CELLS AND MEMBRANES - Nanoindentation with Biological Applications - page 337

Contact Circle

Planar probe surface

Figure 10-7. Sketch of the punch test to measure membrane adhesion.

The limiting case of finite adhesion energy with zero range and
infinite magnitude was derived in our earlier work. The experimentally
verified delamination trajectory for pre-stressed membrane is found to be

I ()( ) ( K I )() K

4 1010 10 10

1/ 2 1/ 2

F () b

(10-24)

0

1/ 2

2 I ()( K ) ( I )() / K

1000 00 10 0

with = c / a . Figure 10-8 shows the delamination trajectory OABC for a

punch radius smaller than the clamped film. As the punch moves in a
displacement controlled manner, the overhanging annulus deforms with
no delamination until point A. An increase in punch displacement
shrinks the contact circle and reduces the applied load along path ABC.
At point C, the contact radius reduces to a critical non-zero value of c *,
where ( w 0 / F ) r=c* = 0. An incremental increase in w 0 leads to “pull-off”
where the film spontaneously detaches from the punch (denoted by *
hereafter). The present model shows 0.1758

ζ

e −1 (= 0.3679), where
the lower and upper limits refer to zero and infinite residual membrane
stress, respectively. One can characterize the mechanical and adhesion
behavior of the film and film-substrate interface using F * and w *. Based
on thermodynamic reversibility, “pull-in” occurs when the film-punch
gap narrows to w *.

ζ *