Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T05:50:13.241Z Has data issue: false hasContentIssue false
  • English
  • Français

Can microscale fracture tests provide reliable fracture toughness values? A case study in silicon

Published online by Cambridge University Press:  09 February 2015

Balila Nagamani Jaya ,
Christoph Kirchlechner  and
Gerhard Dehm
Balila Nagamani Jaya
Affiliation:
Structure and Nano/Micro-mechanics of Materials, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany
Christoph Kirchlechner
Affiliation:
Structure and Nano/Micro-mechanics of Materials, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany; and University of Leoben, Leoben 8700, Austria
Gerhard Dehm*
Affiliation:
Structure and Nano/Micro-mechanics of Materials, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany
*
a)Address all correspondence to this author. e-mail: dehm@mpie.de
Get access

Abstract

Fracture toughness testing of materials at the micrometer scale has become essential due to the continuing miniaturization of devices accompanied by findings of size effects in fracture behavior. Many techniques have emerged in the recent past to carry out fracture toughness measurements at the relevant micro and nanolength scales, but they lack ASTM standards that are prescribed for bulk scale tests. Also, differences in reported values arise at the microscale due to the sample preparation technique, test method, geometry, and investigator. To correct for such discrepancies, we chose four different fracture toughness test geometries in practice, all of them micromachined in the focused ion beam (FIB), to investigate the fracture toughness of Si(100) at the micrometer scale. The average KIC that emerges from all four cases is a constant (0.8 MPa m1/2). The advantages and limitations of each of these geometries in terms of test parameters and the range of materials that can be tested are discussed.

