Fracture mechanics analysis of functionally graded layered structures with a crack crossing the interface

A functionally graded layered structure with a crack crossing the interface is studied analytically. Different layers may have different nonhomogeneity properties in the structure. The problem is solved by using the integral transform, singular integral equation methods and the theory of residues. The influences of the nonhomogeneity constants and geometric parameters on the stress intensity factors (SIFs) are investigated. Especially, the variations of the SIFs with nonhomogeneity constants are depicted when the crack moves from one layer into another layer. It is found that the SIFs usually get to the extremum when the crack tips get to the interface. Many numerical results are provided for further analysis or for other researchers to check their results. Since the fracture problems of FGMs with a crack crossing the interface have been scarcely studied in the past, the present work will be significant for the fracture mechanics analysis and design of functionally graded layered structures.