Relation of the Mayer Index to the Characteristics of the Power Law of Metal Hardening

Abstract:

The issues of determining the Mayer index depending on the parameters of strain hardening of an elastoplastic body described by the Hollomon equation are considered. The analysis of expressions connecting the engineering uniform deformation with the Mayer index is carried out. A new expression is obtained, a particular case of which is the result obtained by V.M. Matyunin et al. Applying the ratio of the maximum Mayer hardness to the Brinell hardness, the relationship of the ultimate strength to the Brinell hardness, and the Hollomon equation, a new expression of the Mayer law is obtained. The description of the radius of the contact area by a power function of the depth of the indenter insertion allowed us to represent the Mayer index as a ratio of known parameters obtained by finite element modeling for other purposes. The graphical dependences of the results obtained are presented.

• Periodical: Key Engineering Materials (Volume 910)
• Pages: 1040-1048
• DOI: https://doi.org/10.4028/p-96ug56
• Online since: February 2022
• Authors: Petr M. Ogar*, Valery A. Shilin, Elena V. Ugryumova
• Keywords: Hardening Parameters, Indentation Depth, Indentation Radius, Mayer Index, Spherical Indenter, Stress-Strain Curves, Ultimate Strength, Yield Strength

References

[1] P.M. Ogar, D.B. Gorokhov, A.S. Kozhevnikov, Contact problems in hermetic sealing studies of fixed joint, BrGU, Bratsk, (2017).

[2] E. Meyer, Untersuchen uber Harteprufung und Harte. Zeitschrift des Vereins Deutschen Ingenieure. 52 (1908) 645-654.

[3] N.B. Demkin, Contacting rough surfaces, Nauka, Moscow, (1970).

[4] N.K. Myshkin, M.I. Petrokovets, Friction, lubrication, wear. Physical basis and engineering applications of tribology., FIZMATLIT, Moscow, (2007).

[5] A.N. Bolotov, V.V. Meshkov, O.V. Sutyagin, M.V. Vasiliev, Influence of hardening on the characteristics of elastic-plastic contact surface roughness. Bulletin of Samara Scientific Center RAS-tion. 15 (2013) 313-315.

[6] P.M. Ogar, V.A. Tarasov, D.B. Gorokhov, A.V. Turchenko, The account of hardening material characteristics in applying of Meyer's empirical law. Syst. Meth. Tech. 4 (2013) 50-54.

[7] P.M. Ogar, D.B. Gorokhov, Meyer law application for solving problems of surface plastic deformation by spherical indentation. Appl. Mech. & Mat. 788 (2015) 199-204.

DOI: 10.4028/www.scientific.net/amm.788.199

[8] S.I. Bulychev, Transition from indentation diagrams to stress-strain diagrams taking into consideration hardened surface layer. Def. and frac. of mat. 2 (2010) 43-48.

[9] S.I. Bulychev, Hardness and hysteresis at the yield strength. Def. and frac. of mat. 1 (2011) 41-45.

[10] P. Jiang, T. Zhang, Y. Feng, R. Yang, N. Liang, Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach. J. of Mat. Res. 24 (2009) 1045-1053.

DOI: 10.1557/jmr.2009.0108

[11] P.M. Ogar, D.B. Gorokhov, The relationship between the deformation of spherical indentation and tensile deformation. Key Engineering Materials. 723 (2016) 363-368.

DOI: 10.4028/www.scientific.net/kem.723.363

[12] J. H. Hollomon, Tensile Deformation, Trans. Metallurgical Society of AIME. 162 (1945) 268-290.

[13] P.M. Ogar, D.B. Gorokhov, Parameters for elastic-plastic body to calculate contact characteristics under the sphere indentation, Syst. Meth. Tech. 1 (2016) 28-32.

[14] M.P. Markovets, Determining metal mechanical properties by their hardness, Mashinostroenie, Moscow, (1979).

[15] S.I. Bulychev, V.P. Alekhin, Testing of materials by continuous depression of an indenter, Mashinostroenie, Moscow, (1990).

[16] M. Gaško, G. Rosenberg, Correlation between hardness and tensile properties in ultra-high strength dual phase steels – short communication, Mat. Eng. 18 (2011) 155-159.

