On the features of inhomogeneous residual stress identification using the digital speckle interferometry and the hole-drilling method

A phenomenological approach to the actual problem of determining the inhomogeneous residual stress-strain state in the components of high-tech engineering systems at the stages of their design and operation is presented. The approach is based on physical and mechanical methods of measuring displacements. Current physical models describe the physical regularities of the residual states attributed to changes in the structure by the interaction of defects and dislocations in the field of micro- and meso-stresses. At the same time, there are the problems of the transition to the macrolevel, the construction of multilevel models, and the conversion of these models in engineering practice. In the framework of phenomenological approaches, in the general case, the solution of this problem requires the solution of three-dimensional inverse problems of thermoelasticity. A well-known mechanical method for determining a uniform field of residual elastic stresses recommended by ASTM E837 is described. The method proposed earlier by one of the authors for determining an inhomogeneous (in the plane) field of residual elastic stresses is discussed. A method of the three-dimensional inhomogeneous residual elastic stress-strain state determination based on the experimental determination of the displacement vector components by the method of step-by-step point hole-drilling and data of digital speckle interferometry and digital image correlation is developed. The constitutive relations for the components of the displacement vector are written in the form of Volterra integral operators. The basic operator functions are the functions of four variables, i.e., the coordinates of the cylindrical system (r, θ, z) associated with the hole, and the hole depth h. A method for verification of the basic functions is presented. The problem is reduced to the determination of three displacement functions of three variables: hole radius r, h, and z. Numerical simulation of basic functions is carried out. The obtained results are consistent with the known experimental data and calculated values of the deformation on the surface depending on the depth of the hole according to the ASTM E837 Standard.

1. Fairfax E. J., Steinzig M. A. Summary of Failures Caused by Residual Stresses / Conf. Proc. of the Soc. for Exp. Mech. Series. — Springer, 2015. P. 209 – 214.

2. Popov A. L., Kozintsev V. M., Chelyubeev D. A., Levitin A. L. Hole-Drilling Method in Residual Stress Diagnostics / Mechanics of Solids. 2021. N 56. P. 1320 – 1339. DOI: 10.3103/S0025654421070190

3. Problems of Strength, Technogenic Safety and Structural Materials Science / Ed. N. A. Makhutov, Yu. G. Matvienko, A. N. Romanov. — Moscow: Lenand, 2018. — 720 p. [in Russian].

4. Monakhov A. D., Yakovlev N. O., Avtaev V. V., Kotova E. A. Destructive methods of residual stress determination / Tr. VIAM. 2021. N 9(103). P. 95 – 104 [in Russian]. DOI: 10.18577/2307-6046-2021-0-9-95-104

5. Makhutov N. A., Gadenin M. M., Odintsev I. N., Razumovsky I. A. Elaboration of the methods for calculation and experimental determination of local residual stresses at complex loading spectra / Probl. Mashinostr. Nadezhn. Mashin. 2015. N 6. P. 53 – 62 [in Russian].

6. Vatulyan A. O., Dudarev V. V., Nedin R. D. Prestressing: Modeling and Identification. — Rostov-on-Don: Izd. Yuzh. Fed. Univ., 2014. — 206 p. [in Russian].

7. Odintsev I. N., Plugatar T. P., Plotnikov A. S. Practical aspects of the application of destructive methods for determining of residual stresses in combination with electronic speckle interferometry / XII All-Russian Congress on fundamental problems of theoretical and applied mechanics in 4 volumes: Ufa, 2019. P. 731 – 733 [in Russian]. DOI: 10.22226/2410-3535-2019-congress-v3

8. Schajer G. S. Universal Calibration Constants for Strain Gauge Hole Drilling Residual Stress Measurements / Experimental Mechanics. 2022. N 62. P. 351 – 358. DOI: 10.1007/s11340-021-00771-0

9. Schajer G. S. Optical Hole Drilling Residual Stress Calculations Using Strain Gauge Formalism / Experimental Mechanics. 2021. N 61. P. 1369 – 1380. DOI: 10.1007/s11340-021-00740-7

10. Harrington J., Schajer G. S. Measurement of Structural Stresses by Hole-Drilling and DIC / Experimental and Applied Mechanics. 2017. N 4. DOI: 10.1007/978-3-319-42028-8_11

11. Cohen R., Noyan I. C. Residual stress — measurement by diffraction and interpretation / Springer Ser. On Mater. Res. And Eng. — Springer-Verlag, 1987. P. 215 – 226.

12. Guo J., Fu H., Pan B., Kang R. Recent progress of residual stress measurement methods: A review / Chinese Journal of Aeronautics. 2021. N 34. P. 54 – 78. DOI: 10.1016/j.cja.2019.10.010

13. Non-destructive testing / Ed. V. V. Klyuev in 8 volumes. — 2005, 2006 [in Russian].

14. Karakozov E., Odintsev I., Plotnikov A., Plugatar T. Determination of High-Gradient Components of Residual Stress by Data of Test Hole Drilling Method / IOP Conf. Series: Mat. Sci. and Eng. Int. Conf. MIKMUS-2019. 2020. P. 90 – 93 [in Russian].

