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Research Papers

Phase Diagrams of Instabilities in Compressed Film-Substrate Systems

[+] Author and Article Information
Qiming Wang

Soft Active Materials Laboratory,
Department of Mechanical Engineering and
Materials Science,
Duke University,
Durham, NC 27708

Xuanhe Zhao

Soft Active Materials Laboratory,
Department of Mechanical Engineering and
Materials Science,
Duke University,
Durham, NC 27708
e-mail: xz69@duke.edu

1Corresponding author.

Manuscript received September 27, 2013; final manuscript received October 23, 2013; accepted manuscript posted October 28, 2013; published online December 10, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051004 (Dec 10, 2013) (10 pages) Paper No: JAM-13-1408; doi: 10.1115/1.4025828 History: Received September 27, 2013; Revised October 23, 2013; Accepted October 28, 2013

Subject to a compressive membrane stress, an elastic film bonded on a substrate can become unstable, forming wrinkles, creases or delaminated buckles. Further increasing the compressive stress can induce advanced modes of instabilities including period-doubles, folds, localized ridges, delamination, and coexistent instabilities. While various instabilities in film-substrate systems under compression have been analyzed separately, a systematic and quantitative understanding of these instabilities is still elusive. Here we present a joint experimental and theoretical study to systematically explore the instabilities in elastic film-substrate systems under uniaxial compression. We use the Maxwell stability criterion to analyze the occurrence and evolution of instabilities analogous to phase transitions in thermodynamic systems. We show that the moduli of the film and the substrate, the film-substrate adhesion strength, the film thickness, and the prestretch in the substrate determine various modes of instabilities. Defects in the film-substrate system can facilitate it to overcome energy barriers during occurrence and evolution of instabilities. We provide a set of phase diagrams to predict both initial and advanced modes of instabilities in compressed film-substrate systems. The phase diagrams can be used to guide the design of film-substrate systems to achieve desired modes of instabilities.

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Figures

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Fig. 1

Schematic illustration of the experimental procedure to observe various modes of instabilities in film-substrate systems under uniaxial compression

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Fig. 2

Schematic illustration of the evolution of a film-substrate system's potential energy with the applied compressive strain and the transition of states

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Fig. 3

The adhesion energy between Sylgard films and prestretched Ecoflex substrates

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Fig. 4

Schematic illustration of a film-substrate system under plane-strain deformation (a-c), and the three initial modes of instabilities (d-f). Optical microscopic images of the wrinkling (g, top view; h, side view), creasing (i, top view; j, side view), and delaminated buckling (k, top view; l, side view) instabilities.

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Fig. 5

A finite-element model for calculating the elastic energy of a film-substrate system at the delaminated buckled state (a). The calculated elastic (b) and potential (c) energy difference between the delaminated buckled and flat states as functions of the applied compressive strain and delaminated length. The calculated energy barrier for the transition from flat to delaminated buckled states (d). Optical microscopic images of the initiation and propagation of a delaminated buckle in a film-substrate system under compression (e). The delaminated buckle initiates at defects on the film-substrate interface as indicated by an arrow.

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Fig. 6

The calculated critical strains (a) and phase diagram (b) of the initial modes of instabilities in film-substrate systems with λp=1

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Fig. 7

The calculated phase diagrams of the initial modes of instabilities in film-substrate systems with λp=2 (a) and λp=3 (b), respectively. Comparison of the experimentally observed instabilities and the calculated phase diagram of instabilities in a film-substrate system with λp=2 is plotted in (a).

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Fig. 8

Schematic illustration of advanced modes of instabilities transited from the wrinkling instability in a film-substrate system with λp=1 (a-d). Optical microscopic images of the double-doubling (e), folding (f), and delaminated buckling (g) instabilities in film-substrate systems with λp=1.

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Fig. 9

Schematic illustration of advanced modes of instabilities transited from the wrinkling instability in a film-substrate system with λp=2 (a-c). Optical microscopic images of the localized ridge (d) and delaminated buckling instabilities (e) in film-substrate systems with λp=2.

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Fig. 10

A finite-element model for calculating the elastic energy of the delaminated buckled state transited from the wrinkled state (a). The calculated potential energy difference between the delaminated buckled and the corresponding wrinkled states as functions of the applied compressive strain and delaminated length (b). The calculated critical strain for the delaminated buckling instability transited from the wrinkling instability (c). It is higher than the critical strain for wrinkling instability.

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Fig. 11

The evolution of potential energies of film-substrate systems from wrinkling to various advanced modes of instabilities calculated by finite element models: from wrinkling to delaminated buckling and period-doubling at λp=1 (a), from wrinkling to delaminated buckling and folding at λp=1 (b), and from wrinkling to delaminated buckling and localized ridge at λp=2 (c). At sufficiently low values of Γ/(μsHf), the delaminated buckling can precede other advanced modes of instabilities.

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Fig. 12

The calculated phase diagrams of advanced modes of instabilities transited from the wrinkling instability in film-substrate systems with λp=1 (a) and λp=2 (b)

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Fig. 13

The nominal stress versus stretch curve of the Sylgard films used in the current study under uniaxial tension. When the stretch is lower than 2.2, the Sylgard films follow the neo-Hookean law.

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Fig. 14

The evolution of potential energies of film-substrate systems from flat state to wrinkled state calculated by the finite-element model as shown in the inset (a). The critical strain for wrinkling for various modulus ratio μf/μs and prestretch λp (b). The calculated critical strain for wrinkling in (a) matches the prediction in (b). In the finite element calculation, the thickness of the substrate and width of the model are much larger than the film thickness. A small force perturbation is applied to the film under compression to trigger the wrinkling.

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