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

#### For citation:

Panfilov I. A., Aizikovich S. M., Vasiliev A. S. Analysis of elastic and elastoplastic models when interpreting nanoindentation results. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 2, pp. 245-253. DOI: 10.18500/1816-9791-2024-24-2-245-253, EDN: CUARKH

Published online:
31.05.2024
Full text:
Language:
Russian
Article type:
Article
UDC:
539.3
EDN:
CUARKH

# Analysis of elastic and elastoplastic models when interpreting nanoindentation results

Autors:
Panfilov Ivan A., Don State Technical University
Aizikovich Sergey M., Don State Technical University
Vasiliev Andrey S. , Don State Technical University
Abstract:

One of the current and widely used non-destructive testing methods for monitoring and determining the elastic properties of materials is nanoindentation. In this case, to interpret the test results, a non-trivial task arises of constructing an adequate mathematical model of the indentation process. As a rule, in many cases, analytical formulas are used that are obtained from an elastic linear formulation of problems about the introduction of a non-deformable stamp into a homogeneous elastic half-space. Currently, the numerical formulation of the problem makes it possible to obtain and use a numerical solution obtained taking into account the complete plastic nonlinear behavior of the material. In this work, a study of contact problems on the introduction of a spherical and conical indenter into an elastoplastic homogeneous half-space was carried out. To verify the numerical solution, the problem of introducing a spherical and conical indenter into an elastic homogeneous half-space was also solved and compared with known analytical solutions. Issues of convergence and tuning of numerical methods, the influence of plasticity and the applicability of analytical solutions are explored. Problems are solved numerically using the finite element method in the Ansys Mechanical software package.

Key words:
Acknowledgments:
This work was supported by the Russian Science Foundation (project No. 22-19-00732).
References:
1. Bulychev S. I., Alekhin V. P. Ispytanie materialov nepreryvnym vdavlivaniem indentora [Testing of Materials by Continuous Indentation of an Indenter]. Moscow, Mashinostroenie, 1990. 224 p. (in Russian).
2. Golovin Yu. I. Nanoindentirovanie i ego vozmozhnosti [Nanoindentation and its Capabilities]. Moscow, Mashinostroenie, 2009. 312 p. (in Russian).
3. Field J. S., Swain M. V. A simple predictive model for spherical indentation. Journal of Materials Research, 1993, vol. 8, iss. 2, pp. 297–306. https://doi.org/10.1557/JMR.1993.0297
4. Oliver W. C., Pharr G. M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research, 1992, vol. 7, iss. 6, pp. 1564–1583. https://doi.org/10.1557/JMR.1992.1564
5. Hertz H. Ueber die Beruhrung fester elastischer Korper.  Journal fur die reine und angewandte Mathematik, 1881, vol. 92, pp. 156–171 (in German). https://doi.org/10.1515/9783112342404-004
6. Dzhonson K. L. Mechanics of Contact. Cambridge, Cambridge University Press, 1987. 452 p. (Russ. ed.: Moscow, Mir, 1989. 510 p.).
7. Galin L. A. Kontaktnye zadachi teorii uprugosti [Contact Problems of the Theory of Elasticity]. Moscow, GITTL, 1953. 264 p. (in Russian).
8. He L. H., Swain M. V. Nanoindentation derived stress-strain properties of dental materials. Dental Materials, 2007, vol. 23, iss. 7, pp. 814–821. https://doi.org/10.1016/j.dental.2006.06.017
9. Potelezhko V. P., Fillipov A. P. Contact problem for a plate lying on an elastic foundation. Soviet Applied Mechanics, 1967, vol. 3, iss. 1, pp. 87–91. https://doi.org/10.1007/BF00885463
10. Landau L. D., Lifshts E. M. Teoreticheskaya fizika. T. 7: Teoriya uprugosti [Theoretical Physics. Vol. 7: Theory of Elasticity]. Moscow, Nauka, 1987. 248 p. (in Russian).
11. Kral E. R., Komvopoulos K., Bogy D. B. Elastic-plastic finite element analysis of repeated indentation of a half-space by a rigid sphere. Journal of Applied Mechanics, 1993, vol. 60, iss. 4, pp. 829–841. https://doi.org/10.1115/1.2900991
12. Mekhanika kontaktnykh vzaimodeystviy [Vorovich I. I., Aleksandrov V. M. (eds.) Mechanics of Contact Interactions]. Moscow, Fizmatlit, 2001. 672 p. (in Russian).
13. Dub S. N. Curves of elasto-plastic deformation of thin coatings obtained in depth-sensing indentation experiments. MRS Symposium Proceedings, 1998, vol. 505, pp. 223–228. https://doi.org/10.1557/PROC-505-223
14. El-Sherbiney M. G. D., Halling J. The Hertzian contact of surfaces covered with metallic films. Wear, 1996, vol. 40, iss. 3, pp. 325–337. https://doi.org/10.1016/0043-1648(76)90124-1
15. Pharr G. M., Oliver W. C. Measurement of thin film mechanical properties using nanoindentation. MRS Bulletin, 1992, vol. 17, pp. 28–33. https://doi.org/10.1557/S0883769400041634
16. Aizikovich S. M. Asymptotic solutions of contact problems of the theory of elasticity for media inhomogeneous in depth. Journal of Applied Mathematics and Mechanics, 1982, vol. 46, iss. 1, pp. 116–124. https://doi.org/10.1016/0021-8928(82)90091-0, EDN: XUXFLE
17. Vasiliev A. S., Volkov S. S., Aizikovich S. M. Approximated analytical solution of a problem on indentation of an electro-elastic half-space with inhomogeneous coating by a conductive punch. Doklady Physics, 2018, vol. 63, iss. 1, pp. 18–22. https://doi.org/10.1134/S1028335818010020, EDN: YVUVSK
18. Volkov S. S., Vasiliev A. S., Aizikovich S. M., Seleznev N. M., Leontieva A. V. Stress-strain state of an elastic soft functionally-graded coating subjected to indentation by a spherical punch. PNRPU Mechanics Bulletin, 2016, iss. 4, pр. 20–34 (in Russian). https://doi.org/10.15593/perm.mech/2016.4.02, EDN: XSESAL
19. Vasiliev A. S., Volkov S. S., Aizikovich S. M., Litvinenko A. N. Indentation of an elastic half-space reinforced with a functionally graded interlayer by a conical punch. Materials Physics and Mechanics, 2018, vol. 40, iss. 2, pp. 254–260. https://doi.org/10.18720/MPM.4022018_14, EDN: VPDWMG
20. Vasiliev A. S., Volkov S. S., Aizikovich S. M. Indentation of an axisymmetric punch into an elastic transversely-isotropic half-space with functionally graded transversely-isotropic coating. Materials Physics and Mechanics, 2016, vol. 28, iss. 1–2, pp. 11–15. EDN: XCQJUT
21. Sadyrin E., Vasiliev A., Volkov S. Mathematical modeling of experiment on Berkovich nanoindentation of ZrN coating on steel substrate. Acta Polytechnica CTU Proceedings, 2020, vol. 27: Proceedings of the 14th International Conference on Local Mechanical Properties – LMP 2019, pp. 18–21. https://doi.org/10.14311/APP.2020.27.0018
22. Ovcharenko A., Halperin G., Verberne G., Etsion I. In situ investigation of the contact area in elastic-plastic spherical contact during loading-unloading. Tribology Letters, 2007, vol. 25, pp. 153–160. https://doi.org/10.1007/s11249-006-9164-y