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The equivalence of axisymmetric indentation model for three-dimensional indentation hardness

Published online by Cambridge University Press:  31 January 2011

J. Qin ,
Y. Huang ,
J. Xiao  and
K.C. Hwang
J. Qin
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Y. Huang*
Affiliation:
Department of Civil and Environmental Engineering and Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208
J. Xiao
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208
K.C. Hwang
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

Nix and Gao [J. Mech. Phys. Solids46, 411 (1998)] established an important relation between the microindentation hardness and indentation depth for axisymmetric indenters. We use the conventional theory of mechanism-based strain gradient plasticity [Huang et al., Int. J. Plast.20, 753 (2004)] established from the Taylor dislocation model [Taylor, Proc. R. Soc. London A145, 362 (1934); Taylor, J. Inst. Met.62, 307 (1938)] to study the Berkovich and other triangular pyramid indenters. The three-dimensional finite element analysis shows that the widely used equivalence of equal base area leads to significant errors, particularly in microindentation. A new equivalence of equal angle is proposed for triangular pyramid indenters, and it has been validated for a large range of indenter angles and indentation depths.

Keywords

Hardness
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 776 - 783
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.Guzman, M.S., Neubauer, G., Flinn, P., and Nix, W.D.: The role of indentation depth on the measured hardness of materials, in Thin Films: Stresses and Mechanical Properties IV, edited by Townsend, P.H., Weihs, T.P., Sanchez, J.E. Jr, and Borgesen, P. (Mater. Res. Soc. Symp. Proc. 308, Pittsburgh, PA, 1993), p. 613.Google Scholar
2.Stelmashenko, N.A., Walls, A.G., Brown, L.M., and Milman, Y.V.: Microindentation on W and Mo oriented single crystals: An STM study. Acta Metall. Mater. 41, 2855 (1993).Google Scholar
3.Ma, Q. and Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10, 853 (1995).CrossRefGoogle Scholar
4.Poole, W.J., Ashby, M.F., and Fleck, N.A.: Micro-hardness of annealed and work-hardened copper polycrystals. Scr. Mater. 34, 559 (1996).CrossRefGoogle Scholar
5.McElhaney, K.W., Vlasssak, J.J., and Nix, W.D.: Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 13, 1300 (1998).CrossRefGoogle Scholar
6.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
7.Fleck, N.A. and Hutchinson, J.W.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825 (1993).Google Scholar
8.Fleck, N.A. and Hutchinson, J.W.: Strain gradient plasticity, in Advances in Applied Mechanics, Vol. 33, edited by Hutchinson, J.W. and Wu, T.Y. (Academic Press, New York, 1997), p. 295.Google Scholar
9.Acharya, A. and Bassani, J.L.: Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48, 1565 (2000).CrossRefGoogle Scholar
10.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
11.Huang, Y., Gao, H., Nix, W.D., and Hutchinson, J.W.: Mechanism-based strain gradient plasticity—II. Analysis. J. Mech. Phys. Solids 48, 99 (2000).Google Scholar
12.Begley, M.R. and Hutchinson, J.W.: The mechanics of size-dependent indentation. J. Mech. Phys. Solids 46, 2049 (1998).Google Scholar
13.Huang, Y., Xue, Z., Gao, H., Nix, W.D., and Xia, Z.C.: A study of microindentation hardness tests by mechanism-based strain gradient plasticity. J. Mater. Res. 15, 1786 (2000).CrossRefGoogle Scholar
14.Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).CrossRefGoogle Scholar
15.Elmustafa, A.A. and Stone, D.S.: Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity. J. Mech. Phys. Solids 51, 357 (2003).Google Scholar
