A thermomechanical analysis is presented for semi-infinite elastic solid sliding against a rigid rough surface characterized by fractal geometry. A piecewise-linear distribution of the contact pressure was obtained by superposition of overlapping triangular pressure elements. The normal surface displacements due to the effects of contact pressure, shear traction, and thermoelastic distortion caused by frictional heating are incorporated in the influence coefficients of the matrix inversion method. Results for a smooth cylindrical surface sliding over a semi-infinite elastic solid demonstrate the accuracy of the analysis and provide reference for comparison with results obtained with the rough (fractal) surface. The effects of surface topography and interaction between neighboring asperity microcontacts on the surface and subsurface temperature rise and stress field of the elastic semi-infinite solid are discussed in the context of numerical results. The significance of frictional heating on the contact pressure, temperature rise, and stresses is interpreted in terms of the Peclet number and topography (fractal) parameters. The results provide insight into the likelihood for cracking and plastic flow at the surface due to the combined effects of mechanical and thermal surface tractions.
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