Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T17:35:42.864Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  31 January 2011

M. Mata ,
M. Anglada  and
J. Alcalá
M. Mata
Affiliation:
Department of Materials Science and Metallurgical Engineering, Universitat Politècnica de Catalunya, E.T.S.E.I.B., Barcelona 08028, Spain
M. Anglada
Affiliation:
Department of Materials Science and Metallurgical Engineering, Universitat Politècnica de Catalunya, E.T.S.E.I.B., Barcelona 08028, Spain
J. Alcalá*
Affiliation:
Department of Materials Science and Metallurgical Engineering, Universitat Politècnica de Catalunya, E.T.S.E.I.B., Barcelona 08028, Spain
*
a)Address all correspondence to this author. e-mail: Jorge.alcala@upc.es
Get access

Extract

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.

Type
Articles
Information
Journal of Materials Research , Volume 17 , Issue 5 , May 2002 , pp. 964 - 976
Copyright
Copyright © Materials Research Society 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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