Vyatka State University, Kirov, Russia:

A. V. Udalov, Cand. Eng., Associate Professor, Dept. of Materials Science and Fundamentals of Design, e-mail: a.v.udalov1960@gmail.com
A. A. Udalov, Senior Lecturer, Basic Dept. of Metallurgy, e-mail: a.a.udalov1992@gmail.com

The hardness of the material hardened in the zone of penetration of the indenter is recorded by standard methods of measuring hardness. This disadvantage is the main reason for the appearance of the size effect (indentation size effect) and a decrease in the measurement accuracy. The aim of the work is to develop a mechanical method for determining the hardness of metals and alloys without taking into account hardening in the zone of penetration of the indenter. Based on the linear relationship between the hardness and the resistance to deformation of the material, a formula was obtained for determining the hardness without taking into account the effect of hardening in the indentation zone, which makes it possible to increase the accuracy of mechanical methods for determining the hardness, expands their functionality and scope. The essence of the proposed method is illustrated by the example of determining the hardness of specimens made of steel 20, subjected to compression at various degrees of deformation. Compression test method was used to construct a hardening curve, which was used to determine the resistance to deformation of the material in the zone of penetration of the indenter and then the hardness of the material without taking into account the hardening in the zone of penetration of the indenter. The developed method for measuring the hardness of metals and alloys makes it possible to increase the accuracy of mechanical methods, to avoid the influence of the indentation size effect on the final result, and can be used to optimize the technologies for manufacturing parts.

1. Flossdorf F. J., Wieland H. J. Material science and steel testing technologies. Chernye Metally. 2010. No. 5. pp. 57–64.
2. Udalov А. V. Study of the influence of the test load on indentation size effect during measuring the materials hardness by a spherical indenter. Chernye Metally. 2020. No. 9. pp. 62–67.
3. Oreshko Е. I., Utkin D. А., Erasov V. S., Lyakhov А. А. Methods for measuring the hardness of materials (review). Trudy VIAM: elektronny nauchno-tekhnicheskiy zhurnal. 2020. No. 1 (85). pp. 10.
4. Udalov A. A., Parshin S. V., Udalov A. V. Indentation size effect during measuring the hardness of materials by pyramidal indenter. Materials Today: Proceedings. 2019. Vol. 19, Iss. 5. pp. 2034–2036.
5. Udalov A. A., Udalov A. V., Parshin S. V. Indentation Size Effect during Measuring the Hardness of Materials by Spherical Indenter. Solid State Phenomena. 2020. Vol. 299. pp. 1172–1177.
6. Udalov A. V., Parshin S. V., Udalov A. A. Determination of the resistance to deformation of metals and alloys by the indenter penetration method. Deformatsiya i razrushenie materialov. 2019. No. 4. pp. 40–44.
7. Huang Y., Gao H., Nix W. D., Hutchinson J. W. Mechanism-based strain gradient plasticity — II. Analysis. Journal of the Mechanics and Physics of Solids. 2000. Vol. 48, Iss. 1. pp. 99–128.
8. Ruiz-Moreno A., Hähner P. Indentation size effects of ferritic/martensitic steels: a comparative experimental and modelling study. Materials & Design. 2018. Vol. 145. pp. 168–180.
9. Rashid K., Abu Al-Rub, Abu Faruk N. M. Prediction of Micro and Nano Indentation Size Effects from Spherical Indenters. Mechanics of Advanced Materials and Structures. 2012. Vol. 19, Iss. 1-3. pp. 119–128.
10. Pharr G. M., Herbert E. G., Gao Y. The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Annual Review of Materials Research. 2010. Vol. 40, Iss. 1. pp. 271–292.
11. Swadener J. G., George E. P., Pharr G. M. The correlation of the indentation size effect measured with indenters of various shapes. Journal of the Mechanics and Physics of Solids. 2002. Vol. 50, Iss. 4. pp. 681–694.
12. Voyiadjis G., Yaghoobi M. Review of Nanoindentation Size Effect: Experiments and Atomistic Simulation. Crystals. 2017. Vol. 7, Iss. 10. pp. 321.
13. Nix W. D., Gao H. Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids. 1998. Vol. 46, Iss. 3. pp. 411–425.
14. Pugno N. M. A general shape/size-effect law for nanoindentation. Acta Materialia. 2007. Vol. 55, Iss. 6. pp. 1947–1953.
15. Matyunin V. М., Dubov А. А., Marchenkov А. Yu. Scale factor in determination of the hardness of metallic materials. Zavodskaya laboratoriya. Diagnostika materialov. 2009. Vol. 75. No. 9. pp. 59–62.
16. Pavlina E. J., Van Tyne C. J. Correlation of Yield Strength and Tensile Strength with Hardness for Steels. Journal of Materials Engineering and Performance. 2008. Vol. 17. pp. 888–893.
17. Rudnitsky V. A., Kren A. P., Lantsman G. A. Determining Yield Strength of Metals by Microindentation with a Spherical Tip. Russian Journal of Nondestructive Testing. 2019. Vol. 55. pp. 162–168.
18. Ngoc-Vinh Nguyen, Viet-Hung Truong, Thai-Hoan Pham, Seung-Eock Kim. Investigating the Relationship Between Hardness and Yield Strength of SS400 Steel Using Nanoindentation. International Journal of Advances in Mechanical and Civil Engineering (IJAMCE). 2017. Vol. 4, Iss. 1. pp. 12–13.
19. Krishna S. Ch., Kumar Gangwar N., Jha K. A., Pant Bh. On the Prediction of Strength from Hardness for Copper Alloys. Journal of Materials. 2013. DOI: 10.1155/2013/352578.
20. Tiryakioğlu M., Robinson J. S., Salazar-Guapuriche M. A., Zhao Y. Y., Eason P. D. Hardness–strength relationships in the aluminum alloy 7010. Materials Science and Engineering. 2015. Vol. 631, Iss. 17. pp. 196–200.
21. Keist J. S., Palmer T. A. Development of strength-hardness relationships in additively manufactured titanium alloy. Materials Science and Engineering. 2017. Vol. 693, Iss. 2. pp. 214–224.
22. GOST 7417–75. Calibrated round steel. Dimensions. Introduced: 01.01.1976.
23. GOST R ISO 6507-1–2007. Metals and alloys. Vickers hardness measurument. Part 1. Test method. Introduced: 01.08.2008.
24. GOST 23677–79. Hardness testing machines for metals. General technical requirements. Introduced: 01.01.1981.