The equivalent axisymmetric model for Berkovich indenters in power-law hardening materials

Z. Shi, X. Feng*, Y. Huang, J. Xiao, K. C. Hwang

*Corresponding author for this work

Research output: Contribution to journalArticle

16 Scopus citations


Nix and Gio [Nix, W.D., Gao, H.J., 1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids 46, 411-425] established an important relation between the micro-indentation hardness and indentation depth for axisymmetric indenters. For the Berkovich indenter, however, this relation requires an equivalent cone angle. Qin et al. [Qin, J., Huang, Y., Xiao, J., Hwang, K.C., 2009. The equivalence of axisymmetric indentation model for three-dimensional indentation hardness. Journal of Materials Research 24, 776-783] showed that the widely used equivalent cone angle from the criterion of equal base area leads to significant errors in micro-indentation, and proposed a new equivalence of equal cone angle for iridium. It is shown in this paper that this new equivalence holds for a wide range of plastic work hardening materials. In addition, the prior equal-base-area criterion does not hold because the Berkovich indenter gives much higher density of geometrically necessary dislocations than axisymmetric indenter. The equivalence of equal cone angle, however, does not hold for Vickers indenter.

Original languageEnglish (US)
Pages (from-to)141-148
Number of pages8
JournalInternational journal of plasticity
Issue number1
StatePublished - Jan 1 2010



  • 3D finite element analysis
  • Berkovich indenter
  • Indenter angle
  • Micro-indentation hardness
  • Strain gradient

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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