Surface roughness and contact: An apology

The Greenwood and Williamson theory of contact has been widely accepted, and perhaps does contain the essential feature needed: that asperities should have a height distribution which approximates to a simple exponential in the relevant range of heights. The Gaussian height distribution often found experimentally does indeed approximate to an exponential as required. It appears that Greenwood and Williamson's second assumption, that asperities may be treated as having spherical caps and as being identical except for their heights, is also useful: little is gained by treating the asperities as ellipsoids, or by introducing a distribution of asperity sizes. But a third, tacit, assumption, that 'peaks' on a surface profile - points higher than their immediate neighbours at the sampling interval used - correspond to asperities is quite wrong, and gives a false idea of both the number and the radius of curvature of the asperities. Instead we need to return to the earlier Archard concept that roughness consists of 'protuberances on protuberances on protuberances', and perhaps also to another Archard idea, the paradox that contact may be plastic at light loads but become elastic at heavier loads!