An approximate solution for the plane stress mode I crack interacting with an inclusion of arbitrary shape

• A general solution is presented for plane stress mode I crack interacting with an inclusion of arbitrary shape.
• Explicit solutions for special inclusion shapes are derived from the general solution.
• The solution has good accuracy for a wide range of modulus ratio between inclusion and matrix.

On the basis of the transformation toughening theory, a general approximate stress intensity factor solution is presented for mode I crack interacting with an inclusion of arbitrary shape under plane stress loading. The transformation strain induced by the inhomogeneity between the inclusion and matrix is obtained by Eshelby inhomogeneity theory. Some explicit solutions for common inclusion shapes are also derived from the general solution. As validated by detailed finite element analyses, the developed formulas have good accuracy for different inclusion shapes of a wide range of modulus ratio between inclusion and matrix.