Research Papers

Modified Stoney's Formulas for Small-Scaled Bilayer Systems

[+] Author and Article Information
Dongying Liu

Department of Civil Engineering,  Zhejiang University, Zijingang Campus, Hangzhou 310058, P. R. China

Weiqiu Chen1

Department of Engineering Mechanics,  Zhejiang University, Yuquan Campus, Hangzhou 310027, P. R. Chinachenwq@zju.edu.cn


Corresponding author.

J. Eng. Mater. Technol 134(3), 031002 (May 07, 2012) (5 pages) doi:10.1115/1.4006509 History: Received September 11, 2011; Revised December 25, 2011; Published May 04, 2012; Online May 07, 2012

The mechanics of a small-scaled bilayer film-substrate system subject to temperature variation is studied. The modified couple stress theory is employed to take account of the size effects that are usually observed in small-scaled structures. In addition, the effect of weak bonding between the film and substrate is examined by using a linear slip-type model. Exact solutions are derived and the closed-form expressions for residual thermal stress and curvature of the system are given. Modified Stoney’s formulas are also presented for the bilayer system with perfect interface or imperfect interface between the film and the substrate.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Schematic sketch of a bilayer beam and the coordinate systems

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Figure 2

Differential element based on the modified couple stress theory

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Figure 3

Curvature of the perfect bilayer system

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Figure 4

Curvature of the imperfect bilayer system



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