Mode-III stress intensity factors of a three-phase composite with an eccentric circular inclusion

An analytical solution to a three-phase composite with an eccentric circular inclusion under a remote uniform shear load is given in this work. Mode- III stress intensity factors for an arbitrarily oriented crack embedded in an infinite matrix or a core inclusion are provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation located either in the core inclusion or in the infinite matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack are established 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 a non-uniformly coated circular inclusion, 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.