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Special Issue Honoring Professor Fazil Erdogan’s Contributions to Mixed Boundary Value Problems of Inhomogeneous and Functionally Graded Materials

Mechanical Modeling of Thin Films and Cover Plates Bonded to Graded Substrates

[+] Author and Article Information
Mehmet A. Guler1

Department of Mechanical Engineering, TOBB University of Economics and Technology, Ankara 06560, Turkeymguler@etu.edu.tr

1

Corresponding author.

J. Appl. Mech 75(5), 051105 (Jul 10, 2008) (8 pages) doi:10.1115/1.2936237 History: Received May 30, 2007; Revised November 02, 2007; Published July 10, 2008

In this study, the contact problems of thin films and cover plates are considered. In these problems, the loading consists of any one or combination of stresses caused by uniform temperature changes and temperature excursions, far field mechanical loading, and residual stresses resulting from film processing or welding. The primary interest in this study is in examining stress concentrations or singularities near the film ends for the purpose of addressing the question of crack initiation and propagation in the substrate or along the interface. The underlying contact mechanics problem is formulated by assuming that the film is a “membrane” and the substrate a graded elastic continuum, and is solved analytically by reducing it to an integral equation. The calculated results are the interfacial shear stress between the film and the graded substrate, the Mode II stress intensity factor at the end of the film, and the axial normal stress in the film. The results indicate that grading the material properties of the substrate helps to decrease the film stresses and the stress intensity factors at the free edges and to lower the axial normal stresses at the midsection where the film is most likely to crack.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 5

Mode II stress intensity factor versus the parameter λ for various values of the aspect ratio l∕hf for homogeneous substrate, l=2a

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Figure 1

Geometry of the problem

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Figure 2

Geometry of the thin film on a graded substrate problem

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Figure 3

Equilibrium diagram of the thin film and the graded substrate

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Figure 4

Interfacial stress σxyf(x,0) and the axial normal stress in the film σxxf(x,0) for various values of the parameter λ for homogeneous substrate, l∕hf=32

Grahic Jump Location
Figure 6

Interfacial stress σxyf(x,0) and the axial normal stress in the film σxxf(x,0) for various values of the nonhomogeneity parameter γa for graded substrate, λ=1∕28, l∕hf=32

Grahic Jump Location
Figure 7

Mode II stress intensity factor versus the nonhomogeneity parameter γa for various values of the parameter λ for graded substrate, l∕hf=32

Grahic Jump Location
Figure 8

Interfacial stress σxyf(x,0) and the axial normal stress in the film σxxf(x,0) for various values of the parameter λ for graded substrate, γa=3, l∕hf=32

Grahic Jump Location
Figure 9

Interfacial stress σxyf(x,0) and the normal stress in the film σxxf(x,0) for various values of the aspect ratio l∕hf for graded substrate, γa=3, λ=1∕28

Grahic Jump Location
Figure 10

Mode II stress intensity factor versus the nonhomogeneity parameter γa for various values of the aspect ratio l∕hf for graded substrate, λ=1∕28

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