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Stress-Induced Wrinkling in Thin Films Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin

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Wrinkles “Wrinkles occur on scales varying from a few nanometers (in thin films) to hundreds of kilometers (on the surface of the earth), in a variety of natural phenomena (see above).” (From http://www.deas.harvard.edu/softmat/)

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Wrinkling in Thin Films

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Applications of Wrinkling (Jones et al., MRS Symp. Proc. 769, H6.12, 2003 ) - Stretchable interconnects/electrodes for flexible electronics - Optical scattering, grating, and waveguide structures - Mechanical characterization of polymer thin films - Reliability of integrated devices containing soft organic materials

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Mechanics of Wrinkling Elastic film on elastic substrate –Equilibrium and Energetics Elastic film on viscous substrate –Non-equilibrium and Kinetics Elastic film on viscoelastic substrate –Evolution of wrinkle patterns

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Freestanding film: Euler buckling Critical load: Other equilibrium states: energetically unfavorable Buckling relaxes compressive stress Bending energy minimizes at long wavelength

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On elastic substrates Deformation of the substrate disfavors wrinkling of long wavelengths and competes with bending to select an intermediate wavelength Elastic substrate Wrinkling: short wavelength, on soft substrates, no delamination Buckling: long wavelength, on hard substrates, with delamination

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Critical Condition for Wrinkling Thick substrate (h s >> h f ): The critical strain decreases as the substrate stiffness decreases. In general, the critical strain depends on the thickness ratio and Poisson’s ratios too. In addition, the interface must be well bonded.

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Equilibrium Wrinkle Wavelength Thick substrate (h s >> h f ): The wrinkle wavelength is independent of compressive strain. The wavelength increases as the substrate stiffness decreases. In general, the wavelength depends on thickness ratio and Poisson’s ratios too. Measure wavelength to determine film stiffness

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Equilibrium Wrinkle Amplitude Thick substrate (h s >> h f ): Measure amplitude to determine film stress/strain. The wrinkle amplitude increases as the compressive strain increases. For large deformation, however, nonlinear elastic behavior must be considered.

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Equilibrium Wrinkle Patterns In an elastic system, the equilibrium state minimizes the total strain energy. However, it is extremely difficult to find such a state for large film areas. More practically, one compares the energy of several possible patterns to determine the preferred pattern. How does the pattern emerge? How to control wrinkle patterns?

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Kinetics: on a viscous substrate Viscous flow controls the growth rate: long-wave wrinkling grows slowly, and an intermediate wavelength is kinetically selected. Viscous layer Rigid substrate Fastest mode m c 0 Growth Rate s Euler buckling smsm (For h s >> h f )

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Kinetically Constrained Equilibrium Wrinkles Infinitely many: each wavelength ( > c ) has an equilibrium state Energetically unstable: longer wavelength lower energy Kinetically constrained: flow is very slow near the equilibrium state Elastic film is bent in equilibrium. Viscous layer stops flowing. Huang and Suo, J. Appl. Phys. 91, 1135 (2002). Viscous layer Rigid substrate

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Simultaneous Expansion and Wrinkling Expansion starts at the edges and propagates toward center Wrinkle grows before expansion relaxes the strain Long annealing removes wrinkles by expansion Liang et al., Acta Materialia 50, 2933 (2002). Viscous layer Rigid substrate

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Wrinkling on Viscoelastic Substrates Cross-linked polymers Compressive Strain Wrinkle Amplitude 0 Evolution of wrinkles: (I)Viscous to Rubbery (II)Glassy to Rubbery Rubbery StateGlassy State

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(Lee at al., 2004)

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Wrinkling Kinetics I: Fastest mode m 0 Growth Rate Wrinkles of intermediate wavelengths grow exponentially; The fastest growing mode dominates the initial growth. For h s >> h f : The kinetically selected wavelength is independent of substrate!

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Wrinkling Kinetics II: Instantaneous wrinkle at the glassy state: Kinetic growth at the initial stage: Long-term evolution:

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t = 0 t = 1 10 4 Numerical Simulation t = 1 10 5 t = 1 10 7 Growing wavelengths Coarsening Equilibrium wavelength

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Evolution of Wrinkle Wavelength Initial stage: kinetically selected wavelengths Intermediate stage: coarsening of wavelength Final stage: equilibrium wavelength at the rubbery state

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Evolution of Wrinkle Amplitude Initial stage: exponential growth Intermediate stage: slow growth Final stage: saturating

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t = 0t = 10 4 t = 10 5 t = 10 7 t = 10 6 2D Wrinkle Patterns I

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t = 0t = 10 5 t = 2X10 7 t = 10 6 t = 5X10 6 2D Wrinkle Patterns II

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t = 10 7 t = 5X10 5 t = 10 6 t = 10 4 2D Wrinkle Patterns III t = 0

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t = 10 4 t = 10 5 t = 10 6 t = 10 7 On a Patterned Substrate

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Circular Perturbation t = 0t = 10 4 t = 10 5 t = 5 10 5 t = 10 6 t = 10 7

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Evolution of Wrinkle Patterns Symmetry breaking in isotropic system: –from spherical caps to elongated ridges –from labyrinth to herringbone. Symmetry breaking due to anisotropic strain –from labyrinth to parallel stripes Controlling the wrinkle patterns –On patterned substrates –By introducing initial defects

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What else? Ultra-thin films –Effect of surface energy and surface stress –Effect of thickness-dependent modulus –Effect of temperature, molecular weight, cross- linking –Other effect at nanoscale? Nonlinear elastic/viscoelastic behavior –Nested wrinkles?

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