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Research Papers

A Generalized Model for Adhesive Contact Between a Rigid Cylinder and a Transversely Isotropic Substrate

[+] Author and Article Information
Haimin Yao

Department of Mechanical Engineering,
The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong, P. R. C.
e-mail: mmhyao@polyu.edu.hk

Manuscript received March 28, 2012; final manuscript received July 15, 2012; accepted manuscript posted July 27, 2012; published online November 19, 2012. Assoc. Editor: Anand Jagota.

J. Appl. Mech 80(1), 011027 (Nov 19, 2012) (7 pages) Paper No: JAM-12-1120; doi: 10.1115/1.4007229 History: Received March 28, 2012; Revised July 15, 2012; Accepted July 27, 2012

In this paper, a solution to the quasi-static adhesive contact problem between a rigid cylinder and a transversely isotropic substrate is extended to the most general case by taking adhesion hysteresis into account. An analytical solution to the contact stress is obtained by solving the integral equations established on the basis of the Green's function for the two-dimensional transversely isotropic half-space problem. By using equilibrium conditions and Griffith's criterion, the adhesion force and resistant moment to rolling are determined as functions of contact geometries and material properties of the contacting solids. Detailed discussions on the adhesion force and resistant moment are presented for some specific cases, revealing adhesion behaviors that have not been predicted by previous models. As the most generalized solution to the discussed problem, our results would have extensive applications in predicting the adhesion behavior between solids undergoing sophisticated mechanical loadings.

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Figures

Grahic Jump Location
Fig. 1

Schematic of a rigid cylinder in adhesive contact with a transversely isotropic half-space. The rigid cylinder is in equilibrium under the external force F and torque M.

Grahic Jump Location
Fig. 4

The variation of pull-off force between a rigid cylinder and an elastic substrate with the pulling angle φ in comparison with that of (wr-wa)/wr|sin ϕ|. Material constants are taken as L22/L11 = 100, θ = 30 deg, μ = 2.0 × 103, ɛ = 0.025, and wr = 15wa. For this case, it can be seen that F¯pf < (wr-wa)/wr| sin | when -25  deg < φ < 10  deg.

Grahic Jump Location
Fig. 2

Variation of the dimensionless contact width as a function of the dimensionless applied force for case with ϕ  =  0  deg. The substrate is assumed isotropic with ER/2(1-ν2)wr=100 and ν=0.375. The open symbols represent the instable equilibrium states with negative derivative of energy release rate with respect to the contact width. For comparison, the 2D JKR solution F=(2πEawr/1-ν2)-(πEa2/4R(1-ν2)) [27] and 2D Hertizan solution F=-(πEa2/4R(1-ν2)) are shown as well.

Grahic Jump Location
Fig. 3

Variation of contact width with external force for single force cases with pulling angle φ =-60  deg,30  deg. Material constants are taken as L22/L11 = 100, θ = 30  deg, μ = 2.0×103, ɛ = 0.025. The open symbols represent the energetically instable states with negative derivative of energy release rate with respect to the contact width.

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