Subsurface stressed state of functionally graded elastic solids involved in dry axially symmetric contacts

Abstract

In general, the goal of most studies of contact problems of elasticity is to determine the contact stress distributions such as pressure and frictional stress. In many cases this information is sufficient to directly or indirectly evaluate the situations with elevated failure risk. However, there are numerous distinct failure processes which get originated below the contact surface. Among these processes are coating delamination and subsurface originated pitting. To be able to consider such processes one has to know the subsurface stressed state of a solid. Therefore, the motivation of this study is to make a first step in addressing the subsurface stress behavior for functionally graded elastic solids. In this work we consider the behavior of the subsurface stresses in a coated elastic solid which is indented by an axially symmetric punch. The contact is assumed to be frictionless. The goal of the paper is to get detailed information on stress behavior at and near the coating/substrate interface. Usually, this is the region where different failure processes get originated. The expressions for subsurface stresses were derived in terms of certain integrals of pressure. The latter were determined using a semi-analytical and asymptotic methods. The distributions of subsurface stresses were determined numerically and analyzed for various functional dependences of the coating and substrate elastic parameters as well as other problem input parameters. Certain peculiar subsurface stress behavior near coating/substrate interface and contact boundary were observed.