Dynamic behavior of a finite crack in the functionally graded materials

In the present paper, the dynamic behavior of a finite crack in the functionally graded materials subjected to the normally incident elastic time harmonic waves is investigated by means of the Schmidt method. The crack arbitrarily oriented with respect to the direction of property gradient is considered. The problem is solved under plane strain or generalized plane stress conditions. By using the Fourier transform and defining the jumps of the displacements across the crack surfaces as unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a Jacobi series. The main results of the paper are calculated mode I and II dynamic stress intensity factors. Numerical examples are provided to show the effect of the gradient parameter δl and the crack configuration on the dynamic stress intensity factors of the functionally graded materials with a crack.