Biomedical Engineering Reference
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r
a
c s
c
w s
F s
w 0
Figure 10-9. Membrane delamination from a substrate surface. Long range surface
forces, F s , are present immediately outside the intimate contact edge, and cut off once the
intersurface separation exceeds the force range, w s .
Figure 10-10 s hows the delamination process for a linear elastic, thin
and flexible membrane with negligible bending rigidity. The interfacial
adhesion energy, essentially the product of the intersurface force
magnitude (normalized force,
ρ s ) and range (normalized range,
ω s ), is
made to be a constant here ( i.e.
s = 1), and the combination of force
magnitude is allowed to vary over a range. The maximum displacement
the probe can travel is identified as the unstable “pull-off ”. The dashed
curve traces the “pull-off ” trajectory in Fig. 10-10.
It is worthwhile to note the changing constitutive relation as the
interface character gradually transits from JKR to DMT. As mentioned
above, the JKR limit requires the contact radius to shrink as the external
diminishes until “pull-off” occurs with a non-zero radius. In the other
extreme, when the force range is large approaching the DMT limit, the
entire overhanging annulus from the contact edge to the clamped
periphery is always under the influence of the surface forces until the
membrane completely detaches from the substrate. Here the applied load
is an increasing function of the probe displacement, contrasting the JKR
limit. It is therefore obvious that the two segments of the “pull-off ”
trajectory separated by the local maximum can be identified with the
JKR (the hook-like envelop) or DMT (monotonic increasing) traits.
Experimental determination of the delamination trajectory allows one
ρ
ω
s
 
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