The dynamic stress intensity factor around the anti-plane crack in an infinite strip functionally graded material under impact loading

In order to dynamically analyze a crack in an infinite strip functionally graded material for anti-plane crack problem under impact loading, a gradient model is established in which the mass density and the shear modulus in the two principal directions of the functionally graded material are assumed to vary proportionally according to the double parameters index function. By using the Laplace and Fourier transforms, the motion equation is first reduced to the Euler equation. By solving dual integral equations derived by applying the solution of the Euler equation with the method of Copson, dynamic stress intensity factor around the crack tip is derived. The variation curves of the normalized stress intensity factor with the inhomogenous coefficient and gradient parameter are obtained from the numerical calculation. The results show that the decrease of the inhomogenous coefficient and the increase of the gradient parameter are beneficial to the decrease of the dynamic stress intensity factor.