Improved Bulge Test Methodology to Characterize Non-buckled and Buckled Ultra Thin Membranes

Research output: Contribution to conferenceAbstractAcademic


Ultra-thin membranes find an increasing amount of applications within the high-tech sector to obtain high performance and reliability. A decrease in membrane thickness could lead to an increase in deviation from the materials bulk behavior. To increase performance and reliability, the material behavior needs to be better understood.

Bulge testing has become the standard technique for mechanical characterization. Still there is only ample of research on improving the accuracy of the bulge setup. Therefore, circular free standing membranes with both compressive and tensile residual stress are manufactured. The height profile, while applying pressure, is measured with a digital holographic microscope, increasing the measurement speed and accuracy. Normally, the deflection of the apex is measured to calculate the stress and strain. This requires a zero stress state reference, which could be difficult or time consuming to measure. Instead, the bulge formulas are rewritten to be used without knowledge of the zero stress state reference and to use the complete measured height profile, improving the accuracy even further.
From these circular samples the biaxial modulus and residual stresses are deduced.

To additionally derive the Young’s Modulus and Poisson ratio, rectangular membranes are needed. Rectangular membranes with a tensile stress and high scaled strain value will deform cylindrically[1]. From these membranes, the plane strain modulus is deduced. Most ultra-thin layers with a compressive residual stress have the tendency to buckle. Generally, it is thought the bulge test is unsuited to analyze these membranes due to the negligible out-of-plane bending stiffness. Accurate but cumbersome time consuming procedures have previously been developed to analyze these membranes[2]. A new improved methodology has been made to quickly analyze the membranes. The new methodology has numerically been validated and an error analysis is performed to find the main causes of errors and reduce them. This new methodology is applied to characterize ultra-thin membranes with a compressive stress.

[1] J. Neggers, J. P. Hoefnagels, and M. G. Geers, “On the validity regime of the bulge equations,”
Journal of Materials Research, vol. 27, no. 9, pp. 1245–1250, 2012

[2] S. Shafqat, O. van der Sluis, M. Geers, and J. Hoefnagels, “A bulge test based methodology for
characterizing ultra-thin buckled membranes,” Thin Solid Films, vol. 660, no. April, pp. 88–
100, 2018
Original languageEnglish
Publication statusPublished - 13 Jun 2022
EventSociety for Experimental Mechanics (SEM) Annual Conference 2022
- Omni William Penn Pittsburgh, Pittsburgh, United States
Duration: 13 Jun 202216 Jun 2022


ConferenceSociety for Experimental Mechanics (SEM) Annual Conference 2022
Country/TerritoryUnited States
Internet address


  • Ultra-thin Membranes
  • bulge testing
  • buckling


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