Anti-plane interaction between a crack and an elliptically cylindrical layered media

Anti-plane interaction of an elliptically cylindrical layered media with an arbitrarily oriented crack embedded in an infinite matrix, intermediate layer, or inner inclusion under a remote uniform shear load is considered in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation in the inclusions and the matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack can easily be obtained by using the screw dislocation solutions as the Green's function together with the principle superposition. The stress intensity factors, which can properly reflect the interaction between a crack and an elliptically cylindrical layered media, are then obtained numerically in terms of the values of the dislocation density functions of the integral equations. The effects of material property combinations and geometric parameters on the normalized mode-III stress intensity factors are discussed in detail and shown in graphic form.