Moving mode III crack in functionally graded strip

In the existing papers, most researchers assume that the material properties of functionally graded material get in accordance with the exponential function or power function. The problem of a moving anti-plane crack in a functionally graded strip is investigated provided the reciprocals of the shear modulus and the density are both linear functions of the coordinate, while Possion ratio keeps constant. With the Fourier integral transform technique and the transfer matrix method, the mixed boundary problem is reduced to a couple of singular integral equations. The mode III dynamic stress intensity factor is obtained by solving the singular integral equations numerically. The influences of the velocity and the size of the moving crack and the material graded parameter on the stress intensity factors is discussed. The numerical results show that the graded parameter, geometrical parameters and velocity of the moving crack exert significant effects on the dynamic fracture behavior.