Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Radchenko V. P., Afanaseva O. S., Glebov V. E. Influence of Residual Stresses on Geometric Parameters of Surface-Strengthened Beam. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 4, pp. 464-478. DOI: 10.18500/1816-9791-2019-19-4-464-478

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 62)
Article type: 

Influence of Residual Stresses on Geometric Parameters of Surface-Strengthened Beam

Radchenko Vladimir P., Samara State Technical University
Afanaseva Olga S., Samara State Technical University
Glebov Victor E., Samara State Technical University

The сomprehensive study of the formation of residual stresses and plastic deformations in prismatic samples of the EP742 alloy after ultrasonic hardening and their influence on the geometric parameters of the beam was conducted. Phenomenological model for the reconstruction of residual stress fields is proposed, and the verification of its adequacy to experimental data with four hardening modes is performed. The correspondence of the calculated and experimental data is observed. To assess the effect of the formed residual stresses on the geometric parameters of the beam the calculation method for initial strains based on using the analogy between the initial (permanent) plastic deformations and temperature deformations in an inhomogeneous temperature field is applied. This enabled us to reduce the consideration of the problem to the boundary value problem of thermoelasticity, which was further solved by numerical methods. The detailed study showed that residual stresses lead to bending effects. For a beam 100 * 10 * 10 mm, the calculated value of the arrow of maximum deflection was 210 um. The kinetics of changes in this quantity is determined depending on the beam thickness which in the calculations ranged from 2 to 10 mm with the same distribution of residual stresses in the hardened layer. It is shown that the magnitude of the deflection nonlinearly increases with a decreasing thickness while with a thickness of 2 mm it is 6.6 mm with a beam length of 100 mm. Illustrated material in the form of graphic and tabular information on the calculation results is given.

