Issues »  Volume 48, Issue 1

Approximation of the Yield Strength in Function of Young’s Modulus and Poisson’s Ratio from Continuous Needle Indentation Testing

A. Boudilmi$^{1,2}$, M. Slamani$^{1}$, L. Bechane$^{1}$, K. Loucif$^{1}$, Kh. Boucherb$^{1}$, M. Silm$^{1}$

$^{1}$Mohamed Boudiaf University, University Pole, Bordj Bou Arreridj Road, DZ-28000 M’Sila, Algeria
$^{2}$Institute of Optics and Precision Mechanics, Ferhat Abbas University of Setif 1, El Bez Campus, DZ-19137 Setif, Algeria

Received: 29.03.2025; final version - 27.10.2025. Download: PDF

Based on mathematical assumptions by Love and Sneddon with co-workers, a yield strength-relationship result from the indentation of a needle of sharp conical tip in elastic materials is determined. This study offers mathematical expressions of the yield strength of solid material, when the penetrator is a sharp needle with a cone tip. According to Love (1939) and by Sneddon (1965) workers, we have deduced the relationship between the yield strength, the Young’s modulus (E), and the Poisson’s ratio (γ) for the tested material andthe semi-included angle of the sharp tip of the needle indenter (θ). Firstly, mathematical concepts of the right circular cone are established. Secondly, the yield strength formula for the bulk material was derived. Thirdly, an approach of the yield strength resulted from the indentation of the sharp conical needle is presented. Finally, yield strength expressions resulted from the indentation of the sharp conical needle of different semi-angles are determined and collected in tables at the last.

Key words: pressure, cone contact, geometric modelling, indentation, yield strength.

URL: https://mfint.imp.kiev.ua/en/abstract/v48/i01/0051.html

DOI: https://doi.org/10.15407/mfint.48.01.0051

PACS: 46.55.+d, 46.80.+j, 62.20.fg, 62.20.Qp, 68.55.jd, 68.60.Bs,81.70.Bt

Citation: A. Boudilmi, M. Slamani, L. Bechane, K. Loucif, Kh. Boucherb, and M. Silm, Approximation of the Yield Strength in Function of Young’s Modulus and Poisson’s Ratio from Continuous Needle Indentation Testing, Metallofiz. Noveishie Tekhnol., 48, No. 1: 51–59 (2026)

REFERENCES
  1. W. C. Oliver and G. M. Pharr, J. Mater. Res., 7, Iss. 6: 1564 (1992).
  2. A. Boudilmi and K. Loucif, Strength of Materials, 48, Iss. 3: 419 (2016).
  3. A. Boudilmi and K. Loucif, Metallofiz. Noveishie Tekhnol., 40, Iss. 12: 1689 (2018).
  4. P. L. Larsson, J. Mater. Eng. Perform., 30, Iss. 4: 2566 (2021).
  5. G. M. Pharr, W. C. Oliver, and F. R. Brotzen, J. Mater. Res., 7, Iss. 3: 613 (1992).
  6. A. Boudilmi and K. Loucif, Trans. Indian Inst. Met., 70, Iss. 6: 1527 (2017).
  7. A. Boudilmi and K. Loucif, Strength of Materials, 54, Iss. 1: 154 (2022).
  8. P. J. Blau and B. R. Lawn, Microindentation Techniques in Materials Science and Engineering (International: 1986).
  9. A. Boudilmi, Contribution à la Caractérisation des Revêtements et des Matériaux stratifiés par micro dureté et tenue à l’usure (Thesis of the Disser. for the Degree of Dr. Phys.-Math. Sci.) (Setif : Université Ferhat Abbas: 2017) (in French).
  10. A. Boudilmi, K. Loucif, M. Slamani, M. Titoum, and K. Bouchareb, Strength of Materials, 55, Iss. 4: 800 (2023).
  11. D. Tabor, The Hardness of Metals (Oxford: Clarendon Press: 1951).
  12. A. Boudilmi and K. Loucif, Metallofiz. Noveishie Tekhnol, 45, Iss. 4: 555 (2023).
  13. M. Gunda, P. Kumar, and M. Katiyar, Crit. Rev. Solid State, 42, Iss. 2: 129 (2017).
  14. A. E. H. Love, Quart. J. Math., 10, Iss. 1: 161 (1939).
  15. A. E. H. Love, Philos. Trans. A, 228: 659 (1929).
  16. J. W. Harding and I. N. Sneddon, Proc. Cambridge Philos. Soc., 41, Iss. 1: 16 (1945).
  17. I. N. Sneddon, Int. J. Eng. Sci., 3, Iss. 1: 47 (1965).
  18. I. N. Sneddon, Fourier Transforms (New York: McGraw-Hill Book Company Inc.: 1951).
  19. O. Neumann, H. V. Surana, S. Melly, P. Steinmann, and S. Budday, Journal of the Mechanical Behavior of Biomedical Materials, 163: 106863 (2025).
  20. J. Boussinesq, Applications des Potentiels a l’etude de Equilibre dt du Mouvement des Solides Elastiques (Paris: Gauthier-Villars: 1885) (in French).
  21. A. S. Alaboodi and Z. Hussain, J. King Saud Univ. - Eng. Sci., 31, Iss. 1: 61 (2019).
  22. Y. Y. Lim and M. M. Chaudhri, Phil. Mag., 84, Iss. 27: 2877 (2004).
  23. M. Munawar Chaudhri, Rev. Mater. Trans., 60, Iss. 8: 1404 (2019).

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License
© 1979 “G. V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine”