Approach to the investigation of residual stress distributions in specimens from rolling sheet

The article presents the results of methodological developments aimed at studying the distribution of residual stresses across the thickness of thin-sheet rolled materials. The specimens subject to direct testing are narrow strips cut from the workpiece along and across the rolling direction. The determination of stresses in the specimen is performed by the method of gradually deepening transverse slit. As a registered response, it is proposed to consider the angle of the arising mutual rotation of the end parts of the sample. For its reliable registration, the most optimal non-contact optical methods should be considered: electronic speckle pattern interferometry or digital image correlation. The choice of a specific one is determined by the test conditions. The procedure for interpreting primary experimental information in terms of residual stresses is formulated as an inverse problem of solid mechanics. Two possible mathematical approaches to data processing are considered, taking into account the incorrectness of the problem statement. Stabilization of the solution is achieved, among other things, through the use of a regularization algorithm. The efficiency of the performed developments is demonstrated by the study’s example of stress distributions in specimens of thin-sheet rolled steel — products of the Novolipetsk Metallurgical Plant. It is shown that different approaches to mathematical processing give practically identical results.

1. Kolmogorov G. L., Kuznetsova E. V., Tiunov V. V. Technological residual stresses and their influence on the durability and reliability of metal products. — Perm: Izd. Perm. Nats. Issl. Politekhn. Univ., 2012. — 226 p. [in Russian].

2. Burkin S. P., Shimov G. V., Andryukova E. A. Residual stresses in metal products. — Ekaterinburg: Izd. Ural. Univ., 2015. — 248 p. [in Russian].

3. Bolobanova N. L., Antonov P. V., Kotov K. A., Yusupov V. S. Modeling and research of forming of rolled steel sheets and improvement of its production processes. — Cherepovets: ChGU, 2023. — 262 p. [in Russian].

4. Kajal G., Tyagi M. R., Kumar G. A review on the effect of residual stresses in incremental sheet metal forming used in automotive and medical sectors / Mater. Today: Proc. 2023. Vol. 78. Part 3. P. 524 – 534. DOI: 10.1016/j.matpr.2022.11.235

5. Struzhanov V. V. On residual stresses after rolling and delamination of two-layer strips / Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki. 2010. No. 5(21). P. 55 – 63 [in Russian]. DOI: 10.14498/vsgtu823

6. Maksimov E. A., Shatalov R. L., Shalamov V. G. Development of a methodology for calculating residual stresses and springback parameters of a sheet on a roller straightening machine / Izv. Vuzov. Cher. Met. 2021. Vol. 64. No. 1. P. 14 – 20 [in Russian]. DOI: 10.17073/0368-0797-2021-1-14-20

7. Witek S., Milenin A. Numerical analysis of temperature and residual stresses in hot-rolled steel strip during cooling in coils / Arch. Civil Mech. Eng. 2018. Vol. 18. Issue 2. P. 659 – 668. DOI: 10.1016/j.acme.2017.11.002

8. Milenin A., Kuziak R., Lech-Grega M., et al. Numerical modeling and experimental identification of residual stresses in hot-rolled strips / Arch. Civil Mech. Eng. 2016. Vol. 16. Issue 1. P. 125 – 134. DOI: 10.1016/j.acme.2015.08.002

9. Díaz A., Cuesta I. I., Alegre J. M., et al. Residual stresses in cold-formed steel members: review of measurement methods and numerical modelling / Thin-Walled Structures. 2021. Vol. 159. DOI: 10.1016/j.tws.2020.107335

10. Kargapol’tsev S. K., Gozbenko V. E., Bol’shakov R. S. On the issue of assessing the presence of residual stresses on aluminum plates / Sist. Met. Tekhnol. 2023. No. 3(59). P. 52 – 58 [in Russian].

11. Ponomaryev K. E., Strelnikov I. V., Antonov A. A., Bondarenko A. A. Application of laser interferometry to the choice of processing modes by the criterion of the residual stress level / Industr. Lab. Mater. Diagn. 2020. Vol. 86. No. 2. P. 54 – 60 [in Russian]. DOI: 10.26896/1028-6861-2020-86-2-54-60

12. Khlybov A. A., Ryabov D. A., Minkov K. A. Acoustic control of the residual stresses in steel 5KhNM samples. Industrial laboratory / Industr. Lab. Mater. Diagn. 2020. Vol. 86. No. 9. P. 30 – 36 [in Russian]. DOI: 10.26896/1028-6861-2020-86-9-30-36

13. Degtyareva S. P., Vorozhtsova E. V., Peskishev S. A. X-ray determination and modeling of macro-stresses in products / Industr. Lab. Mater. Diagn. 2021. Vol. 87. No. 2. P. 38 – 42 [in Russian]. DOI: 10.26896/1028-6861-2021-87-2-38-42

14. Razumovskii I. A., Odintsev I. N., Plugatar’ T. P. Methodology of experimental and computational study of residual stresses in structural elements / Akt. Vopr. Mashinoved. 2022. Vol. 11. P. 116 – 119 [in Russian].

