The effect of elevated temperature and tensile force loading on the relaxation

V. P. Radchenko ; E. E. Derevyanka

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 3, pp. 497-524.

Résumé

A mathematical model for the relaxation of residual stresses in surface-hardened cylindrical elements of statically indefinable rod systems under creep conditions with elevated temperature and tensile force loading was developed. The following problems were solved during the modeling: reconstruction of the stress-strain state in a cylindrical rod after the surface treatment by microspheres; consideration of the influence of temperature loading on the magnitude and the fields of residual stresses due to the temperature dependence of Young's modulus; calculation of relaxation of residual stresses in hardened elements of the system under the influence of elevated temperature and tensile force loading under creep conditions; analysis of the final residual stresses after creep and reduced temperature and tensile force unloading. The problems were solved within the first two stages of creep of the system of material elements. For a detailed analysis a three-element statically indefinable system with hardened elements at the temperature of 20$\,^\circ$C and an operating temperature of 675$\,^\circ$C made of ZhS6U alloy was used. To implement the solutions of the problems mentioned, numerical algorithms were developed using discretization by spatial and temporal coordinates and using the method of time steps. For a posteriori estimation of the convergence and stability of the numerical method the numerical results were compared for large values of the calculation time with the asymptotic values of the stress-strain state characteristics corresponding to the steady-state creep stage obtained by the analytical method. The results obtained by both approaches are consistent. The results of calculations were illustrated the kinetics of residual stresses in all three rods of the system during creep under the influence of elevated temperature and tensile force loading, starting from the moment of their formation after hardening. It was shown that a stepwise change in the magnitude and the distribution of residual stresses occurs only due to the “instantaneous” temperature heating of the elements of the rod structure due to the temperature dependence of the Young's modulus. It was also established by calculations that the relaxation of residual stresses in the most loaded rods system is much slower than in less loaded ones. To illustrate the main results obtained in this paper, we plotted the distribution of residual stresses along the depth of the hardened layer.

Détail

Keywords: solid rod system, elevated temperature tensile testing, surface hardening, residual stresses, creep, stress relaxation.

Bibliographie

[1] Altenberger I., Nalla R. K., Sano Y., et. al., “On the effect of deep-rolling and laser-peening on the stress-controlled low- and high-cycle fatigue behavior of Ti–6Al–4V at elevated temperatures up to 550$^\circ$C”, Intern. J. Fatigue, 44 (2012), 292–302 | DOI

[2] Dai K., Shaw L., “Analysis of fatigue resistance improvements via surface severe plastic deformation”, Intern. J. Fatigue, 30:8 (2008), 1398–1408 | DOI

[3] James M. N., Hughes D. J., Chen Z., et al., “Residual stresses and fatigue performance”, Engng Failure Anal., 14:2 (2007), 384–395 | DOI

[4] Majzoobi G. H., Azadikhah K., Nemati J., “The effects of deep rolling and shot peening on fretting fatigue resistance of Aluminum-7075-T6”, Mater. Sci. Engng: A, 516:1–2 (2009), 235–247 | DOI

[5] McClung R. C., “A literature survey on the stability and significance of residual stresses during fatigue”, Fatigue Fract. Engng Mater. Struct., 30:3 (2007), 173–205 | DOI

[6] Soady K. A., “Life assessment methodologies incorporating shot peening process effects: mechanistic consideration of residual stresses and strain hardening. Part 1. Effect of shot peening on fatigue resistance”, Mater. Sci. Technol., 29:6 (2013), 637–651 | DOI

[7] Terres M., Laalai N., Sidhom H., “Effect of nitriding and shot-peening on the fatigue behavior of 42CrMo4 steel: Experimental analysis and predictive approach”, Mater. Design., 35:6 (2013), 741–748 | DOI

[8] Pavlov V. F., Kirpichev V. A., Vakulyuk V. S., Prognozirovanie soprotivleniia ustalosti poverkhnostno uprochnennykh detalei po ostatochnym napriazheniiam [Prediction of fatigue resistance of surfacehardened parts by residual stresses], Samara Scientific Center of RAS, Samara, 2012, 125 pp. (In Russian)

[9] Nozhnitskii Yu. A., Fishgoit A. V., Tkachenko R. I., Teplova S. V., “Development and application of new methods of hardening GTE parts, which are based on the plastic deformation of surface layers (review)”, Vestn. Dvigatelestr., 2 (2006), 8–16 (In Russian)

[10] Birger I. A., Ostatochnye napryazheniya [Residual Stresses], M., 1963, 262 pp. (In Russian)

[11] Kravchenko B. A., Krucilo V. G., Gutman G. N., Termoplasticheskoe uprochnenie – rezerv povysheniya prochnosti i nadezhnosti detalei mashin [Thermoplastic hardening as a reserve for increasing the strength and reliability of machine parts], Samara State Technical Univ., Samara, 2000, 216 pp. (In Russian)

