| Quasicrystal(QC) is a novel kind of solid material,which the orderly arrangement does not have the lattice periodic but show long-range patterns.It is new solid material completely different from conventional crystals and amorphous solids. The so-called long-range patterns of QC, it points that in a certain direction often expresses in the form of irrational number sequence,while the sequence as irrational infinite loop. Owing the "abnormal" way arrangement of atoms in the QC, the QC symmetry break the traditional crystal symmetry theory which has been rejected more than five or six times the existence of the axis of symmetry. For this special structure,the QC elastic problems are more complicated than the classical elastic problems.Because the description of QC elasticity needs to introduce two displacement fields,namely the description of lattice vibrated phonon field and atom quasi-periodic arranged phason field.Meanwhile,its mechanical property,electrical,thermal,magnetic,related physical and chemical performance also has essential difference with common crystals. Researching on such problems, therefore, have both the theory value and the significance of practice.Fracture phenomenon is always connected with the defect of materials(e.g., orifice, inclusions or cracks, etc.)and the stress distribution is extremely uneven caused by the discontinuity,this phenomenon is called the stress concentration in mechanics. Defects and stress concentration are the most important reasons to cause the materials damage and the stress intensity factor as a physical quantity reflected the elasticity of the crack tip stress field intensity, which is an important parameter of fracture characterization of materials. So the material fracture problem is the key to solve all kinds of defects by the external force under stress field and determine the field intensity factors of crack tip. This paper mainly studies QC elastic spatial axisymmetric problems and QC fracture problems of piezoelectric materials,the concrete content is as follows:The first chapter is introduction.In this chapter mainly introduces thediscovery of quasicrystals, the present situation of quasicrystals research and development.And also discuss the classic piezoelectric materials and the development of piezoelectric materials.At last simply introduced the main job in this paper.The second chapter studies elastic axisymmetric problems of one-dimensional(1D) QC. First of all, using cylindrical coordinate system and rectangular coordinate system to establish the general equations of QC elastic under cylindrical coordinate system. Then, according to the property of the axisymmetry to simplify the equations for axisymmetric equations. Finally,using the method of successive introduction of displacement potential function to find the general solution of the axisymmetric equations, and according to the general solution of the form, discuss the semi-infinite body surface by axisymmetric distribution load specific issues.The third chapter will introduce the fracture mechanics of piezoelectric material of QCs.This chapter mainly discusses the piezoelectric material of1 D hexagonal QC.Mainly using the conformal mapping, Cauchy integral formula and Stroh formula, the Griffith crack, two asymmetrical edge cracks emanating from an elliptical,round with many cracks and infinite plane of semi-infinite crack problems are discussed.Then we obtained the analytic expression of the field intensity factors and energy release rate. We also discuss the piezoelectric material of 1D hexagonal interaction between screw dislocation and elliptic hole.At last the antiplane problems of electric plastic field of the piezoelectric material of 1D QC is reseached and the size of the crack of plastic area is obtained. At last we disccusse the piezoelectric effect of 2D QC with tenfold rotational symmetry.In the fourth chapter is summary and outlook. Using briefly words to summarize this paper and making some prospects of the application of QC material. |
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