The strength of interfaces involving rubbery polymers

The rate of energy input needed to advance a crack unit area, the adhesive fracture energy G, can be written in a form that emphasises the contribution of 

The importance of viscoelastic effects in adhesion as measured by methods such as peeling tests means that it is quite difficult to measure the limiting fracture energy Gq. One method that has been used successfully for elastomers was developed by Johnson, Kendall and Roberts (Johnson et al. 1971) and is commonly known as the JKR experiment. The experimental arrangement is 

This additional force means that, even in the absence of an external load, the hemisphere will be distorted and there will be a finite radius of contact a. The modified relation between the radius of contact and the applied load may be found by more detailed analysis (Johnson et al. 1971). Equation (7.2.3) is modified to 

Two obvious consequences follow from this equation firstly, in the absence of an external load, the contaet radius takes a non-zero value ao given by 

Moreover, a remains positive even if a small negative load is applied. One can find the minimum negative load - the pull-off force - by noting that, in order for equation (7.2.6) to have a real solution, ( Gq7iRP + TtGqtiR) 0. This gives for the pull-off force i puii-off 

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