Abstract
The two-dimensional contact problem for two elastic half-spaces of identical materials with a periodic system of grooves, in the surface of one of them is considered when partial slip is taken into account. It is assumed that there is initially complete contact between the surfaces of the bodies under the action of a normal load and that a tangential load is then added to them with the resultant appearance of frictional slip zones within each groove. The stress-strain state of the bodies is represented in terms of a specified function of the groove height and an unknown function of the relative displacement of the boundaries of the bodies in the slip zones. To determine the latter, a singular integral equation with a Hilbert kernel is obtained and solved analytically. The width of the slip zones is found from the condition that the contact shear stresses are limited. The dependences of the contact parameters on the applied load and the groove width are analysed.
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