Solutions of a crack interacting with a three-phase composite in plane elasticity

The interaction between a crack and a circularly cylindrical layered media under a remote uniform load for plane elasticity is investigated. Based on the method of analytical continuation associated with the alternation technique, the solutions to the crack problem for a three-phase composite are derived. A rapidly convergent series solution for the stress field, expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The solution procedures for solving this problem consist of two parts. In the first part, the complex potential functions of dislocation interacting with a three-phase composite are obtained. In the second part, the derivation of logarithmic singular integral equations by introducing the complex potential functions of dislocation along the crack border is made. The stress intensity factors (SIFs) are then obtained numerically in terms of the dislocation density functions of the logarithmic singular integral equations. The stress intensity factors (SIFs) as a function of the dimensionless crack length for various material properties and geometric parameters are shown in graphic form. The obtained results may provide some guidance for material and geometry selections by minimizing the SIF.