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Research Papers

Confined Thin Film Delamination in the Presence of Intersurface Forces With Finite Range and Magnitude

[+] Author and Article Information
Kai-tak Wan, Scott E. Julien

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115

J. Appl. Mech 76(5), 051005 (Jun 18, 2009) (9 pages) doi:10.1115/1.3112745 History: Received July 01, 2008; Revised February 02, 2009; Published June 18, 2009

A circular membrane clamped at the periphery is allowed to adhere to or to delaminate from a planar surface of a cylindrical punch in the presence of intersurface forces with finite range and magnitude. Assuming a uniform disjoining pressure within the cohesive zone at the delamination front, the adhesion-delamination mechanics is obtained by a thermodynamic energy balance. Interrelations between the instantaneous applied load, punch displacement, and contact circle, and the resulting critical thresholds of “pinch-off,” “pull-off,” and “pull-in” are derived from the first principles. Two limiting cases are obtained: (i) intersurface force with long range and small magnitude in reminiscence of the classical Derjaguin–Muller–Toporov (DMT) model and (ii) short range and large magnitude alluding to the Johnson–Kendall–Roberts (JKR) model. The DMT-JKR transitional behavior has significant impacts on adhesion measurements, micro-electromechanical systems, and life-sciences.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Schematic of a clamped membrane adhered to planar punch surface. (b) Drawing in normalized coordinates and variables.

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Figure 2

(a) Lennard-Jones potential and the uniform disjoining pressure approximation as function of intersurface separation (w0−w). (b) Disjoining pressure distribution and (c) surface energy density as function of radial distance in the membrane-punch interface for a range of decreasing disjoining pressure.

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Figure 3

Membrane profile for fixed contact radius c=0.3 and a range of disjoining pressure. The delamination front is shaped as a cusp in all the curves and in the DMT-limit, besides the JKR-limit.

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Figure 4

The JKR-limit follows path OSRQP with contact radii, cO=cS=1.00, cR=0.7792, cQ=0.5395, and cP=c=∗0.1945. Load-controlled pull-off occurs at S, and displacement-controlled pull-off at P. The branch OP (dashed) is physically inaccessible. The DMT-limit follows path OAB with cA=0.49649 and cB=0.

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Figure 5

Energy as a function of contact radius for punch displacement w0=0.5 and a range of disjoining pressure: (a) elastic energy stored in the membrane, (b) surface energy, and (c) total energy of the membrane-punch system.

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Figure 6

Total energy of the membrane-punch system for disjoining pressure (a) p=0.5, (b) p=5, and (c) p→∞ (JKR-limit). Dashed curves joining the minima of individual curves indicate mechanical equilibrium and delamination process.

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Figure 7

Mechanical response for a range of disjoining pressure. The dashed curve OABCD corresponds to pinch-off with zero contact radius, and curve DH is pull-off with nonzero contact radius.

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Figure 8

Mechanical response for a range of disjoining pressures

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Figure 9

Mechanical response for a range of disjoining pressures. The dashed curve DMT-JKR indicates the transitional behavior.

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Figure 10

Pull-off radius as a function of disjoining pressure. The critical radius approaches the JKR-limit at large p.

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Figure 11

Cohesive edge as a function of contact radius for a range of disjoining pressures. Delamination proceeds from right to left. All curves initiate at c=1 and b=1 until deviation occurs at critical contact radii.

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Figure 12

Cohesive zone width as a function of contact radius for a range of disjoining pressure. Delamination proceeds from right to left. All curves initiate at c=1 and b−c=0 until deviation occurs at critical contact radii.

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Figure 13

Mechanical force measured by a punch probe as it moves toward a clamped membrane. The dashed curve is a reference to the pinch-off-pull-off locus. (a) For p=1.25 and range y=0.8, probe senses the membrane at A. Loading-unloading follows ABCO-OCBA. No hysteresis is expected. (b) For p=1.86 and y=0.5373, loading-unloading follows ABC-CBA. No hysteresis is expected. (c) For p=5 and y=0.2, loading-unloading follows ABC-CDA. Hysteresis is expected.

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