Hysteresis and Drag in the Contact of Spheres

When particles make elastic contact with a surface, equilibrium is not attained immediately. Time is required for the contact spot to enlarge, and more time is needed for the contact to separate when a tensile force is imposed. This is adhesive drag. Indeed, equilibrium may never be attained. On making the contact, the spot size has a certain diameter at a given load. When breaking the contact at an identical load, the contact spot is bigger. This is known as adhesive hysteresis, which was observed by Drutowski in 1969. These effects may be studied systematically with smooth elastomer spheres at zero load as shown in Fig. 9.23.  

These observations demonstrate that adhesive drag and hysteresis are not caused by the solid nature of the materials, but by intrinsic properties of the interface, moderated by lossy effects within the materials. 

The phenomena of adhesive drag and hysteresis are relevant to the tack of solids. Certain adhesive tapes need to be tacky so as to grab the attaching 

To obtain a more genanl explanation of these complex effects, Kendall separated out the drag and hysteresis terms. The drag was viewed as an interface reaction which was kinetically controlled by a surface energy barrier, whereas the hysteresis was viewed as a crack stopping effect brought about by the lossy relaxation of the inelastic matoial. The influence of these two separate phenomena was best demonstiated by measuring the contact spot size at various times and temperatures, as shown in Fig. 9.25. 

The experiment was conducted as before, measuring the contact spot size d both making and breaking the contact, then calculating the adhesive energy T and crack speed v from the TV record using the equation derived from equation 9.7 

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