Modeling thermal contact resistance between elastic hemisphere and elastic layer bonded to elastic substrate

An approximate thermo-mechanical model is developed to predict thermal contact resistance of a hemisphere in elastic contact with a layered substrate. Numerical data are obtained for several combinations of layer material. It is shown that with the proper selection of dimensionless parameters the numerical results fall on a single curve that is easily correlated. The complex solution is reduced to a simple closed form solution for the unknown contact radius. The proposed thermo-mechanical model is applicable for any layer-substrate material combination over the full range of the layer thicknesses. The agreement between the theoretical predictions and experimental data is good at the light loads. A method for correcting the contact radius for elastic-plastic behavior at higher loads is presented.