Integral Equation Method For Crack Problems In One-Dimensional Hexagonal Quasicrystals

Quasicrystal is a new type of material with a special structure between amorphous and crystalline states.Its atomic arrangement has both a certain degree of disorder and long-range ordering,making it excellent in properties such as high hardness,corrosion resistance,wear resistance,and oxidation resistance.Due to their excellent properties,quasicrystal materials are widely used in automotive manufacturing,aerospace,coating and thin film technologies,which greatly improve the service life and performance of materials.However,the local stress concentrations formed under external loads can lead to damage and destruction of quasicrystal structures.Researchers have addressed this problem by controlling the synthesis of quasicrystal materials,changing their crystal structure and grain size,and improving their durability and mechanical properties.Researchers have found that defects in quasicrystal materials,such as cracks,can greatly affect the mechanical properties of the material.Therefore,it is of theoretical importance to study the cracking problem of quasicrystals.The main work of this thesis is as follows:In the first chapter,the background and research significance of quasicrystal materials,the fracture mechanics of quasicrystal materials and the research status of functionally graded quasicrystals are introduced.The basic theory and dual Integral equation method of one-dimensional hexagonal quasicrystals are introduced in chapter 2.The problem of dynamic cracks in one-dimensional hexagonal quasicrystal strips is investigated in Chapter 3.The dynamic fracture of the crack is studied by using the integral transform technique,and the Fourier transform is applied to transform the side value problem of the partial differential equation describing the fracture problem into two dual integral equations,which are solved by Copson method.The explicit expressions for the phonon and phason on the crack surface are determined,and the dynamic stress intensity factors are obtained.The results show that the standard stress intensity factor at the crack tip increases with the increase of crack length and coupling coefficient.In Chapter 4,one-dimensional hexagonal functional graded quasicrystal center crack is considered.The Fourier integral transform is used to transform the mixed-edge problem into a pair of dual integral equations,and the Copson method is used to transform the dual integral equations into the second type of Fredhoml integral equations to obtain the field intensity factor.It is shown that as the crack length,coupling coefficient and graded index increases,the standard stress intensity factor at the crack tip also increases.In Chapter 5,one-dimensional hexagonal functional graded piezoelectric quasicrystal containing central crack is investigated by transforming the mixed-edge problem of a system of partial differential equations into a triple-pair dual integral equation with the help of the integral transformation technique.The results show that the standard stress intensity factor of the crack tip increases with the increase of crack length and functional graded index.The coupling coefficient is not related to the stress intensity factor of phonon field and electric field,while the stress intensity factor of phonon field increases with the increase of coupling coefficient.The full thesis is summarized in Chapter 6 and prospects for future work are presented.