16.Zong, Z., Lou, J., Adewoye, O.O., Elmustafa, A.A., Hammad, F., and Soboyejo, W.O.: Indentation size effects in the nano- and micro-hardness of fcc single crystal metals. Mater. Sci. Eng., A 434, 178 (2006).CrossRefGoogle Scholar
17.Saha, R., Xue, Z., Huang, Y., and Nix, W.D.: Indentation of a soft metal film on a hard substrate: Strain gradient hardening effects. J. Mech. Phys. Solids 49, 1997 (2001).CrossRefGoogle Scholar
18.Zhang, F., Saha, R., Huang, Y., Nix, W.D., Hwang, K.C., Qu, S., and Li, M.: Indentation of a hard film on a soft substrate: Strain gradient hardening effects. Int. J. Plast. 23, 25 (2007).Google Scholar
19.Durst, K., Goken, K.M., and Pharr, G.M.: Indentation size effect in spherical and pyramidal indentations. J. Phys. D: Appl. Phys. 41, 1 (2008).CrossRefGoogle Scholar
20.Abu, R.K.Al-Rub: Prediction of micro and nanoindentation size effect from conical or pyramidal indentation. Mech. Mater. 39, 787 (2007).Google Scholar
21.Xue, Z., Huang, Y., Hwang, K.C., and Li, M.: The influence of indenter tip radius on the micro-indentation hardness. J. Eng. Mater. Tech. Trans. ASME 124, 371 (2002).Google Scholar
22.Qu, S., Huang, Y., Nix, W.D., Jiang, H., Zhang, F., and Hwang, K.C.: Indenter tip radius effect on the Nix-Gao relation in micro- and nanoindentation hardness experiments. J. Mater. Res. 19, 3423 (2004).CrossRefGoogle Scholar
23.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
24.Qin, J., Huang, Y., Hwang, K.C., Song, J., and Pharr, G.M.: The effect of indenter angle on the microindentation hardness. Acta Mater. 55, 6127 (2007).CrossRefGoogle Scholar
25.Taylor, G.I.: The mechanism of plastic deformation of crystals. Part I.-Theoretical. Proc. R. Soc. London A 145, 362 (1934).Google Scholar
26.Taylor, G.I.: Plastic strain in metal. J. Inst. Met. 62, 307 (1938).Google Scholar
27.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
28.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).Google Scholar
29.Huang, Y., Zhang, F., Hwang, K.C., Nix, W.D., Pharr, G.M., and G Feng: A model of size effects in nano-indentation. J. Mech. Phys. Solids 54, 1668 (2006).CrossRefGoogle Scholar
30.Huang, Y., Feng, X., Pharr, G.M., and Hwang, K.C.: A nano-indentation model for spherical indenters. Model. Simul. Mater. Sci. Eng. 15, S255 (2007).CrossRefGoogle Scholar
31.Zhang, F., Huang, Y., Hwang, K.C., Qu, S., and Liu, C.: A three-dimensional strain gradient plasticity analysis of particle size effect in composite materials. Mater. Manuf. Process. 22, 140 (2007).CrossRefGoogle Scholar
32.Li, M., Chen, W.M., Liang, N.G., and Wang, L.D.: A numerical study of indentation using indenters of different geometry. J. Mater. Res. 19, 73 (2004).Google Scholar
33.Ashby, M.F.: The deformation of plastically non-homogeneous alloys. Philos. Mag. 21, 399 (1970).Google Scholar
34.Nye, J.F.: Some geometrical relations in dislocated crystal. Acta Metall. Mater. 1, 153 (1953).CrossRefGoogle Scholar
35.Cottrell, A.H.: The Mechanical Properties of Materials (J. Wiley, New York, 1964), p. 277.Google Scholar
36.Arsenlis, A. and Parks, D.M.: Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density. Acta Mater. 47, 1597 (1999).Google Scholar
37.Shi, M., Huang, Y., and Gao, H.: The J-integral and geometrically necessary dislocations in nonuniform plastic deformation. Int. J. Plast. 20, 1739 (2004).Google Scholar
38.Bishop, J.F.W. and Hill, R.: A theory of plastic distortion of a polycrystalline aggregate under combined stresses. Philos. Mag. 42, 414 (1951).CrossRefGoogle Scholar
39.Bishop, J.F.W. and Hill, R.: A theoretical derivation of the plastic properties of a polycrystalline face-centered metal. Philos. Mag. 42, 1298 (1951).CrossRefGoogle Scholar
40.Kocks, U.F.: The relation between polycrystal deformation and single crystal deformation. Metall. Mater. Trans. 1, 1121 (1970).Google Scholar
41.ABAQUS/Standard User's Manual Version 6.2 (Hibbitt, Karlsson & Sorenson, Inc., 2001).Google Scholar