  2. Altenberger I., Nalla R. K., Sano Y. On the affect of deep-rolling and laser-peening on the stress-controlled low- and high-cycle fatigue behavior of Ti-6-Al-4V at elevated temperatures up to 550 ∘C. Intern. J. Fatigue, 2012, vol. 44, pp. 292–302. DOI: https://doi.org/10.1016/j.ijfatigue.2012.03.008
  3. Brockman R. A., Braisted W. R., Olson S. E. [et. al.]. Prediction and characterization of residual stresses from laser shock peening. Intern. J. Fatigue, 2012, vol. 36, pp. 96–108. DOI: https://doi.org/10.1016/j.ijfatigue.2011.08.011
  4. McClung R. C. Aliterature survey on the stability and significance of residual stresses during fatigue. Fatigue Fract. Engng. Mater. Struct., 2007, vol. 30, pp. 173–205. DOI: https://doi.org/10.11111/j.1406-2695.2007.01102.x
  5. Soady K. A. Life assessment methodologies incorporating shot peening process effects: mechanistic consideration of residual stresses and strain hardening. 1. Effeact of shot peening on fatigue resistance. Mater. Sci. Technol., 2013, vol. 29, no. 6, pp. 673–651. DOI: https://doi.org/10.1179/1743284713Y.0000000222
  6. 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, 2012, vol. 35, pp. 741–748. DOI: https://doi.org/10.1016/j.matdes.2011.09.055
  7. Pavlov V. F., Kirpichev V. A., Vakuluk V. S. Prognozirovanie soprotivleniya ustalosti poverkhnostno uprochnionnykh detalei po ostatochnym napriazheniyam [Prediction of fatigue resistance of surface reinforced parts by residual stresses]. Samara, Izd-vo STsN RAN, 2012. 125 p. (in Russian).
  8. Kravchenko V. A., Krucilo V. G., Gutman G. N. Termoplasticheskoe uprochnenie – rezerv povyshenija prochnosti i nadjozhnosti detalej mashin [Thermoplastic Hardening – Reserve for Increased Strength and Reliability of Machine Parts]. Samara, Izd-vo SamGTU, 2000. 216 p. (in Russian).
  9. Ivanov S. I. To determination of residual stresses in the cylinder by means of rings and strips. Ostatochnye napriazheniya [Residual tension. Collected papers]. Kujbyshev, Izd-vo KuAI, 1971. Iss. 53, pp. 32–42 (in Russian).
  10. Ivanov S. I. Examination of residual tangential stresses in cylindrical part by means of rings. Ostatochnye napriazheniya [Residual tension. Collected papers]. Kujbyshev, Izd-vo KuAI, 1971. Iss. 53, pp. 107–115 (in Russian).
  11. Davidenkov N. N. Calculation of Residual Stresses in Cold Drawn Tubes. Zeitschrift fur¨ Metallkunde. 1932, vol. 24. no. 25, pp. 25–29.
  12. Birger I. A. Ostatochnye napriazheniya [Residual tension]. Moscow, Mashgiz, 1963. 232 p. (in Russian).
  13. Schajer G. S. Advaces in Hole-Drilling Residual Stress Measurements. Exp. Mech. 2010, vol. 50. no. 2, pp. 159–168. DOI: https://doi.org/10.1007/s11340-009-9228-7
  14. Fitspatrick M. E., Lodini A. Analysis of Residual Stress by Diffraction using Neutron and Synchrotron Radiation. London, CRC Press, 2003. 368 p. DOI: https://doi.org/10.1201/9780203608999
  15. Rouhaud E., Deslaef D., Lu J., Chaboche J.-L. Modeling of residual stress, shot peening. In: Handbook on Residual Stress, ed. Jian Lu. Society of Experimental Mechanics. 2005, pp. 116–148.
  16. Gallitelli D., Boyer D., Gelineau M., Colaitis Y. [et al.]. Simulation of sHot peening: From process parameters to residual stress fields in a structure. Comptes Rendus Mecanique ´ , 2016, vol. 344, no. 4–5, pp. 355–374. DOI: https://doi.org/10.1016/j.crme.2016.02.006
  17. Musinski W. D., McDowell D. L. On the eigenstrain aplication 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
  18. Purohit R., Verma C. S., Rana R. S. Simulation of shot peening process. Material Today: Proceedings, 2017, vol. 4, no. 2, pp. 1244–1251. DOI: https://doi.org/10.1016/j.matpr.2017.01.144
  19. Xie L., Wang Ch., Wang L. [et al.]. Numerical analysis and experimental validation on residual stress distribution of titanium matrix composite after shot peening treatment. Mech. Mat., 2016, vol. 99, pp. 2–8. DOI: https://doi.org/10.1016/j.mechmat.2016.05.005
  20. Jebahi M., Gakwaya A., Levesque J. [et al.]. Robust methodology to simulate real shot pe- ´ ening process using discrete-cotinuum coupling method. Int. J. Mech. Sci., 2016, vol. 107, pp. 21–33. DOI: https://doi.org/10.1016/j.ijmecsci.2016.01.005
  21. Keller S., Chupakhin S., Staron P., Maawad E., Kashaev N., Klusemann B. Experimental and numerical investigation of residual stresses in laser shock peened AA2198. Jour. of Mater. Proc. Tech., 2018, vol. 255, pp. 294–307. DOI: https://doi.org/10.1016/j.j0atprotect.2017.11.023
  22. Badredding J., Rouhaud E., Micoulaut M., Rerny S. Simulation of shot dynamics for ultrasonic shot peening: Effects of process parameters. Int. J. Mech. Sci., 2014, vol. 82, pp. 179–190. DOI: https://doi.org/10.1016/j.ijmecsci.2014.03.006
  23. Pavlov V. F., Stoljarov A. K., Vakuljuk V. S., Kirpichev V. A. Raschiot ostatochnykh napriazheniy v detaliakh s kontsentratorami napriazheniy po pervonachal’nym deformatsiyam [Calculation of residual stresses in parts with stress concentrators by initial deformations]. Samara, Izd-vo SNTs RAN, 2008. 124 p. (in Russian).
  24. Sazanov V. P., Kirpichev V. A., Vakuljuk 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, 2015, vol. 19, no. 2 (68), pp. 35–40 (in Russian).
  25. 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. Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, vol. 22, no. 1, pp. 40–64 (in Russian). DOI: https://doi.org/10.14498/vsgtu1602
  26. Radchenko V. P., Kurov A. Yu. Effect of anisotropy of surface plastic hardening on formation of residual stresses in cylindrical samples with semicircular notch. Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. & Math. Sci.], 2016, vol. 20, no. 4, pp. 675–690 (in Russian). DOI: https://doi.org/10.14498/vsgtu1513
  27. Sazanov V. P., Semenova O. Yu., Pismarov A. V., Churikov D. S. On the influence of the original radial deformations on the development of the fatigue cracks of strengthened parts from construction steels. In: Proc. of the XI All-Russian Scientific Conference with International Participation “Mathematical Modeling and Boundary Value Problems” (May 27–30, 2019, Samara, Russian Federation) : in 2 vols. Samara, Izd-vo SamGTU, 2019. Vol. 1. pp. 168–171 (in Russian).
  28. 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, pp. 93–112 (in Russia). DOI: https://doi.org/10.15593/perm.mech/2016.1.07
  29. 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, pp. 130–147. DOI: https://doi.org/10.15593/perm.mech/2015.1.09
  30. Saushkin M. N., Radchenko V. P., Pavlov V. F. Method of Calculating the fields of residual stresses and plastic strains in cylindrical specimens with allowance for surface hardening anisotropy. Jour. of Appl. Mech. and Tech. Phys., 2011, vol. 52, no. 2, pp. 303–310. DOI: https://doi.org/10.1134/S0021894411020180