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Slip distance model for the indentation size effect at the initiation of plasticity in ceramics and metals

Published online by Cambridge University Press:  31 January 2011

A.J. Bushby ,
T.T. Zhu  and
D.J. Dunstan
A.J. Bushby*
Affiliation:
Centre for Materials Research and Department of Materials, School of Engineering and Materials Science, Queen Mary, University of London, London, E1 4NS, United Kingdom
T.T. Zhu
Affiliation:
Centre for Materials Research and Department of Materials, School of Engineering and Materials Science, Queen Mary, University of London, London, E1 4NS, United Kingdom
D.J. Dunstan
Affiliation:
Centre for Materials Research and Department of Physics, Queen Mary, University of London, London, E1 4NS, United Kingdom
*
a) Address all correspondence to this author. e-mail: a.j.bushby@qmul.ac.uk
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Abstract

The indentation size effect, in which the contact pressure increases as the size of contact decreases, has been observed for many years for both spherical and pointed indenters. The concept of strain gradient plasticity has been used to describe this phenomenon, but it is often necessary to introduce a material length scale l* to fit experimental data. Here we present a theory based on the concept of dislocation slip distance, which naturally generates the scaling and incorporates the material parameters that influence the size effect. We compare this model with experimental data for a range of ceramics and tungsten metal and show that the yield strain and Burgers vector are the important material parameters in the indentation size effect.

Keywords

CeramicMetalNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 966 - 972
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.Ma, Q. and Clark, D.R.: Size dependent hardness of silver single crystals., J. Mater. Res. 10, 853 (1995).CrossRefGoogle Scholar
2.Lim, Y.Y. and Chaudhri, M.M.: The effect of the indenter load on the nanohardness of ductile metals: An experimental study on polycrystalline work-hardened and annealed oxygen-free copper. Philos. Mag. A 79, 2879 (1999).CrossRefGoogle Scholar
3.Swadener, J.G., George, E.P., and Pharr, G.M.: The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50, 681 (2002).CrossRefGoogle Scholar
4.Spary, I.J., Bushby, A.J., and Jennett, N.M.: On the indentation size effect in spherical indentation. Philos. Mag. 86, 5581 (2006).CrossRefGoogle Scholar
5.Zhu, T.T., Hou, X.D., Bushby, A.J., and DDunstan, J.: Indentation size effect at the initiation of plasticity for ceramics and metals. J. Phys. D: Appl. Phys. 41, 074004 (2008).CrossRefGoogle Scholar
6.Zhu, T.T., Bushby, A.J., and Dunstan, D.J.: Size effect in the initiation of plasticity for ceramics in nanoindentation. J. Mech. Phys. Solids 56, 1170 (2008).CrossRefGoogle Scholar
7.Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).CrossRefGoogle Scholar
8.Huang, Y., Qu, S., Hwang, K.C., Li, M., and Gao, H.: A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plast. 20, 753 (2004).CrossRefGoogle Scholar
9.Qin, J., Huang, Y., Hwang, K.C., Song, J., and Pharr, G.M.: The effect of indenter angle on the micronindentation hardness. Acta Mater. 55, 6127 (2007).CrossRefGoogle Scholar
10.Qu, S., Huang, Y., Pharr, G.M., and Hwang, K.C.: The indentation size effect in the spherical indentation of Iridium: A study via the conventional theory of mechanism-based strain gradient plasticity. Int. J. Plast. 22, 1265 (2006).CrossRefGoogle Scholar
11.Fleck, N.A. and Hutchinson, J.W.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49, 2245 (2001).CrossRefGoogle Scholar
12.Gao, H., Huang, Y., Nix, W.D., and Hutchinson, J.W.: Mechanism based strain gradient plasticity—I. Theory. J. Mech. Phys. Solids 47, 1239 (1999).CrossRefGoogle Scholar
13.Conrad, H., Feuerstein, S., and Rice, L.: Effects of grain size on the dislocation density and flow stress of niobium. Mater. Sci. Eng. 2, 157 (1967).CrossRefGoogle Scholar
14.Field, J.S. and Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
15.Bushby, A.J.: Nano-indentation using spherical indenters. Nondestruct. Test. Eval. 17, 213 (2001).CrossRefGoogle Scholar
16.Swadener, J.G. and Pharr, G.M.: Indentation modulus of elastically anisotropic half-spaces by cones and parabola of revolution. Philos. Mag. A 81, 447 (2001).CrossRefGoogle Scholar
17.Oliver, W.C. and Pharr, G.M.: Improved technique for determining hardness and elastic modulus using loading and displacement sensing indentation. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
18.Hou, X.D., Bushby, A.J., and Jennett, N.J.: Study of the interaction between the indentation size effect and Hall–Petch effect with spherical indenters on annealed polycrystalline copper. J. Phys. D: Appl. Phys. 41, 074006 (2008).CrossRefGoogle Scholar
19.Kocks, U.F.: The relation between polycrystal deformation and single crystal deformation. Metall. Mater. Trans. 1, 1121 (1970).CrossRefGoogle Scholar
20.Tabor, D.: The Hardness of Metals (Clarendon Press, Oxford, UK, 1951).Google Scholar
21. HHackelöer, J., Selbach, H., Kanert, O., Sleeswyk, A.W., and Hut, G.: Determination of the velocity of mobile dislocations by nuclear spin relaxation measurements. Phys. Status Solidi B 80, 235 (1977).CrossRefGoogle Scholar
22.Gao, H., Huang, Y., and Nix, W.D.: Modeling plasticity at the micrometer scale. Naturwissenschaften 86, 507 (1999).CrossRefGoogle ScholarPubMed