Research Papers

Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface

[+] Author and Article Information
Jia-Wen Wang, Bo Li, Yan-Ping Cao

Department of Engineering Mechanics,
Institute of Biomechanics
and Medical Engineering,
Tsinghua University,
Beijing 100084, China

Xi-Qiao Feng

Department of Engineering Mechanics,
Institute of Biomechanics
and Medical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: fengxq@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 4, 2015; final manuscript received March 7, 2015; published online March 31, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(5), 051009 (May 01, 2015) (7 pages) Paper No: JAM-15-1066; doi: 10.1115/1.4030010 History: Received February 04, 2015; Revised March 07, 2015; Online March 31, 2015

Wrinkling of thin films resting on compliant substrates has emerged as a facile means to create well-ordered surface patterns. In this paper, both theoretical analysis and numerical simulations are presented to study the surface wrinkling of a film–substrate system with periodic interfacial structures. It is demonstrated that a variety of novel surface wrinkling patterns can be generated through the introduction of interfacial architectures. These surface patterns can be easily tuned by adjusting two geometric parameters: the lengths of the thin films in the thick and the thin regions. A phase diagram is established for the onset of different wrinkling morphologies with respect to the two geometric dimensions. This study offers a promising route for engineering the surfaces of materials endowed with tunable properties and functions.

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Fig. 1

(a) Film–substrate system with periodic interfacial microstructures and (b) a finite element method (FEM) model. The insets in (b) show the amplified mesh in the finite element simulations. (c) The system has stress concentration near the interfacial corners, where the elastic moduli μf=80μs=80 MPa, the film lengths L¯1=L¯2/8=0.7, and the compressive strain is 15%. The legend indicates the maximal principal stress Smax.

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Fig. 2

Six wrinkling patterns observed in FEM simulations: (a) sinusoidal wrinkles, (b) periodic tilted sawteeth, (c) slope–sine pattern consisting of rotated thick films and wrinkled thin films, (d) alternating upward–downward arcs, (e) sinusoidal wrinkles separated by shallow arcs, and (f) folded thin films separated by unbuckled thick films. The legend denotes the Lagrange strain in the x-direction.

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Fig. 3

Phase diagram of six wrinkling patterns with respect to the film lengths, where the modulus ratio is in the range of 70 < μf/μs < 1000

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Fig. 4

Phase diagram of the buckling modes in the thick film regions. The diamonds, triangles, and circles represent the results of finite element simulations for the sinusoidal wrinkling, Euler buckling, and rigid rotation modes, respectively.

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Fig. 5

(a) Theoretical model of a film–substrate system with a finite-length L1, (b) FEM model with L1 = 40 μm, (c) equivalent stiffnesses Kw, Kr, and Ke as functions of Es* when L1 = 20 μm, and (d) equivalent stiffnesses Kw, Kr, and Ke as functions of L1 when Es* = 1.3 MPa

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Fig. 6

(a) Schematic of the sinusoidal wrinkling morphology of the film in a thick region and (b) the finite element simulation result for the surface morphology of pattern VI. The legend denotes the Lagrange strain in the x-direction.

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Fig. 7

The critical strains ɛc for the occurrence of the sinusoidal wrinkling, Euler buckling, and rigid rotation modes, where Ef*/Es* is taken as 100. The magnitude of Ef*/Es* does not affect the critical lengths L¯1crot and L¯1csin.

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Fig. 8

(a) Schematic of the Euler buckling mode of a film, and the finite element simulation results for the surface morphologies of: (b) pattern V and (c) pattern IV. The legend denotes the Lagrange strain in the x-direction.

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Fig. 9

(a) Schematic of the pure rotation mode of a film, and the finite element simulation results for the surface morphologies of: (b) pattern I, (c) pattern III, and (d) pattern II. The legend denotes the Lagrange strain in the x-direction.




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