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On the validity regime of the bulge equations

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Abstract

The plane strain bulge test technique is a powerful and acknowledged technique for characterizing the mechanical behavior of thin films. In a bulge test analysis, the stress and strain are derived from the measured quantities using analytical approximations of the deformed geometry (bulge equations). To improve the bulge test, the systematic error introduced by these approximations is evaluated and quantified by scrutinizing the method on a finite element model of the bulge test, used as an idealized experiment.

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References

  1. W.D. Nix: Mechanical properties of thin films. Metall. Trans. A 20, 2217–2245 (1989).

    Article  Google Scholar 

  2. A.J. Kalkman, A.H. Verbruggen, G.C.A.M. Janssen, and S. Radelaar: Transient creep in free-standing thin polycrystalline aluminum films. J. Appl. Phys. 92 (9), 4968–4975 (2002).

    Article  CAS  Google Scholar 

  3. R. Ramesh and N.A. Spaldin: Multiferroics: Progress and prospects in thin films. Nat. Mater. 6, 21–29 (2007).

    CAS  Google Scholar 

  4. C.V. Thompson: The yield stress of polycrystalline thin films. J. Mater. Res. 8 (2), 237–238 (1993).

    Article  Google Scholar 

  5. R.P. Vinci and J.J. Vlassak: Mechanical behavior of thin films. Annu. Rev. Mater. Sci. 26, 432–462 (1996).

    Article  Google Scholar 

  6. J.R. Greer, W.C. Oliver, and W.D. Nix: Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients. Acta Mater. 53, 1821–1830 (2005).

    Article  CAS  Google Scholar 

  7. P.A. Gruber, J. Böhm, F. Onuseit, A. Wanner, R. Spolenak, and E. Arzt: Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: A study by synchrotron and bulge test techniques. Acta Mater. 56, 2318–2335 (2008).

    Article  CAS  Google Scholar 

  8. E. Arzt: Size effects in materials due to microstructural and dimensional constraints: A comparative review. Acta Mater. 46 (16), 5611–5626 (1998).

    Article  CAS  Google Scholar 

  9. L.B. Freund and S. Suresh: Thin Film Materials: Stress, Defect Formation, and Surface Evolution (Cambridge University Press, New York, 2003).

    Google Scholar 

  10. J.J. Vlassak and W.D. Nix: A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J. Mater. Res. 7 (12), 3242–3249 (1992).

    Article  CAS  Google Scholar 

  11. A.J. Kalkman, A.H. Verbruggen, and S. Radelaar: High-temperature tensile tests and activation volume measurement of free-standing submicron Al films. J. Appl. Phys. 92 (11), 6612–6615 (2002).

    Article  CAS  Google Scholar 

  12. Y. Xiang, X. Chen, and J.J. Vlassak: Plane-strain bulge test for thin films. J. Mater. Res. 20 (9), 2360–2370 (2005).

    Article  CAS  Google Scholar 

  13. Y. Xiang and J.J. Vlassak: Bauschinger and size effects in thin-film plasticity. Acta Mater. 54, 5449–5460 (2006).

    Article  CAS  Google Scholar 

  14. T. Tsakalakos: The bulge test: A comparison of theory and experiment for isotropic and anisotropic films. Thin Solid Films 75, 293–305 (1981).

    Article  CAS  Google Scholar 

  15. J.W. Beams: Mechanical properties of thin films of gold and silver, in Structure and Properties of Thin Films, edited by C.A. Neugebauer (Wiley and Sons, New York, 1959) pp. 183–192.

    Google Scholar 

  16. M.K. Small and W.D. Nix: Analysis of the accuracy of the bulge test in determining the mechanical properties of thin-films. J. Mater. Res. 7, 1553–1563 (1992).

    Article  CAS  Google Scholar 

  17. P. Martins, P. Delobelle, C. Malhaire, S. Brida, and D. Barbier: Bulge test and AFM point deflection method, two technics for the mechanical characterisation of very low stiffness freestanding films. Eur. Phys. J. Appl. Phys. 45, 10501 (2009).

    Article  Google Scholar 

  18. L.I.J.C. Bergers, N.K.R. Delhey, J.P.M. Hoefnages, and M.G.D. Geers: Measuring time-dependent deformations in metallic MEMS. Microelectron. Reliab. 51 (6), 1054–1059 (2011).

    Article  CAS  Google Scholar 

  19. M. Hetényi: Application of Maclaurin series to the analysis of beams in bending. J. Franklin Inst. 254, 369–380 (1952).

    Article  Google Scholar 

  20. F.P.K. Hsu, A.M.C. Liu, J. Downs, D. Rigamonti, and J.D. Humphrey: A triplane video-based experimental system for studying axisymmetrically inflated biomembranes. IEEE Trans. Biomed. Eng. 42 (5), 442–450 (1995).

    Article  Google Scholar 

  21. J. Neggers, J.P.M. Hoefnagels, F. Hild, S. Roux, and M.G.D. Geers: A global digital image correlation enhanced full-field bulge test method. Procedia IUTAM (2011, accepted).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ, Eindhoven, The Netherlands

    Jan Neggers, Johan P. M. Hoefnagels & Marc G. D. Geers

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  1. Jan Neggers
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  2. Johan P. M. Hoefnagels
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  3. Marc G. D. Geers
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Correspondence to Johan P. M. Hoefnagels.

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Neggers, J., Hoefnagels, J.P.M. & Geers, M.G.D. On the validity regime of the bulge equations. Journal of Materials Research 27, 1245–1250 (2012). https://doi.org/10.1557/jmr.2012.69

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  • DOI: https://doi.org/10.1557/jmr.2012.69

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