The cycle configuration at two-frequency loading modes depends on the number of parameters, including the absolute values of the frequencies and amplitudes of the low-frequency and high-frequency loads added during this mode, the ratio of their frequencies and amplitudes, and the phase shift between these harmonic components, with the latter having a significant effect only when the ratio of frequencies is small. Such two-frequency regimes of service loading of parts of machines and structures can significantly reduce their endurance. Using the results of experimental studies of changes in the endurance of a two-frequency loading of specimens of cyclically stable, cyclically softened, and cyclically hardened steels under rigid conditions, we have shown that decrease in the endurance under the aforementioned conditions depends on the ratio of frequencies and amplitudes of operating low-frequency low-cycle and high-frequency vibration stresses, and, moreover, the higher the level of the ratios of amplitudes and frequencies of those stacked harmonic processes of loading, the greater the effect. It is shown that estimation of such a decrease in the endurance compared to a single frequency loading equal in the total stress (strains) amplitudes can be carried out using an exponential expression coupling those endurances through a parameter (reduction factor) containing the ratio of frequencies and amplitudes of operation cyclic loads and characteristic of the material. The reduction is illustrated by a set of calculation-experimental curves on the corresponding diagrams for each of the considered types of materials and compared with the experimental data.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Kogaev V.P., Makhutov N.A., and Gusenkov A.P., Raschety detalei mashin i konstruktsii na prochnost’ i dolgovechnost’ (Calculations of Machine Parts and Constructions for Strength and Life-Time), Moscow: Mashinostroenie, 1985.
Makhutov, N.A., Prochnost’ i bezopasnost’: fundamental’nye i prikladnye issledovaniya (Strength and Safety: Fundamental and Applied Studies), Novosibirsk: Nauka, 2008.
Bezopastnost’ Rossii. Pravovye, sotsial’no-ekonomicheskie i nauchno-tekhnicheskie aspekty. Upravlenie resursom ekspluatatsii vysokoriskovykh ob”ektov (Safety of Russia: Legal, Social-Economic, and Scientific-Engineering Aspects. Management of Service Resource for Highly Risk Objects), Moscow: Znanie, 2013.
Gadenin, M.M., The multiple parameter analysis of safe service conditions and protectability of machines and structures by criteria of strength, resource and survivability, Probl. Bezop. Chrezvychainykh Situatsii, 2012, no. 6, pp. 22–36.
Strength and resource of water-moderated power reactors, in Issledovaniya napryazhenii i prochnosti yadernykh reaktorov (Researches of Stresses and Strength of Nuclear Reactors), Moscow: Nauka, 1988.
Dynamics and strength of water-moderated power reactors, in Issledovaniya napryazhenii i prochnosti yadernykh reaktorov (Researches of Stresses and Strength of Nuclear Reactors), Moscow: Nauka, 2004.
Strength and resource of liquid-fuel rocket engines, in Issledovaniya napryazhenii i prochnosti raketnykh dvigatelei (Researches of Stresses and Strength of Rocket Engines), Moscow: Nauka, 2011.
Gadenin, M.M. and Romanov, A.N., The arrangement for reproduction of a two-frequency loading mode on monofrequent fatigue test machines, Zavod. Lab., 1974, vol. 40, no. 4, pp. 463–465.
Gadenin, M.M., The method of cyclic tests automation on basis of URS 50/50 electrohydraulic test machine and IVK-2 measuring-computer complex, Zavod. Lab., 1985, vol. 51, no. 12, pp. 61–65.
Gadenin, M.M., Peculiarities of strains evolution and damages accumulation at two-frequency low-cycle loading and heightened temperatures, Mashinovedenie, 1976, no. 1, pp. 69–77.
Gadenin, M.M., Resistance change to low-cycle deformation and fracture for two-frequency process of a loading, Materialy XIII Nauchno-tekhnicheskoi konferentsii “Problemy nadezhnosti i dolgovechnosti elementov konstruktsii v mashinostroenii i stroiindustrii,” Tezisy dokladov (Proc. XIII Sci.-Tech. Conf. “Reliability and Durability of Construction Elements in Machine engineering and Construction Industry,” Abstracts of Papers), Sverdlovsk: Sverdlovskii Obl. Sov. NTO, 1978, pp. 5–6.
Gadenin, M.M., Study on damaging and fatigue life of constructions under single- and two-frequency loading modes based on deformational and energy approaches, Inorg. Mater., 2018, vol. 54, no. 15, pp. 1543–1550.
Locati, L., Essais de fatigue par flexion avec fréquences superposées, in Colloquium on Fatigue, Berlin: Springer-Verlag, 1956, p. 160.
Gadenin, M.M., Study of the effect of strain amplitude ratio at two-frequency cyclic loading, Inorg. Mater., 2019, vol. 55, no. 15, pp. 1523–1532.
Makhutov, N.A. and Gadenin, M.M., Fatigue resistance at variation of temperature-time factors, Int. J. Fract., 2008, vol. 150, no. 1, pp. 105–127.
Bezopastnost’ Rossii. Pravovye, sotsial’no-ekonomicheskie i nauchno-tekhnicheskie aspekty. Fundamental’nye issledovaniya problem tekhnogennoi bezopasnosti (Safety of Russia: Legal, Social-Economic, and Scientific-Engineering Aspects. Fundamental Studies of Engineering Safety), Moscow: Znanie, 2013.
Gadenin, M.M., Characteristics of mechanical properties of materials in studies of conditions of attainment of marginal states, Inorg. Mater., 2013, vol. 49, no. 15, pp. 1352–1356.
Makhutov, N.A. and Gadenin, M.M., Resource estimation at combination of extreme low-cycle and vibrating impacts, Trudy chetvertoi Vserossiiskoi nauchno-tekhnicheskoi konferentsii “Dinamika i prochnost' konstruktsii aerogidrouprugikh sistem. Chislennye metody,” Moskva, 14–15 noyabrya 2017 g. (Proc. 4th All-Russian Sci.-Tech. Conf. “Dynamics and Strength of Constructions of Aerial- and Hydroelastic Systems. Numerical Methods,” Moscow, November 14–15, 2017), Moscow: Inst. Mashinoved. im. A.A. Blagonravova, Ross. Akad. Nauk, 2017, pp. 40–41.
This work was supported by Russian Foundation for Basic Research (project no. 18-08-00572_a).
The authors declare that they have no conflicts of interest.
Translated by V. Alekseev
About this article
Cite this article
Gadenin, M.M. Calculation and Experimental Estimation of the Role of the Frequency Ratio in Changing the Durability at Two-Frequency Deformation Modes. Inorg Mater 56, 1485–1491 (2020). https://doi.org/10.1134/S0020168520150042
- two-frequency loading regime
- low-cycle fatigue
- vibration loads
- structural materials
- ratios of frequencies and amplitudes of stresses