Type
Articles
Information
Journal of Materials Research , Volume 30 , Issue 5 , 14 March 2015 , pp. 686 - 698
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Dehm, G., Motz, C., Scheu, C., Clemens, H., Maryhofer, P.H., and Mitterer, C.: Mechanical size effects in miniaturized and bulk materials. Adv. Eng. Mater. 8(11), 1033–1045 (2006).Google Scholar
Kraft, O., Gruber, P.A., Moenig, R., and Weygand, D.: Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40, 293–317 (2010).Google Scholar
Greer, J.R. and Hosson, J.D.: Plasticity in small scale metallic systems: Intrinsic vs extrinsic size effect. Prog. Mater. Sci. 56(6), 654–724 (2011).CrossRefGoogle Scholar
Chokshi, A.H., Rosen, A., Karch, J., and Gleiter, H.: On the validity of Hall-Petch relationship in nanocrystalline materials. Scr. Metall. 23, 1679–1684 (1989).Google Scholar
Carlton, C.E. and Ferreira, P.J.: What is behind the inverse Hall-Petch effect in nanocrystalline materials? Acta Mater. 55, 3749–3756 (2007).Google Scholar
Chen, C.P. and Leipold, M.H.: Fracture toughness of Si. Am. Ceram. Soc. Bull. 59, 469–472 (1980).Google Scholar
Ebrahimi, F. and Kalwani, L.: Fracture anisotropy in silicon single crystal. Mater. Sci. Eng., A 268, 116–126 (1999).CrossRefGoogle Scholar
Sundararajan, S. and Bhushan, B.: Development of AFM based techniques to measure mechanical properties of nanoscale structures. Sens. Actuators, A 101, 338–351 (2002).Google Scholar
Ando, T., Li, X., Nakao, S., Kasai, T., Tanaka, H., Shikida, M., and Sato, K.: Fracture toughness measurement of thin film silicon. Fatigue Fract. Eng. Mater. Struct. 28, 687–694 (2005).Google Scholar
Tanaka, M., Higashida, K., Nakashima, H., Takagi, H., and Fujiwara, M.: Orientation dependence of fracture toughness measured by indentation methods and its relation to surface energy in single crystal silicon. Int. J. Fract. 139, 383–394 (2006).Google Scholar
Ritchie, R.O.: Failure of silicon: Crack formation and propagation. In 13th Workshop on Crystalline Solar Cell Materials and Processes, Vail, Colorado, 2003.Google Scholar
ASTM E 1820-01: Standard test method for measurement of fracture toughness. In Ann Book ASTM Std, Vol. 03.01, 2001, pp. 1–46.Google Scholar
Yawny, A., Malarria, J., Soukup, E., and Sade, M.: Stage for in-situ mechanical loading experiments in a scanning electron microscope with a small chamber. Rev. Sci. Instrum. 68, 1500154 (1997).Google Scholar
Jaya, B.N. and Alam, M.Z.: Small-scale mechanical testing of materials. Curr. Sci. 105, 1073–1099 (2013).Google Scholar
Ipina, J.E.P. and Yawny, A.A.: In-situ observation of damage evolution and fracture toughness measurement by SEM. In Damage Prognosis for Aerospace, Civil and Mechanical Systems, edited by Inman, D. J., Farrar, D. J., Lopes, V. Jr, and Steffen, V. Jr. (2005); pp. 61–73.Google Scholar
Podor, R., Ravaoux, J., and Brau, H.: In-situ experiments in the scanning electron microscope chamber. In Scanning Electron Microscopy, edited by Kazmiruk, V.. (InTech, 2012); pp. 32–54.Google Scholar
Jaya, B.N., Bhowmick, S., S Asif, S.A., Warren, O.L. and Jayaram, V.: Optimisation of clamped beam geometry for fracture toughness testing of micron-scale samples. Philos (2015, in press). DOI.10.1080/14786435.2015.1010623.Google Scholar
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, 1564–1583 (1992).Google Scholar
Vliet, K.J.V., Prchlik, L., and Smith, J.F.: Direct measurement of indentation frame compliance. J. Mater. Res. 19, 325–331 (2004).Google Scholar
Asif, S.A.S., Wahl, K.J., and Colton, R.J.: Nanoindentation and contact stiffness measurement suing force modulation with a capacitive load-displacement transducer. Rev. Sci. Instrum. 70, 2408–2413 (1999).Google Scholar
Kupka, D.: Fracture experiments of single grain boundaries in ductile metals. PhD Thesis, Helmholtz-Zentrum Geesthacht, Germany, 2013.Google Scholar
Huerta, E., Corona, J.E., Oliva, A.I., Aviles, F., Gonzalez-Hernandez, J.: Universal testing machine for mechanical properties of thin materials. Rev. Mex. Fis. 56(4), 317–322 (2010).Google Scholar
Fischer-Cripps, A.C.: Nanoindentation, 2nd ed. (Springer, New York, NY, 2004).Google Scholar
Peret, C.M. and Rodrigues, J.M.: Stability of crack propagation during bending tests on brittle materials. Ceramica 54, 382–387 (2008).Google Scholar
Matoy, K., Schoenherr, H., Detzel, T., Pippan, R., Motz, C., and Dehm, G.: A comparative microcantilever study of the mechanical behavior of silicon based passivation films. Thin Solid Films 518, 247–256 (2009).Google Scholar
Jaya, B.N., Jayaram, V., and Biswas, S.K.: A new method for fracture toughness determination of graded (Pt, Ni)Al bond coats by microbeam bend tests. Philos. Mag. 92, 3326–3345 (2012). Special Issue: Nano-mechanical testing in materials research and development III.Google Scholar
Liu, S., Wheeler, J.M., Howie, P.R., Zeng, X.T., Michler, J., and Clegg, W.J.: Measuring the fracture resistance of hard coatings. Appl. Phys. Lett. 102, 1719071–1719074 (2013).Google Scholar
Sebastiani, M., Johanns, K.E., Herbert, E.G., Carasitti, F., and M Pharr, G.: A novel pillar indentation splitting test for measuring fracture toughness of thin ceramic coatings. Philos. Mag. (2014). DOI: 10.1080/14786435.2014.913110.Google Scholar
Jaya, B.N. and Jayaram, V.: Crack stability in edge notched clamped beam specimen: Modeling and experiments. Int. J. Fract. 188, 213–228 (2014).Google Scholar
