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Research Papers

A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space

[+] Author and Article Information
Xu Guo

e-mail: guoxu@dlut.edu.cn

Wei Zhang

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
Dalian University of Technology,
Dalian 116023, China

1Corresponding author.

Manuscript received January 10, 2013; final manuscript received January 31, 2013; accepted manuscript posted March 7, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061024 (Aug 21, 2013) (9 pages) Paper No: JAM-13-1016; doi: 10.1115/1.4023980 History: Received January 10, 2013; Revised January 31, 2013; Accepted March 07, 2013

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a power-law graded elastic half-space is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closed-form solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)-type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.

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Figures

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Fig. 1

Schematic of an elastically graded half-space in contact with (a) a rigid punch with an arbitrary profile, and (b) a circular flat-ended cylinder

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Fig. 6

Adhesive contact between an elastically graded half-space and a concave punch. The axisymmetric punch is characterized by a radius R and a maximum depth of concavity h at the central axis.

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Fig. 4

Schematic of the optimal punch profile of radius R for the elastically graded half-space

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Fig. 3

Comparison of equilibrium P − δ curves between an exact spherical punch (red solid line) and a parabolic punch (blue dashed line) for (a) different E*Rγ, and (b) different R/c0, respectively

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Fig. 5

Optimal punch profiles in contact with an elastically graded half-space for (a) different gradient exponents k, and (b) different gradient variation rates R/c0

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Fig. 2

Magnitude of pull-off force as a function of the gradient exponent k for power-law punch profiles with different shape indexes m

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Fig. 9

Effects of the nondimensional gradient variation rate R/c0 on the pull-off force for spherical and hypergeometric concave punch profiles with a given maximum concave depth. The actually measured evolutions are shaded. A logarithmic scale on the horizontal axis is used.

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Fig. 7

Comparison of normalized pull-off force for spherical and hypergeometric concave punch profiles with given parameters (a) E*Rγ = 500, R/c0 = 10, and (b) E*Rγ = 100, R/c0 = 5. The actually measured evolutions are shaded.

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Fig. 8

Effects of the gradient exponent k on the pull-off force for spherical and hypergeometric concave punch profiles with different maximum concave depths (a) h/R = 0.02, (b) h/R = 0.08, and (c) h/R = 0.15. The actually measured evolutions are shaded.

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