Method of calculating the fatigue life of parts under the non-regular loading in the presence of surface residual stresses

Machining the aircraft engine critical parts ensures formation of the surface residual compressive stresses and increasing service life under the low-cycle fatigue, and it is used in practice for a long time. However, questions remain open regarding the computation methodology to assess fatigue strength in such situations. The problem of correct accounting for the surface residual compressive stresses is debatable. It is preferable to use the data on fatigue testing with the machined samples that have the same surface residual compressive stresses and strength characteristics as the part under study, but the methodology for such testing is still missing. The influence of the order of cycles in a flight pattern and presence of the low-amplitude cycles in it for the fatigue life is also not entirely clear, as it is not taken into account by methodologies used in practice. The paper considers a problem of identifying the service life of a high-pressure turbine disk, which surfaces were subjected to shot blasting, in the flight loading cycles. The plastic deformations profile is determined from the laboratory data obtained by the N.N. Davidenkov’s method using the proposed reconstruction formulas. To introduce surface plastic deformations in the finite element model, shell elements are used with attributes of amplitude and thickness of the preliminary deformation layer. The paper computes distribution of the residual stresses generated by incompatible part of the specified deformations, as well as stresses caused by centrifugal forces and non-uniform thermal expansion. Residual stresses move the existing hazardous points from the surface to beneath the hardened layer, almost without changing stresses inside the part. An evolutionary model is used to compute the fatigue life that takes into account the non-stationary loading history in the flight cycles. Due to the lack of data on fatigue destruction originating under the hardened surface layer, the required W?hler diagrams are simulated by shifting the diagrams for samples without the surface hardening. Analyzing computation results for four flight cycle schematizations makes it possible to determine the ranges of fatigue life predictions depending on the surface machining and irregular loading, as well as the proposed methodology applicability.
EDN: FIGBGA, https://elibrary/figbga

References

[1] Porter A.M., Leshin D.P., Bukatyy S.A. et al. Experiment-calculated research of the influence of the shot-peening strengthening upon the low-cycle fatigue of the gas turbine parts with the stress concentrator. Vestnik SGAU, 2011, no. 3–2, pp. 40–46. (In Russ.).

[2] Pavlov V.F., Kirpichev V.A., Vakulyuk V.S. Prognozirovanie soprotivleniya ustalosti poverkhnostno uprochnennykh detaley po ostatochnym napryazheniyam [Prediction of fatigue resistance of surface hardened parts by residual stresses]. Samara, SNTs RAN Publ., 2012. 125 p. (In Russ.).

[3] Bagmutov V.P. Reshenie pryamykh i obratnykh zadach mekhaniki formirovaniya poverkhnostno-uprochnennykh titanovykh splavov so sbalansirovannym kompleksom tribotekhnicheskikh i ustalostnykh kharakteristik [Solution of direct and inverse problems of mechanics of formation of surface-hardened titanium alloys with a balanced complex of tribotechnical and fatigue characteristics]. Project card RNF 22-29-01078. URL: https://www.rscf.ru/project/22-29-01078/ (accessed: 15.05.2024). (In Russ.).

[4] Marines I., Bin X., Bathias C. An understanding of very high cycle fatigue of metals. Int. J. Fatigue, 2003, vol. 25, no. 9, pp. 1101–1107, doi: https://doi.org/10.1016/S0142-1123(03)00147-6

[5] Shiozawa K., Lu L., Ishihara S. S-N curve characteristics and subsurface crack initiation behaviour in ultra-long life fatigue of a high carbon-chromium bearing steel. Fatigue Fract. Eng. Mater. Struct., 2001, vol. 24, no. 12, pp. 781–790, doi: https://doi.org/10.1046/j.1460-2695.2001.00459.x

[6] Kashaev N., Plekhov O.A., Gachegova E.A. et al. Influence of laser shock peening on low- and high-cycle fatigue of an OT4-0 titanium alloy. Prikladnaya mekhanika i tekhnicheskaya fizika, 2022, vol. 63, no. 2, pp. 182–191, doi: https://doi.org/10.15372/PMTF20220217 (in Russ.). (Eng. version: J. Appl. Mech. Tech. Phy., 2022, vol. 63, no. 2, pp. 335–342, doi: https://doi.org/10.1134/S0021894422020171)

[7] Nikitin I.S., Burago N.G., Nikitin A.D. Damage and fatigue fracture of structural elements in various cyclic loading modes. Prikladnaya matematika i mekhanika, 2022, vol. 86, no. 2, pp. 276–290. (In Russ.).

[8] Naumann E.C., Hardrath H.R., Guthrie E.C. Axial load fatigue tests of 2024-T3 and 7075-T6 aluminum alloy sheet specimens under constant- and variable-amplitude loads. Techchnical report. NASA TN D-212. Langley Research Center, NASA, 1959. 40 p.

[9] Naumann E.C. Fatigue under random and programmed loads. Technical report NASA TN D-2629. Langley Research Center, NASA, 1965. 42 p.

[10] Schutz W. The fatigue life under three different load spectra tests and calculations. Symp. on Random Load Fatigue. AGARD CP-118, 1972.

