Explicit equations for sub-surface stress field in plane contacts

This paper presents a new method to directly and explicitly calculate all of the components of the sub-surface stress field in plane contacts once the surface contact stress distributions are known. The method is applicable when the contacting bodies have isotropic elastic behaviour, identical mechanical properties and can be modelled as elastic half-planes. Although the method presented here has direct application in the case of plane contacts, it is also applicable in other mechanical problems that lead to a stress distribution at the surface. The procedure described here is applied to find the interior stress field generated by the well-known Carter's solution for a rolling contact.

► A new method for obtaining the sub-surface stress field in plane contact is proposed.
► The method produces explicit equations based on the Muskhelishvili's complex potential.
► The method is used to find the interior stress field generated in a bi-dimensional rolling contact.