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

  • In-suk Choi (a1), Yixiang Gan (a2), Daniel Kaufmann (a3), Oliver Kraft (a3) and Ruth Schwaiger (a3)...

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.

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a)Address all correspondence to this author. e-mail: insukchoi@kist.kr

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1.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).
2.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).
3.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).
4.Uchic, M.D., Dimiduk, D.M., Florando, J.N., and Nix, W.D.: Sample dimensions influence strength and crystal plasticity. Science 304, 986 (2004).
5.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).
6.Kraft, O., Gruber, P., Mönig, R., and Weygand, D.: Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40, 8.18.25 (2010).
7.Volkert, C.A. and Lilleodden, E.T.: Size effects in the deformation of sub-micron Au columns. Philos. Mag. 86, 5567 (2006).
8.Volkert, C.A., Donohue, A., and Spaepen, F.: Effect of sample size on deformation in amorphous metals. J. Appl. Phys. 103, 083539 (2008).
9.Kiener, D., Motz, C., and Dehm, G.: Micro-compression testing: A critical discussion of experimental constraints. Mater. Sci. Eng., A 505, 79 (2009).
10.Zhang, H., Schuster, B.E., Wei, Q., and Ramesh, K.T.: The design of accurate microcompression experiments. Scr. Mater. 54, 181 (2006).
11.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).
12.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).
13.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).
14.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).
15.Brantley, W.A.: Calculated elastic constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44, 534 (1973).
16.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).
17.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).
18.Ballato, A.: Poisson’s ratio for tetragonal, hexagonal, and cubic crystals. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 56 (1996).
19.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).
20.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).
21.Domnich, V. and Gogotsi, Y.: Phase transformation in silicon under contact loading. Rev. Adv. Mater. Sci. 3, 1 (2002).
22.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).
23.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).

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

  • In-suk Choi (a1), Yixiang Gan (a2), Daniel Kaufmann (a3), Oliver Kraft (a3) and Ruth Schwaiger (a3)...

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