Determining the elastic modulus of thin films using a buckling-based method

Computational study

Xiu Peng Zheng, Yan Ping Cao*, Bo Li, Xi Qiao Feng, Hanqing Jiang, Yonggang Huang

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The buckling mode of a thin film lying on a soft substrate has been used to determine the elastic modulus of thin films and one-dimensional objects (e.g. nanowires and nanotubes). In this paper, dimensional analysis and three-dimensional nonlinear finite element computations have been made to investigate the buckling of a film with finite width bonded to a compliant substrate. Our study demonstrates that the effect of Poisson's ratio of the film can be neglected when its width-thickness ratio is smaller than 20. For wider films, omitting the influence of Poisson's ratio may lead to a significant systematic error in the measurement of the Young's modulus and, therefore, the film should be treated as a plate. It is also found that the assumption of the uniform interfacial normal stress along the width of the film made in the theoretical analysis does not cause an evident error, even when its width is comparable to its thickness. Based on the computational results, we further present a simple expression to correlate the buckling wavelength with the width and thickness of the film and the material properties (Young's moduli and Poisson's ratios) of the film and substrate, which has a similar form to that in the classical plane-strain problem. The fundamental solutions reported here are not only very accurate in a broad range of geometric and material parameters but also convenient for practical use since they do not involve any complex calculation.

Original languageEnglish (US)
Article number175506
JournalJournal of Physics D: Applied Physics
Volume42
Issue number17
DOIs
StatePublished - Sep 17 2009

Fingerprint

buckling
Computational methods
Buckling
modulus of elasticity
Elastic moduli
Thin films
thin films
Poisson ratio
Substrates
thickness ratio
Systematic errors
dimensional analysis
plane strain
systematic errors
Nanotubes
Nanowires
nanotubes
Materials properties
nanowires
Wavelength

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Surfaces, Coatings and Films

Cite this

Zheng, Xiu Peng ; Cao, Yan Ping ; Li, Bo ; Feng, Xi Qiao ; Jiang, Hanqing ; Huang, Yonggang. / Determining the elastic modulus of thin films using a buckling-based method : Computational study. In: Journal of Physics D: Applied Physics. 2009 ; Vol. 42, No. 17.
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Determining the elastic modulus of thin films using a buckling-based method : Computational study. / Zheng, Xiu Peng; Cao, Yan Ping; Li, Bo; Feng, Xi Qiao; Jiang, Hanqing; Huang, Yonggang.

In: Journal of Physics D: Applied Physics, Vol. 42, No. 17, 175506, 17.09.2009.

Research output: Contribution to journalArticle

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