Skip to main content
SpringerLink
Log in

Re-Examination of Correlation between Hardness and Tensile Properties by Numerical Analysis

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Contact, singular-field, and large-deformation numerical analyses were performed to re-examine the correlation between hardness and tensile properties. Materials have single hardness values, but continuous changes in stress-strain diagrams; it is impossible, in principle, to correlate the hardness to one stress-strain value. Therefore, there must exist an application limit, which is discussed in this study. Because discretization error is unavoidable in such analyses, a method for leveling the discretization error regardless of the analysis condition was introduced. Moreover, in order to generalize the analysis results, the stress-strain diagram used for this analysis was considered as a dimensionless expression in arranging the results. From the analytical results, the following conclusions were deduced. The range in which the empirical equation between hardness and tensile strength is applicable depends on only the value of the work hardening exponent. Moreover, for the 0.05–0.2 range of the work hardening exponent for general steel, the prediction of tensile strength from the hardness is possible with 10% error at indenter face angles between 110° and 136° in case of the wedge indentation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Tabor D (1956) The physical meaning of indentation and scratch hardness. Br J Appl Phys 7(5):159–166. doi:10.1088/0508-3443/7/5/301

    Article  Google Scholar 

  2. Pavlina EJ, Van Tyne CJ (2008) Correlation of yield strength and tensile strength with hardness for steels. J Mater Eng Perform 17(6):888–893. doi:10.1007/s11665-008-9225-5

    Article  Google Scholar 

  3. Brooks I, Lin P, Palumbo G, Hibbard GD, Erb U (2008) Analysis of hardness–tensile strength relationships for electroformed nanocrystalline materials. Mater Sci Engng A 491(1–2):412–419. doi:10.1016/j.msea.2008.02.015

  4. Boyer HE, Gall TL (1985) Metals Handbook, Desk edn. ASM International, Metals Park, Ohio

    Google Scholar 

  5. Ashby MF, Jones DRH (2012) Engineering materials 1: an introduction to properties, applications and design. Elsevier, Oxford

    Google Scholar 

  6. Tabor D (1948) A simple theory of static and dynamic hardness. Proc R Soc Lond Ser A Math Phys Sci 192(1029):247–274. doi:10.1098/rspa.1948.0008

    Article  Google Scholar 

  7. Tabor D (1951a) The hardness and strength of metals. J Inst Met 79(7):1–18

    Google Scholar 

  8. Tabor D (1951b) The hardness of metals. Monographs on the physics and chemistry of materials. Clarendon Press, Oxford

    Google Scholar 

  9. Cahoon JR, Broughton WH, Kutzak AR (1971) The determination of yield strength from hardness measurements. Metall Trans A 2(7):1979–1983. doi:10.1007/BF02913433

    Google Scholar 

  10. Cahoon JR (1972) An improved equation relating hardness to ultimate strength. Metall Trans A 3(11):3040. doi:10.1007/BF02652880

    Article  Google Scholar 

  11. Johnson KL (1970) The correlation of indentation experiments. J Mech Phys Solids 18(2):115–126. doi:10.1016/0022-5096(70)90029-3

    Article  Google Scholar 

  12. Giannakopoulos AE, Larsson PL, Vestergaard R (1994) Analysis of Vickers indentation. Int J Solids Struct 31(19):2679–2708. doi:10.1016/0020-7683(94)90225-9

    Article  MATH  Google Scholar 

  13. Larsson P-L (2001) Investigation of sharp contact at rigid–plastic conditions. Int J Mech Sci 43(4):895–920. doi:10.1016/S0020-7403(00)00056-4

    Article  MATH  Google Scholar 

  14. Mata M, Anglada M, Alcalá J (2002) Contact deformation regimes around sharp indentations and the concept of the characteristic strain. J Mater Res 17(05):964–976. doi:10.1557/JMR.2002.0144

    Article  Google Scholar 

  15. Ogasawara N, Chiba N, Chen X (2005) Representative strain of indentation analysis. J Mater Res 20(08):2225–2234. doi:10.1557/JMR.2005.0280

    Article  Google Scholar 

  16. Cao Y, Huber N (2006) Further investigation on the definition of the representative strain in conical indentation. J Mater Res 21(07):1810–1821. doi:10.1557/jmr.2006.0224

    Article  Google Scholar 

  17. Jayadevan KR, Narasimhan R (1995) Finite element simulation of wedge indentation. Comput Struct 57(5):915–927. doi:10.1016/0045-7949(94)00557-J

    Article  MATH  Google Scholar 

  18. Jayaraman S, Hahn GT, Oliver WC, Rubin CA, Bastias PC (1998) Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests. Int J Solids Struct 35(5–6):365–381

    Article  MATH  Google Scholar 

  19. Tekkaya AE, Lange K (2000) An improved relationship between Vickers hardness and yield stress for cold formed materials and its experimental verification. CIRP Ann Manuf Technol 49(1):205–208. doi:10.1016/S0007-8506(07)62929-1

    Article  Google Scholar 

  20. Tekkaya AE (2001) Improved relationship between Vickers hardness and yield stress for cold formed materials. Steel Research 72(8):304–310

    Article  Google Scholar 

  21. Antunes JM, Menezes LF, Fernandes JV (2006) Three-dimensional numerical simulation of Vickers indentation tests. Int J Solids Struct 43(3–4):784–806. doi:10.1016/j.ijsolstr.2005.02.048

    Article  MATH  Google Scholar 

  22. Saito Y, Oztop MS, Kysar JW (2012) Wedge indentation into elastic–plastic single crystals. 2: simulations for face-centered cubic crystals. Int J Plast 28(1):70–87. doi:10.1016/j.ijplas.2011.05.013

    Article  Google Scholar 

  23. Dahlberg CFO, Saito Y, Öztop MS, Kysar JW (2014) Geometrically necessary dislocation density measurements associated with different angles of indentations. Int J Plast 54:81–95. doi:10.1016/j.ijplas.2013.08.008

    Article  Google Scholar 

  24. Dieter GE (1988) Mechanical metallurgy. McGraw-hill series in materials science and engineering. SI metric ed. / adapted by David Bacon edn, McGraw-Hill Book Company, London

    Google Scholar 

  25. Chakrabarty J (2006) Theory of plasticity, Third edn. Elsevier Butterworth-Heinemann, Oxford

    MATH  Google Scholar 

  26. Hill R, Lee EH, Tupper SJ (1947) The theory of wedge indentation of ductile materials. Proc R Soc Lond Ser A Math Phys Sci 188(1013):273–289. doi:10.1098/rspa.1947.0009

    Article  MathSciNet  Google Scholar 

  27. Hill R (1950) The mathematical theory of plasticity. Oxford University Press Inc., New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, 744 Moto-oka Nishi-Ku, Fukuoka, 819-0395, Japan

    S. Hamada & H. Noguchi

  2. Graduate School of Engineering, Kyushu University, 744 Moto-oka Nishi-Ku, Fukuoka, 819-0395, Japan

    M. Nakanishi & T. Moriyama

Authors
  1. S. Hamada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Nakanishi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Moriyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Noguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Hamada.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hamada, S., Nakanishi, M., Moriyama, T. et al. Re-Examination of Correlation between Hardness and Tensile Properties by Numerical Analysis. Exp Mech 57, 773–781 (2017). https://doi.org/10.1007/s11340-017-0272-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-017-0272-4

Keywords

Search

Navigation