Explicit solution and invariance of the singularities at an interface crack in anisotropic composites

Assuming that stress distribution near the tip of an interface crack in an anisotropic composite is proportional to rδ, application of the interface and boundary conditions yields ||K(δ)|| = 0, where K is a 12 × 12 complex matrix. The surfaces of the crack can be free-free, fixed-fixed or free-fixed. For the cases of free-free and fixed-fixed cracks, explicit solutions for all δ's are obtained. For the case of free-fixed crack, the determinant of K is reduced to a 3 × 3 determinant which yields a sextic equation. Explicit solutions are obtained only for isotropic composites. The special cases of a homogeneous anisotropic material with a semi-infinite crack and the half-plane problems are also considered. Explicit solutions for δ's are obtained for all three boundary conditions. Finally, it is shown that δ is invariant with respect to the orientation of the plane boundary (in the case of half-plane problems), the semi-infinite crack (in the case of a crack in a homogeneous material) and the crack and interface (in the case of a composite with an interface crack) relative to the materials. This is a somewhat surprising result not expected of anisotropic materials.

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