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Research Papers

Thermomechanical Analysis of Film-on-Substrate System With Temperature-Dependent Properties

[+] Author and Article Information
YongAn Huang1

State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R. Chinayahuang@hust.edu.cn

ZhouPing Yin, YouLun Xiong

State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R. China

1

Corresponding author.

J. Appl. Mech 77(4), 041016 (Apr 16, 2010) (9 pages) doi:10.1115/1.4000927 History: Received August 07, 2009; Revised December 09, 2009; Published April 16, 2010; Online April 16, 2010

Thermomechanical analysis of global and local buckling is presented to show temperature effects on the stress/strain and shape of a film-on-substrate system. First, the strain is expressed as a function of three key temperatures (room, working, and deposit temperatures). Through sensitivity analysis on temperature, polydimethylsiloxane (PDMS) selection is determined to theoretically design film-on-substrate systems with the minimum variation in stress caused by temperatures. Then, the wrinkling behaviors are studied to establish the relationships of critical strain, wavelength, and amplitude with temperature. In addition, the critical working temperature is determined for local buckling. The approximate semi-analytical solution and the finite element simulation are compared by the use of a two-dimensional case of film on a half-space substrate.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Wrinkling steps for thin films onto a prestretched and thermally expanded PDMS substrate. (a) PDMS substrate with L0 when relaxed; (b) prestretched PDMS with L1 when stretched in Troom by external mechanical load F; (c) prestretched PDMS with L2 when stretched in Tdeposited by external mechanical load F and thermal load Tdeposited−Troom; (d) thin films evaporated on the stretched substrate; (e) release from prestretch in Twork environment, and thin films wrinkle or bend. When the structure is stretched, thin films deflect out of plane so that large elongation of substrate induces only small elastic strains in thin films.

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Figure 2

Normalized strain in the film as a function of film/substrate thickness ratio

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Figure 3

Normalized strain as a function of Young’s modulus of substrate. (a) Normalized strain as a function of film/substrate Young’s modulus ratio. (b) Normalized strain as a function of temperature.

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Figure 4

Substrate strain εf(Tref) as a function of the temperature and the initial stress. (a) Without external stress, temperature independent or dependent moduli are considered. (b) The degree of nonlinearity is dependent on the external stress. T-independent and T-dep mean temperature independent and dependent, respectively.

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Figure 5

The relationship of critical strain with temperature

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Figure 6

The relationship of wavelength with temperature

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Figure 7

The relationship of wave amplitude with temperature

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Figure 8

The critical working temperature with deposit temperature 200°C. (a) Calculation of critical strain for three kinds of thickness of substrate. (b) The law of the critical working temperature relative to the thickness of the substrate.

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Figure 9

The peak strains of thin film

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Figure 10

The maximum allowable prestrain

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Figure 11

Different number of waves at different temperatures

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Figure 12

The analytical solution and the finite element simulation of wavelength with temperature

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