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Measuring anisotropy in Young’s modulus of copper using microcantilever testing

Published online by Cambridge University Press:  31 January 2011

David E.J. Armstrong*
Affiliation:
Department of Materials, University of Oxford, Oxford, United Kingdom OX1 3PH
Angus J. Wilkinson
Affiliation:
Department of Materials, University of Oxford, Oxford, United Kingdom OX1 3PH
Steve G. Roberts
Affiliation:
Department of Materials, University of Oxford, Oxford, United Kingdom OX1 3PH
*
a) Address all correspondence to this author. e-mail: david.armstrong@materials.ox.ac.uk
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Abstract

Focused ion beam machining was used to manufacture microcantilevers 30 μm by 3 μm by 4 μm with a triangular cross section in single crystal copper at a range of orientations between. These were imaged and tested using AFM/nanoindentation. Each cantilever was indented multiple times at a decreasing distance away from the fixed end. Variation of the beam’s behavior with loading position allowed a critical aspect ratio (loaded length:beam width) of 6 to be identified above which simple beam approximations could be used to calculate Young’s modulus. Microcantilevers were also milled within a single grain in a polycrystalline copper sample and electron backscattered diffraction was used to identify the direction of the long axis of the cantilever. The experimentally measured values of Young’s modulus and their variation with orientation were found to be in good agreement with the values calculated from the literature data for bulk copper.

