Numerical analysis of frictional contact in the presence of a surface crack in a functionally graded coating substrate system

In this paper, the frictional two-dimensional contact in the presence of a surface crack in a functionally graded coating substrate system is studied for rigid circular and flat stamps. A computational method based on finite difference (FD) is developed to evaluate the contact stresses and also the fracture parameters, which are KI and KII due to mixed mode fracture. The FD method applied here, uses a mapping technique which enable the analysis to consider any geometry of the punch and the crack. The Coulomb's dry friction law is considered in the contact area. The advantage of this study, compared to the efforts done by other researchers, is the ability to analysis a system with any arbitrary material properties distribution. Here, the elastic material properties distribution is estimated by TTO model which takes into account the interaction between the constituting phases as well, and the Poisson's ratio is assumed to be constant. The effect of material nonhomogeneity, the interaction of the constituting phases, the thickness of the graded coating layer, the size of the punch and the coefficient of friction is studied. In a general case, the findings of this research show that increasing the size of the punch, the coefficient of friction and the thickness of the graded layer increase the contact force and hence the contact stress; however, the interaction of the constituting phases does not have any effects on the contact parameters. In frictionless contact, the stress intensity factor is negative. In addition, increasing the coefficient of friction increases KI but decreases KII. These results are valid for any materials properties distribution.