Semi-analytical study of microscopic two-dimensional partial slip contact problem within the framework of couple stress elasticity: Cylindrical indenter

In the present work, a size-dependent partial slip contact model of an elastic half-plane indented by a rigid cylindrical punch is established within the framework of couple stress elasticity. The proposed model introduces an internal material length to characterize the size effect of materials and assumes that the friction between two bodies is one of the Coulomb friction type. The Fourier transform in conjunction with the generalized stress function formulation is adopted to obtain the relationship between the coupled normal pressure and tangential traction in the form of a set of singular integral equations. Employing an iterative approach, the coupled system of integral equations is numerically solved and the effects of the couple stress and the friction coefficient upon the contact response are highlighted. The results show significant departure from the predictions of previous contact models based on the classical elasticity or the couple stress elasticity under frictionless condition. Moreover, it is demonstrated that the predicted contact responses of microindentation problems are underestimated if the material is assumed to have a smooth surface or treated as a classical elastic material.