Stressed state of functionally graded elastic solids involved in dry contacts

Ilya I. Kudish¹, Andrey S. Vasiliev ², Sergey S. Volkov ², Sergey M. Aizikovich ³

¹Mathematics, Kettering University, Flint, MI, USA, ²Research Fellow, National Research Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia, ²Materials Laboratory, Don State Technical University, Rostov-on-Don, Russia

It has been shown that functionally graded coatings may significantly alter contact pressure and subsurface stress distributions. One of the questions left not addressed is how the elastic properties of coatings and substrates affect subsurface stress distribution. The principal stresses and displacements vary within a coating depending on whether the coating elastic parameters are constant or vary with depth. Depending on the functional dependence of the Young's modulus it is possible to reduce or increase the concentration of the principal stresses near the coating surface and the interface of the coating and the substrate. Therefore, using the appropriate/optimal selection of elastic properties of the coating and substrate it is possible to affect a contact tribological  properties  and  to  increase its  fatigue  life  and coating delamination life.

To analyze the subsurface stress behavior for a dry contact the expressions for contact pressure, subsurface displacements and stresses were derived in terms of certain integrals of contact pressure distribution. The latter were determined using a semi-analytical and asymptotic methods. The distributions of subsurface displacements and stresses were determined numerically and analyzed for various functional dependences of the coating and substrate elastic parameters and coating thickness. Certain peculiar subsurface stress behavior in the zones near the contact boundary has been observed.

Acknowledgement. This research was supported by Russian Science Foundation grant no. 15-19-10056.