The interaction of mode I crack with multi-inclusions in a three-phase model

An approximately close form solution has been developed for mode I crack interacting with multi-inclusions in composite materials. The crack-tip stress intensity factor is evaluated in a three-phase model, which combines the present knowledge that the inclusions only in the immediate neighborhood of the crack-tip have strong effect on the stress intensity factor and that the far inclusions have an overall effects which can be estimated by effective properties of the composites. As validated by numerical examples, the solution has good accuracy for a wide range of the modulus ratios between the inclusion and matrix material.