Smart Search 


KREN Alexander P., D. Sc. in Eng., Assoc. Prof., Head of the Laboratory of Contact-Dynamic Control Methods, Institute of Applied Physics of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

Year 2022
Issue 1(58)
Pages 56–63
Type of article RAR
Index UDK 620.17, 539.3
Abstract The aim of this paper is to study and describe the behavior features of metals under impact loading in the area of elastic-plastic transition, with strains not exceeding 3–4 %, which are typical for measuring the hardness of materials during dynamic indentation. It has been established that until the state of full plasticity is reached, the excess of the dynamic hardness over the static one cannot be explained only by an increase of the strain rate and requires taking into account the elastic properties of the material. It is shown that a grow of the yield stress and the part of elastic deformation leads to a significant increase in the dynamic hardness of the material. This is due to the feature of measurements, which consists in fixing the value of the initial impact energy, which is distributed between elastic and plastic part of strain, depending on the characteristics of the material: yield stress, elastic modulus, strain-hardening coefficient.
Keywords indentation, metals, deformation, impact, elastoplasticity
  You can access full text version of the article.
  1. Tirupataiah Y., Sundararajan G. A comprehensive analysis of the static indentation process. Materials science and engineering, 1987, vol. 91, pp. 169–180. DOI:
  2. Oliver W.C., Pharr G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of materials research, 1992, vol. 7, iss. 6, pp. 1564–1583. DOI:
  3. VanLandingham M.R. Review of instrumented indentation. Journal of research of the National Institute of Standards and Technology, 2003, vol. 108, no. 4, pp. 249–265. DOI: https://
  4. Bahr D.F., Gerberich W.W. Plastic zone and pileup around large indentations. Metallurgical and materials transactions A, 1996, vol. 27, iss. 12, pp. 3793–3800. DOI:
  5. Mok C.H., Duffy J. The dynamic stress-strain relation of metals as determined from impact tests with a hard ball. International journal of mechanical sciences, 1965, vol. 7, iss. 5, pp. 355–366. DOI:
  6. Lu J., Suresh S., Ravichandran G. Dynamic indentation for determining the strain rate sensitivity of metals. Journal of the mechanics and physics of solids, 2003, vol. 51, iss. 11–12, pp. 1923–1938. DOI:
  7. Koeppel B.J., Subhash G. Dynamic indentation hardness of metals. Proc. IUTAM symposium on micro- and macrostructural aspects of thermoplasticity. Bochum, 1997, vol. 62, pp. 447–456. DOI
  8. Sundararajan G., Tirupataiah Y. The localization of plastic flow under dynamic indentation conditions: I. Experimental results. Acta materialia, 2006, vol. 54, iss. 3, pp. 565–575. DOI: https://
  9. Tabor D. The hardness of metals. Oxford, Clarendon Press, 1951. 176 p.
  10. Johnson K.L. Contact mechanics. Cambridge, Cambridge University Press, 1985. DOI:
  11. Mesarovic S.Dj., Fleck N.A. Spherical indentation of elastic-plastic solids. Proceedings of the Royal Society A. Mathematical physical and engineering sciences, 1999, vol. 455, iss. 1987, pp. 2707–2728. DOI:
  12. Kren A.P., Protasenya T.A. Determination of the physic and mechanical characteristics of isotropic pyrolitic graphite by dynamic indentation method. Russian journal of nondestructive testing, 2014, vol. 50, iss. 7, pp. 419–425. DOI:
  13. Kren A.P. Determination of the critical stress intensity factor of glass under conditions of elastic contact by the dynamic indentation method. Strength of materials, 2009, vol. 41, iss. 6, pp. 628–636. DOI:
  14. Wu C.-Y., Li L.-Y., Thornton C. Rebound behaviour of spheres for plastic impacts. International journal of impact engineering, 2003, vol. 28, iss. 9, pp. 929–946. DOI:
  15. Alcalá J., Esqué-De Los Ojos D. Reassessing spherical indentation: Contact regimes and mechanical property extractions. International journal of solids and structures, 2010, vol. 47, iss. 20, pp. 2714–2732. DOI: 2010.05.025.
  16. Gao X.-L., Jing X.N., Subhash G. Two new expanding cavity models for indentation deformations of elastic strain-hardening materials. International journal of solids and structures, 2006, vol. 43, iss. 7–8, pp. 2193–2208. DOI: ijsolstr.2005.03.062.
  17. Kren A.P., Rudnitskii V.A. Determination of the strainhardening exponent of a metallic material by low-speed impact indentation. Russian metallurgy (metally), 2019, vol. 2019, iss. 4, pp. 478–483. DOI: