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Research Papers

Analysis of Sinusoidal Interfacial Wrinkling of an Anisotropic Film Sandwiched Between Two Compliant Layers

[+] Author and Article Information
J. W. Yang

Institute of Applied Mechanics,
School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China

G. H. Nie

Institute of Applied Mechanics,
School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China
e-mail: ghnie@tongji.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 26, 2014; final manuscript received July 6, 2014; accepted manuscript posted July 9, 2014; published online July 21, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(9), 091013 (Jul 21, 2014) (11 pages) Paper No: JAM-14-1227; doi: 10.1115/1.4027974 History: Received May 26, 2014; Revised July 06, 2014; Accepted July 09, 2014

When a stiff film is bonded to a compliant layer and meanwhile encapsulated by another compliant layer on top, the film may form wrinkles under applied compressive stress. Inspired by the recent development of foldable circuit sealed in an encapsulating layer to improve bendability, unlike the wide study of surface wrinkling in a bilayer system, this paper presents a study of possible sinusoidal interfacial wrinkling in such sandwich system. The film is assumed to be anisotropic with arbitrary orientation of elastic axis while both layers are isotropic. A linear perturbation analysis is performed to predict critical membrane stress, wave number and equilibrium amplitude for the onset of interfacial wrinkles. The effect of parameters such as elastic axis orientation of the film and moduli, thicknesses, and Poisson's ratios of the layers on the wrinkling is evaluated in detail. The results show that compared to two compliant layers, the stiffer and thinner the film is, the smaller the values of both the critical stress and wave number for wrinkling will be. Especially, we illustrate three limiting cases: two layers both reach thick-layer limit, two layers both reach thin-layer limit and one layer reaches thick-layer limit while the other layer reaches thin-layer limit. Analytical solutions are obtained for first two cases and numerical solutions are plotted for the third case. It is found that as long as the thin-layer is near incompressible, the interfacial wrinkles can be suppressed. In addition, the equilibrium wave modes for the three limiting cases are also given. The resulting solutions for the sandwich system can be reduced to the classic solutions for a bilayer system.

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Figures

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Fig. 1

(a) Schematics of undeformed sandwich system that a stiff film is in between of two finite-thickness compliant layers which in turn are bonded to rigid supports. (b) Deformed sandwich system that film forms interfacial wrinkles with wavelength described as λ and the wave number can be calculated as k = 2π/λ.

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Fig. 2

(a) Schematics of in-plane elastic axis of anisotropic material labeled as 1,2 and Cartesian coordinates as global coordinates labeled as x,y. The rotate angle between the two set of coordinates is θ, which is also defined as elastic axis orientation angle. (b) The in-plane modulus of film in x direction with variation of θ.

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Fig. 3

The normalized membrane stress as a function of normalized wave number with variations of two layers' (a) moduli, (b) thicknesses, (c) Poisson's ratios, and (d) elastic axis orientation angle of the film

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Fig. 4

The critical normalized membrane stress, wave number and the equilibrium amplitude as a function of thicknesses ratio of the layers and film with variations of both layers' moduli. Left column shows νu = νl = 0.3 and right column shows νu = 0.1,νl = 0.49. The insets show the close-up view of rectangular region in the figure.

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Fig. 5

The effects of elastic axis orientation angle of film on the critical membrane stress and wave number with variations of moduli, thicknesses, and Poisson's ratios of both layers

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Fig. 6

The normalized critical membrane stress and wave number as a function of elastic axis orientation angle of film with variations of moduli and Poisson's ratios of both layers for a film sandwiched between a thick layer and a thin layer

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Fig. 7

The equilibrium wave modes for the three limiting cases when E¯u/C¯¯11 = E¯l/C¯¯11 = 0.01, t/Hu = t/Hl = 10, νu = νl = 0.3, σxx0/C¯¯11 = -0.5

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