Frictionally excited thermoelastic instability in the presence of contact resistance

In sliding systems, frictional heating generates a well-known instability above a certain critical speed V-cr, which is a function of geometrical and material properties only. Similar instabilities are known to occur in the static problem, driven by temperature differences, in the presence of thermal contact resistance. Thermal contact resistance at the interface has seldom been considered and gives rise to full coupling of the problem. Generally, the resistance decreases nonlinearly when pressure is increased. Here, the critical condition (in terms of heat flux and sliding speed) for the stability of the uniform pressure solution for a half-plane in frictional contact with a rigid wall at fixed temperature is studied for a general resistance function R(p). It is found that the heat flux direction increases the instability as in the case of zero speed, i.e. when directed into the half-plane (which is the only distortive material), whereas frictional heating can have also a stabilizing effect, for a given heat flux, specifically when R(p) +pR'(p) < 0. Also, an isothermal critical speed has been defined, and the actual critical speed is found to be smaller or larger depending on the temperature difference sign. Longer wavelengths are always more unstable so that the critical wavelength is still dictated by the real size of the system