Some Crack Problems In An Infinite Space Of Two Dimensional Hexagonal Quasicrystals

Quasicrystals (QCs) are a new structural form between crystals and glass, with a long-range quasi-periodic translational order and a long-range orientation order. Due to its unique structural form, QC materials have following excellent properties compared with traditional materials, such as low friction coefficient, low porosity, low adhesion, low thermal conductivity, high wear resistance and high corrosion resistance. Therefore, QCs have a plenty of potential applications in a wide range of high and new technology fields. Owing to the brittleness of QC materials at room temperature, the research on the crack problems of the QCs is of scientific value and practical significance. In the present work, two aspects concerning the crack problems of QCs have been carried out.(1) In the framework of elasticity of two-dimensional QCs, three-dimensional elastic fundamental solutions to the problem that crack surface subjected to a pair of concentrated normal loadings (mode I) in an infinite two-dimensional hexagonal QC space are derived. By virtue of the elastic general solutions of two-dimensional hexagonal QCs conjugated with the method of potential theory, the three-dimensional elastic fundamental solutions in terms of elementary functions are obtained. On the basis of the fundamental solutions, the physical quantities, for instance, the stress intensity factor, crack surface displacement and energy release rate, which are important parameters in fracture mechanics, are explicitly derived. The phonon-phason coupling effects are revealed as well.(2) In the context of thermo-elasticity of two-dimensional QCs, three-dimensional thermo-elastic fundamental solutions to the problem that crack surface subjected to a pair of identical thermal loadings in an infinite two dimensional hexagonal QC space are obtained. Based on the thermo-elastic general solutions of two-dimensional hexagonal QCs along with the method of potential theory, the three-dimensional thermo-elastic fundamental solutions are expressed in terms of elementary functions. The physical quantities, for example, stress intensity factor and crack surface displacement, which are important in fracture mechanics, are explicitly derived on the basis of the fundamental solutions. The thermo-phonon-phason coupling effects are also discussed.The problems studied in the present work improve the research on the fracture aspects of QCs. The present analytical solutions can serve as benchmarks for numerous simplified analyses and various numerical codes in future investigations.