%0 Journal Article
%T Closed
%A CuiYing Fan
%A MingHao Zhao
%A Qing-Hua Qin
%A Yuan Li
%J Mathematics and Mechanics of Solids
%@ 1741-3028
%D 2019
%R 10.1177/1081286518807513
%X An elliptical crack subjected to coupled phonon¨Cphason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method
%K Two-dimensional hexagonal quasicrystals
%K elliptical crack
%K coupled phonon¨Cphason loadings
%K analytical solutions
%K displacement discontinuities
%U https://journals.sagepub.com/doi/full/10.1177/1081286518807513