A sensitive interval of imperfect interface parameters based on the analysis of general solution for anisotropic matrix containing an elliptic inhomogeneity

A general solution is proposed to solve the plane problem for infinite anisotropic medium containing an elliptic inhomogeneity with imperfect interface. The imperfect interface is usually described as a spring model with vanishing thickness based on the assumption that the tractions are continuous but the normal or tangential displacements are discontinuous due to a jump at the interface. By means of the series expansion of the complex stress functions and the factor functions for the imperfect elliptic interface, a general procedure to determine the coefficients in the series is illustrated and the convergent solutions are obtained by truncating finite number of terms in the series. The present solutions are verified with available analytical results for the cases of perfect interface and debonded interface (or hole). The patterns of the stresses in the anisotropic medium (or matrix) and inhomogeneity due to the eigenstrains and far-filed stresses are presented, respectively. A sensitive interval of interface parameters is suggested, in which the influence of the change of interface parameters on the stress field is very obvious. Monotonic and non-monotonic change of peak stresses on a subset of interface parameters is also discussed. The method and the procedure proposed in this work can be used in the analysis of strength and failure of anisotropic materials containing an elliptic inhomogeneity with imperfect interface.