[11] Schutz W., Heuler P. Miner’s rule revisited. Mater. Test., 1994, vol. 42, no. 6, pp. 245–251, doi: https://doi.org/10.1515/mt-2000-420612

[12] Jacoby G.H. Comparison of fatigue lives under conventional program loading and digital random loading. In: Effects of environment and complex load history on fatigue life. ASTM Int., 1970, pp. 184–202, doi: https://doi.org/10.1520/STP32042S

[13] Ekvall J.C., Young L. Converting fatigue loading spectra for flight-by-flight testing of aircraft and helicopter components. J. Test. Eval., 1976, vol. 4, no. 4, pp. 231–247, doi: https://doi.org/10.1520/JTE10207J

[14] Basov V.N., Nesterenko G.I. Mechanical and fatigue strength of skin materials for civil airplane structures. Nauchnyy vestnik MGTU GA [Civil Aviation High Technologies], 2010, no. 153, pp. 15–23. (In Russ.).

[15] Jurcevic R., DuQuesnay D.L., Topper T.H. et al. Fatigue damage accumulation in 2024-T351 aluminium subjected to periodic reversed overloads. Int. J. Fatigue, 1990, vol. 12, no. 4, pp. 259–266, doi: https://doi.org/10.1016/0142-1123(90)90453-L

[16] Borrego L.P., Ferreira J.M., Pinho da Cruz J.M. et al. Evaluation of overload effects on fatigue crack growth and closure. Eng. Fract. Mech., 2003, vol. 70, no. 11, pp. 1379–1397, doi: https://doi.org/10.1016/S0013-7944(02)00119-4

[17] Haibach F. Modifizierte lineare Schadensakkumulationshypothese zur Beräcksichtigung des Dauerfestigkeitsabfalls mit fortschreitender. Technische Mitteilungen TM 50. Sch?digung, Laboratorium für Betriebsfestigkeit, 1970.

[18] Eurocode 3: Design of steel structures — Part 1-9: Fatigue. Vol. EN 1993-1-9:2005-05 +AC:2009-04. Brussels, ECS, 2009. 36 p.

[19] Zenner H., Liu J. Vorschlag zur Verbesserung der Lebensdauerabschätzung nach dem Nennspannungskonzept. Konstruktion, 1992, vol. 44, no. 1, pp. 9–17.

[20] Strizhius V.E. Fatigue curve equation under quasi-random loading of elements of the longitudinal wing set of a non-maneuvering aircraft wing. Uchenye zapiski TsAGI, 1998, vol. 29, no. 3–4, pp. 144–152. (In Russ.).

[21] Haibach E. Betriebsfestigkeit. Verfahren und Daten zur Bauteilberechnung. Springer, 2006. 759 p.

[22] Kuzmin V.R., Prokhorov V.A., Borisov A.Z. et al. Ustalostnaya prochnost metallov i dolgovechnost elementov konstruktsiy pri neregulyarnom nagruzhenii vysokogo urovnya [Fatigue strength of metals and durability of structural elements under irregular high-level loading]. Moscow, Mashinostroenie Publ., 1998. 256 p. (In Russ.).

[23] Strizhius V.E. Method for fatigue analysis of airframe elements, operating under biharmonical loading. Nauchnyy vestnik MGTU GA [Civil Aviation High Technologies], 2012, no. 175, pp. 55–61. (In Russ.).

[24] Pereira H., DuQuesnay D., De Jesus A. et al. Analysis of variable amplitude fatigue data of the P355NL1 steel using the effective strain damage model. J. Pressure Vessel Technol., 2009, vol. 131, no. 5, art. 051402, doi: https://doi.org/10.1115/1.3147986

[25] Sines G. Failure of materials under combined repeated stresses with superimposed static stresses. Technical report NACA TN-3495. NACA, 1955.

[26] Crossland B. Effect of large hydrostatic pressures on torsional fatigue strength of an alloy steel. Proc. Int. Conf. on Fatigue of Metals, 1956, pp. 138–149.

[27] Manson S.S. Thermal stress and low-cycle fatigue. McGraw-Hill, 1966. ?404 p. (Russ. ed.: Temperaturnye napryazheniya i malotsiklovaya ustalost. Moscow, Mashinostroenie Publ., 1974. 344 p.)

[28] Smith K., Topper T., Watson P. A stress–strain function for the fatigue of metals. J. Mater., 1970, vol. 5, pp. 767–778.

[29] Fatemi A., Socie D.F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading. FFEMS, 1988, vol. 11, no. 3, pp. 149–165, doi: https://doi.org/10.1111/j.1460-2695.1988.tb01169.x

[30] You C., Achintha M., Soady K.A. et al. Low cycle fatigue life prediction in shot-peened components of different geometries – part II: life prediction. FFEMS, 2017, vol. 40, no. 5, pp. 749–760, doi: https://doi.org/10.1111/ffe.12542

[31] Cruces A.S., Lopez-Crespo P., Moreno B. et al. Multiaxial fatigue life prediction on S355 structural and offshore steel using the SKS critical plane model. Metals, 2018, vol. 8, no. 12, art. 1060, doi: https://doi.org/10.3390/met8121060

[32] Lemaitre J., Chaboche J.L. Mechanics of solid materials. Cambridge University Press, 1994. 556 p.

