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Research Papers

Nonslipping Contact Between a Mismatch Film and a Finite-Thickness Graded Substrate

[+] Author and Article Information
Chen Peijian

State Key Laboratory for Geomechanics
and Deep Underground Engineering,
School of Mechanics and Civil Engineering,
China University of Mining and Technology,
Xuzhou 221116, Jiangsu, China
e-mail: chenpeijian@cumt.edu.cn;
chen_peijian@hotmail.com

Chen Shaohua

LNM,
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: shchen@LNM.imech.ac.cn;
chenshaohua72@hotmail.com

Yao Yin

LNM,
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 7, 2015; final manuscript received November 1, 2015; published online November 13, 2015. Editor: Yonggang Huang.

J. Appl. Mech 83(2), 021007 (Nov 13, 2015) (8 pages) Paper No: JAM-15-1543; doi: 10.1115/1.4031936 History: Received October 07, 2015; Revised November 01, 2015

The contact behavior of an elastic film subjected to a mismatch strain on a finite-thickness graded substrate is investigated, in which the contact interface is assumed to be nonslipping and the shear modulus of the substrate varies exponentially in the thickness direction. The Fourier transform method is adopted in order to reduce the governing partial differential equations to integral ones. With the help of numerical calculation, the interfacial shear stress, the internal normal stress in the film and the stress intensity factors are predicted for cases with different material parameters and geometric ones, including the modulus ratio of the film to the substrate, the inhomogeneous feature of the graded substrate, as well as the profile of the contacting film. All the physical predictions can be used to estimate the potential failure modes of the film–substrate interface. Furthermore, it is found that the result of a finite-thickness model is significantly different from the prediction of a generally adopted half-plane one. The study should be helpful for the design of film–substrate systems in real applications.

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Topics: Stress , Shear stress
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Figures

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Fig. 1

The perfectly adhesive contact model between an elastic film of length lf and a finite-thickness graded substrate. The variation of environmental temperature induces a mismatched strain at the contact interface. The shear modulus of the substrate abides by a graded law μ2(y)=μ1 exp(γy); h is the thickness of the graded substrate.

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Fig. 2

Schematic of the mechanical behavior of the bonded interface between a deformable film and an elastically graded substrate

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Fig. 3

Comparison of the distribution of the nondimensional interface shear stress σxyf/p1 and the normal stress in the film σxxf/p1 for the model of an elastic film in adhesive contact with a homogeneous half-plane and the present one with a relatively thick substrate, where the ratio of the film length to its thickness is lf/hf=32, μf is the shear modulus of the film and μ1 denotes the shear modulus of the upper surface of the graded substrate

Grahic Jump Location
Fig. 4

The distribution of the nondimensional interface shear stress σxyf/p1 and the normal stress in the film σxxf/p1 for the model of a deformable film in adhesive contact with a finite-thickness graded substrate with determined parameters h/a = 1 and lf/hf = 32, but with different ratios μf/μ1. (a) and (b) for μ3/μ1 = 1/7 ; (c) and (d) for μ3/μ1 = 7.

Grahic Jump Location
Fig. 5

The distribution of the interface shear stress σxyf/p1 and the normal stress in the film σxxf/p1 for the model of a deformable film in adhesive contact with a finite-thickness graded substrate with determined parameters h/a = 1, μf/μ1 = 28, lf/hf = 32, but with different inhomogeneity parameters μ3/μ1 of the substrate

Grahic Jump Location
Fig. 6

The distribution of the interface shear stress σxyf/p1 and the normal stress in the film σxxf/p1 for the model of a deformable film in adhesive contact with a finite-thickness graded substrate with determined parameters μf/μ1 = 28, lf/hf = 32, but with different ratios h/a. (a) and (b) for μ3/μ1 = 7; (c) and (d) for μ3/μ1 = 1/7.

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Fig. 7

Variation of the Mode II stress intensity factor KII/p1a versus the ratio of the substrate thickness to half of the film length h/a for different ratios μ3/μ1, where μf/μ1=28

Grahic Jump Location
Fig. 8

The distribution of the interface shear stress σxyf/p1 and the normal stress in the film σxxf/p1 for the model of a deformable film in adhesive contact with a finite-thickness graded substrate with determined parameters μf/μ1=28, h/a=1, but with different values lf/hf. (a) and (b) for μ3/μ1=1/7; (c) and (d) for μ3/μ1=7.

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Fig. 9

The profile of the bonded film in the thickness direction with different shape parameters λ

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