Determination of the Tensile Strain by Indenting the Sphere

Abstract:

The value of the parameter m (previously the Mayer index) has been interpreted in a new way. For this purpose, in determining m, a new parameter was introduced consisting of a factor obtained from the Hollomon equation and a factor used in transforming the Mayer equation. Taking into account the new parameter, the dependences are determined that allow determining the tensile deformation. The essential significance of the new parameter is shown at its values of 0.95 ... 1.05. It is noted that the calculations of representative deformations and stresses according to Tabor are a small special case of the proposed method. On examples with a clear physical meaning, the possibility of using the proposed approach to determine representative deformations and stresses for the range of values of the hardening exponent has been confirmed. The graphical dependences of the results obtained are presented.

• Periodical: Key Engineering Materials (Volume 910)
• Pages: 1049-1055
• DOI: https://doi.org/10.4028/p-90b7md
• Online since: February 2022
• Authors: Petr M. Ogar*, Valery A. Shilin, Elena V. Ugryumova
• Keywords: Indentation Parameters, Mayer Index, Representative Deformations, Spherical Indenter, Stresses, Tensile Deformations, Uniform Deformation

References

[1] 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

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

[3] H.A. Francis, Phenomenological Analysis of Plastic Spherical Indentation. J. of Eng. Mat. and Tech. Trans. ASME 98 H (1976) 272.

[4] F.M. Haggag, In-Situ Measurements of Mechanical Properties Using Novel Automated Ball Indentation System (1993) 27-44.

[5] B. Taljat, T. Zacharia, and F. Kosel, New analytical procedure to determine stress-strain curve from spherical indentation data, Int. J. of Sol. and Struct. 35(33) (1998) 4411–4426.

DOI: 10.1016/s0020-7683(97)00249-7

[6] J.-H. Ahn, D. Kwon, Derivation of plastic stress–strain relationship from ball indentations: examination of strain definition and pileup effect, J. of Mat. Research 16 (11) (2001) 3170–3178.

DOI: 10.1557/jmr.2001.0437

[7] F. O. Sonmez, A. Demir, Analytical relations between hardness and strain for cold formed parts, J. of Mat. Proc. Tech. 186 (1–3) (2007) 163–173.

DOI: 10.1016/j.jmatprotec.2006.12.031

[8] J. R. Matthews, Indentation hardness and hot pressing, Acta Metallurgica 28 (3) (1980) 311–318.

DOI: 10.1016/0001-6160(80)90166-2

[9] O. Richmond, H. Morrison, M. Devenpeck, Sphere indentation with application to the Brinell hardness test, Int. J. of Mech. Sc. 16 (1) (1974) 75–82.

DOI: 10.1016/0020-7403(74)90034-4

[10] E. G. Herbert, W. Oliver, G. Pharr, On the measurement of yield strength by spherical indentation, Philos. Mag. 86 (33–35) (2006) 5521–5539.

DOI: 10.1080/14786430600825103

[11] H. Habbab, B. Mellor, S. Syngellakis, Post-yield characterization of metals with signi:cant pile-up through spherical indentations, Acta Materialia 54(7) (2006) 1965–(1973).

DOI: 10.1016/j.actamat.2005.12.021

[12] B. Xu, X. Chen, Determining engineering stress–strain curve directly from the load–depth curve of spherical indentation test, J. of Mat. Research 25 (12) (2010) 2297–2307.

DOI: 10.1557/jmr.2010.0310

[13] P. Haušild, A. Materna, J. Nohava. On the identification of stress–strain relation by instrumented indentation with spherical indenter, Mat. & Design 37 (2012) 373-378.

DOI: 10.1016/j.matdes.2012.01.025

[14] M.Y. N'Jock, D. Chicot, X. Decoopman, J. Lesage, J. M. Ndjaka, A. Pertuz, Mechanical tensile properties by spherical macroindentation using an indentation strainhardening exponent, Int. J. of Mech. Sc. 75 (2013) 257–264.

DOI: 10.1016/j.ijmecsci.2013.07.008

[15] K. Fu, L. Chang, B. Zheng, Y. Tang, H. Wang, On the determination of representative stress–strain relation of metallic materials using instrumented indentation, Mat. & Design 65 (2015) 989–994.

DOI: 10.1016/j.matdes.2014.10.018

[16] Chao Chang, M. A. Garrido, J. Ruiz-Hervias, Zhu Zhang, Le-le Zhang, Representative stress-strain curve by spherical indentation on elastic-plastic materials, Advances in Mat. Sci. and Eng. (2018) 1–9.

DOI: 10.1155/2018/8316384

[17] 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

[18] P.M. Ogar, V.A. Shilin, E.V. Ugryumova, Relation of the Mayer Index to the Characteristics of the Power Law of Metal Hardening. Mat. Sci. Forum (in print).

DOI: 10.4028/p-96ug56

[19] 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.

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

[21] 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.

[22] GOST R 56232-2014 Determination of the «stress – strain» diagram by the method of instrumental indentation of the ball, Standartinform, Moscow, (2015).

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