Type
Articles
Copyright
Copyright © Materials Research Society 2009

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References

1.Ritchie, I.G.: Improved resonant bar techniques for measurement of dynamic elastic-moduli and test of Timoshenko beam theory. J. Sound Vib. 31(4), 453 (1973).CrossRefGoogle Scholar
2.Ledbetter, H.: Dynamic vs static Young moduli: A case study. Mater. Sci. Eng., A 165(1), L9 (1993).CrossRefGoogle Scholar
3.Sirdeshmukh, D.B. and Subhadra, K.G.: Consistency checks on elastic properties of crystals. J. Mater. Sci. 40(7), 1553 (2005).CrossRefGoogle Scholar
4.Talling, R.J., Dashwood, R.J., Jackson, M., Kurarnoto, S., and Dye, D.: Determination of (C-11-C-12) in Ti-36Nb-2Ta-3Zr-0.3O (wt%) (gum metal). Scr. Mater. 59(6), 669 (2008).CrossRefGoogle Scholar
5.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564 (1992).CrossRefGoogle Scholar
6.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(1), 3 (2004).CrossRefGoogle Scholar
7.Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42(8), 1223 (1994).CrossRefGoogle Scholar
8. D. Di Maio and Roberts, S.G.: Measuring fracture toughness of coatings using focused-ion-beam-machined microbeams. J. Mater. Res. 20(2), 299 (2005).Google Scholar
9.Kiener, D., Grosinger, W., Dehm, G., and Pippan, R.: A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples. Acta Mater. 56(3), 580 (2008).CrossRefGoogle Scholar
10.Kiener, D., Motz, C., Schoberl, T., Jenko, M., and Dehm, G.: Determination of mechanical properties of copper at the micron scale. Adv. Eng. Mater. 8(11), 1119 (2006).CrossRefGoogle Scholar
11.Uchic, M.D., Dimiduk, D.M., Florando, J.N., and Nix, W.D.: Sample dimensions influence strength and crystal plasticity. Science 305(5686), 986 (2004).CrossRefGoogle ScholarPubMed
12.Johansson, S., Schweitz, J.A., Tenerz, L., and Tiren, J.: Fracture testing of silicon microelements in situ in a scanning electronmicroscope. J. Appl. Phys. 63(10), 4799 (1988).CrossRefGoogle Scholar
13.Weihs, T.P., Hong, S., Bravman, J.C., and Nix, W.D.: Mechanical deflection of cantilever microbeamsA new technique for testing the mechanical-properties of thin-films. J. Mater. Res. 3(5), 931 (1988).CrossRefGoogle Scholar
14.Uchic, M.D. and Dimiduk, D.A.: A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing. Mater. Sci. Eng., A 400, 268 (2005).CrossRefGoogle Scholar
15.Ng, K.S. and Ngan, A.H.W.: Stochastic nature of plasticity of aluminum micro-pillars. Acta Mater. 56(8), 1712 (2008).CrossRefGoogle Scholar
16.Frick, C.P., Clark, B.G., Orso, S., Schneider, A.S., and Arzt, E.: Size effect on strength and strain hardening of small-scale [111] nickel compression pillars. Mater. Sci. Eng., A 489(12), 319 (2008).CrossRefGoogle Scholar
17.Uchic, M.D., Dimiduk, D.M., Wheeler, R., Shade, P.A., and Fraser, H.L.: Application of micro-sample testing to study fundamental aspects of plastic flow. Scr. Mater. 54(5), 759 (2006).CrossRefGoogle Scholar
18.Greer, J.R. and Nix, W.D.: Size dependence of mechanical properties of gold at the sub-micron scale. Appl. Phys. A 80(8), 1625 (2005).CrossRefGoogle Scholar
19.Greer, J.R. and Nix, W.D.: Nanoscale gold pillars strengthened through dislocation starvation. Phys. Rev. B 73(24), 245410 (2006).CrossRefGoogle Scholar
20.Volkert, C.A., Lilleodden, E.T., Kramer, D., and Weissmuller, J.: Approaching the theoretical strength in nanoporous Au. Appl. Phys. Lett. 89(6), 061920 (2006).CrossRefGoogle Scholar
21.Kiener, D., Motz, C., and Dehm, G.: Dislocation-induced crystal rotations in micro-compressed single crystal copper columns. J. Mater. Sci. 43(7), 2503 (2008).CrossRefGoogle Scholar
22.Lai, Y.H., Lee, C.J., Cheng, Y.T., Chou, H.S., Chen, H.M., Du, X.H., Chang, C.I., Huang, J.C., Jian, S.R., Jang, J.S.C., and Nieh, T.G.: Bulk and microscale compressive behavior of a Zr-based metallic glass. Scr. Mater. 58(10), 890 (2008).CrossRefGoogle Scholar
23.Schuster, B.E., Wei, Q., Hufnagel, T.C., and Ramesh, K.T.: Sizeindependent strength and deformation mode in compression of a Pd-based metallic glass. Acta Mater. 56(18), 5091 (2008).CrossRefGoogle Scholar
24.Nadgorny, E.M., Dimiduk, D.M., and Uchic, M.D.: Size effects in LiF micron-scale single crystals of low dislocation density. J. Mater. Res. 23(11), 2829 (2008).CrossRefGoogle Scholar
25.Shim, S., Bei, H., Miller, M.K., Pharr, G.M., and George, E.P.: Effects of focused-ion-beam milling on the compressive behavior of directionally solidified micropillars and the nanoindentation response of an electropolished surface. Acta Mater. 57(2), 503 (2009).CrossRefGoogle Scholar
26.Motz, C., Schoberl, T., and Pippan, R.: Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique. Acta Mater. 53(15), 4269 (2005).CrossRefGoogle Scholar
27.Epstein, S.G. and Carlson, O.N.: Elastic constants of nickel-copper alloy single crystals. Acta Metall. 13(5), 487 (1965).CrossRefGoogle Scholar
28.Ledbetter, H.N. and Naimon, E.R.: Elastic properties of copper. J. Phys. Chem. Ref. Data 3(4), 897 (1974).CrossRefGoogle Scholar
29.Jacobsen, E.H.: Elastic spectrum of copper from temperature scattering of x-rays. Phys. Rev. 94(5), 1420 (1954).Google Scholar
30.Hiki, Y. and Granato, A.V.: Anharmonicity in noble metals Higher order elastic constants. Phys. Rev. 144(2), 411 (1966).CrossRefGoogle Scholar
31.Hearmon, R.F.S.: The elastic constants of anisotropic materials. Rev. Mod. Phys. 18(3), 409 (1946).CrossRefGoogle Scholar
32.Hearmon, R.F.S.: The elastic constants of anisotropic materials II. Adv. Phys. 5(19), 323 (1956).CrossRefGoogle Scholar