Adhesion of a Rigid Cylinder to an Incompressible Film
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ADHESION OF A RIGID CYLINDER TO AN INCOMPRESSIBLE FILM Fuqian Yang a, b , Xinzhong Zhang b and J.C.M. Li b a Xerox Corporation, MS: 147-54A, 800 Phillips Road, Webster, NY 14580 b Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627 ABSTRACT The adhesion between a rigid cylindrical particle with a flat end of radius a and an incompressible elastic film of thickness h deposited on a rigid substrate was studied. The contact surfaces between the particle and the film and between the film and the substrate are either frictionless (slip) or perfectly bonded (stick). Using integral equations, the stress distribution in the contact area was solved and used to obtain the load required to press the particle onto the thin film. Using a thermodynamic method, the pull-off force to separate the particle from the film was obtained numerically and analytically. For a>>h, the pull-off force is proportional to a2/h1/2 if it is frictionless on both contact interfaces and is proportional to a3/h3/2 if it is frictionless between the particle and thin film and bonded between the thin film and the substrate. For a a (5) Eq. (4) is an approximation for z=δ. From our experience, this approximation is very good as long as δ is only a fraction of a. Four special cases are considered here for the other boundary conditions. Case I: frictionless on all contact faces, σ rz (r ,0) = 0 for r ≤ a (6) σ rz ( r , h ) = 0 , and u z ( r , h ) = 0 (7) Case II: frictionless on the interface between the particle and the elastic film and bonded between the elastic film and the substrate, σ rz (r ,0) = 0 for r ≤ a (8) uz (r , h) = ur (r , h) = 0 (9) Case III: bonded between the particle and the elastic film and frictionless on the interface between the elastic film and the substrate, Q6.5.2
ur (r ,0) = 0 for r ≤ a (10) σ rz (r , h) = 0 , and uz (r , h) = 0 (11) Case IV: bonded on all the contact faces, ur (r ,0) = 0 for r ≤ a (12) uz (r , h) = ur (r , h) = 0 (13) The above equations have been solved by using integral transforms [6, 7]. For the adhesion between a rigid cylindrical particle and an elastic thin film ( h
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