The Hertzian contact surface

It is tempting to accept the predictions regarding indentation depth and radius of circle of contact between two elastic bodies in contact given by the well-known Hertz equations at face value. However, it is nevertheless of interest to examine these predictions either by experiment or by independent computation. Indentation depth may be readily compared using standard experimental apparatus but in this paper, attention is given to the radius of curvature of the indented surface for a condition of full load. The conclusion arising from the Hertz equations, that contact between a flat surface and a non-rigid indenter of radius R is equivalent to that between the flat surface and a perfectly rigid indenter of a larger radius, has not thus far been examined in detail in the literature, possibly because of the difficulty in measuring such a radius of curvature in situ while load is applied to the indenter. This feature of contact between two solids is of interest since it has been often used as the basis for various hardness theories which involve an elastic–plastic contact. This paper addresses the issue by utilizing the finite-element method to compute the radius of curvature of the contact surface for both elastic and elastic–plastic contacts. It is shown that indentations involving elastic–plastic deformations within either or both the specimen and the indenter are equivalent to indentations with a perfectly rigid spherical indenter whose radius is somewhat smaller than that calculated using the Hertz equations for elastic contact. An experimental compliance response is used to indirectly validate the finite-element results.