A singular stress field develops at the corner of rectangular inclusion which is placed in the medium. It can be assumed that the cracking from this singular point is generated by singular stress field at the corner. When the length of crack is small compared to the other specific length scales characterizing the geometry, a simple universal relation exists between the complex stress intensity factors for the interface crack tip and the singularity intensity factors for the corner singular stress field.
In this rectangular inclusion problem, the singular stress field can be characterized by the stress singularity orders and singularity intensity factors for each loading mode as in the typical form $H_{Ⅰ}\gamma^{\lambda 11-1}$ and $H_{Ⅱ}\gamma^{\lambda 21-1}$, where γ is the radius from the corner of rectangular inclusion, $\lambda_{11}-1$ and $\lambda_{21}-1$ are the orders of the stress singularity for mode Ⅰ and mode Ⅱ. And also $H_Ⅰ$ and $H_Ⅱ$ are the singularity intensity factors with respect to mode Ⅰ and mode Ⅱ. Unfortunately, the dominant region of H-field characterized by the only first term has too small to include the K-field. It means that the singular stress field of the corner including the corner crack is not only described by $H_Ⅰ$ and $H_{Ⅱ}$. The next term $H_Ⅰ^*\gamma^{\lambda 21-1}$ for mode Ⅰ is introduced into the eigenfunction expansion in order to expand the H-dominant region. The next term for mode Ⅱ does not contribute to the corner singular stress field of rectangular inclusion.
The singularity intensity factor H can be evaluated by M-based mutual integral and the stress intensity factor K can be evaluated by J-based mutual integral. And then we can obtain the universal relation between singular intensity factors H and stress intensity factor K.
In the result of this work, it is found that there is a universal relation between the corner singular stress field of the rectangular inclusion expanded by next term in eigenfunction expansion and the crack tip singular stress field from the corner which has the right angle. This universal relation can be used to evaluate the stress intensity factors for the interface crack tip embedded into the corner singular stress field of the different shape of rectangular inclusion having the same corner shape treated in this work. This universal relation must be modified whenever the shape of the corner of rectangular inclusion is changed.
