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Effect of elastic surface deformation on the relation between hardness and yield strength

Published online by Cambridge University Press:  01 December 2004

L.J. Vandeperre ,
F. Giuliani  and
W.J. Clegg
L.J. Vandeperre
Affiliation:
Ceramics Laboratory, Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 3QZ, United Kindgom
F. Giuliani
Affiliation:
Ceramics Laboratory, Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 3QZ, United Kindgom
W.J. Clegg
Affiliation:
Ceramics Laboratory, Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 3QZ, United Kindgom
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Abstract

The use of an analytical approach to determine the relation between hardness and yield strength for materials with a high ratio of yield strength to Young's modulus is re-examined. It is shown that predictions using the analogy of the spherical cavity fail to reproduce experimental and finite element results because the surface deflection that occurs during loading is not taken into account. A modification is proposed to allow this. This gives a greatly improved prediction of the relationship between the hardness and yield strength of a material. It also enables the effect of the indenter shape on the measured hardness to be incorporated and explains why in some very hard materials, indentation is observed to be completely elastic.

Keywords

HardnessMechanical properties
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 12 , December 2004 , pp. 3704 - 3714
Copyright
Copyright © Materials Research Society 2004

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References

REFERENCES

1Atkins, A.G. and Tabor, D.: Plastic indentation in metals with cones. J. Mech. Phys. Solids 13, 149 (1965).CrossRefGoogle Scholar
2Cheng, Y.T. and Cheng, C.M.: What is indentation hardness? Surf. Coat. Technol. 133, 417 (2000).CrossRefGoogle Scholar
3Dao, M., Chollacoop, N., Vliet, K.J.V., Venkatesh, T.A. and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
4Mata, M., Anglada, M. and Alcala, J.: Contact deformation regimes around sharp indentations and the concept of the characteristic strain. J. Mater. Res. 17, 964 (2002).CrossRefGoogle Scholar
5Mata, M. and Alcala, J.: Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).CrossRefGoogle Scholar
6Marsh, D.M.: Plastic flow in glass. Proc. R. Soc. A 279, 420 (1963).Google Scholar
7Hill, R.: The Mathematical Theory of Plasticity (Clarendon Press, Oxford, U.K., 1950)Google Scholar
8Johnson, K.L.: The correlation of indentation experiments. J. Mech. Phys. Solids 18, 115 (1970).CrossRefGoogle Scholar
9Hirst, W. and Howse, G.J.W.: The indentation of materials by wedges. Proc. Roy. Soc. A 311, 429 (1969).Google Scholar
10Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
11Sneddon, I.N.: Boussinesq’s problem for a rigid cone. Proc. Cambridge Phil. Soc. 44, 492 (1948).CrossRefGoogle Scholar
12Sneddon, I.N.: Boussinesq’s problem for a flat-ended cylinder. Proc. Cambridge Phil. Soc. 42, 29 (1946).CrossRefGoogle Scholar
13Chiang, S.S., Marshall, D.B. and Evans, A.G.: The response of solids to elastic/plastic indentation: I. Stresses and residual stresses. J. Appl. Phys. 53, 298 (1982).CrossRefGoogle Scholar
14Fischer-Cripps, A.C.: Analysis of instrumented indentation test data for functionally graded materials. Surf. Coat. Technol. 168, 136 (2003).CrossRefGoogle Scholar
15Mulhearn, T.O.: The deformation of metals by Vickers-type pyramidal indenters. J. Mech. Phys. Solids 7, 85 (1959).CrossRefGoogle Scholar
16Samuels, L.E. and Mulhearn, T.O.: An experimental investigation of the deformed zone associated with indentation hardness impressions. J. Mech. Phys. Solids 5, 125 (1957).CrossRefGoogle Scholar
17Singh, A.P. and Padmanabhan, K.A.: Axisymmetrical compression of solid cylinders. 1. Slow loading conditions. J. Mater. Sci. 26, 5481 (1991).CrossRefGoogle Scholar
18Cheng, Y.T. and Cheng, C.M.: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284 (1998).CrossRefGoogle Scholar
19Xu, Z-H. and Rowcliffe, D.: Method to determine the plastic properties of bulk materials by nanoindentation. Philos. Mag. A82, 1893 (2002).CrossRefGoogle Scholar
20Hultman, L., Neidhardt, J., Hellgren, N., Sjostrom, H. and Sundgren, J-E.: Fullerene-like carbon nitride: A resilient coating material. MRS Bull. 28, 194 (2003).CrossRefGoogle Scholar
21Cheng, Y.T. and Li, Z.: Hardness obtained from conical indenters with various cone angles. J. Mater. Res. 15, 2830 (2000).CrossRefGoogle Scholar
22Hill, R., Lee, E.H. and Tupper, S.J.: The theory of wedge indentation of ductile materials. Proc. R. Soc. A 188, 273 (1947).Google Scholar
23Lockett, F.J.: Indentation of a rigid/plastic material by a conical indenter. J. Mech. Phys. Solids 11, 345 (1963).CrossRefGoogle Scholar
24Fischer-Cripps, A.C.: Elastic-plastic behaviour in materials loaded with a spherical indenter. J. Mater. Sci. 32, 727 (1997).CrossRefGoogle Scholar
25Mata, M., Anglada, M. and Alcala, J.: A hardness equation for sharp indentation of elastic-power law strain-hardening materials. Philos. Mag. A82, 1831 (2002).CrossRefGoogle Scholar
26Giuliani, F., Lloyd, S.J., Vandeperre, L.J. and Clegg, W.J. Deformation of GaAs under Nanoindentation, in Electron Microscopy and Analysis 2003 (Institute of Physics, Oxford, U.K., 2003)Google Scholar
27Timoshenko, S.P. and Goodier, J.N.: Theory of Elasticity. Engineering Societies Monographs (McGraw-Hill, New York, NY, 1984).Google Scholar
28Tabor, D.: The Physical meaning of indentation and scratch tests. Br. J. Appl. Phys. 7, 159 (1956).CrossRefGoogle Scholar