Skip to main content Accessibility help

Contact Deformation Regimes Around Sharp Indentations and the Concept of the Characteristic Strain

  • M. Mata (a1), M. Anglada (a1) and J. Alcalá (a1)


Finite element simulations are performed to analyze the contact deformation regimes induced by a sharp indenter in elastic – power-law plastic solids. As the yield strength (σys) and strain hardening coefficient (n) decrease or, alternatively, as Young's modulus (E) increases, the contact regime evolves from (i) an elastic–plastic transition, to (ii) a fully plastic contact response, and to (iii) a fully plastic regime where piling-up of material at the contact area prevails. In accordance with preliminary analyses by Johnson, it is found that Tabor's equation, where hardness (H) = 2.7σr, applies within the fully plastic regime of elastic – power-law plastic materials. The results confirm the concept of the uniqueness of the characteristic strain, ∈r = 0.1, that is associated with the uniaxial stress, σr. A contact deformation map is constructed to provide bounds for the elastic–plastic transition and the fully plastic contact regimes for a wide range of values of σ ys, n, and E. Finally, the development of piling-up and sinking-in at the contact area is correlated with uniaxial mechanical properties. The present correlation holds exclusively within the fully plastic contact regime and provides a tool to estimate σ ys and n from indentation experiments.


Corresponding author

a)Address all correspondence to this author. e-mail:


Hide All
1.Tabor, D., Hardness of Metals, (Clarendon Press, Oxford, United Kingdom, 1951).
2.Hill, R., Lee, E.H., and Tupper, S.J., Proc. R. Soc. A 188, 273 (1947).
3.Lockett, F.J., J. Mech. Phys. Solids 11, 345 (1963).
4.Yu, W. and Blanchard, J.P., J. Mater. Res. 11, 2358 (1996).
5.Bishop, R.F., Hill, R., and Mott, N.F., Proc. Phys. Soc. 57, 147 (1945).
6.Marsh, D.M., Proc. R. Soc. A 279, 420 (1964).
7.Hill, R., The Mathematical Theory of Plasticity (Clarendon Press, Oxford, United Kingdom, 1950).
8.Hirst, W. and Howse, M.G.J.W., Proc. R. Soc. A 311, 429 (1969).
9.Johnson, K.L., J. Mech. Phys. Solids 18, 115 (1970).
10.Laursen, Y.A. and Simo, J.C., J. Mater. Res. 7, 618 (1992).
11.Giannakopoulos, A.E., Larsson, P-L., and Vestergaard, R., Int. J. Solids Struct. 31, 2679 (1994).
12.Larsson, P-L., Giannakopoulos, A.E., So¨derlund, E., Rowcliffe, D.J., and Vestergaard, R., Int. J. Solids Struct. 33, 221 (1996).
13.Marx, V. and Balke, H., Acta Mater. 45, 3791 (1997).
14.Bolshakov, A. and Pharr, G.M., J. Mater Res. 13, 1049 (1998).
15.Chaudhri, M.M., Acta Mater. 46, 3047 (1998).
16.Cheng, Y-T. and Li, Z., J. Mater. Res. 45, 2830 (2000).
17.Biwa, S. and Storåkers, B., J. Mech. Phys. Solids 43, 1303 (1995).
18.Bower, A.F., Fleck, N.A., Needleman, A., and Ogbonna, N., Proc. R. Soc. A 441, 97 (1993).
19.Komvopoulos, K., J. Tribol. 110, 477 (1988).
20.Mesarovic, S.D. and Fleck, N.A., Proc. R. Soc. A 455, 2707 (1999).
21. ABAQUS User’s Manual V5.8 (Hibbitt, Karlsson & Sorensen Inc., 1999).
22.Sneddon, I.N., Int. J. Eng. Sci. 3, 47 (1965).
23.Alcala´, J., Barone, A.C., and Anglada, M., Acta Mater. 48, 3451 (2000).
24.Eason, G. and Shield, R.T., ZAMP 11, 33 (1960).
25.Alcala, J., J. Am. Ceram. Soc. 83, 1977 (2000).
26.Hill, R., Storåkers, B., and Zdunek, A.B., Proc. R. Soc. A 423, 301 (1989).
27.Norbury, A.L. and Samuel, T., J. Iron Steel Inst. 17, 673 (1928).
28.Johnson, K.L., Contact Mechanics (Cambridge University Press, Cambridge, United Kingdom, 1985).
29.Mata, M., Anglada, M., and Alcala, J., Philos. Mag. A (in press).
30.Larsson, P-L., Int. J. Mech. Sci. 43, 895 (2001).
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: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed