Two-dimensional Hertzian contact problem with surface tension

In the present paper, we consider a two-dimensional contact problem of a rigid cylinder indenting on an elastic half space with surface tension. Based on the solution of a point force acting on a substrate with surface tension, we derive the singular integral equation of this problem. By using the Guass-Chebyshev quadrature formula, the integral equation is solved numerically to illuminate the influence of surface tension on the contact response. It is found that when the contact width is comparable with the ratio of surface tension to elastic modulus, surface tension significantly alters the pressure distribution in the contact region and the contact width. Compared to that of the classical Hertzian contact, the existence of surface tension decreases the displacements on the half plane and yields a continuous slope of normal stress and displacements across the contact fringe. In addition, it predicts the increase of hardness as the radius of indent cylinder decreasing. The obtained results are useful for the measurement of mechanical properties of materials based on the indentation technique.