A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials

Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension-shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex representation of stress and displacement is given. Using the mixed boundary conditions, the closed-form expressions for the stresses and the displacement jumps in the phonon field and phason field on the material interface are obtained. The results show that the stress intensity factor at the crack tip is zero for the phason field. The variation in the stress intensity factor and the length of the contact zone in the phonon field is given, and the result is consistent with the properties of the crystal. The design of safe engineering structures and the formulation of reasonable quality acceptance standards may benefit from the theoretical research carried out here.