Elastic Analysis of Interaction between Circular Inclusion and Crack

Abstract

A crack problem near a circular inclusion is analyzed numerically. The method of continuously distributed dislocations model is applied to the present problem, and the boundary condition on the crack surface is reduced to a set of singular integral equations of the Cauchy type in which the dislocation density functions are unknown. The obtained singular integral equations are solved numerically and the stress intensity factors are obtained with changing the configuration parameters of the crack and/or the elastic moduli of the matrix and the circular inclusion. The normal stress and the shearing stress acting on the bimaterial interface are also calculated quantitatively. The numerical results are reliable and accurate enough to be used for the confirmation of the reliability and the accuracy of another analysis method. As a result of these calculations, it has been clarified that when the rigidity of the inclusion is high, the stress level on the interface becomes large in spite of the fact that the stress intensity factors of the crack become small.