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Measurement of Young’s modulus of anisotropic materials using microcompression testing

Published online by Cambridge University Press:  21 February 2012

In-suk Choi ,
Yixiang Gan ,
Daniel Kaufmann ,
Oliver Kraft  and
Ruth Schwaiger
In-suk Choi*
Affiliation:
Karlsruhe Institute of Technology, Institute for Applied Materials, 76131 Karlsruhe, Germany; and High Temperature Energy Materials Center, Korea Institute of Science and Technology, Seongbuk-gu, Seoul 136-791, Republic of Korea
Yixiang Gan
Affiliation:
Karlsruhe Institute of Technology, Institute for Applied Materials, 76131 Karlsruhe, Germany; and School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Daniel Kaufmann
Affiliation:
Karlsruhe Institute of Technology, Institute for Applied Materials, 76131 Karlsruhe, Germany
Oliver Kraft
Affiliation:
Karlsruhe Institute of Technology, Institute for Applied Materials, 76131 Karlsruhe, Germany
Ruth Schwaiger
Affiliation:
Karlsruhe Institute of Technology, Institute for Applied Materials, 76131 Karlsruhe, Germany
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

Microcompression test was applied to determine the Young’s modulus for elastically anisotropic materials for two different orientations of single crystalline Si. Although there is a clear difference in the apparent Young’s moduli for the different orientations, a significant underestimation of Young’s modulus was observed resulting from the substrate deformation as observed in both finite element simulation and experiment. This effect decreases with increasing aspect ratio. To correct the deviation of the apparent Young’s modulus from the theoretical values, a systematic framework of microcompression test is suggested. The modified Sneddon correction using the indentation modulus instead of Young’s modulus successfully yields Young’s moduli of single crystalline silicon in the [100] and [111] directions to within 5.3% and 2.0% deviation, respectively.

Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 21 , 14 November 2012 , pp. 2752 - 2759
Copyright
Copyright © Materials Research Society 2012

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References

REFERENCES

Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).CrossRefGoogle Scholar
Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223 (1994).CrossRefGoogle Scholar
Vlassak, J.J., Ciavarella, M., Barber, J.R., and Wang, X.: The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, 1701 (2003).CrossRefGoogle Scholar
Uchic, M.D., Dimiduk, D.M., Florando, J.N., and Nix, W.D.: Sample dimensions influence strength and crystal plasticity. Science 304, 986 (2004).CrossRefGoogle Scholar
Greer, J.R. and De Hosson, J.T.M.: Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect. Prog. Mater Sci. 56, 654 (2011).CrossRefGoogle Scholar
Kraft, O., Gruber, P., Mönig, R., and Weygand, D.: Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40, 8.1–8.25 (2010).CrossRefGoogle Scholar
Volkert, C.A. and Lilleodden, E.T.: Size effects in the deformation of sub-micron Au columns. Philos. Mag. 86, 5567 (2006).CrossRefGoogle Scholar
Volkert, C.A., Donohue, A., and Spaepen, F.: Effect of sample size on deformation in amorphous metals. J. Appl. Phys. 103, 083539 (2008).CrossRefGoogle Scholar
Kiener, D., Motz, C., and Dehm, G.: Micro-compression testing: A critical discussion of experimental constraints. Mater. Sci. Eng., A 505, 79 (2009).CrossRefGoogle Scholar
Zhang, H., Schuster, B.E., Wei, Q., and Ramesh, K.T.: The design of accurate microcompression experiments. Scr. Mater. 54, 181 (2006).CrossRefGoogle Scholar
Choi, Y.S., Uchic, M.D., Parthasarathy, T.A., and Dimiduk, D.M.: Numerical study on microcompression tests of anisotropic single crystals. Scr. Mater. 57, 849 (2007).CrossRefGoogle Scholar
Moser, B., Wasmer, K., Barbieri, L., and Michler, J.: Strength and fracture of Si micropillars: A new scanning electron microscopy-based micro-compression test. J. Mater. Res. 22, 1004 (2007).CrossRefGoogle Scholar
Sneddon, I.N.: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
Greer, J.R., Oliver, W.C., and Nix, W.D.: Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients. Acta Mater. 53(6), 1821 (2005); Corrigendum. Acta Mater. 54(6), 1705 (2006).CrossRefGoogle Scholar
Brantley, W.A.: Calculated elastic constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44, 534 (1973).CrossRefGoogle Scholar
Schwaiger, R., Weber, M., Moser, B., Gumbsch, P., and Kraft, O.: Mechanical assessment of ultrafine-grained nickel by microcompression experiment and finite element simulation. J. Mater. Res. 27(1), 266 (2012).CrossRefGoogle Scholar
Yang, Y., Ye, J.C., Lu, J., Liu, F.X., and Liaw, P.K.: Effects of specimen geometry and base material on the mechanical behavior of focused-ion-beam-fabricated metallic-glass micropillars. Acta Mater. 57, 1613 (2009).CrossRefGoogle Scholar
Ballato, A.: Poisson’s ratio for tetragonal, hexagonal, and cubic crystals. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 56 (1996).CrossRefGoogle Scholar
Franca, D.R. and Blouin, A.: All-optical measurement of in-plane and out-of-plane Young’s modulus and Poisson’s ratio in silicon wafers by means of vibration modes. Meas. Sci. Technol. 15, 859 (2004).CrossRefGoogle Scholar
Kailer, A., Nickel, K.G., and Gogotsi, Y.G.: Raman microspectroscopy of nanocrystalline and amorphous phases in hardness indentations. J. Raman Spectrosc. 30, 939 (1999).3.0.CO;2-C>CrossRefGoogle Scholar
Domnich, V. and Gogotsi, Y.: Phase transformation in silicon under contact loading. Rev. Adv. Mater. Sci. 3, 1 (2002).Google Scholar
Jang, J., Lance, M.J., Wen, S., Tsui, T.Y., and Pharr, G.M.: Indentation-induced phase transformations in silicon: Influences of load, rate and indenter angle on the transformation behavior. Acta Mater. 53, 1759 (2005).CrossRefGoogle Scholar
Bolshakov, A. and Pharr, G.M.: Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques. J. Mater. Res. 13, 4 (1998).CrossRefGoogle Scholar