ABSTRACT
The second choice, implemented in the JKR (Johnson, Kendall and Roberts) model [33], results in a different stress distribution: compressive in the center of the contact zone, changing to tensile when approaching the boundary (and zero outside the contact circle). Using the energy minimization approach, JKR predicted that the contact radius can be derived from Hertz equation when the external load P is substituted by an apparent load P\:
R = a/Ri + I/R2) (1)
K (2)
where
Alternatively, the problem of separation of the two surfaces can be treated within the formalism of the linear fracture mechanics: the mechanical energy made available through the crack growth, the energy release rate G (i.e. rate of change in strain energy with area), is used to overcome the surface energy of newly created surfaces (so-called Griffith criterion for stability of the crack: G = W\32). This leads to an equation for the energy release rate equivalent to the energy minimization result above [34]:
The requirement for Pi to remain real results in the JKR expression for the force of adhesion:
P a = ^nRWl32 (6)
The JKR theory predicts a finite radius of contact under zero external load and when surfaces separate:
respectively. Dividing the contact area at pull-off, a s, by the area occupied by a single functional group allows an estimate of the number of molecular contacts to be made. The corresponding quantities for the DMT theory are
{27tWl32R2\l/3 ao(DMT) = I ~ I ana #S(DMT) = u.
