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Novel technique for measuring the mechanical properties of porous materials by nanoindentation

  • Xi Chen (a1), Yong Xiang (a2) and Joost J. Vlassak (a2)


A new technique for measuring the elastic-plastic properties of porous thin films by means of nanoindentation is proposed. The effects of porosity on indentation hardness and modulus are investigated through finite element analyses based on the Gurson model for plastic deformation of ductile porous materials. Intrinsic mechanical properties of the thin film are obtained by eliminating both substrate and densification effects. The technique is applied to the special case of a porous, low-permittivity dielectric thin film. The results are in good agreement with those obtained independently using the plane-strain bulge test.


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1.Huang, H.B., Spaepen, F.: Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers. Acta Mater. 48, 3261 (2000).
2.Xiang, Y., Chen, X., Vlassak, J.J.: The plane-strain bulge test for thin films. J. Mater. Res. 20, 2360 (2005).
3.Vlassak, J.J., Nix, W.D.: A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J. Mater. Res. 7, 3242 (1992).
4.Baker, S.P., Nix, W.D.: Mechanical properties of compositionally modulated Au-Ni thin films: Nanoindentation and microcantilever deflection experiments. J. Mater. Res. 9, 3131 (1994).
5.Weihs, T.P., Hong, S., Bravman, J.C., Nix, W.D.: Mechanical deflection of cantilever microbeams—A new technique for testing the mechanical-properties of thin films. J. Mater. Res. 13, 931 (1998).
6.Baker, S.P., Kretschmann, A., Arzt, E.: Thermomechanical behavior of different texture components in Cu thin films. Acta Mater. 49, 2145 (2001).
7.Keller, R.M., Baker, S.P., Arzt, E.: Stress-temperature behaviour of unpassivated thin copper films. Acta Mater. 47, 415 (1999).
8.Oliver, W.C., 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).
9.Doerner, M.F., Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).
10.Pharr, G.M.: Measurement of mechanical properties by ultra-low-load indentation. Mater. Sci. Eng. A 253, 151 (1998).
11.Pharr, G.M., Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).
12.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, UK, 1985).
13.Hay, J.C., Bolshakov, A., Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).
14.Chen, X., Vlassak, J.J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16, 2974 (2001).
15.Vlassak, J.J., Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223 (1994).
16.Tabor, D.: The Hardness of Metals (Clarendon Press, Oxford, UK, 1951).
17.Saha, R., Nix, W.D.: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50, 23 (2002).
18.Fleck, N.A., Otoyo, H., Needleman, A.: Indentation on porous solids. Int. J. Solids Struct. 29, 1613 (1992).
19.Volinsky, A.A., Vella, J.B., Gerberich, W.W.: Fracture toughness, adhesion and mechanical properties of low-K dielectric thin films measured by nanoindentation. Thin Solid Films 429, 201 (2003).
20.Chen, X., Wang, R., Yao, N., Evans, A.G., Hutchinson, J.W., Bruce, R.W.: Foreign object damage in a thermal barrier system: Mechanisms and simulations. Mater. Sci. Eng. A 352, 221 (2003).
21.Chen, X., He, M.Y., Spitsberg, I., Fleck, N.A., Hutchinson, J.W., Evans, A.G.: Mechanisms governing the high temperature erosion of thermal-barrier coatings used in gas turbines. Wear 256, 735 (2004).
22.Chen, X., Hutchinson, J.W., Evans, A.G.: Simulation of the high temperature impression of thermal-barrier coatings with columnar microstructure. Acta Mater. 52, 565 (2004).
23.Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth. I. Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2 (1977).
24.Xiang, Y., Chen, X., Tsui, T.Y., Jang, J.I. and Vlassak, J.J.: Mechanical properties of porous and fully dense low-κ dielectric thin films measured by means of nanoindentation and the plane-strain bulge test technique. J. Mater. Res. 21, 386 (2006).
25.Bückle, H. Use of hardness test to determine other material properties, in The Science of Hardness Testing and Its Research Applications, edited by Westbrook, J.W. and Conrad, H. (American Society for Metals, Metals Park, OH, 1971), p. 453.
26. ABAQUS 5.8 User's Manual (ABAQUS Inc., Pawtucket, RI, 1998).
27.Mesarovic, S.D., Fleck, N.A.: Spherical indentation of elastic-plastic solids. Proc. R. Soc. London A455, 2707 (1999).


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Novel technique for measuring the mechanical properties of porous materials by nanoindentation

  • Xi Chen (a1), Yong Xiang (a2) and Joost J. Vlassak (a2)


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