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On the validity regime of the bulge equations

Published online by Cambridge University Press:  04 April 2012

Jan Neggers
Affiliation:
Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
Johan P.M. Hoefnagels*
Affiliation:
Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
Marc G.D. Geers
Affiliation:
Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
*
a)Address all correspondence to this author. e-mail: [email protected]
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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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Articles
Copyright
Copyright © Materials Research Society 2012

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References

REFERENCES

1.Nix, W.D.: Mechanical properties of thin films. Metall. Trans. A 20, 22172245 (1989).CrossRefGoogle Scholar
2.Kalkman, A.J., Verbruggen, A.H., Janssen, G.C.A.M., and Radelaar, S.: Transient creep in free-standing thin polycrystalline aluminum films. J. Appl. Phys. 92(9), 49684975 (2002).CrossRefGoogle Scholar
3.Ramesh, R. and Spaldin, N.A.: Multiferroics: Progress and prospects in thin films. Nat. Mater. 6, 2129 (2007).CrossRefGoogle ScholarPubMed
4.Thompson, C.V.: The yield stress of polycrystalline thin films. J. Mater. Res. 8(2), 237238 (1993).CrossRefGoogle Scholar
5.Vinci, R.P. and Vlassak, J.J.: Mechanical behavior of thin films. Annu. Rev. Mater. Sci. 26, 432462 (1996).CrossRefGoogle Scholar
6.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, 18211830 (2005).CrossRefGoogle Scholar
7.Gruber, P.A., Böhm, J., Onuseit, F., Wanner, A., Spolenak, R., and Arzt, E.: 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, 23182335 (2008).CrossRefGoogle Scholar
8.Arzt, E.: Size effects in materials due to microstructural and dimensional constraints: A comparative review. Acta Mater. 46(16), 56115626 (1998).CrossRefGoogle Scholar
9.Freund, L.B. and Suresh, S.: Thin Film Materials: Stress, Defect Formation, and Surface Evolution (Cambridge University Press, New York, 2003).Google Scholar
10.Vlassak, J.J. and Nix, W.D.: A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J. Mater. Res. 7(12), 32423249 (1992).CrossRefGoogle Scholar
11.Kalkman, A.J., Verbruggen, A.H., and Radelaar, S.: High-temperature tensile tests and activation volume measurement of free-standing submicron Al films. J. Appl. Phys. 92(11), 66126615 (2002).CrossRefGoogle Scholar
12.Xiang, Y., Chen, X., and Vlassak, J.J.: Plane-strain bulge test for thin films. J. Mater. Res. 20(9), 23602370 (2005).CrossRefGoogle Scholar
13.Xiang, Y. and Vlassak, J.J.: Bauschinger and size effects in thin-film plasticity. Acta Mater. 54, 54495460 (2006).CrossRefGoogle Scholar
14.Tsakalakos, T.: The bulge test: A comparison of theory and experiment for isotropic and anisotropic films. Thin Solid Films 75, 293305 (1981).CrossRefGoogle Scholar
15.Beams, J.W.: Mechanical properties of thin films of gold and silver, in Structure and Properties of Thin Films, edited by Neugebauer, C.A. (Wiley and Sons, New York, 1959) pp. 183192.Google Scholar
16.Small, M.K. and Nix, W.D.: Analysis of the accuracy of the bulge test in determining the mechanical properties of thin-films. J. Mater. Res. 7, 15531563 (1992).CrossRefGoogle Scholar
17.Martins, P., Delobelle, P., Malhaire, C., Brida, S., and Barbier, D.: 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).CrossRefGoogle Scholar
18.Bergers, L.I.J.C., Delhey, N.K.R., Hoefnages, J.P.M., and Geers, M.G.D.: Measuring time-dependent deformations in metallic MEMS. Microelectron. Reliab. 51(6), 10541059 (2011).CrossRefGoogle Scholar
19.Hetényi, M.: Application of Maclaurin series to the analysis of beams in bending. J. Franklin Inst. 254, 369380 (1952).CrossRefGoogle Scholar
20.Hsu, F.P.K., Liu, A.M.C., Downs, J., Rigamonti, D., and Humphrey, J.D.: A triplane video-based experimental system for studying axisymmetrically inflated biomembranes. IEEE Trans. Biomed. Eng. 42(5), 442450 (1995).CrossRefGoogle Scholar
21.Neggers, J., Hoefnagels, J.P.M., Hild, F., Roux, S., and Geers, M.G.D.: A global digital image correlation enhanced full-field bulge test method. Procedia IUTAM (2011, accepted).Google Scholar