Edge effect and indentation depth-dependent contact behavior in contact of an elastic quarter-space

Abstract

The edge effect in contact of an elastic quarter-space is numerically studied in this work. The extension of Hetényi’s approach of overlapping two elastic half-spaces is implemented in the boundary element method to obtain the solution of an elastic quarter-space whose top and side surfaces could be both loaded. In the study on the indentation test of a rigid sphere on an elastic quarter-space, the dependencies of the normal force, mean contact radius, and pressure distribution in contact area as well as the internal von Mises stress in relation to the position of the sphere from the side edge are obtained numerically and expressed by fitting the numerical results. These equations can be also used to interpret the indentation depth-dependent contact behavior: from Hertzian contact at the beginning of the indentation to the non-circular contact at large indentation depth.In addition, the results are compared with a contact case of a quarter-space in which the side surface of the quarter-space is not completely free: shear stresses on the side surface vanish but normal stress exists. The latter case generates very similar results, especially the contact area, but its solutions are much easier to achieve by applying a symmetrical loading on an elastic half-space, offering an effective way to approximate the solution of a quarter-space.