"The design and structural reliability of advanced materials, like composites or functionally graded, require a better understanding of how the fracture process initiates and progresses to final failure. There is a demand for these materials to support both static and dynamic loads without the risk of brittle fracture. The performance of advanced materials is directly linked to the reliability of interfaces. Starting from these aspects the main objectives of the research are: - a better understanding of the failure mechanisms in composite materials with the focus on the interface reliability. - to completely describe the asymptotic stress field around interface cracks and bonded –joints interfaces as an initial stage of crack initiation, and to study the effect of the interface on the fracture parameters. To introduce new parameters for better characterizing of fracture of interfaces. - investigating the influence of the material properties (considering elastic and elasto-plastic materials) on the crack path for the interface cracks and cracks approaching an interface. The novelty of the work will consist in using the Runge – Kutta method in combination with the shooting method for solving stress and displacement asymptotic fields with boundary conditions problem at both interval ends. Based on the linear elastic and elasto-plastic numerical investigations new parameters are expected to be obtained like split singularities for inclined cracks reaching a bi-material interface, mode mixity parameter and interface load phase-angle. Some simple but original design formulas will be developed based on analytical and numerical investigations for the stress singularity at bonded joints and/or interface cracks. Experimental techniques like digital image correlation and photoelastic stress analysis will be applied for identification of the crack path propagation and to validate the numerical simulations."