This paper develops a model for evolving wrinkles in a bilayer thin film consisting of an elastic layer and a viscoelastic layer. The elastic layer is subjected to a compressive residual stress and is modeled by the nonlinear von Karman plate theory. A thin-layer approximation is developed for the viscoelastic layer. The stability of the bilayer and the evolution of wrinkles are studied first by a linear perturbation analysis and then by numerical simulations. Three stages of the wrinkle evolution are identified: initial growth of the fastest growing mode, intermediate growth with mode transition, and, finally, an equilibrium wrinkle state.
Issue Section:
Technical Papers
1.
Iacopi
, F.
, Brongersma
, S. H.
, and Maex
, K.
, 2003, “Compressive Stress Relaxation Through Buckling of a Low-k Polymer-Thin Cap Layer System
,” Appl. Phys. Lett.
0003-6951, 82
, pp. 1380
–1382
.2.
Yin
, H.
, Huang
, R.
, Hobart
, K. D.
, Liang
, J.
, Suo
, Z.
, Shieh
, S. R.
, Duffy
, T. S.
, Kub
, F. J.
, and Sturm
, J. C.
, 2003, “Buckling Suppression of SiGe Islands on Compliant Substrates
,” J. Appl. Phys.
0021-8979, 94
, pp. 6875
–6888
.3.
Watanabe
, M.
, Shirai
, H.
, and Hirai
, T.
, 2002, “Wrinkled Polypyrrole Electrode for Electroactive Polymer Actuators
,” J. Appl. Phys.
0021-8979, 92
, pp. 4631
–4637
.4.
Lacour
, S. P.
, Wagner
, S.
, Huang
, Z. Y.
, and Suo
, Z.
, 2003, “Stretchable Gold Conductors on Elastomeric Substrates
,” Appl. Phys. Lett.
0003-6951, 82
, pp. 2404
–2406
.5.
Cerda
, E.
, and Mahadevan
, L.
, 2003, “Geometry and Physics of Wrinkling
,” Phys. Rev. Lett.
0031-9007, 90
, 074302
.6.
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 (London)
0028-0836, 393
, pp. 146
–149
.7.
Chua
, D. B. H.
, Ng
, H. T.
, and Li
, S. F. Y.
, 2000, “Spontaneous Formation of Complex and Ordered Structures on Oxygen-Plasma-Treated Elastometric Polydimenthylsiloxane
,” Appl. Phys. Lett.
0003-6951, 76
, pp. 721
–723
.8.
Martin
, S. J.
, Godschalx
, J. P.
, Mills
, M. E.
, Shaffer
II, E. O.
, and Townsend
, P. H.
, 2000, “Development of a Low-Dielectric-Constant Polymer for the Fabrication of Integrated Circuit Interconnect
,” Adv. Mater. (Weinheim, Ger.)
0935-9648, 12
, pp. 1769
–1778
.9.
Stafford
, C. M.
, Harrison
, C.
, Beers
, K. L.
, Karim
, A.
, Amis
, E. J.
, Vanlandingham
, M. R.
, and Kim
, H.-C.
, Volksen
, W.
, Miller
, R. D.
, and Simonyi
, E. E.
, 2004, “A Buckling-Based Metrology for Measuring the Elastic Moduli of Polymeric Thin Films
,” Nat. Mater.
1476-1122, 3
, pp. 545
–550
.10.
Groenewold
, J.
, 2001, “Wrinkling of Plates Coupled With Soft Elastic Media
,” Physica A
0378-4371, 298
, pp. 32
–45
.11.
Chen
, X.
, and Hutchinson
, J. W.
, 2004, “Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates
,” J. Appl. Mech.
0021-8936, 72
, pp. 597
–603
.12.
Huang
, Z. Y.
, Hong
, W.
, and Suo
, Z.
, 2005, “Nonlinear Analysis of Wrinkles in Films on Soft Elastic Substrates
,” J. Mech. Phys. Solids
0022-5096, 53
, pp. 2101
–2118
.13.
Sridhar
, N.
, Srolovitz
, D. J.
, and Suo
, Z.
, 2001, “Kinetics of Buckling of a Compressed Film on a Viscous Substrate
,” Appl. Phys. Lett.
0003-6951, 78
, pp. 2482
–2484
.14.
Huang
, R.
, and Suo
, Z.
, 2002, “Wrinkling of an Elastic Film on a Viscous Layer
,” J. Appl. Phys.
0021-8979, 91
, pp. 1135
–1142
.15.
Yoo
, P. J.
, and Lee
, H. H.
, 2003, “Evolution of a Stress-Driven Pattern in Thin Bilayer Films: Spinodal Wrinkling
,” Phys. Rev. Lett.
0031-9007, 91
, 154502
.16.
Huang
, R.
, 2005, “Kinetic Wrinkling of an Elastic Film on a Viscoelastic Substrate
,” J. Mech. Phys. Solids
0022-5096, 53
, pp. 63
–89
.17.
Timoshenko
, S.
, and Woinowsky-Krieger
, S.
, 1987
, Theory of Plates and Shells
, 2nd Edition, McGraw-Hill
, New York.18.
Freund
, L. B.
, and Suresh
, S.
, 2003
, Thin Film Materials
, Cambridge University Press
, Cambridge.19.
Christensen
, R. M.
1982
, Theory of Viscoelasticity
, Academic Press
, New York.20.
Reynolds
, O.
, 1886, “On the Theory of Lubrication and its Applications to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,” Philos. Trans. R. Soc. London
0370-2316, 177
, pp. 157
–234
.21.
Xia
, Z. C.
, and Hutchinson
, J. W.
, 2000, “Crack Patterns in Thin Films
,” J. Mech. Phys. Solids
0022-5096, 48
, pp. 1107
–1131
.22.
Huang
, R.
, Prevost
, J. H.
, and Suo
, Z.
, 2002, “Loss of Constraint on Fracture in Thin Film Structures Due to Creep
,” Acta Mater.
1359-6454, 50
, pp. 4137
–4148
.23.
Allen
, H. G.
, 1969
, Analysis and Design of Structural Sandwich Panels
, Pergamon
, New York.24.
Huang
, Z. Y.
, Hong
, W.
, and Suo
, Z.
, 2004, “Evolution of Wrinkles in Hard Films on Soft Substrates
,” Phys. Rev. E
1063-651X, 70
, 030601
(R).25.
Huang
, R.
, and Suo
, Z.
, 2002, “Instability of a Compressed Elastic Film on a Viscous Layer
,” Int. J. Solids Struct.
0020-7683, 39
, pp. 1791
–1802
.Copyright © 2005
by American Society of Mechanical Engineers
You do not currently have access to this content.