Introduction

Classical elastic contact stress theory concerns bodies whose temperature is uniform. Variation in temperature within the bodies may, of itself, give rise to thermal stresses but may also change the contact conditions through thermal distortion of their surface profiles. For example if two non-conforming bodies, in contact over a small area, are maintained at different temperatures, heat will flow from the hot body to the cold one through the ‘constriction’ presented by their contact area. The gap between their surfaces where they do not touch will act more or less as an insulator. The interface will develop an intermediate temperature which will lie above that of the cold body, so that thermal expansion will cause its profile to become more convex in the contact region. Conversely the interface temperature will lie below that of the hot body, so that thermal contraction will lead to a less convex or a concave profile. Only if the material of the two bodies is similar, both elastically and thermally, will the expansion of the one exactly match the contraction of the other; otherwise the thermal distortion will lead to a change in the contact area and contact pressure distribution. This problem will be examined in §4 below.

A somewhat different situation arises when heat is generated at or near to the interface of bodies in contact. An obvious example of practical importance is provided by frictional heating at sliding contacts.