Explicit equations for the half-plane sub-surface stress field under a flat rounded contact

Abstract

In this article, the interior half-plane stress field resulting from the contact between a half-plane and a flat rounded punch is obtained in an explicit form. The punch is first subjected to a normal load, N, and later to a tangential load Q = µN, so a global sliding condition is achieved. The equations presented here are obtained assuming that the contacting bodies exhibit isotropic elastic behaviour and have identical mechanical properties and that both bodies can be modelled as half-planes. In addition to the equations describing the interior stress field, the maximum value of the von Mises parameter and the location of this maximum value are obtained as a function of the b/a ratio, a and b being the semi-widths of the contact zone and flat section, respectively. Finally, the direct stress, σ ^t _xx (x, 0), due to the tangential load is calculated using the formulae developed here.