JKR Contact Mechanics Theory (contd...)

Here we'll find out how to obtain this actual contact radius

Consider the situation when no surface forces act, the contact radius is given as . The movement of the applied load is given by

When attractive forces act between the surfaces the contact radius in equilibrium will be . Although, applied load remains at , an apparent Hertz load corresponding to the contact radius , defined as:

	(9.2)

Then the energy required to load the system of spheres to a contact radius with a load , in the absence of surface forces, can be calculated as:
Say, an intermediate load is , and the corresponding contact radius is , then and the movement of the applied load is,

	(9.3)

The differential movement and the energy is

	(9.4)

Hence the total energy stored in the spheres is

	(9.5)