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TECHNICAL PAPERS

Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates

[+] Author and Article Information
X. Chen

Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027

John W. Hutchinson

Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

J. Appl. Mech 71(5), 597-603 (Nov 09, 2004) (7 pages) doi:10.1115/1.1756141 History: Received May 14, 2003; Revised October 30, 2003; Online November 09, 2004
Copyright © 2004 by ASME
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References

Figures

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Buckling of a 50 nm gold film on a thick elastomer (PDMS) substrate. On the right, the substrate has been patterned with alternating flat depressions, 2. The substrate on the left two-thirds of the figure is flat and not patterned. The herringbone pattern is on the left. The wavelength of the pattern across the crests is approximately 30 μm while the distance between jogs of the herringbone mode is approximately 100 μm.
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Gold film on a substrate which has been patterned with a circular flat depression of several millimeters in diameter, 1. The herringbone pattern emerges in the center of the spot and outside the edges of the spot.
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An example from 3 of a highly organized buckling pattern for a film/substrate system. As depicted, the film is forced to buckle into a mold with a square pattern, after which the mold is removed.
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Ratio of average elastic energy per unit area in the film/substrate system in the buckled state to that in the unbuckled state, U/U0, as a function of σ00C for the one-dimensional mode. Results are shown for several wavelengths. Note that the wavelength that is critical at the onset of buckling (k1=k1C) produces the minimum energy in the buckled state even when σ0 is well above σ0C.
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Buckling amplitude of the film, w⁁/t, as a function of σ00C for the three modes considered. The wavelengths (and inclination in the case of the herringbone mode) correspond to the critical at the onset of buckling.
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Ratio of average elastic energy per unit area in the film/substrate system in the buckled state to that in the unbuckled state, U/U0, as a function of σ00C for the three modes considered. The wavelengths (and inclination in the case of the herringbone mode) correspond to the critical at the onset of buckling. At σ00C well above unity, the herringbone mode lowers the energy more than the other two modes.
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Periodic cell of the herringbone mode
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Contour plots of the normal deflection of the film in the herringbone mode at σ00C=26 (a,b) and σ00C=4 (c) for several values of the breadth of the periodic cell, all with a/L=2 and α=45 deg
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Variation of U/U0 as a function of σ00C for the herringbone mode. (a) Dependence on L/LC with a/L=2 and α=45 deg. (b) Dependence on a/L with L/LC=1 and α=45 deg. (c) Dependence on α with L/LC=1 and a/L=2.

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