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Research Papers

Buckling of Stressed and Pressurized Thin Films on Substrates

[+] Author and Article Information
Éloi Dion1

PHYMAT-CNRS UMR6630, University of Poitiers, 2 Bd Pierre et Marie Curie, Futuroscope 86962, Franceeloi.dion@univ-poitiers.fr

Jean Grilhé, Jérôme Colin, Christophe Coupeau

 University of Poitiers, SP2MI Teleport, 2 Bd Marie et Pierre Curie - BP 30179, Futuroscope 86962, France

1

Corresponding author.

J. Appl. Mech 77(4), 041012 (Apr 14, 2010) (5 pages) doi:10.1115/1.4000923 History: Received June 30, 2009; Revised December 08, 2009; Published April 14, 2010; Online April 14, 2010

The buckling solutions for a stressed thin film deposited on a semi-infinite rigid substrate have been determined in the framework of the Föppl–von Karman’s theory of thin plates and the perturbed bifurcation theory when pressures are applied onto the lower and upper free surfaces of the buckled film. It is found that the equilibrium solutions of the film are modified compared with the classical case of the Euler column, as well as the critical stress above which the film buckles.

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Figures

Grahic Jump Location
Figure 1

A thin film of thickness h under compression stress σ0 is considered on a stiff substrate. The film/substrate interface is initially delaminated on a distance 2b along the (Ox) axis. The pressure mismatch is defined as Δp=pint−pext with pint the pressure between the substrate and the film, and pext the pressure acting on the upper part of the film. σxx corresponds to the stress in the buckled part.

Grahic Jump Location
Figure 2

Case of a nickel thin film under tension. δ versus σ0 for a positive pressure mismatch Δp=0.02, 0.04, and 0.08 GPa. The stress values for the fully relaxed films are σ0=0.27, 1.1, and 4.4 GPa, respectively. E=200 GPa, ν=0.312, and b=10h with h=400 nm.

Grahic Jump Location
Figure 3

Case of a nickel thin film under compression. E=200 GPa, ν=0.312, b=4275 nm, and h=400 nm. (a) δ as a function of σ0 for a positive pressure mismatch Δp=10−4 GPa and for Δp=0. The zero pressure curve corresponds to the classical Euler column. (b) δ versus σ0 for a negative pressure mismatch Δp=−10−4 GPa and for Δp=0.

Grahic Jump Location
Figure 4

Variation in the new critical stress σc∗ with respect to the Euler critical stress σc versus the absolute value of the pressure mismatch |Δp|. E=200 GPa, ν=0.312, b=4275 nm, and h=400 nm.

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