15. Zavoychinskaya E. B. On the Theory of Scale Structural Fatigue of Metals at the Proportional Loading / Journal of Physics. 2020. N 1431. P. 012024-012032. DOI: 10.1088/1742-6596/1431/1/012024

16. Mironov S., Ozerov M., Kalinenko A., et al. On the relationship between microstructure and residual stress in laser- shock-peened Ti-6Al-4V / Journal of Alloys and Compounds. 2022. N 163383. DOI: 10.1016/j.jallcom.2021.163383

17. Ovchinnikov E. I., Volegov P. S. Study of the stress-strain state of crystallites in the framework of residual mesostress determinstion in the model of inelastic deformation of a polycrystal / Vestn. Tambov. Univ. Ser. Estestv. Tekhn. Nauki. 2016. Vol. 21. N 3. P. 1199 – 1201 [in Russian]. DOI: 10.20310/1810-0198-2016-21-3-1199-1202

18. Seifi R., Salimi-Majd D. Effects of Plasticity on Residual Stresses Measurement by Hole Drilling Method / Mechanics of Materials. 2012. Vol. 53. P. 72 – 79. DOI: 10.1016/j.mechmat.2012.05.009

19. Anpilov A. V., Kisilev A. S., Larkin A. I., et al., Determination of residual welding stresses based on the combined holographic interferometry and finite element methods. — Moscow: MIFI, 2007. — 124 p.

20. Apal’kov A. A., Odintsev I. N., Plotnikov A. S. Estimation of Range of Reliable Measurements of Residual Stresses by Hole Drilling Method / Inorganic Materials. 2017. Vol. 53. N 15. P. 1496 – 1501. DOI: 10.1134/S0020168517150031

21. Plotnikov A. S. Hole-drilling method for residual stress determining: current state and perspective / Sci. Proc. of the VII Int. Sci. Conf. «Fundamental Research and Innovative Technologies in Mech. Eng». — Moscow: IMASh RAN, 2021. P. 197 – 199 [in Russian].

22. Apalkov A. A., Odintsev I. N., Plotnikov A. S. Evaluation of the reliable measurement range of residual stresses by drilling holes / Industr. Lab. Mater. Diagn. 2016. Vol. 82. N 2. P. 47 – 52 [in Russian].

23. Plugatar T. P., Odintsev I. N., Plotnikov A. S. A Study of Residual Stress Distributions in Case-Hardened Material Layers / AIP Conference Proceedings 2315. 2020. 040028. DOI: 10.1063/5.0037301

24. Peng Y., Zhao J., Chen L., Dong J. A residual stress measurement combining blind-hole drilling and digital image correlation approach / Journal of Constructional Steel Research. 2021. N 176. 10634. DOI: 10.1016/j.jcsr.2020.106346

25. Hagara M., Trebun F., Pástor M., et al. Analysis of the aspects of residual stresses quantification performed by 3D DIC combined with standardized hole-drilling method / Measurement. 2019. N 137. P. 238 – 256. DOI: 10.1016/j.measurement.2019.01.028

26. Olson M. D., DeWald A. T., Hill M. R. Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator / Exper. Mech. 2021. N 61. P. 549 – 564. DOI: 10.1007/s11340-020-00679-1

27. Pineda O. J. O. Investigation of the measurement of through- thickness residual stress by combining digital speckle pattern interferometry and the slitting method. — Florianópolis, 2020. — 89 p.

28. Pástor M., Hagara M., Virgala I., et al. Design of a Unique Device for Residual Stresses Quantification by the Drilling Method Combining the PhotoStress and Digital Image Correlation / Materials. 2021. Vol. 14. N 314. DOI: 10.3390/ma14020314

29. Rahimi S., Violatos I. Comparison Between Surface and Near-Surface Residual Stress Measurement Techniques Using a Standard Four-Point-Bend Specimen / Exp. Mech. 2022. N 62. P. 223 – 236. DOI: 10.1007/s11340-021-00779-6

30. Razumovskii I. A., Usov S. M. Development of the Hole-Drilling Method as Applied to the Study of Inhomogeneous Residual Stress Fields / Journal of Machinery Manufacture and Reliability. 2021. Vol. 50. N 8. P. 727 – 734. DOI: 10.3103/S1052618821080100

31. Kohri A., Mikami T., Suzuki Y. Residual Stress Measurement of the Engineering Plastics by the Hole-Drilling Strain- Gage Method / ECRS-10 Materials Research Forum LLC Materials Research Proceedings. 2018. N 6. P. 101 – 106. DOI: 10.21741/9781945291890-17

32. Wern H. Finite-element solutions for mechanical drilling methods: A new integral formalism / Journal of Computational and Applied Mathematics. 1995. N 63. P. 365 – 372.

33. Release 2021R1 Documentation for ANSYS, ANSYS Inc..

34. Razumovskii I. A., Chernyatin A. S. Determination of workload and defectiveness of structural elements based on minimization of displacements between experimental and calculated data / Industr. Lab. Mater. Diagn. 2012. Vol. 78. N 1. P. 71 – 78 [in Russian].

35. Schajer G. S. Advances in Hole-Drilling Residual Stress Measurement / Experimental Mechanics. 2010. Vol. 50. P. 159 – 168. DOI: 10.1007/s11340-009-9228-7