This paper gives an energy analysis of an elastic solid with a crack which penetrates an elastic inclusion. The purpose of our work is to evaluate the energy release rates (ERR) associated with crack tip extension while the inclusion is stationary, and to evaluate the ERR due to inclusion translation, rotation and expansion with respect to the crack tip. Reduction and increase in the crack ERR caused by an inclusion (shielding and amplification effects of the inclusion) are expressed in terms of the inclusion elastic properties normalized by Young's modulus of the bulk material. The variation in ERR as a crack approaches and passes through a circular inclusion is also examined.

The Green's function is constructed for the stress intensity factor due to the unit dipole force applied to the crack surface in the presence of a circular inclusion in front of the crack tip. An explicit functional form of the Green's function is proposed in terms of dipole force location, Young's modulus ratio and the inclusion size and position with respect to the crack tip. This is achieved through a combination of the dimensional analysis and parametric studies by means of the finite element method. The purpose of this paper is to provide the basis for further studies of a crack interaction with an array of microdefects and/or inclusions.

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