| In this dissertation the basic axisymmetric and antiplane crack problems in a nonhomogeneous solid with continuously varying elastic properties are considered. The problem is encountered in studying the fracture mechanics of certain geophysical materials such as shale-sandstone interfaces, tailored materials with graded properties such as the nonhomogeneous cermets, and interfacial zones in a variety of bonded materials. In this study the effect of the material nonhomogeneity parameters on the stress intensity factors in "functionally gradients materials" containing a crack parallel to the nominal interface is investigated.;By using Hankel integral transforms for the displacements in axisymmetric crack problems and Fourier integral transform for the displacement in the antiplane crack problems, the mixed boundary conditions are first reduced to a system of dual integral equations, and then, by a systematic approach, to a system of singular integral equations. Finally, by using certain approximate techniques,the resulting system is converted to a system of functional equations. In the numerical examples, such physically important quantities as stress intensity factors and the strain energy release rates are obtained and plotted. A detailed discussion of the results is given. |