Hopcroft, M.A., Nix, W.D., and Kenny, T.W.: What is the Young’s modulus of Si? J. Microelectromech. Syst. 19, 229–238 (2010).Google Scholar
Timoshenko, S. and Goodier, J.N.: Theory of Elasticity, 2nd ed. (McGraw-Hill, New York, NY, 1951).Google Scholar
Sebastiani, M.: Private communication, 2014.Google Scholar
Li, H. and Vlassak, J.J.: Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation. J. Mater. Res. 24, 1114–1126 (2009).Google Scholar
Di Maio, D. and Roberts, S.G.: Measuring fracture toughness of coatings using focused-ion-beam-machined microbeams. J. Mater. Res. 20, 299–302 (2005).CrossRefGoogle Scholar
Takashima, K. and Higo, Y.: Fatigue and fracture of a Ni-P amorphous alloy thin film on the micrometer scale. Fatigue Fract. Eng. Mater. Struct. 28, 703–710 (2005).Google Scholar
Halford, T.P., Rudinal, D., Takashima, K., and Higo, Y.: The effect of sample preparation upon the fracture toughness of microsized TiAl. Key Eng. Mater. 297–300, 2416–2422 (2005).Google Scholar
Wurster, S., Motz, C., and Pippan, R.: Characterisation of fracture toughness of micron-sized tungsten single crystal notched specimens. Philos. Mag. 92, 1803–1825 (2012).Google Scholar
Iqbal, F., Ast, J., Goeken, M., and Durst, K.: In-situ microcantilever tests to study fracture properties of NiAl single crystals. Acta Mater. 60, 1193–1200 (2012).Google Scholar
Armstrong, D.E.J., Wilkinson, A.J., and Roberts, S.G.: Micro-mechanical measurements of fracture toughness of bismuth embrittled copper grain boundaries. Philos. Mag. Lett. 91(6), 394–400 (2011).Google Scholar
Mueller, M.: Microscopic chevron-notch fracture test of alumina reinforcements. Nanobruecken (2014).Google Scholar
Iqbal, F.: Fracture mechanisms of γ-TiAl alloys investigated by in-situ experiments in a scanning electron and atomic force microscope. PhD Thesis, Universität Erlangen-Nürnberg, Erlangen, Germany, 2012.Google Scholar
Noyen, I.C. and Cohen, J.B.: Residual Stress Measurement by Diffraction and Interpretation (Springer-Verlag, New York, 1987).Google Scholar
Brenner, A. and Senderoff, S.: Calculation of stress in electrodeposits from the curvature of a plated strip. J. Res. Natl. Bur. Stand. 42, 105–123 (1949).Google Scholar
Ager, J.W. III and Drory, M.D.: Quantitative measurement of residual biaxial stress by Raman spectroscopy in diamond grown on a Ti alloy by chemical vapor deposition. Phys. Rev. B. 48, 2601–2607 (1993).Google Scholar
Fang, W. and Wickert, J.: Determining mean and gradient residual stresses in thin films using micromachined cantilevers. J. Micromech. Microeng. 6, 301–309 (1996).Google Scholar
Sebastiani, M., Bemporad, E., Carasitti, F., and Schwarzer, N.: Residual stress measurement at the micrometer scale: Focused ion beam milling and nanoindentation testing. Philos. Mag. 91, 1121–1136 (2011).Google Scholar
Beres, W., Koul, A.K., and Thamburaj, R.: A tapered double cantilever beam specimen designed for constant K-testing at elevated temperatures. J. Test. Eval. 25, 536–542 (1997).Google Scholar
Brown, E.N.: Use of the tapered double-cantilever beam geometry for fracture toughness measurements and its application to the quantification of self-healing. J. Strain Anal. Eng. Des. 46, 167–186 (2010).Google Scholar
Qiao, Y.: PhD Thesis, MIT, 2002.Google Scholar
Gatzen, H.H. and Beck, M.: Investigations on the friction force anisotropy of the silicon lattice. Wear 254, 1122–1126 (2003).CrossRefGoogle Scholar
Pharr, G.M.: The anomalous behavior of silicon during nanoindentation. Mater. Res. Soc. Symp. Proc. 239, 301–312 (1992).Google Scholar
Gerberich, W.W., Stauffer, D.D., Beaber, A.R., and Tymiak, N.I.: A brittleness transition in silicon due to scale. J. Mater. Res. 27, 552–567 (2012).CrossRefGoogle Scholar
Han, Z., Zheng, K., Zhang, Y.F., Zhang, Z., and Wang, Z.L.: Low temperature in-situ large strain plasticity of silicon nanowires. Adv. Mater. 19, 2112–2118 (2007).Google Scholar
Oestlund, F., Malyska, K.R., Leifer, K., Hale, L.M., Tang, Y., Ballarini, R., Gerberich, W.W., and Michler, J.: Brittle to ductile transition in uniaxially compression of silicon pillars at room temperature. Adv. Funct. Mater. 19, 2439–2444 (2009).Google Scholar
Gludovatz, P., Wuster, S., Hoffmann, A., and Pippan, R.: A study into the crack propagation resistance of pure tungsten. Eng. Fract. Mech. 100, 76–85 (2013).CrossRefGoogle Scholar
Tsuchiya, T., Sakata, J., and Taga, Y.: Tensile strength and fracture toughness of surface micromachined polycrystalline silicon thin films prepared under various conditions. MRS Symp. Proc. 505, 285–290 (1997).CrossRefGoogle Scholar
Myers, R.J. and Hillberry, B.M.: Effect of notch root radius on the fracture behavior of monocrystalline silicon. In Proceedings, 4th International Conference on Fracture, Waterloo, Canada, Vol. 3, 1001–1005 (1977).Google Scholar
Sharpe, W.N., Yuan, B., and Edwards, R.L.: Fracture tests of polysilicon film. MRS Symp. Proc. 505, 51–56 (1997).Google Scholar
Rubanov, S. and Munroe, P.R.: FIB induced damage in silicon. J. Microsc. 24, 213–221 (2004).Google Scholar
Kahn, H., Tayebi, N., Ballarini, R., Mullen, R.L., and Heuer, A. H.: Fracture toughness of polysilicon MEMS devices. Sens. Actuators, A 82, 274–280 (2000).Google Scholar
Chasiotis, I., Cho, S.W., and Jonnalagadda, K.: Fracture toughness and subcritical crack growth in polycrystalline silicon. J. Appl. Mech. 73, 714–722 (2005).CrossRefGoogle Scholar