Effects of nonhomogeneity on dynamic stress intensity factors for an antiplane interface crack in a functionally graded material bonded to an elastic semi-strip

The transient response of a crack lying at the interface between a functionally graded material (FGM) and an elastic substrate of finite width is analyzed when subjected to antiplane shear impact loads. The results for the cases of applied impacts acting on the material surface and on the crack surface are presented and compared, where the two flank-edges are assumed to be traction-free and traction-free, clamped and clamped, or one free of traction and the other clamped. Using the Fourier and Laplace transforms, the mixed initial-boundary value problem is reduced to triple series equations, then to a singular integral equation of the first kind. The resulting singular integral equation is solved numerically by using the Lobatto–Chebyshev collocation quadrature method, and dynamic stress intensity factors are determined by a numerical inversion of the Laplace transform. The effects of the FGM nonhomogeneity on dynamic stress intensity factors are examined and shown graphically. The results indicate that the overshoot of the normalized stress intensity factors increases or decreases and even disappears depending on the sign of the nonhomogeneity exponential of FGM, particularly for sudden impacts acting at the surface of the FGM coating.