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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,
AML,
Tsinghua University,
Beijing 100084, China

Xi-Qiao Feng

Department of Engineering Mechanics,
Institute of Biomechanics
and Medical Engineering,
AML,
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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References

Cerda, E., 2005, “Mechanics of Scars,” J. Biomech., 38(8), pp. 1598–1603. [CrossRef] [PubMed]
Jeng, F. S., and Huang, K. P., 2008, “Buckling Folds of a Single Layer Embedded in Matrix-Theoretical Solutions and Characteristics,” J. Struct. Geol., 30(5), pp. 633–648. [CrossRef]
Lambert, R. K., Codd, S. L., Alley, M. R., and Pack, R. J., 1994, “Physical Determinants of Bronchial Mucosal Foldings,” J. Appl. Physiol., 77(3), pp. 1206–1216. [PubMed]
Li, B., Cao, Y. P., Feng, X. Q., and Gao, H., 2012, “Mechanics of Morphological Instabilities and Surface Wrinkling in Soft Materials: A Review,” Soft Matter, 8(21), pp. 5728–5745. [CrossRef]
Cao, Y. P., and Hutchinson, J. W., 2012, “Wrinkling Phenomena in Neo-Hookean Film/Substrate Bilayers,” ASME J. Appl. Mech., 79(3), p. 031019. [CrossRef]
Zang, J., Zhao, X., Cao, Y. P., and Hutchinson, J. W., 2012, “Localized Ridge Wrinkling of Stiff Films on Compliant Substrates,” J. Mech. Phys. Solids, 60(7), pp. 1265–1279. [CrossRef]
Wang, Q., and Zhao, X., 2014, “Phase Diagrams of Instabilities in Compressed Film–Substrate Systems,” ASME J. Appl. Mech., 81(5), p. 051004 [CrossRef].
Bowden, N., Brittain, S., Evans, A. G., Hutchinson, J. W., and Whitesides, G. M., 1998, “Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer,” Nature, 393(6681), pp. 146–149 [CrossRef].
Watanabe, M., and Mizukami, K., 2012, “Well-Ordered Wrinkling Patterns on Chemically Oxidized Poly(Dimethylsiloxane) Surfaces,” Macromolecules, 45(17), pp. 7128–7134. [CrossRef]
Vandeparre, H., Gabriele, S., Brau, F., Gay, C., Parker, K. K., and Damman, P., 2010, “Hierarchical Wrinkling Patterns,” Soft Matter, 6(22), pp. 5751–5756. [CrossRef]
Genzer, J., and Groenewold, J., 2006, “Soft Matter With Hard Skin: From Skin Wrinkles to Templating and Material Characterization,” Soft Matter, 2(4), pp. 310–323. [CrossRef]
Jiang, H., Khang, D. Y., Song, J., Sun, Y., Huang, Y., and Rogers, J. A., 2007, “Finite Deformation Mechanics in Buckled Thin Films on Compliant Supports,” Proc. Natl. Acad. Sci. U.S.A., 104(40), pp. 15607–15612. [CrossRef] [PubMed]
Song, J., Jiang, H., Liu, Z., Khang, D., Huang, Y., Rogers, J., Lu, C., and Koh, C., 2008, “Buckling of a Stiff Thin Film on a Compliant Substrate in Large Deformation,” Int. J. Solids Struct., 45(10), pp. 3107–3121. [CrossRef]
Shu, Y., Khare, K., and Pei-Chun, L., 2010, “Harnessing Surface Wrinkle Patterns in Soft Matter,” Adv. Funct. Mater., 20(16), pp. 2550–2564 [CrossRef].
Rogers, J. A., Someya, T., and Huang, Y., 2010, “Materials and Mechanics for Stretchable Electronics,” Science, 327(5973), pp. 1603–1607. [CrossRef] [PubMed]
Kim, J. B., Kim, P., Pegard, N. C., Soong Ju, O., Kagan, C. R., Fleischer, J. W., Stone, H. A., and Yueh-Lin, L., 2012, “Wrinkles and Deep Folds as Photonic Structures in Photovoltaics,” Nat. Photonics, 6(5), pp. 327–332. [CrossRef]
Huang, J., Juszkiewicz, M., de Jeu, W. H., Cerda, E., Emrick, T., Menon, N., and Russell, T. P., 2007, “Capillary Wrinkling of Floating Thin Polymer Films,” Science, 317(5838), pp. 650–653. [CrossRef] [PubMed]
Harris, A. K., Wild, P., and Stopak, D., 1980, “Silicone Rubber Substrata: New Wrinkle in the Study of Cell Locomotion,” Science, 208(4440), pp. 177–179. [CrossRef] [PubMed]
Chen, X., and Hutchinson, J. W., 2004, “Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates,” ASME J. Appl. Mech., 71(5), pp. 597–603. [CrossRef]
Song, J., Jiang, H., Choi, W., Khang, D., Huang, Y., and Rogers, J., 2008, “An Analytical Study of Two-Dimensional Buckling of Thin Films on Compliant Substrates,” J. Appl. Phys., 103(1), p. 014303. [CrossRef]
