Partial closure analysis of a surface crack in a graded medium loaded by a frictional flat stamp

In this study the behavior of a surface crack in a graded isotropic elastic medium is examined under the effect of loading due to a frictional rigid flat stamp. The contact between the graded medium and the rigid stamp is assumed to transfer both normal and tangential forces which are related through Coulomb's friction law. The elastic modulus of the graded medium is assumed to increase exponentially in depth direction. The surface crack is oriented parallel to the material property gradation. The coupled crack and contact problem is formulated using transform techniques and reduced to a system of singular integral equations. The main emphasis is on the partial closure of the crack surfaces for small values of the friction coefficient at the material surface. The surfaces of the crack are assumed to be in smooth contact. This leads to a boundary value problem which is highly nonlinear in terms of the unknown length of the closed portion of the crack. An expansion - collocation technique is used to convert the integral equations to a system of linear algebraic equations and an iterative solution algorithm is developed to compute the length of the closed portion of the crack and the modified mode II stress intensity factors. It is found that for frictionless contact at the material surface, the surface crack is completely closed in both homogeneous and graded media. Some other sample results are also provided to present the effects of the material nonhomogeneity parameter and friction coefficient on the contact stresses, stress intensity factors and length of the closed portion of the crack.