Numerical method for calculating the stress-strain state in~a~prismatic surface-hardened spacemen with a~notch in elastic and~elastoplastic formulations

V. P. Radchenko ; D. M. Shishkin

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 21 (2021) no. 4, pp. 503-519.

Résumé

The problem of calculating the stress-strain state in the region of through stress concentrators in the form of a transverse notch of semicircular, through and V-shaped shape in a prismatic sample after advanced surface plastic deformation in elastic and elastoplastic formulations based on the finite element method is solved. The initial formulations are reduced to fictitious problems of thermoelasticity and thermoelastoplasticity using the method of initial deformations. At the first stage, the field of residual stresses and plastic deformations in a smooth sample after hardening is determined. At the second stage, residual plastic deformations are modeled by temperature deformations in an inhomogeneous temperature field along the depth of the hardened layer. At the third stage, a through notch of a given geometric shape is applied, and the problem of fictitious thermoelasticity or thermoelastoplasticity on the redistribution of stresses in the concentrator area is solved. Model calculations were performed on the basis of experimental data for a smooth sample made of EP742 alloy after vibro-shock ultrasonic hardening of one of its faces. There is a significant discrepancy between the solutions for the elastic and elastoplastic formulations in the notches, the depth of which does not exceed the thickness of the hardened layer. The results obtained for problems with notches in linear elastic and elastoplastic formulations, along with the results for a smooth sample, were subjected to a comparative analysis of the distribution of residual stresses to establish the influence area of the stress concentrator. It was found that, regardless of the shape of the notch, the values of residual stresses outside the stress concentrator zone when solving elastic or elastoplastic problems practically coincide with the corresponding values for a smooth sample.

Bibliographie

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

[2] Grinchenko I. G., The Hardening of Parts of Heat-resistant and Titanium Alloys, Mashinostroenie, M., 1971, 120 pp. (in Russian)

[3] Sulima A. M., Shuvalov V. A., Yagodkin Yu. D., Surface Layer and Performance of Machine Parts, Mashinostroenie, M., 1988, 240 pp. (in Russian)

[4] Kudryavtsev I. V., Surface Strain Hardening to Increase the Strength and Durability of Machine Parts, Mashinostroenie, M., 1969, 100 pp. (in Russian)

[5] Nozhnitskii Yu. 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”, International Journal of Fatigue, 36:1 (2012), 96–108 | DOI

[7] Dai K., Shaw L., “Analysis of fatigue resistance improvements via surface severe plastic deformation”, International Journal of 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

[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”, Materials Science and Technology, 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”, Materials Design, 35 (2012), 741–748 | DOI

[12] Pavlov V. F., Kirpichev V. A., Vakulyuk V. S., Prediction of Fatigue Resistance of Surface Reinforced Parts by Residual Stresses, Samara Sci. Center of RAS, Samara, 2012, 125 pp. (in Russian)

[13] Pavlov V. F., Petrova Yu. N., Vakulyuk V. S., Sazanov V. P. Katanaeva Yu. A., “Appointment of the optimal for fatigue resistance types of surface hardening of details with the use of residual voltage distribution”, Progressive Technologies and Systems of Mechanical Engineering, 2021, no. 1 (72), 65–70 (in Russian)

[14] 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 (in Russian) | DOI

[15] 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

[16] 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

[17] Sazanov V. P., “Analysis of the mechanism of fatigue crack arrest in a cylindrical notched specimen”, Vestnik of Samara University. Aerospace and Mechanical Engineering, 17:1 (2018), 160–169 (in Russian) | DOI

[18] Doremus L., Cormier J., Villechaise P., Henaff G., Nadot Y., Pierret S., “Influence of residual stresses on the fatigue crack growth from surface anomalies in a nickel-based superalloy”, Materials Science and Engineering: A, 644 (2015), 234–246 | DOI

[19] Fleury R. M. N., Nowell D., “Evaluating the influence of residual stresses and surface damage on fatigue life of nickel superalloys”, International Journal of Fatigue, 105 (2017), 27–33 | DOI

[20] Vakulyuk V. S., Sazanov V. P., Shadrin V. K., Mikushev N. N., Zlobin A. S., “Thermoelasticity method application on finite elements modeling of residual strained state in surface hardened parts”, Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 16:4 (2014), 168–174 (in Russian)

[21] Surgutanov N. A., “Influence of crack depth on the stress intensity coefficient in notched and smooth plates”, Vestnik of Samara University. Aerospace and Mechanical Engineering, 16:1 (2017), 176–185 (in Russian) | DOI

[22] 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

[23] Radchenko V. P., Shishkin D. M., “The method of reconstruction of residual stresses in a prismatic specimen with a notch of a semicircular profile after advanced surface plastic deformation”, Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 20:4 (2020), 478–492 (in Russian) | DOI

[24] 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

[25] Zimmermann M., Klemenz M., Schulze V., “Literature review on shot peening simulation”, International Journal of Computational Materials Science and Surface Engineering, 3:4 (2010), 289–310 | DOI

[26] Purohit R., Verma C. S., Rana R. S., Dwivedi R., Dwivedi S., “Simulation of shot peening process”, Materials Today: Proceedings, 4:2 (2017), 1244–1251 | DOI

[27] Xie L., Wang C., Wang L., Wang Z., Jiang C., Lu W., Ji V., “Numerical analysis and experimental validation on residual stress distribution of titanium matrix composite after shot peening treatment”, Mechanics of Materials, 99 (2016), 2–8 | DOI

[28] Jebahi M., Gakwaya A., Levesque J., Mechri O., Ba K., “Robust methodology to simulate real shot peening process using discrete-continuum coupling method”, International Journal of Mechanical Sciences, 107 (2016), 21–33 | DOI

[29] Keller I. E., Trofimov V. N., Vladykin A. V., Plyusnin 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

[30] 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”, Vestnik UGATU, 19:2 (68) (2015), 35–40 (in Russian)

[31] Pavlov V. F., Sazanov V. P., Vakulyuk V. S., Shadrin V. K., “Initials deformations employment in the study of harden parts residual stress strained state”, Pumps. Turbines. Systems, 2019, no. 1 (30), 76–81 (in Russian)

[32] Radchenko V. P., Eremin Yu. A., Rheological Deformation and Fracture of Materials and Structural Elements, Mashinostroenie-1, M., 2004, 265 pp. (in Russian)