Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems

V. P. Radchenko ; E. E. Derevyanka

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 4, pp. 647-668.

Résumé

We propose a method for modeling stress-strain state in surface-hardened elements of statically indefinable rod systems under creep. A method we propose is considered for a three-element asymmetric rod system. The solution consists of two steps: reconstruction of the stress-strain state after the procedure of surface plastic hardening of the cylindrical elements of the system (pneumatic blasting with micro balls) and the method for calculating the relaxation of residual stresses in the hardened elements amidst the creep state of rod system (as a whole structure). Rheological relations are determined on the basis of a model describing the first and second phases of creep. The solution of both stages and special aspects of the problem is illustrated on a model example of creep of systems with hardened elements made of ZhS6U alloy at the temperature of 650 °C. For hardening the rods of this alloy, real experimental data were used for axial and circumferential residual stresses. The technique of reconstruction of the stress-strain state after pneumatic blasting treatment is illustrated in detail. To build a rheological model, experimental data were used for the uniaxial creep curves of the ZhS6U alloy under various constant stresses at the temperature of 650 °C. The numerical values of the model parameters are given in the article. The uniaxial model is generalized to a complex stress state. The main problem is solved numerically using discretization by spatial and temporal coordinates. The stationary asymptotic stress-strain state of the rod system is investigated, which corresponds to the steady-state creep stage, which was used to estimate the convergence of the numerical method. The dependencies of the kinetics of all components of the residual stress tensor in all three strengthened elements of the system due to creep under a given external load are obtained. A comparative analysis of the residual stress relaxation rate in different rods is performed. The algorithm and software for solving the problem is developed. The main results of the work are illustrated by the residual stresses graphs over the depth of the hardened layer. Issues of applying the results obtained in the work to practical problems of assessing the reliability of hardened rod systems are discussed.

Détail

Keywords: three-element statically indefinable system, 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 °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 incoroporating shot peening process effects: mechanistic consideration of residual stresses and strain hardening. 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., Vakuliuk 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 for hardening GTE parts based on plastic deformation of surface layers (Review)”, Vestnik dvigatelestroeniia, 2006, no. 2, 8–16 (In Russian)

[10] Kravchenko B. A., Krucilo V. G., Gutman G. N., Termoplasticheskoe uprochnenie – rezerv povysheniya prochnosti i nadezhnosti detalei mashin [Thermoplastic Hardening as a Reserve Increase of Strength and Reliability of Machine Parts], Samara State Technical Univ., Samara, 2000, 216 pp. (In Russian)

[11] Radchenko V. P., Saushkin M. N., Polzuchest' i relaksatsiia ostatochnykh napriazhenii v uprochnennykh konstruktsiiakh [Creep and Relaxation of Residual Stresses in Hardened Structures], Mashinostroenie-1, Moscow, 2005, 226 pp. (In Russian)

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

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

[15] 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”, Mater. Sci. Engng: A, 528:21 (2011), 6478–6489 | DOI

[16] 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

[17] 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)

[18] Hoffmann J., Scholtes B., Vöhringer O., Macherauch E., “Thermal relaxation of shot peening residual stresses in the differently heat treated plain carbon steel Ck 45”, Proc. of the 3rd International Conference on Shot Peening (ICSP3), DGM Informationsgesellschaft Verlag, Oberursel, 1987, 239–246

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

[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] 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

[22] Benedetti M., Fontanari V., Scardi P. et al., “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

[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] 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

[25] 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

[26] Radchenko V. P., Saushkin M. N., Bochkova T. I., “A 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 high-temperature creep conditions”, PNRPU Mechanics Bulletin, 2016, no. 1, 93–112 (In Russian) | DOI

[27] Samarin Yu. P., Uravneniia sostoyaniia materialov so slozhnymi reologicheskimi svoistvami [Equations of State of Materials with Complex Rheological Properties], Kuibyshev State Univ., Kuibyshev, 1979, 84 pp. (In Russian)

[28] 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