[17] A.V. Grushko, Determination of the material flow curve by standard mechanical characteristics, Bulletin of Kiev Polytechnic Institute,. Series: mech. Eng., 60 (2010) 223-227.

[18] D.Tabor, The hardness of metals, Oxford University press, Great Britain, (1951).

[19] V.M. Zaitsev, Brinell hardness as a function of the plasticity parameters of materials, Factory laboratory. 15 (1949) 704-717.

[20] P.Ogar, D.Gorokhov, S. Belokobylsky, The elastic-plastic contact of a single asperity of a rough surface, MATEC Web of Conferences. 129 (2017) 06017.

DOI: 10.1051/matecconf/201712906017

[21] V.M. Matyunin, Express-diagnosis of mechanical properties of constructional materials, Izd. dom MEI, Moscow, (2006).

[22] V.M. Matyunin, A.Y. Marchenkov, Interrelation between strains and parameters of metal strengthening upon tension and indentation in plastic region, Inorg. Mat. 53 (2017) 1555-1561.

DOI: 10.1134/s0020168517150110

[23] GOST R 56232-2014, Standartinform, Moscow, (2015).

[24] X. Hernot, O. Bartier, Y. Bekouche, R. El Abdi, G. Mauvoisin, Influence of penetration depth and mechanical properties on contact radius determination for spherical indentation, Int. J. Sol. & Struct. 43 (2006) 4136-4153.

DOI: 10.1016/j.ijsolstr.2005.06.007

[25] J.-M. Collin, G. Mauvoisin, R. El Abdi, An experimental method to determine the contact radius changes during a spherical instrumented indentation, Mech. of Mat. 40 (2008) 401–406.

DOI: 10.1016/j.mechmat.2007.10.002

[26] H. Lee, J.H. Lee, G.M. Pharr, A numerical approach to spherical indentation techniques for material property evaluation, J. Mech. Phys. Solids. 53 (2005) 2037-2069.

DOI: 10.1016/j.jmps.2005.04.007

[27] H. Lee, T. Kim, H. Lee, A study on robust indentation techniques to evaluate elastic–plastic properties of metals, Int. J. Sol. & Struct. 47 (2010) 647–664.

DOI: 10.1016/j.ijsolstr.2009.11.003

[28] S.H. Kim, B.W. Lee, Y. Choi, D. Kwon, Quantitative determination of contact depth during spherical indentation of metallic materials-a FEM study, Mat. Sci. & Eng. 415 (2006) 59-65.

DOI: 10.1016/j.msea.2005.08.217

[29] T. Zhang, S. Wang, W. Wang, An energy-based method for flow property determination from a single-cycle spherical indentation test (SIT), Int. J. of Mech. Sci. 171 (2020) 105369.

DOI: 10.1016/j.ijmecsci.2019.105369

[30] J.L. Hay and P.J. Wolff, Small correction required when applying the Hertzian contact model to instrumented indentation data, J. Mater. Res. 16 (2001) 1280-1285.

DOI: 10.1557/jmr.2001.0179

[31] J.-M. Collin, Correction factor for contact radius in spherical indentation measurements, Mech. of Mat. 50 (2012) 47–52.

DOI: 10.1016/j.mechmat.2012.02.007

[32] P.M. Ogar, V.A Tarasov, Kinetic Indentation Application to Determine Contact Characteristics of Sphere and Elastoplastic Half-Space, Adv. Mat. Res. 664 (2013) 625-631.

DOI: 10.4028/www.scientific.net/amr.664.625

[33] P. Ogar, D.Gorokhov, A. Zhuk, V. Kushnarev, Contact geometry during indentation of a sphere into an elastoplastic half-space, MATEC Web of Conf.. 298 (2019) 00093.

DOI: 10.1051/matecconf/201929800093

[34] J.-M. Collin, G. Mauvoisin, P. Pilvin, Materials characterization by instrumented indentation using two different approaches, Mat. & Desing. 31 (2010) 636-640.

DOI: 10.1016/j.matdes.2009.05.043

[35] T. Zhang, S. Wang, W. Wang, Method to determine the optimal constitutive model from spherical indentation tests, Results in Physics 8 (2018) 716–727.

DOI: 10.1016/j.rinp.2018.01.019