Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

Abstract

An analysis solution method (ASM) is proposed for analyzing arbitrarily shaped planar cracks in two-dimensional (2D) hexagonal quasicrystal (QC) media. The extended displacement discontinuity (EDD) boundary integral equations governing three-dimensional (3D) crack problems are transferred to simplified integral-differential forms by introducing some complex quantities. The proposed ASM is based on the analogy between these EDD boundary equations for 3D planar cracks problems of 2D hexagonal QCs and those in isotropic thermoelastic materials. Mixed model crack problems under combined normal, tangential and thermal loadings are considered in 2D hexagonal QC media. By virtue of ASM, the solutions to 3D planar crack problems under various types of loadings for 2D hexagonal QCs are formulated through comparison to the corresponding solutions of isotropic thermoelastic materials which have been studied intensively and extensively. As an application, analytical solutions of a penny-shaped crack subjected uniform distributed combined loadings are obtained. Especially, the analytical solutions to a penny-shaped crack subjected to the anti-symmetric uniform thermal loading are first derived for 2D hexagonal QCs. Numerical solutions obtained by EDD boundary element method provide a way to verify the validity of the presented formulation. The influences of phonon-phason coupling effect on fracture parameters of 2D hexagonal QCs are assessed.