Dynamic investigation of a functionally graded layered structure with a crack crossing the interface

The dynamic response of a functionally graded layered structure with a crack crossing the interface is analyzed. The in-plane impact loading condition is considered. By using the Laplace and Fourier integral transforms, singular integral equation method and residue theory, the present problem is reduced to a singular integral equation in the Laplace transform domain. The influences of Young’s modulus ratio, thickness ratio, and crack length and location on the dynamic stress intensity factors (DSIFs) are investigated. Particularly, the DSIFs corresponding to different crack locations are shown in the case when the crack center moves from one layer to another layer through the interface. The peak and static values and overshoot characteristics of the DSIFs are analyzed. It is found that these values typically exhibit kinking behavior when the crack tips arrive at the interface. This study is different from previous other investigations in the following respects: (1) the dynamic response of a crack crossing the interface of a functionally graded structure is studied analytically, which has hardly been done in the past and (2) the present model can be reduced to some important problems, such as a functionally graded coating-substrate structure with a crack in the graded coating or homogeneous substrate or one intersecting the interface.