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Research Papers

Adhesion Map for Thin Membranes

[+] Author and Article Information
Kai-tak Wan

Associate Professor
e-mail: ktwan@coe.neu.edu
Mechanical and Industrial Engineering,
Northeastern University,
Boston, MA 02115

1Current address: Texas Instruments, Dallas, TX 75243.

2Corresponding author.

Manuscript received February 22, 2013; final manuscript received August 21, 2013; accepted manuscript posted August 28, 2013; published online October 16, 2013. Assoc. Editor: Anand Jagota.

J. Appl. Mech 81(2), 021018 (Oct 16, 2013) (7 pages) Paper No: JAM-13-1089; doi: 10.1115/1.4025303 History: Received February 22, 2013; Revised August 21, 2013; Accepted August 28, 2013

A new Tabor's parameter ψ is defined for adhesion-delamination of thin membranes. A small ψ corresponds to a thick, small, and stiff membrane under the influence of a long-range weak surface force, as in the Derjaguin–Muller–Toporov (DMT) limit. A large ψ corresponds to a thin, large, and flexible membrane under the influence of a short-range strong surface force, as in the Johnson–Kendall–Roberts (JKR) limit. A new adhesion map based on ψ is drawn to summarize the “pull-off” events and the delamination trajectory for membranes under mixed stretching-bending deformation. Maps are generated for one- and two-dimensional membranes clamped at the edge.

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Figures

Grahic Jump Location
Fig. 3

Behavior of 1D rectangular membranes. (a) F(w0) for membranes under pure stretching for ψ = 1 (path OA), ψ = 2 (OB), ψ = 4 (OCD), ψ = 10 (OGD), and ψ → ∞ (OJK). Loci of fixed-load and fixed-grips pinch-off events are shown as lower dashed curve OABDHK marking the termini of the F(w0) curves. Fixed-load pull-off Fmax along JGCB is shown as upper dashed curve. Bifurcation of fixed-load and fixed-grips pull-offs as well as DMT-JKR transition at ψ* = 2 occurs at D. The JKR limit (OJK) is shown as a thick dashed curve, terminating at K. (b) F(w0) for membranes under pure bending for ψ = 2 (path OA), ψ* = 0.4899 (OB), ψ = 6 (OCD), ψ = 10 (OGH), ψ = 50 (terminating at J), and ψ → ∞ (terminating at K). Loci of fixed-grips pinch-off and pull-off events are shown as lower dashed curve OABDHJK, marking the termini of the F(w0) curves. Fixed-load pull-off Fmax along GCB is shown as upper dashed curve. Bifurcations of fixed-load and fixed-grips as well as DMT-JKR transition at ψ* occur at B. The JKR limit is shown as a thick dashed curve, terminating at K.

Grahic Jump Location
Fig. 2

Behavior of 2D circular membranes. (a) Delamination trajectories of applied load versus punch displacement F(w0) for membrane under pure stretching with ψ = 1 (path OA), ψ = 2 (OBC), ψ = 3 (OGH), ψ = 10 (OJK), and ψ → ∞ (OLM). Loci of fixed-grips pinch-off and pull-off events are shown as lower dashed curve OADCHKM, marking the termini of the F(w0) curves. Fixed-load pull-off Fmax along LJGBD is shown as upper dashed curve. Bifurcation of fixed-load and fixed-grips pull-offs as well as DMT-JKR transition at ψ* = 1.86 occurs at D. The JKR limit with ψ → ∞ (OLM) is shown as a thick dashed curve. (b) Mechanical response of membrane under pure bending for ψ = 2 (path OA), ψ* = 5.657 (OB), ψ = 8 (OCD), ψ = 10 (OGH), and ψ → ∞. Loci of fixed-grips pinch-off and pull-off events are shown as lower dashed curve OABDHJ, marking the termini of the F(w0) curves. Fixed-load pull-off Fmax along GCB is shown as upper dashed curve. Bifurcations of fixed load and fixed grips as well as DMT-JKR transition at ψ* occur at B. The JKR limit terminates at J.

Grahic Jump Location
Fig. 1

Schematics of confined membrane delamination. (a) 2D circular membrane clamped at the periphery delaminates from the planar surface of a cylindrical punch. (b) 1D rectangular membrane clamped at the two opposite ends delaminates from the rectangular punch. (c) Cross section of either 1D or 2D membrane. Surface force is present immediately outside the contact edge and is bounded by the cohesive zone (c < r < b or c < x < b).

Grahic Jump Location
Fig. 4

Adhesion map for 2D membranes for γ2D = 1. (a) Fixed-grips pull-off displacement, w0*, as a function of the Tabor parameter, ψ, for pure stretching (upper) and pure bending (lower). (b) Fixed-grips pull-off force, F *(ψ). Points A and D marked on the stretching curve are the same points in Figs. 2(a) and 2(b), and B on the bending curve is the same as in Figs. 3(a) and 3(b). The shaded area corresponds to membranes under mixed stretching-bending deformation. B marks the demarcation of fixed-load and fixed-grips as well as DMT-JKR transition. The dashed curves emanating from D in the upper curve and B in the lower curve show the loci of fixed-load pull-off or Fmax.

Grahic Jump Location
Fig. 5

Adhesion map for 1D rectangular membranes for γ1D = 1, showing (a) w0* and (b) F * as functions of ψ. Point B on the stretching curve is the same point as in Figs. 2(a) and 2(b), and B on the bending curve is the same as in Figs. 3(a) and 3(b). The shaded area corresponds to membranes under mixed stretching-bending deformation. The two dashed curves emanating from B in either curve show the loci of fixed-load pull-off or Fmax.

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