When a crack is lodged in an inclusion, differences between the moduli of the inclusion and the bulk material can cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous body. To study the influence of such moduli differences, we solve the problem of a semi-infinite crack half-way penetrating a circular inclusion. The field equations are automatically satisfied by choosing appropriate series expansions for the complex stress potentials; a doubly-infinite system of linear algebraic equations for the series coefficients then enforces continuity of traction and displacement at the inclusion boundary. Results for the reduction (or enhancement) of the stress intensity factor are given for the entire range of material parameters.

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