Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

Abstract

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method of two-dimensional QCs is developed to solve the plane elasticity problem of two-dimensional decagonal QCs containing complex defects. The analytical solutions for the stress field and the stress intensity factors near the crack tip are expressed by using a conformal mapping technique and complex potential theory. Some special cases of the results are also obtained, such as the T-type crack, cross crack, and Griffith crack. The effects of geometrical parameters of crack configuration on the stress intensity factors are presented graphically.

Keywords

• two-dimensional decagonal quasicrystals
• Mode-I plane problem
• cracks emanating from an elliptical hole
• stress intensity factors
• analytical solution