| In this study, the basic interface crack problems in a nonhomogeneous coating with continuously varying elastic properties bonded to a homogeneous semi-infinite medium and subjected to mechanical loading conditions are examined. The underlying mechanics problems are encountered in studying the fracture mechanics of functionally graded materials (FGMs) which are mostly two-phase particulate composites with continuously varying volume fractions. The objective of the study is to determine the effect of the material inhomogeneity parameter and relative dimensions such as thickness of the coating and the bond coat on the stress intensity factors. With the application to fracture mechanics in mind, the main results given in this study are the stress intensity factors as a function of the inhomogeneity parameter and the dimensionless length parameters for various loading conditions. Some sample results on the crack opening displacements are also presented. In the last part of the study, thermal stresses around an insulated barrier due to the constant heat flux in a homogeneous semi-infinite medium are considered. Temperature distribution and thermal stresses are given for different values of the thickness parameter representing the ratio of the length of the barrier to its distance from the free surface. The main objective of this part of the study is to obtain thermal stresses around the insulated barrier and to show that the superposition may be used to solve the corresponding crack problem by using thermally rather than mechanically induced stresses as the crack surface tractions. In all problems, results agree with the closedform solutions obtained for special cases. In thermal stress problem, the closedform solution is given in Appendix D for the infinite medium. Using Fourier transforms for displacements in the plane strain crack problem, the mixed boundary conditions are analytically reduced to a system of dual integral equations and then, by a systematic approach, to a system of singular integral equations. After converting the system of singular integral equations to a system of functional equations, such physically important quantities as stress intensity factors and crack opening displacements are obtained numerically by using certain approximate techniques. |
