Indentation by nominally flat or conical indenters with rounded corners

Abstract

Axisymmetric indentation of a flat surface is considered: specifically, the case of flat-ended indenter with rounded edges, and the case of a shallow cone with a rounded tip. Analytical solutions are obtained for the normal and sequential tangential loading, in both full or partial slip conditions (with the Cattaneo fn9 fn9 degree polynomial in x and y. The most relevant are Hertzian elliptical contacts (as proved explicitly by Cattaneo, 1938) and plane problems ( Ciavarella, 1998a, Ciavarella, 1998b) . Indeed, for plane problems, with no dependence, say, on y, Δ V ( x) = (d 2V ( x) /d x 2) = h 1+ h 2 has a general solution V ( x) = [ ( h 1+ h 2) /2] x 2+ c. Other particular cases of such exact solutions may exist, with a more general shape of stick area, but the question of limited practical interest, as long as the surface profiles to produce that contact area and symmetry are of rather particular form, so that the property will hold only for very special values of geometry and load. Mindlin approximation) , and for the complete interior stress field in all these conditions. Implications for strength of the contact are discussed with reference to metallic or brittle materials, with the intention to shed more light in particular to the understanding of common fretting fatigue or indentation testings with nominally flat or conical indenters. It is found that the strength of the contact, which is nominally zero for perfectly sharp flat or conical indenters, is well defined even for a small radius of curvature. This is particularly true for the flat indenter, for which the strength is even significantly higher than for the classical Hertzian indenter for a wide range of geometrical and loading conditions, rendering it very attractive for design purposes.