An Experimental Study of the Apparent Area of Contact under Nominally Hertzian Contact of Rough Surfaces

For bodies in contact it is usual to assume that the real area of contact is proportional to the applied normal load. For Hertzian type contacts the apparent area of contact is also dependent on load. Thus, in contacts of the latter kind the divergence of the apparent contact area from the classical Hertzian predictions leads to further understanding of the actual nature of contact of rough surfaces. In the work reported in this paper, results are presented for experimentally determined values of the apparent contact size in Hertzian conditions over a wide range of applied load. It is demonstrated that the Hertzian values are generally valid at higher loads, provided bulk plastic yielding does not occur. At lower loads the size of the contact zone is greater than that predicted by Hertz, the discrepancy being greater for rough surfaces and the contact being almost independent of the normal load. This confirms the general theoretical prediction for the contact of rough surfaces. The results of such a study, therefore, demonstrate the regime in which the usual Hertzian analysis is valid for defining the apparent contact size. Nonetheless, even where agreement exists, the actual contacts occur only over a discrete population of the surface asperities. The effect of ball size is also shown to be of reducing significance in defining the contact size at small loads, again justifying the basic theoretical arguments. At higher loads it is found that the Hertz solution is substantially valid even where a marked geometric conformity exists between the ball and its track.