A surface crack in a graded medium loaded by a sliding rigid stamp

In this article the coupled problem of crack/contact mechanics in a nonhomogeneous medium is considered. The underlying physical problem to which the results might be applicable is the initiation and the subcritical growth of surface cracks in a graded medium loaded by a sliding rigid stamp in the presence of friction. The dimensions of the graded medium are assumed to be very large in comparison with the local length parameters of the crack/contact region. Thus in formulating the problem the graded medium is assumed to be semi-infinite. The objective of the study is to determine, in addition to contact stresses, the in-plane component of the surface stress and the stress intensity factors at the crack tip. These are the primary load factors controlling the initiation and the subsequent growth of surface cracks in the graded medium. The coupled mixed boundary value problem is solved and the results are presented for various combinations of friction coefficient, material nonhomogeneity constant and crack/contact length parameters.