Multiple-zone sliding contact with friction on an anisotropic thermoelastic half-space

The paper studies a class of multiple-zone sliding contact problems. This class is general enough to include frictional and thermal effects, and anisotropic response of the indented material. In particular, a rigid die (indenter) slides with Coulomb friction and at constant speed over the surface of a deformable and conducting body in the form of a 2D half-space. The body is assumed to behave as a thermoelastic transversely isotropic material. Thermoelasticity of the Green–Lindsay type is assumed to govern. The solution method is based on integral transforms and singular integral equations. First, an exact transform solution for the auxiliary problem of multiple-zone (integer n > 1) surface tractions is obtained. Then, an asymptotic form for this auxiliary problem is extracted. This form can be inverted analytically, and the result applied to sliding contacts with multiple zones. For illustration, detailed calculations are provided for the case of two (n = 2) contact zones. The solution yields the contact zone width and location in terms of sliding speed, friction, die profile, and also the force exerted. Calculations for the hexagonal material zinc illustrate effects of speed, friction and line of action of the die force on relative contact zone size, location of maximal values for the temperature and the compressive stress, and the maximum temperature for a given maximum stress. Finally, from our general results, a single contact zone solution follows as a simple limit.