Analysis of Crack-Inclusion Interaction in an Anisotropic Medium by Eshelby Equivalent Inclusion Method

The problem of a semi-infinite crack in anisotropic medium interacting with a near-tip inclusion is analyzed by the Eshelby equivalent inclusion method. The change of mode I stress intensity factor due to crack-inclusion interaction is evaluated using a novel analytical solution for the model I stress intensity factor at the tip of a semi-infinite crack due to near-tip eigenstrains. Numerical results of the mode I stress intensity factor due to the presence of a near-tip circular inclusion are presented to show the influence of the elastic stiffness of an inclusion on the near-tip elastic field. The present scheme can be applied to calculate the stress intensity at a crack-tip in anisotropic media due to the interaction of inclusions with arbitrary shapes.

Eshelby Equivalent Inclusion Method for Composites with Interface Effects

The Eshelby equivalent inclusion method is generalized to calculate the stress fields related to spherical inhomogeneities with two interface conditions depicted by the interface stress model and the linear-spring model. It is found that the method gives the exact results for the hydrostatic loading and very accurate results for a deviatoric loading. The method can be used to predict the effective properties of composites with the interface effects.