structures parts on strength. — Moscow: Mashinostroenie, 1981. — 272 p. [in Russian].

9. Makhutov N. A. Structural integrity, life-time and technogenic safety. — Novosibirsk: Nauka. 2005. Part 1. — 493 p.; Part 2. — 610 p. [in Russian].

10. Gadenin M. M. Characteristics of the mechanical properties of materials in analysis of achieving limiting state / Zavod. Lab. Diagn. Mater. 2012. Vol. 78. N 2. P. 58 – 63 [in Russian].

11. Gadenin M. M. Features of the kinetics of cyclic elastoplastic deformation diagrams at dwells in cycles and superimposition of variable stresses on them / Zavod. Lab. Diagn. Mater. 2020. Vol. 86. N 12. P. 46 – 53 [in Russian]. DOI: 10.26896/1028-6861-2020-86-12-46-53

12. Makhutov N. A., Burak M. I., Gadenin M. M., et al. Mechanics of low cycle fracture. — Moscow: Nauka, 1986. — 264 p. [in Russian].

13. Makhutov N. A., Chernyavsky O. F., Chernyavsky A. O., Gadenin M. M. Living conditions of a sign-variable inelastic deformation at a low cycle loading / Probl. Mashinostr. Nadezhn. Mashin. 2008. N 5. P. 53 – 63 [in Russian].

14. Gokhfeld D. A., Getsov L. B., Kononov K. M., et al. Mechanical properties of steels and alloys at a non-stationary loading. Hand-book. — Yekaterinburg: Izd. UrO RAN, 1996. — 408 p. [in Russian].

15. Ponter A. P. The general limit theorems for a quasistatic deformation of bodies of inelastic materials with the application to a creep of metals / Mechanic of deformable bodies and structures. — Moscow: Mashinostroenie, 1975. P. 395 – 402 [in Russian].

16. Cherniavsky O., Rebiakov Yu., Cherniavsky A. Properties of steels and chromium-nickel alloys under low-cycle combined deformation / International Journal of Fatigue. October 2017. Vol. 103. P. 415 – 418.