Research On The Problem Of Uniform Moving Defect In Quasicrystal Materials

Quasicrystal is a novel kind of solid material, which is different from conventional crystals and amorphous solids.This novel kind of solid material has long-range patterns but its orderly arrangement does not have the lattice periodic. The defects in the quasicrystals have been observed since it has been observed. Compared to quasicrystal static problems, the defect dynamics of quasicrystal is still very limited. The physical mechanism of the phason field dynamics is still fuzzy, there are several different views on the phason field dynamics of the quasicrystal. Bak thinks that the phonon field and the phason field represent the wave propagation, the motion equation of the phonon field and the phason field should be fluctuating form. Lubensky thinks that the phonon field and the phason field represent the diffusion, the motion equation of the phonon field and the phason field should be diffusion mode. In this paper,based on the dynamic model of quasicrystals followed Bak's argument, the dynamic problems of several kinds of special defects in two-dimensional and three-dimensional quasicrystals are studied.For the two-dimensional anisotropic elasticity problem, this problem is independent of displacement and coordinate. According to the Stroh's intrinsic theory, the matrix operation is introduced into the elastic theory. Using some properties of the matrix, the form of the solution of the stress and displacement in two-dimensional elasticity can be expressed simply and clearly.In this paper, the Stroh formula is extended to the quasicrystal dynamics problem. Based on the dynamic model of quasicrystals followed Bak's arguments, the dynamics of cracks and dislocations in two-dimensional and three-dimensional quasicrystals are studied. The concrete contents are as follows:The first chapter is introduction, mainly introduces the discovery of solid quasicrystals and soft matter quasicrystals. The classification, application and defects of quasicrystal materials are introduced, the present situation of quasicrystals research and development are also discussed. Finally, the Stroh formula and main job in this paper are briefly introduced.In the second chapter, based on the dynamic model of quasicrystals followed Bak's arguments, a finite Griffith crack moving constant velocity in a decagonal quasicrystals is discussed. The explicit expressions for stresses and displacements of the phonon and phason fields are obtained by the extended Stroh formalism, then the normalized hoop stress near the crack tip for different normalized crack speeds are studied. Then the numerical solution of the general solution is analyzed and the normalized hoop stress near the crack tip for different normalized crack speeds are studied.In the third chapter, based on the dynamic model of quasicrystals followed Bak's arguments, · a · moving straight dislocation in decagonal quasicrystals is investigated in detail. The closed-form expressions for the elastic displacement and stress fields are obtained by the extended Stroh formalism. The effects of the velocity of dislocations and phonon-phason coupling elastic constant on the hoop displacements and stresses are discussed. Finally, the dynamic physical characteristics of dislocation are revealed and the wave behavior is checked in phonon and phason fields.In the fourth chapter, the motion crack problem of two-dimensional quasicrystals is extended into three-dimensional quasicrystals, a finite Griffith crack moving with constant velocity in an icosahedral quasicrystal is discussed.The explicit expressions for stresses and displacements of the phonon and phason fields are obtained by the extended Stroh formalism, then the normalized hoop stress near the crack tip for different crack speeds are studied.In the fifth chapter is summary and outlook. Using briefly words to summarize this paper and making some prospects of quasicrystal defect dynamics is studied deeply.