Lin, P. C., and Yang, S., 2007, “Spontaneous Formation of One-Dimensional Ripples in Transit to Highly Ordered Two-Dimensional Herringbone Structures Through Sequential and Unequal Biaxial Mechanical Stretching,” Appl. Phys. Lett., 90(24), p. 241903. [CrossRef]
Chan, E. P., and Crosby, A. J., 2006, “Fabricating Microlens Arrays by Surface Wrinkling,” Adv. Mater., 18(24), pp. 3238–3242. [CrossRef]
Breid, D., and Crosby, A. J., 2009, “Surface Wrinkling Behavior of Finite Circular Plates,” Soft Matter, 5(2), pp. 425–431. [CrossRef]
Xuan, Y., Guo, X., Cui, Y., Yuan, C., Ge, H., Cui, B., and Chen, Y., 2012, “Crack-Free Controlled Wrinkling of a Bilayer Film With a Gradient Interface,” Soft Matter, 8(37), pp. 9603–9609. [CrossRef]
Vella, D., Ajdari, A., Vaziri, A., and Boudaoud, A., 2011, “Wrinkling of Pressurized Elastic Shells,” Phys. Rev. Lett., 107(17), p. 174301. [CrossRef] [PubMed]
Li, B., Jia, F., Cao, Y. P., Feng, X. Q., and Gao, H., 2011, “Surface Wrinkling Patterns on a Core–Shell Soft Sphere,” Phys. Rev. Lett., 106(23), p. 234301. [CrossRef] [PubMed]
Wang, J. W., Cao, Y. P., and Feng, X. Q., 2014, “Archimedean Spiral Wrinkles on a Film–Substrate System Induced by Torsion,” Appl. Phys. Lett., 104(3), p. 031910. [CrossRef]
Zheng, X. P., Cao, Y. P., Li, B., Feng, X. Q., and Yu, S. W., 2010, “Surface Wrinkling of Nanostructured Thin Films on a Compliant Substrate,” Comput. Mater. Sci., 49(4), pp. 767–772. [CrossRef]
Lin, P. C., and Yang, S., 2009, “Mechanically Switchable Wetting on Wrinkled Elastomers With Dual-Scale Roughness,” Soft Matter, 5(5), pp. 1011–1018. [CrossRef]
Efimenko, K., Rackaitis, M., Manias, E., Vaziri, A., Mahadevan, L., and Genzer, J., 2005, “Nested Self-Similar Wrinkling Patterns in Skins,” Nat. Mater., 4(4), pp. 293–297. [CrossRef] [PubMed]
Huang, Y., Chen, H., Wu, J., and Feng, X., 2014, “Controllable Wrinkle Configurations by Soft Micro-Patterns to Enhance the Stretchability of Si Ribbons,” Soft Matter, 10(15), pp. 2559–2566. [CrossRef] [PubMed]
Ohzono, T., Matsushita, S. I., and Shimomura, M., 2005, “Coupling of Wrinkle Patterns to Microsphere-Array Lithographic Patterns,” Soft Matter, 1(3), pp. 227–230. [CrossRef]
Jungwook, K., Jinhwan, Y., and Hayward, R. C., 2010, “Dynamic Display of Biomolecular Patterns Through an Elastic Creasing Instability of Stimuli-Responsive Hydrogels,” Nat. Mater., 9(2), pp. 159–164 [CrossRef]. [PubMed]
Rudykh, S., and Boyce, M. C., 2014, “Transforming Wave Propagation in Layered Media Via Instability-Induced Interfacial Wrinkling,” Phys. Rev. Lett., 112(3), p. 034301. [CrossRef] [PubMed]
Harrison, C., Stafford, C. M., Zhang, W. H., and Karim, A., 2004, “Sinusoidal Phase Grating Created by a Tunably Buckled Surface,” Appl. Phys. Lett., 85(18), pp. 4016–4018. [CrossRef]
Wirgin, A., and Deleuil, R., 1969, “Theoretical and Experimental Investigation of a New Type of Blazed Grating,” J. Opt. Soc. Am., 59(10), pp. 1348–1357. [CrossRef]
Chung, J. Y., Youngblood, J. P., and Stafford, C. M., 2007, “Anisotropic Wetting on Tunable Micro-Wrinkled Surfaces,” Soft Matter, 3(9), pp. 1163–1169. [CrossRef]
Mei, Y., Kiravittaya, S., Harazim, S., and Schmidt, O. G., 2010, “Principles and Applications of Micro and Nanoscale Wrinkles,” Mater. Sci. Eng. R, 70(3–6), pp. 209–224. [CrossRef]
Huang, Z., Hong, W., and Suo, Z., 2005, “Nonlinear Analyses of Wrinkles in a Film Bonded to a Compliant Substrate,” J. Mech. Phys. Solids, 53(9), pp. 2101–2118. [CrossRef]
Celep, Z., 1988, “Circular Plate on Tensionless Winkler Foundation,” J. Eng. Mech., 114(10), pp. 1723–1739. [CrossRef]
Biot, M., 1937, “Bending of an Infinite Beam on an Elastic Substrate,” ASME J. Appl. Mech., 4, pp. A1–A7.

Figures

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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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