On the reconstruction of residual stresses and strains of~a~plate after shot peening

I. E. Keller ; V. N. Trofimov ; A. Vladykin ; V. V. Plyusnin ; D. S. Petukhov ; I. Vindokurov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 1, pp. 40-64.

Résumé

The subject of this research is a mathematical description of the shape and the stress-strain state of a steel plate subjected to unilateral shot peening, its experimental verification and application of the results for verification of methods for reconstruction of residual stress and strain fields according to experimental data. Such plate is used in manufacturing as a calibrating sample to determine of shot peening duration required for formation of proper compressive tangential stress in the surface layer of the processed product. The method of calibration is convenient and widely applied in different technologies of surface hardening. In that case the source of the residual stresses is plastic strains in surface layer produced by shot peening. For the statement of the problem a plastic strain tensor field is defined up to an arbitrary function. The shape and the stress-strain state of an elastic plate with the surface layer of plastic strains were calculated numerically. The qualitative behavior of numerical solution allowed us to accept the set of hypotheses to find an analytical solution of the spatial problem of elasticity theory and to weaken the boundary conditions. The exact solution has been found analytically. Within the framework of the plane stress state along the thickness and transverse directions, the result exactly corresponds to the Davidenkov–Birger formula connected the tangential residual stress distribution on depth with the function of deflections. An explicit formula for the dependence of the residual (plastic) deformation on the thickness coordinate is obtained. Sources of errors of the received expressions and methods of their correction are analyzed. An experiment has been carried out on the one-sided shot peening of calibration plate made of hardened 65G steel, for which the layer-by-layer etching of the treated surface and the measurement of the flexure of the plate were made (by Davidenkov method). The profiles of residual stresses and strains were reconstructed numerically with reasonable accuracy using the obtained experimental data. The result is applicable to a wide class of problems for elastic bodies with hardened surface layers. It may serve as a base for experimental research of such problems, help to formulate hypotheses and test them by experiment, help to study relation between physical fields in asymptotic case, help to verify applicability of different ways to account residual stresses in numerical solution. The solution found can be used for verification of stress and displacement fields in different cases of preliminarily stressed shell elements in engineering software for calculation of fatigue endurance of different machine parts with hardened surface layer. It also seems to be a reference for the study of surface-hardened bodies with curved free boundary, to which most of the practically important tasks are reduced.

Détail

Keywords: residual stresses, boundary layer, shot peening, surface treatment, experiment
Mots-clés : calculation, exact solution, reconstruction.

Bibliographie

[1] Kopp R., Schulz J., “Flexible sheet forming technology by double-sided simultaneous shot peen forming”, CIRP Annals, 51:1 (2002), 195–198 | DOI

[2] Dounde A. A., Seemikeri C. Y., Tanpure P. R., “Study of shot peening process and their effect on surface properties: A Review”, International Journal of Engineering, Business and Enterprise Applications (IJEBEA), 2:12 (2015), 104–107

[3] Badreddine J., Rouhaud E., Micoulaut M., Remy S., “Simulation of shot dynamics for ultrasonic shot peening: Effects of process parameters”, International Journal of Mechanical Sciences, 82 (2014), 179–190 | DOI

[4] Liu Yu, Wang L., Wang D., “Finite element modeling of ultrasonic surface rolling process”, Journal of Materials Processing Technology, 211:12 (2011), 2106–2113 | DOI

[5] Han B., Ju D. Y., “Compressive residual stress induced by water cavitation peening: A finite element analysis”, Materials and Design, 30:8 (2009), 3325–3332 | DOI

[6] Champaigne J., Shot Peening Overview, 2001, 37 pp. Retrieved from (February 14, 2018) https://www.shotpeener.com/library/pdf/2001012.pdf

[7] Li J. K., Mei Y., Duo W., Renzhi W., “Mechanical approach to the residual stress field induced by shot peening”, Materials Science and Engineering: A, 147:2 (1991), 167–173 | DOI

[8] Franchim A. S., de Campos V. S., Travessa D. N., de Moura Neto C., “Analytical modelling for residual stresses produced by shot peening”, Materials and Design, 30:5 (2009), 1556–1560 | DOI

[9] Sherafatnia K., Farrahi G.H., Mahmoudi A.H., Ghasemi A., “Experimental measurement and analytical determination of shot peening residual stresses considering friction and real unloading behavior”, Materials Science and Engineering: A, 657:7 (2016), 309–321 | DOI

[10] Davis J., Ramulu M., “A study of the residual stress induced by shot peening for an isotropic material based on Prager’s yield criterion for combined stresses”, Meccanica, 50:6 (2015), 1593–1604 | DOI | MR | Zbl

