Approximate analytical solution for plane stress mode II crack interacting with an inclusion of any shape

•Approximate solution for plane stress mode II crack interacting with an inclusion is developed.•The solution is applicable to an arbitrary-shaped inclusion of any elastic modulus.•Explicit solutions for special inclusion shapes are obtained.

In this paper, a general approximate solution is developed for plane stress mode II crack interacting with an arbitrary-shaped inclusion of any elastic modulus on the basis of the Eshelby equivalent inclusion theory and the transformation toughening theory. Some simple solutions for special 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 with a wide range of modulus ratio between inclusion and matrix. Furthermore, the comparison of the present plane stress solution with the previous plane strain solution gives insight into the complex three-dimensional interaction between a crack and an inclusion.