Research On Some Problems Of Two-imensional Octagonal Quasicrystals Fracture Mechanics

The discovery of quasicrystals in 1984 was a major breakthrough in condensed matter physics in recent years.As a new type of material,quasicrystals have great significance in studying their mechanical properties,especially the elasticity and defects.Based on the elasto-hydrodanamics model,dynamic problem of octagonal two dimensional quasicrystals was investigated by using the finite difference scheme,and calculated the Eshelby tensor of octagonal two dimensional quasicrystals.There are four chapters.Preliminary knowladge,the numerical analysis about fracture problems of a octagonal quasicrystals with a mode I Griffith crack,dynamic problems of a mode II crack in two dimensional octagonal quasicrystals,derived the formulas of Eshelby tensor and calculated the Eshelby tensor of an octahedral quasicrystal containing elliptical inclusions.In chapter one,we introduced the theory of quasicrystal related elasticity.In chapter two,the finite difference method was used in the fracture problem of a octagonal quasicrystals with a mode I Griffith crack.By using the finite difference method to discretize elasto-hydro-danamics mode,the regular pattern of stress intensity factors on the different dynamic loading following the change of time was expounded.In chapter three,based on the elasto-hydrodanamics model,dynamic problem of a mode II crack in octagonal two dimensional quasicrystals was investigated by using the finite difference scheme.The dynamic responses of stress intensity factors for different loading time and different material size were analyzed,respectively.And the influence of different phonon-phason coupling elastic constants on displacement component of phason field was demonstrated.The results indicates that,the value of stress intensity factor increases as the loading time longer,and the curve approaches the curve of step load.The wider of the material size,the longer the stress wave reaches the crack tip.And the value of stress intensity factor increases.The crack loading is different from board loading,the former change is greater than the latter change.With the phone-phason coupling constant increasing the displacement component of phason field leads to greater.Because of the influence of the phonon and phonon-phason coupling effect,the displacement component of phason field equals to zero when the phone-phason coupling constant is zero.In chapter four,based on the elastic theory of quasicrystals,the Eshelby inclusion theory was generalized and the Eshelby tensor with ellipsoid inclusions was obtained.