Thermal and Mechanical Model for Rigid Cylinder Indenting an Elastic Layer Resting on Rigid Base: Application to Turned Surfaces

Models are presented for the solution of the thermal and mechanical problem of a rigid metallic cylinder indenting an elastic layer with finite thickness which rests on a rigid substrate without friction. The models were extended to turned surfaces applications. With introduction of an equivalent isothermal flux distribution for the mixed boundary problem—constant temperature over the contact area while adiabatic elsewhere along the top surface—an approximate analytical thermal model was developed. The solution was compared to a numerical solution under certain cases. Both solutions in turn compare very well with the generalized three-dimensional expression proposed by prior investigators. The mechanical model predicts the contact half-width under varying mechanical properties, layer dimensions, and applied load. The mechanical contact problem was solved numerically by substituting the displacement variable with a truncated polynomial to get a system of linear equations from which the dimensionless contact half-width was derived. The model is valid throughout a wide range of parameters, including mechanical properties and geometric dimensions. To explicitly predict the dimensionless contact half-width as a function of dimensionless load, a curve was fitted to the numerically obtained solution.