15. Makhutov N. A., Razumovskii I. A. Methods for analysis of the fields of residual stresses in spatial structural components / Industr. Lab. Mater. Diagn. 2017. Vol. 83. No. 1. Part I. P. 56 – 64 [in Russian].

16. Monakhov A. D., Yakovlev N. O., Avtaev V. V., Kotova E. A. Destructive methods for determining residual stresses / Tr. VIAM. 2021. Vol. 103. No. 9. P. 95 – 104 [in Russian]. DOI: 10.18577/2307-6046-2021-0-9-95-104

17. Usov S. M., Razumovsky I. A., Odintsev I. A. Study of inhomogeneous fields of residual stresses using step-by-step enlarged crack method in combination with electronic speckle pattern interferometry (ESPI) / Industr. Lab. Mater. Diagn. 2021. Vol. 87. No. 9. P. 50 – 58 [in Russian]. DOI: 10.26896/1028-6861-2021-87-9-50-58

18. Plotnikov A. S., Zavoychinskaya E. B. On the features of inhomogeneous residual stress identification using the digital speckle interferometry and the hole-drilling method / Industr. Lab. Mater. Diagn. 2023. Vol. 89. No. 12. P. 60 – 73 [in Russian]. DOI: 10.26896/1028-6861-2023-89-12-60-73

19. Dreiera S., Denkenaa B. Determination of residual stresses in plate material by layer removal with machine-integrated measurement / Procedia CIRP 24. 2014. P. 103 – 107. DOI: 10.1016/j.procir.2014.07.137

20. Oleinik B. D., Vinokurov N. V., Nurtdinov A. S. Determination of residual surface stresses by etching a cantilever-mounted sample / Deform. Razr. Mater. 2015. No. 4. P. 12 – 16 [in Russian].

21. Belousov Yu. B. Determination of residual stresses during etching of a cantilever-mounted sample / Stroit. Mekh. Inzh. Konstr. Sooruzh. 2016. No. 1. P. 55 – 59 [in Russian].

22. Prime M. B. Residual stress measurement by successive extension of a slot: the crack compliance method / Appl. Mech. Rev. 1999. Vol. 52. No. 2. P. 75 – 96. DOI: 10.1115/1.3098926

23. Prime M. B., Hill M. R. Residual stress, stress relief, and inhomogeneity in aluminum plate / Scripta Mater. 2002. Vol. 46. No. 1. P. 77 – 82. DOI: 10.1016/s1359-6462(01)01201-5

24. Schajer G. S., Prime M. B. Use of inverse solutions for residual stress measurements / J. Eng. Mater. Technol. 2006. Vol. 128. No. 3. P. 375 – 382. DOI: 10.1115/1.2204952

25. Tikhonov A. N., Arsenin V. Ya. Solutions of ill-posed problems. — Washington: Halsted Press, 1977. — 258 p.

26. Plugatar T. P., Odintsev I. N., Plotnikov A. S. A study of residual stress distributions in case-hardened material layers / AIP conference proceedings. 14th Int. Conf. on Mechanics, Resource and Diagnostics of Materials and Structures, MRDMS 2020. Vol. 2315. DOI: 10.1063/5.0037301

27. Odintsev I. N., Plugatar T. P., Volkov A. N. Methodology for studying residual stresses in sheet metal products / Proc. of the 7th Int. Sci. Tech. Conf. «Survivability and Structural Materials Science». 2024. P. 261 – 268 [in Russian].

28. Razumovsky I. A. Interference-optical methods of solid mechanics. — Berlin: Springer, 2011. — 180 p.

29. Sutton M. A., Orteu J. J., Schreier H. Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. — N.-Y.: Springer, 2009. — 332 p.

30. Korn G. A., Korn T. M. Mathematical handbook for scientists and engineers. — N.Y.: McGraw-Hill, 1968. — 1130 p.

31. Goncharskiy A. V., Tikhonov A. N., Yagola A. G., Stepanov V. V. Numerical methods for solving ill-posed problems. — Moscow: Nauka, 1990. — 232 p. [in Russian].

32. Seber G. A., Lee A. J. Linear Regression Analysis. — N.Y.: John Wiley & Sons, 2012. — 592 p.