Dynamic analysis of a crack in a functionally graded material sandwiched between two elastic layers under anti-plane loading

The transient response of a crack embedded in a functionally graded material (FGM) layer sandwiched between two dissimilar elastic layers is analyzed under anti-plane shear impact loads. The material properties of the FGM is assumed to be an exponential function of the thickness. The problem is reduced to a singular integral equation via the Fourier and Laplace transforms, and the resulting equation is solved numerically. Dynamic stress intensity factors are determined by a numerical inversion of the Laplace transform. The results indicate that in addition to the crack geometry, the dynamic stress intensity factors depend upon the material properties and the crack position. Moreover, there is a significant error in the obtained dynamic stress intensity factors for applied impacts acting at the material surface and at the crack surfaces.