Extension of the Adhesive-Junction Model for Friction

Neither departure from Amontons laws of friction nor the occurrence of values greater than 0.2 for the coefficient of friction should be regarded as aberrations from a fundamentally ideal mode of frictional behavior. The theoretical basis of friction can be extended to these cases. To avoid the restrictions imposed by a limiting value of 0.2 for 

Tangential force coefficients can be determined by direct measurement of the tangential tractive force and the normal loading force of the system, but the ratio A /A is usually obtained by indirect methods. McFarlane and Tabor [9] found that the adhesion of indium to steel under the influence of a normal preload was so strong that the tractive force to initiate sliding after removal of the preload was essentially a measure of the shear force in indium. From this measurement they calculated a value of a =3.3 for indium. Courtney-Pratt and Eisner [10] evaluated A /A by electrical resistance and obtained a value of a = 11.66 for platinum. 

in Eqn 8-9b, p approaches zero for pure shear under an extremely light load and p is assigned a value equal to 5a [5], then a = a and a assumes the value 25. The following relation can then be obtained from Eqn B-9b  

Since the stresses in real asperities are not restricted to pure shear, 25 is probably too high a value for a. Tabor [5] argued that 3.3, the value obtained from experiments with indium, is so low because of the experimental difficulty of measuring the adhesion and because of the plowing contribution to the force of friction for such a soft metal. The value of ca. 12 from the results of Courtney-Pratt and Eisner [10] for platinum may be imprecise because of the influence of surface film error on the conductivity measurements. The value of 9 was selected for a as a useful magnitude representative of the metals usually encountered. Setting = 3i then gives 

The exact value of a, so long as it is consistent with observed behavior, does not influence the logical conclusions drawn from the model. 

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