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TECHNICAL PAPERS

Adherence of an Axisymmetric Flat Punch Onto a Clamped Circular Plate: Transition From a Rigid Plate to a Flexible Membrane

[+] Author and Article Information
K.-T. Wan

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Norris Hall 106, Mail Code 0219, Blacksburg, VA 24061e-mail: kwan@vt.edu

J. Appl. Mech 69(2), 110-116 (Oct 15, 2001) (7 pages) doi:10.1115/1.1433477 History: Received February 12, 2001; Revised October 15, 2001
Copyright © 2002 by ASME
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References

Figures

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The critical load φ and punch displacement W0 at pull-off as functions of Γ* (solid lines), along with the bending and stretching limits (dashed lines).
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Constitutive relations with delamination for various Γ* as indicated (solid lines), along with the no-delamination relations for ζ=0 to 0.9 with an interval of 0.1 and ζ=0.95 (gray lines).
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Curve ABC shows the constitutive relation with delamination for Γ*=104. The solid gray line is the mixed bending-stretching constitutive relation without delamination for a central point load (ζ=0). The two dashed gray curves AMP and JKL show the bending and stretching limits, respectively.
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A pure membrane. (a) The enthalpy (H̃/Γ*) as a function of contact area ζ2 under fixed load for [φ/(Γ*)3/4]=0.5, 1.0, 2.0 and 2.74636. The dashed line joining the maximum of every curve represents the unstable equilibrium. Spontaneous delamination occurs at φ. (b) The internal energy (Ũ/Γ*) as a function of contact area ζ2 under fixed grips for [W0/(Γ*)1/4]=0.3, 0.4, 0.5 and 0.562441. The dashed line represents the delamination process. Pull-off occurs at the point of inflexion at W0.
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A pure plate. (a) The enthalpy (H̃/Γ*) as a function of contact area ζ2 under fixed load for [φ/(Γ*)1/2]=1, 2, 5 and 10. The dashed line joining the maximum of each curve represents the unstable equilibrium. (b) The internal energy (Ũ/Γ*) as a function of contact area ζ2 under fixed grips for [W0/(Γ*)1/2]=0.01, 0.04, 0.08, 0.112761. The dashed line represents the stable delamination process. Pull-off occurs at the point of inflexion at W0.
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Gradient of the constitutive relation n as a function of W0 for various ζ as indicated. When bending dominates at small W0,n≈1; and when stretching prevails at large W0,n≈3. In the intermediate region (0.1<W0<10),n lies between 1 and 3.
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Constitutive relation φ(W0) for various ζ as indicated. The pure bending and pure stretching limits are shown as dashed lines. There exists an intermediate bending-stretching transition region.
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Film profiles for ζ=0.1 and β=1, 10, 100. Note that the gradients at the outer and inner circles are zero at small β.
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Sketch of a circular cylindrical flat punch adhered onto a thin membrane constrained at the circular rim. A free-body diagram showing the external force, bending moments and tensile membrane stress.

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