Research On Problems Of Some Cracks In Piezoelectric Material Of One-dimensional Quasicrystals Under The Different Electric Boundary Conditions

Quasicrystals(QCs) is a kind of solid different from crystals and amorphous. And its quasi-periodic leads to its particularity. Because of its particularity, the study of QCs is much more complicated than that of classical crystals. So it is necessary to investigate the problem of QCs.Fracture of QCs materials is connected with the defect of QCs materials.So, in the study, the materials fracture problem is the key to observe the relation between the field intensity factors of crack tip and materials and the shape of defects, so that it will get a better application in practice.QCs fracture problems of one-dimensional hexagonal and one-dimensional orthorhombic with the piezoelectric effect are studied in this paper. The material fracture problems of one-dimensional hexagonal and one-dimensional orthorhombic are to study all kinds of defects by the external force and electricity under stress field and the field intensity factors of cracks tip. The concrete content is as follows:In the first chapter, the discovery and the classification of QCs are briefly introduced. In addition, one-dimensional QCs systems and corresponding elastic constants are listed. The research process of QCs since its discovery and the research results that have been made are also reviewed, and the significance of studying QCs and its development prospect are described in this chapter.In the second chapter, two specific problems are solved by using two different kinds of methods. Using the complex variable function method,the antiplane problems of curved cracks with power function type in an one-dimensional hexagonal piezoelectric QCs are researched and using the Stroh method, the analytical solution of the problems of the lip crack in an infinite one-dimensional hexagonal piezoelectric QCs under the partial electrically permeable boundary conditions are obtained.In the third chapter, the problems of parabolic crack in the periodic plane and nonperiodic plane of one-dimensional orthorhombic QCs materials are studied. At first, the governing equations of the problems are derived by using the method of introducing displacement potential function. Then using the complex variable function, complex representation of stress fields in the mathematical plane and SIFs of the parabolic crack tip were obtained.In the forth chapter, the fracture problems of piezoelectric materials of the one-dimensional orthorhombic QCs are studied. The antiplane problems of parabolic crack and the circular hole with two asymmetry collinear cracks and semi-infinite crack in a piezoelectric material of one-dimensional orthorhombic QCs are studied.Using the complex variable function, complex representation of stress field and electric displacement in the mathematical plane and SIFs of the parabolic crack tip are obtained.This paper's study results are summarized in the fifth chapter.