Interfacial circular crack in cylindrically anisotropic composites under antiplane shear

The paper investigates the antiplane shear problem of a dissimilar interfacial circular crack in cylindrically anisotropic composites. Using the theory of analytical functions, a general solution based on a complex variable displacement function is obtained, which is similar to Lekhnitskii's stress potentials for rectilinearly anisotropic material. For some cases, the circular crack problems are reduced to Hilbert problems which are solved in a closed form. The first three-term asymptotic expansions of the near crack-tip stress field are given to identify the role of the curvature effect. The asymptotic solutions are further compared with exact solutions. These solutions show that the leading term exhibits an inverse square root stress singularity regardless of the material properties. In order to compare the stress field near the crack tip for a curved crack with that of a planar crack, a solution for a rectilinearly anisotropic body with a centered straight interfacial crack is also presented.