[33] Murakami S. Continuum damage mechanics. Springer, 2012. 402 p.

[34] Nikitin I.S., Nikitin A.D., Stratula B.A. A comprehensive study of fatigue crack initiation and growth under very high cycle torsional fatigue loading. Fizicheskaya mezomekhanika, 2023, vol. 26, no. 3, pp. 50–61, doi: https://doi.org/10.55652/1683-805X_2023_26_3_50 (in Russ.).

[35] Marmi A.K., Habraken A.M., Duchene L. Multiaxial fatigue damage modelling at macro scale of Ti–6Al–4V alloy. Int. J. Fatigue, 2009, vol. 31, no. 11-12, pp. 2031–2040, doi: https://doi.org/10.1016/j.ijfatigue.2009.03.003

[36] Lu R.S., Tan J.P., Yang J. et al. A new creep-fatigue crack growth model and a correlation of the creep-fatigue crack growth rate with unified constraint parameter. Int. J. Fatigue, 2023, vol. 166, art. 107248, doi: https://doi.org/10.1016/j.ijfatigue.2022.107248

[37] Bondar V.S., Abashev D.R. Inelastic behavior and destruction of materials under isothermal and non-isothermal, simple and complex loads. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin], 2020, no. 4, pp. 107–119, doi: https://doi.org/10.15593/perm.mech/2020.4.10 (in Russ.).

[38] Volkov I.A., Igumnov L.A. Vvedenie v kontinualnuyu mekhaniku povrezhdennoy sredy [Introduction to continuum mechanics of damaged media]. Moscow, Fizmatlit Publ., 2017. 300 p. (In Russ.).

[39] Ottosen N.S., Stenström R., Ristinmaa M. Continuum approach to high-cycle fatigue modeling. Int. J. Fatigue, 2008, vol. 30, no. 6, pp. 996–1006, doi: https://doi.org/10.1016/j.ijfatigue.2007.08.009

[40] Petukhov D.S., Keller I.E. Evolutionary model of fatigue fracture under irregular loading. Izvestiya RAN MTT, 2022, no. 2, pp. 72–81, doi: https://doi.org/10.31857/S0572329922020167 (in Russ.). (Eng. version: Mech. Solids, 2022, vol. 57, no. 2, pp. 263–270, doi: https://doi.org/10.3103/S0025654422020194)

[41] Korsunsky A. Variational eigenstrain analysis of synchrotron diffraction measurements of residual elastic strain in a bent titanium alloy bar. J. Mech. Mat. Struct., 2006, vol. 1, no. 2, pp. 259–277, doi: http://dx.doi.org/10.2140/jomms.2006.1.259

[42] Musinski W.D., McDowell D.L. On the eigenstrain application of shot-peened residual stresses within a crystal plasticity framework: application to Ni-base superalloy specimens. Int. J. Mech. Sci., 2015, vol. 100, pp. 195–208, doi: https://doi.org/10.1016/j.ijmecsci.2015.06.020

[43] Saushkin M.N., Radchenko V.P., Kurov A.Yu. Method of calculating residual stresses in semicircular notches in a surface hardened hollow cylindrical specimen. Prikladnaya mekhanika i tekhnicheskaya fizika, 2013, vol. 54, no. 4, pp. 150–157. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phy., 2013, vol. 54, no. 4, pp. 644–650, doi: https://doi.org/10.1134/S0021894413040159)

[44] Gallitelli D., Boyer V., Gelineau M. et al. Simulation of shot peening: from process parameters to residual stress fields in a structure. Comptes Rendus M?ecanique, 2016, vol. 344, no. 4–5, pp. 355–374, doi: https://doi.org/10.1016/j.crme.2016.02.006

[45] Cochennec F., Rouhaud E., Roucoules L. et al. Numerical and experimental investigation on shot-peening induced deformation: application to sheet metal forming. Powder Diffr., 2008, vol. 23, no. 2, p. 183, doi: https://doi.org/10.1154/1.2951767

[46] Petukhov D.S., Keller I.E. Exact reconstruction formulas for plastic strain dis­tribution in the surface-treated plate and their applications. Acta Mech., 2020, vol. 231, no. 5, pp. 1849–1866, doi: https://doi.org/10.1007/s00707-020-02625-7

[47] Cai X., Li X., Xu J. Fatigue limit and life evaluation formulae for compres­sive mean stress states. Mater. Sci. Technol., 2018, vol. 34, no. 17, pp. 2166–2173, doi: https://doi.org/10.1080/02670836.2018.1522100

[48] Thiago R. Zum Schwingfestigkeitsverhalten von Gusseisenwerkstoffen unter einachsiger und mehrachsiger Beanspruchung am Beispiel von EN-GJV-450. Doktorarbeit. Shaker, 2011. 192 p.

[49] Forrest P.G. Fatigue of metals. Pergamon Press, 1963. 425 p.