Features and uniform description of I, II, and III stages of the creep in single-crystal superalloys

Features of the creep process in single-crystal nickel-based superalloys are studied in a wide range of temperatures and holding time for different crystallographic orientations. The results of experimental study of high-temperature creep obtained for different single-crystal superalloys are presented. The dominance of stage III of creep is observed for considered temperature range and loads. Uniform creep models describing I, II, and III stages, are proposed taking into account damage accumulation based on the Norton – Bailey relations and power law of evolution for the scalar damage measure of Kachanov – Rabotnov. A hierarchical sequence of creep models of various degrees of complexity is suggested depending on the necessity of taking into account stage I. A material model including six constants is sufficient to describe stages II and III. Simultaneous accounting of all three stages of creep can be carried out using model with nine constants. The assumption on the absence of damage at the first stage leads to a material model with ten constants. The entered additional tenth parameter characterizes the duration of the first stage. Identification methods for the parameters of the introduced models based on using the least-squares method and Nedeler – Mead method for solving the problem of minimizing the error functional are proposed. The results of verification of the proposed inelastic deformation models are presented for various nickel-based single-crystal superalloys. The standard deviation between the experimental and computation results for all the proposed creep models does not exceed 10%. This allows us to recommend the developed approach for estimating the level of irreversible accumulated strains and durability of the structural elements made of single-crystal superalloys.

1. Katanakha N. A., Semenov A. S., Getsov L. B. A modified version of creep model ensuring more accurate prediction under long term loading conditions and identification of its parameters / Deform. Razrush. Mater. 2013. N 10. P. 16 – 23 [in Russian].

2. Lokoshenko A. M. Simulation of the process of creep and long-term strength of metals. — Moscow: MSIU, 2007. — 263 p. [in Russian].

3. Naumenko K., Altenbach H. Modeling of Creep for Structural Analysis. — Springer, 2007.

4. Semenov S. G., Semenov A. S., Getsov L. B., Petrushin N. V., Ospennikova O. G., Zhivushkin A. A. Increasing the lifetime of gas-turbine engine nozzle blades using a new monocrystalline alloy / J. Machin. Manufact. Reliability. 2016. Vol. 45. N 4. P. 316 – 323.

5. Semenov S. G., Getsov L. B., Tikhomirova E. A., Semenov A. S. Special features of creep and long-term strength of single-crystal refractory nickel-base alloys / Metal Science and Heat Treatment. 2015. N 12(726). P. 29 – 37 [in Russian].

6. Semenov A. S., Beliaev M. O., Grishchenko A. I. Modeling of cross-section ovality of single crystal nickel-based superalloy samples under tension / PNRPU Mechanics Bulletin. 2017. N 2. P. 153 – 177.

7. Getsov L. B., Semenov A. S., Tikhomirova E. A., Rybnikov A. I. Thermocyclic-and static-failure criteria for single-crystal superalloys of gas-turbine blades / Materiali in Tehnologije. 2014. Vol. 48. Issue 2. P. 255 – 260.

8. Semenov A. S., Getsov L. B. Thermal fatigue fracture criteria of single crystal heat-resistant alloys and methods for identification of their parameters / Strength of Materials. 2014. Vol. 46. N 1. P. 38 – 48.

9. Pollock T. M., Argon A. S. Creep resistance of CMSX-3 nickel base superalloy single crystals / Acta Metallurgica et Materialia. 1992. Vol. 40. N 1. P. 1 – 30.

10. Radaev Yu. N. Tensor damage measures and harmonic analysis of the fine damage structure / Vestn. Samar. Gos. Univ. 1998. N 2(8). P. 79 – 105 [in Russian].

11. Semenov A. S. The identification of anisotropy parameters of phenomenological plasticity criterion for single crystals worked out on the micromechanical model basis / St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 2014. Vol. 194. N 2. P. 17 – 29.

12. Murakami S., Ohno N. A continuum theory of creep and creep damage / Creep in structures. A. R. S. Ponter, D. R. Hayhurst (eds.). — Berlin: Springer, 1981. P. 422 – 443.

13. Betten J. Damage tensors in continuum mechanics / Journal de Mйcanique thйorique et appliquй. 1983. Vol. 2. N 1. P. 13 – 32.

14. Getsov L. B. Materials and strength of gas turbine parts. Vol. 1. — Rybinsk: Izd. dom «Gazoturbinnye tekhnologii», 2011. — 611 p. [in Russian].

15. Katanakha N. A., Semenov A. S., Getsov L. B. Unified model of steady-state and transient creep and identification of its parameters / Strength of Materials. 2013. Vol. 45. N 4. P. 495 – 505.

16. Katanakha N. A., Semenov A. S., Getsov L. B. Durability of bends in high-temperature steam lines under the conditions of long-term operation / Thermal Engineering. 2015. Vol. 62. N 4. P. 260 – 270.

17. Cormier J., Milhet X., Mendez J., Cailletaud G. Modeling the [001] non-isothermal creep behavior of a second generation single crystal NI-based superalloy submitted to very high temperature overheat / Trudy TsKTI. 2009. Issue 296. P. 199 – 215.

18. Himmelblau D. Applied Nonlinear Programming. — McGraw-Hill, 1972. — 536 p.

19. Getsov L. B., Semenov A. S., Grudinin A. N., Rybnikov A. I. Fracture Behavior of Single-Crystal Alloys Under Thermocyclic Loading / Strength of Materials. 2019. Vol. 51(2). P. 202 – 213.

20. Semenov A. S., Grishchenko A. I., Kolotnikov M. E., Getsov L. B. Finite element analysis of thermocyclic strength of gas turbine blades. Part 1 / Vestn. UGATU. 2019. Vol. 23. N 1(83). P. 70 – 81 [in Russian].

21. Semenov A. S., Grishchenko A. I., Kolotnikov M. E., Getsov L. B. Finite element analysis of thermocyclic strength of gas turbine blades. Part 2 / Vestn. UGATU. 2019. Vol. 23. N 2(84). P. 61 – 74 [in Russian].