Partial slip contact problem for solids with regular surface texture assuming thermal insulation or thermal permeability of interface gaps

• We investigate partial slip of solids with a periodic array of gaps at the interface.
• The slip is induced by thermal strains due to the imposed heat flow.
• The extent of slip zones nonlinearly increases as the heat flow increases.
• The slip zones are the largest for the case of thermal insulation of the gaps.
• The extent of slip zones decreases with increasing thermal permeability of the gaps.

The stick-slip thermoelastic contact problem for two solids, one of which has regular surface texture in the form of periodically arranged grooves, is investigated. The materials of the solids are supposed to be identical. The interface between the solids consists of a periodic array of gaps, which are assumed to be thermoinsulated or to be filled with a heat-permeable medium, and a periodic array of contact regions, where perfect thermal and stick-slip contact occurs. Partial slip of the surfaces is induced by thermal strains due to imposed heat flow, and the first points to slip are the ends of each gap. The effect of the medium in the gaps on heat transfer between the solids is simulated by thermal resistance which is a function of a height of the gaps. The contact problem is reduced to a system of three singular integral equations for the case of thermoinsulated gaps and to a system of two singular integral equation and one singular integro-differential equation for the case of heat-permeable gaps. Solutions of the systems are constructed for an arbitrary smooth function describing a shape of the grooves, and numerical results are given for a certain shape of the grooves. The comparison of contact parameters for the case of heat-permeable gaps with those for the case of thermoinsulated gaps is provided. The effects of the thermal conductivity of the interstitial medium and the imposed heat flow on the slip evolution are also studied.