Interface crack embedded in a bi-material plane under shear and compression

•An interface crack of a bi-material plane under shear is studied.•No oscillatory singularity, but square-root singularity occurs near the crack tips.•Mode-I stress intensity factor depends on Dundurs’ parameter.•Full stress fields in a bi-material are derived for uniform and linear shear stress.•Dundurs’ parameter affects the crack initiation direction.

A two-dimensional elastic analysis is made for a crack lying at the interface between two bonded dissimilar homogeneous isotropic media subjected to shear and compression. The Fourier transform technique is applied to reduce the problem to dual integral equations, and the solution is obtained in closed form. Full stress fields at an arbitrary position of the whole bi-material plane induced by a closed mode-II interface crack are explicitly obtained for uniform and linearly distributed shear stress at the crack surface, respectively. The stress intensity factors are gained in closed form. Obtained results indicate that the shear stresses ahead of the crack tip exhibit a usual square-root singularity, rather than oscillatory singularity. Disturbed normal stresses are also singular at the crack surfaces behind the crack tips and depend on a Dundurs’ parameter. Using the maximum tangential stress criterion, the Dundurs’ parameter has an influence on the initiation angle of an interface crack in mixed compression–shear mode.