The method of reconstruction of residual stresses in a prismatic specimen with a notch of a semicircular profile after advanced surface plastic deformation

V. P. Radchenko ; D. M. Shishkin

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 20 (2020) no. 4, pp. 478-492.

Résumé

The stress-strain state in a surface-hardened bar (beam) with a stress concentrator of the semicircular notch type is investigated. A numerical method for calculating the residual stresses in the notch region after an advanced surface plastic deformation is proposed. The problem is reduced to the boundary-value problem of fictitious thermoelasticity, where the initial (plastic) deformations of the model are simulated by temperature deformations in an inhomogeneous temperature field. The solution is constructed using the finite element method. For model calculations, experimental data on the distribution of residual stresses in a smooth beam made of EP742 alloy after ultrasonic mechanical hardening were used. The effect of the notch radius and beam thickness on the nature and magnitude of the distribution of the residual stress tensor components in the region of the stress concentrator is studied. For the normal longitudinal component of the residual stress tensor, which plays an important role in the theory of high-cycle fatigue, it was found that if the radius of a semicircular notch is less than the thickness of the hardened layer (area of material compression), an increase (in modulus) of this component of residual stresses occurs in the smallest section of the part (in the volume immediately adjacent to the bottom of the concentrator). If the depth of the notch is greater than the thickness of the hardened layer, then a decrease (in magnitude) of this value is observed in comparison with a smooth hardened sample. It is shown that in a reinforced notched beam, the deflection value due to induced self-balanced residual stresses is less than in a smooth beam. Experimental verification of the developed numerical method is done for a surface-hardened smooth beam made of EP742 alloy.

Bibliographie

[1] Birger I. A., Residual tension, Mashgiz, M., 1963, 232 pp. (in Russian)

[2] Grinchenko I. G., The hardening of parts of heat-resistant and titaniumalloys, Mashinostroenie, M., 1971, 120 pp. (in Russian)

[3] Sulima G. N., Shuvalov V. A., Iagodkin Yu. D., Surface layer and performance of machine parts, Mashinostroenie, M., 1988, 240 pp. (in Russian)

[4] Kudryavtsev V. S., Surface cold working for increased strength and durability of machine parts by surface plastic deformation, Mashinostroenie, M., 1969, 100 pp. (in Russian)

[5] Nozhnitskii Iu. A., Fishgoit A. V., Tkachenko R. I., Teplova S. V., “Development and application of new GTE parts hardening methods based on the plastic deformation of the surface layers”, Vestnik dvigatelestroeniia, 2006, no. 2, 8–16 (in Russian)

[6] Brockman R. A., Braisted W. R., Olson S. E., Tenaglia R. D., Clauer A. H., Langer K., Shepard M. J., “Prediction and characterization of residual stresses from laser shock peening”, Intern. J. Fatigue, 36:1 (2012), 96–108 | DOI

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

[8] James M. N., Hughes D. J., Chen Z., Lombard H., Hattingh D. G., Asquith D., Yates J. R., Webster P. J., “Residual stresses and fatigue performance”, Engineering Failure Analysis, 14:2 (2007), 384–395 | DOI | MR

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

[10] 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), 673–651 | DOI

[11] Terres M. A., Laalai N., Sidhom H., “Effect of hitriding and shot peening on the fatigue behavior of 42CrMo4 steel: Experimantal analysis and predictive approach”, Mater. Design, 35 (2012), 741–748 | DOI

[12] Pavlov V. F., Kirpichev V. A., Vakuluk V. S., Prediction of fatigue resistance of surface reinforced parts by residual stresses, Samarskij nauchnyj tsentr RAN, Samara, 2012, 125 pp. (in Russian)

[13] Bukatyi' A. S., “Finite element modeling and re-search of residual stresses and deformations of parts after shot peening”, Russian Engineering Research, 2016, no. 6, 52–57 (in Russian)

[14] Jebahi M., Gakwaya A., Lévesque J., Mechri O., Ba K., “Robust methodology to simulate real shot peening process using discrete-cotinuum coupling method”, Int. J. Mech. Sci., 107 (2016), 21–33 | DOI

[15] Gallitelli D., Boyer V., Gelineau M., Colaitis Y., Rouhaud E., Retraint D., Kubler R., Desvignes M., Barrallier L., “Simulation of shot peening: From process parameters to residual stress fields in a structure”, C. R. Mécanique, 344:4–5 (2016), 355–374 | DOI

[16] Keller I. E., Trofimov V. N., Vladykin A. V., Plusnin V. V., Petukhov D. S., Vindokurov I. V., “On the reconstruction of residual stresses and strains of a plate after shot peening”, J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 22:1 (2018), 40–64 (in Russian) | DOI | Zbl

[17] Radchenko V. P., Afanaseva O. S., Glebov V. E., “Influence of Residual Stresses on Geometric Parameters of Surface-Strengthened Beam”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 19:4 (2019), 464–478 (in Russian) | DOI | MR

[18] Pavlov V. F., Bukatyj A. S., Semjonova O. Ju., “Forecasting of the endurance limit of surface-hardened parts with stress concentrators”, Russian Engineering Research, 2019, no. 1, 3–7 (in Russian)

[19] Ivanov S. I., Shatunov M. P., Pavlov V. F., “Influence of residual stresses on notched specimen endurance”, Problems of strength of aircraft structure elements, 1, KuAI (Kuibyshev Aviation Institute), Kuibyshev, 1974, 88–95 (in Russian)

[20] Pavlov V. F., Stoljarov A. K., Vakuljuk V. S., Kirpichev V. A., Calculation of residual stresses in parts with stress concentrators by initial deformations, Samarskij nauchnyj tsentr RAN, Samara, 2008, 124 pp. (in Russian)

[21] Vakuljuk V. S., “Investigation of influence of thickness hardened layer on the redisiual stresses in basin concentrator using initial strain”, J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 2010, no. 1 (20), 222–225 (in Russian) | DOI

[22] Sazanov V. P., Kirpichev V. A., Vakulyuk V. S., Pavlov V. F., “The definition of initial deformations in the cylindrical parts surface layer by Finite Elements Modeling method using PATRAN/NASTRAN program complex”, Vestn. UGATU, 19:2 (68) (2015), 35–40 (in Russian)

[23] Saushkin M. N., Kurov A. Yu., “Analysis of stress state in semicircular profile notches after preliminary surface plastic deformation of solid cylindrical specimens”, J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 2012, no. 1 (26), 133–140 (in Russian) | DOI | Zbl

[24] Radchenko V. P., Kurov A. Yu., “Effect of anisotropy of surface plastic hardening on formation of residual stresses in cylindrical samples with semicircular notch”, J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 20:4 (2016), 675–690 (in Russian) | DOI

[25] 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

[26] Radchenko V. P., Afanaseva O. S., Glebov V. E., “The effect of surface plastic hardening technology, residual stresses and boundary conditions on the buckling of a beam”, PNRPU Mechanics Bulletin, 2020, no. 1, 87–98 | DOI

[27] Radchenko V. P., Pavlov V. Ph., Saushkin M. N., “Investigation of surface plastic hardening anisotropy influence on residual stresses distribution in hollow and solid cylindrical specimens”, PNRPU Mechanics Bulletin, 2015, no. 1, 130–147 | DOI