Skip to main content
    • Aa
    • Aa

Understanding nanoindentation unloading curves

  • G. M. Pharr (a1) and A. Bolshakov (a2)

Experiments have shown that nanoindentation unloading curves obtained with Berkovich triangular pyramidal indenters are usually welldescribed by the power-law relation P = α(hhf)m, where hf is the final depth after complete unloading and α and m are material constants. However, the power-law exponent is not fixed at an integral value, as would be the case for elastic contact by a conical indenter (m = 2) or a flat circular punch (m = 1), but varies from material to material in the range m = 1.2–1.6. A simple model is developed based on observations from finite element simulations of indentation of elastic–plastic materials by a rigid cone that provides a physical explanation for the behavior. The model, which is based on the concept of an indenter with an “effective shape” whose geometry is determined by the shape of the plastic hardness impression formed during indentation, provides a means by which the material constants in the power law relation can be related to more fundamental material properties such as the elastic modulus and hardness. Simple arguments are presented from which the effective indenter shape can be derived from the pressure distribution under the indenter.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. J.B. Pethica , R. Hutchings , and W.C. Oliver , Philos. Mag. A 48, 593 (1983).

2. J.L. Loubet , J.M. Georges , O. Marchesini , and G. Meille , J. Tribol. 106, 43 (1984).

6. G.M. Pharr , Mater. Sci. Eng. A 253, 151 (1998).

8. I.N. Sneddon , Int. J. Eng. Sci. 3, 47 (1965).

12. N.A. Stelmashenko , M.G. Walls , L.M. Brown , and Y.V. Milman , Acta Metall. 41, 2855 (1993).

14. W.D. Nix and H. Gao , J. Mech. Phys. Solids 46, 411 (1998).

21. W. Hirst and M.G.J.W. Howse , Proc. R. Soc. A 311, 429 (1969).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 242 *
Loading metrics...

Abstract views

Total abstract views: 419 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th May 2017. This data will be updated every 24 hours.