[12] Radchenko V. P., Saushkin M. N., Polzuchest' i relaksatsiya ostatochnykh napryazheniy v uprochnonnykh konstruktsiyakh [Creep and Relaxation of Residual Stresses in Hardened Structures], Mashinostroenie-1, Moscow, 2005, 226 pp. (In Russian)

[13] Kolotnikova O. V., “Effectiveness of hardening by methods of plastic surface deformation of components operating at high temperatures”, Strength of Materials, 15:2 (1983), 292–295 | DOI

[14] Tseitlin V. I., Kolotnikova O. V., “Relaxation of residual stresses in gas-turbine engine parts”, Strength of Materials, 12:8 (1980), 982–984 | DOI

[15] Foss B. J., Gray S., Hardy M. C., et al., “Analysis of shot-peening and residual stress relaxation in the nickel-based superalloy RR1000”, Acta Materialia, 61:7 (2013), 2548–2559 | DOI

[16] Hoffmann J., Scholtes B., Vohringer O., et al., “Thermal relaxation of shot peening residual stresses in the differently heat treated plain carbon steel Ck 45”, Shot Peening: Sci., Technol., Appl., 61:7 (1987), 239–246 https://www.shotpeener.com/library/pdf/1987102.pdf

[17] Khadraoui M., Cao W., Castex L., “Experimental investigations and modeling of relaxation behavior of shot peening residual stresses at high temperature for nickel base superalloys”, Materials Science and Technology, 13:4 (1997), 360–367 | DOI

[18] Xie L., Jiang C., Ji V., “Thermal relaxation of residual stresses in shot peened surface layer of (TiB + TiC)/Ti-6Al-4V composite at elevated temperatures”, Materials Science and Engineering: A, 528:21 (2011), 6478–6489 | DOI

[19] Zaharova T. P., Rozanov M. A., Teplova S. V., “Influence of operation conditions at the residual stress relaxation in turbine root slots of HPT, made of monocrystal nickel super alloys”, Vestnik UGATU, 19:3 (69) (2015), 21–27 (In Russian) | MR

[20] Radchenko V. P., Kocherov E. P., Saushkin M. N., Smyslov V. A., “Experimental and theoretical studies of the influence of a tensile load on the relaxation of residual stresses in a hardened cylindrical specimen under creep conditions”, J. Appl. Mech. Tech. Phys., 56:2 (2015), 169–177 | DOI | DOI

[21] Buchanan D. J., John R., “Relaxation of shot-peened residual stresses under creep loading”, Scripta Materialia, 59:3 (2008), 286–289 | DOI

[22] Evans A., Kim S-B., Shackleton J., et al., “Relaxation of residual stress in shot peened Udimet 720Li under high temperature isothermal fatigue”, Int. J. Fatigue, 27:10–12 (2005), 1530–1534 | DOI

[23] Kim J.-C., Cheong S.-K., Noguchi H., “Residual stress relaxation and low- and high-cycle fatigue behavior of shot-peened medium-carbon steel”, Int. J. Fatigue, 56 (2013), 114–122 | DOI

[24] Benedetti M., Fontanari V., Scardi P., Ricardo C. L. A., Bandini M., “Reverse bending fatigue of shot peened 7075-T651 aluminium alloy: The role of residual stress relaxation”, Int. J. Fatigue, 31:8 (2009), 1225–1236 | DOI

[25] Radchenko V. P., Saushkin M. N., “Direct method of solving the boundary-value problem of relaxation of residual stresses in a hardened cylindrical specimen under creep conditions”, J. Appl. Mech. Tech. Phys., 50:6 (2009), 989–997 | DOI | Zbl

[26] Radchenko V. P., Saushkin M. N., Tsvetkov V. V., “Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions”, J. Appl. Mech. Tech. Phys., 57:3 (2016), 559–568 | DOI | DOI | MR

[27] Radchenko V. P., Saushkin M. N., Bochkova T. I., “Mathematical modeling and experimental study of forming and relaxation of the residual stresses in plane samples made of EP742 alloy after the ultrasonic hardening under the hightemperature creep conditions”, PNRPU Mechanics Bulletin, 2016, no. 1, 93–112 (In Russian) | DOI

[28] Radchenko V. P., Derevyanka E. E., “Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:4 (2018), 647–668 (In Russian) | DOI | Zbl

[29] Samarin Yu. P., Uravneniya sostoyaniya materialov so slozhnymi reologicheskimi svoystvami [Equations of state of materials with complex rheological properties], Kuibyshev State Univ., Kuibyshev, 1979, 84 pp. (In Russian)

[30] Radchenko V. P., Tsvetkov V. V., “The stress-strain state of cylindrical sample from alloy D16T under axial tension and torsion creep”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, no. 3(32), 77–86 (In Russian) | DOI | Zbl

[31] Radchenko V. P., Pavlov V. F., Saushkin M. N., “Mathematical modeling of the stress-strain state in surface hardened thin-walled tubes with regard to the residual shear stresses”, PNRPU Mechanics Bulletin, 2019, no. 1, 138–150 (In Russian) | DOI