Boundary element analysis for finite-size quasicrystal plates with a hole

Abstract

The quasicrystal thermal barrier coating technology for engines is one effective means to address the energy-saving and emission-reduction issues in fuel-powered vehicles. It is noted that under loads, quasicrystal components with holes will experience stress concentration at hole edges, which can induce cracks and lead to material failure. Therefore, studying the mechanical behavior of quasicrystal defects is of great significance for improving the reliability of components. However, the boundary value problem of finite-sized icosahedral quasicrystal plates with holes is very complex and difficult to solve analytically. In the article, based on the extended Stroh method, a boundary element analysis is conducted for finite-size quasicrystal plates with a hole. Mainly, Green’s function is derived to obtain the fundamental solutions of an infinite-sized quasicrystal specimen with a hole, and linear interpolation functions and the Gauss integral formula are used to discretize integral equations. Finally, the effects of the size of the medium and the coupling elastic constant on the stress around the hole are discussed. The numerical results show that the boundary element method can be used to analyze both the finite-sized problem and the infinite-sized problem.