Sliding contact between a rigid cylindrical punch and a functionally graded semi-infinite medium in the presence of a surface crack

In this article two dimensional sliding contact of a rigid cylindrical punch on a functionally graded (FG) semi-infinite medium is studied. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions between the constituting phases. The governing equations are solved by finite difference (FD) method by means of MATLAB software. The effects of different parameters such as non-homogeneity­, q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction are investigated on the force-displacement diagram of the punch, stress distribution and modes I and II stress intensify factors (KI and KII). The results show that the contact force and the stress distribution under the punch are affected by the thickness of the graded layer, radius of the punch and the non-homogeneity­ coefficient. But the variation of q has no effects on the contact force and the stress distribution under the punch. In the absence of the friction, KI is always non-positive and the crack has no tendency to grow under this mode. Increasing the friction coefficient, increases KI but decreases KII.