The Analysis Of The Fracture Behaviors Of Functionally Graded Materials Under Moving Crack And Elastic Wave

FGM which is considered to be the most promising composite material under the high temperature working condition, as a kind of designable composite material, has an important application and potential prospect in the areas of astronautics and aeronautics. With Functionally Graded Materials widely used in the astronautic and aeronautic fields, the mechanics problems research in Functionally Graded Materials become more and more important. FGMs are non homogeneous solid and the nonhomogeneality of FGMs has a great influence on their mechanical behavior. However, the studies on the dynamic fracture mechanics of FGMs are not enough, especially for the problems on moving and expanding cracks. We thoroughly explored several of these difficult issues mentioned and obtained some very important results.The main contributions of this dissertation can be read as follow:1. The stress at the crack tip on moving crack in an infinite body for FGM subjected to shear loading are studied. The dual integral equation of antiplane moving problem through Fourier transform with the help of the exponent model of the shear modulus and density is obtained. The displacement is expanded into series form using Jacobi Polynomial by Schmidt method, then the semi-analytic and numerical solutions of dynamic stress intensity factor are attained. and the Influences of the crack velocity, graded parameter, and orthotropic coefficient on the stress at crack tip are considered.2. The theoretical treatment of an interface moving crack is provided for laminated media. Two physical models, namely homogeneous bonded media and a functionally graded coating-substrate structure, are considered respectively. Using conditions of the welding surface of different media, we express all the quantities in terms of a single unknown function. Using method of integral transform, we formulate the moving crack problem as dual integral equations, then the semi-analytic of dynamic stress intensity factor are attained by Schmidt method. The influences of parameters such as crack velocity, graded parameter and laminated height on dynamic stress intensity factor are studied. 3. The stress at the crack tip on moving crack in an infinite length strip for FGM subjected to shear loading are studied and the Influences of the crack velocity and graded parameter on the stress at crack tip are considered. The results show that stress intensity factor at the crack tip decrease with increasing crack velocity for the clamped boundary problems of moving crack in an infinite length strip, but for the problem of free boundary, the maximum value of stress at the crack tip increase with increasing crack velocity. Stress field at the crack tip decrease with increasing graded parameter.4. The problem of elastic waves scattering and dynamic stress concentration by FGM plane with cracks of any limited lengths near the gap is investigated. Due to the same time factor of scattering wave and incident wave, the scattering model of the crack tip can be constructed by making use of the displacment function of harmonic load on any point of the infinite plane. With the use of the integral transform, the dual integral equation for determining the external forces can be abtained, then have some process on the even and odd term of the integral kernel, the expression of displacement and stress is established while the interaction of infinite plate with cracks is studied with Schmidt method. Dynamic stress concentration near the plate is studied, and dynamic stress intensity factor at crack tip is discussed. Some examples and results are given. The influences of wave number, incident angles of electic wave, and graded parameter are discussed.5. Consider the propagation of P-wave and SV-wave, produced by the action of oscillating compressional and shear forces, which vary harmonically in time and are applied in the xy-plane. These input waves are diffracted at the crack in FGM. The indicates that the waves scattered by the crack are composed of both compression and shear waves even if the incident wave may only be of one type, either the P- or SV-waves. By semi-analytic solutions the influences of wave number, incident angles of electic wave, graded parameter and Poisson's ratio are discussed.This work can provide a foundation for the optimization design and property evaluation of Functionally Graded Materials in theory. The results provide valuable conclusion on the displacement field and the stress field of a crack tip.