[11] 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

[12] Rouhaud E., Deslaef D., Lu J., Chaboche J.-L., “Modeling of Residual Stress, Shot Peening”, Handbook on Residual Stress, eds. Jian Lu, Society of Experimental Mechanics, 2005, 116–148

[13] 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”, Comptes Rendus Mécanique, 344:4–5 (2016), 355–374 | DOI

[14] Musinski W. D., McDowell D. L., “On the eigenstrain application of shot-peened residual stresses within a crystal plasticity framework: Application to Ni-base superalloy specimens”, International Journal of Mechanical Sciences, 100 (2015), 195–208 | DOI

[15] Bhuvaraghan B., Srinivasan R.M., Maffeo B., “Optimization of the fatigue strength of materials due to shot peening: A survey”, IJSCS–Mechanics and Applications, 2:2 (2010), 33–63 Retrieved from (February 14, 2018) https://journals.tdl.org/ijscs/index.php/ijscs/article/view/2338/2021

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

[17] Xie L., Wang Ch., Wang L., Wang Zh., Jiang Ch., 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

[18] Jebahi M., Gakwaya A., Lévesque 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

[19] Birger I. A., Ostatochnye napriazheniia [Residual Stresses], Mashgiz, Moscow, 1963, 232 pp. (In Russian)

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

[21] 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)

[22] Ivanov S. I., “The Way to Determine the Residual Stresses in a Cylinder by Using the Rings and Stripes Method”, Ostatochnye napriazheniia [Residual Stresses], KuAI, Kuibyshev, 1971, 32–42 (In Russian)

[23] 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”, J. Appl. Mech. Tech. Phys., 52:2 (2011), 303–310 | DOI | Zbl

[24] Zakharova 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 (2015), 21–27 (In Russian) | MR

[25] 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 (2015), 35–40 (In Russian)

[26] Sazanov V. P., Semenova O. Yu., Kirpichev V. A., Vakulyuk V. S., “Mathematical modeling of initial deformations in surface hardened parts for the choice of a reference specimen”, Vestnik UGATU, 20:3 (2016), 31–37 (In Russian)

[27] Saushkin M. N., Radchenko V. P., Kurov A. Yu., “Method of calculating residual stresses in semicircular notches in a surface hardened hollow cylindrical specimen”, J. Appl. Mech. Tech. Phys., 54:4 (2013), 644–650 | DOI | Zbl

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

[29] Kuznetsov N. D., Tseitlin V. I., Volkov V. I., Tekhnologicheskie metody povysheniia nadezhnosti detalei mashin [Technological Techniques for Improving Reliability of Machine Parts], Mashinostroenie, Moscow, 1993, 304 pp. (In Russian)

[30] Mattsen R. L., Fonda H. E., Peening Intensity Measurement, Memorandum Report S-200-9C, General Motors, March, 1945, 13 pp.

[31] Lurie A. I., “To the theory of thick plates”, Prikl. Mat. Mekh., 6:2–3 (1942), 151–168 (In Rusiian)

[32] Aksentian O. K., Vorovich I. I., “The state of stress in a thin plate”, J. Appl. Math. Mech., 27:6 (1963), 1621–1643 | DOI | MR | Zbl

[33] Vorovich I. I., Malkina O. S., “The state op stress in a thick plate”, J. Appl. Math. Mech., 31:2 (1967), 252–264 | DOI | MR | Zbl

[34] Ustinov Yu. A., “The structure of the boundary layer in laminated plates”, Dokl. Akad. Nauk SSSR, 229:2 (1976), 325–328 (In Russian) | MR | Zbl

[35] Merkulova N. S., Monitoring of residual stresses at the installation for the Automation of the Residual Stresses Determination Process (ARSDP), The procedures manual, NIAT PI 1.4.804-84, National Institute of Aviation Technologies, Moscow, 1985, 50 pp. (In Russian)

[36] Keller I. E., Tenzornoe ischislenie [Tensor Calculus], Lan', St. Petersburg, 2012, 176 pp. (In Russian)

[37] Koiter W. T., “General theorems of elastic-plastic solids”, Progress in Solid Mechanics, v. 1, ed. J. N. Sneddon, R. Hill, North Holland, Amsterdam, 1960, 167–221 | MR

[38] Zarka J., Frelat J., Inglebert G., Kasmai-Navidi P., A New Approach in Inelastic Analysis of Structures, CADLM, Gif-sur-Yvette, France, 1990, 300 pp.

[39] Birger I. A., Kruglye plastinki i obolochki vrashcheniia [Round Plates and Shells of Revolution], Oborongiz, Moscow, 1961, 368 pp. (In Russian) | MR