Plane-strain bulge test for thin films


*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

188 Citations (Scopus)


The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress-strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress-strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress-strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations. © 2005 Materials Research Society.
Original languageEnglish
Pages (from-to)2360-2370
Number of pages11
JournalJournal of Materials Research
Issue number9
Early online date1 Sept 2005
Publication statusPublished - Sept 2005
Externally publishedYes

Bibliographical note

The authors are grateful for the support from the Division of Engineering and Applied Sciences and the Materials Research Science and Engineering Center at Harvard University, Cambridge, MA. This research was funded by National Science Foundation (NSF) Grant Nos. DMR-0133559 and DMR-0215902 at Harvard University and by NSF Grant No. CMS-0407743 at Columbia University, New York, NY.


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