Problems Of Wave Scattering By Interface Crack And Thermal Fracture In Functionally Graded Materials

Functionally graded materials (FGMs) are new type of composites which can satisfy the harsh requirements of materials used in high-technology fields of astronautics, aeronautics, national defense, etc. Because FGMs are multiple phase materials with spatially and continuously varying properties, they can maintain the structural rigidity, reduce the thermal stress and resist the severe thermal loading from the high temperature environment. Although FGMs possess many good comprehensive thermal-elastic properties, there are all kinds of cracks or defects under dynamic loading and high temperature, which may cause the failure of FGMs. Therefore, it is important to investigate the dynamic fracture behaviors and thermal fracture behaviors for the design, optimization and application of FGMs.The advance of FGMs including theoretical analysis, numerical simulation and experiments is reviewed in details in Chapter 1.The scattering of the anti-plane incident time-harmonic wave with arbitrary degree by the interface crack between the functionally graded coating and the homogeneous substrate is investigated in Chapter 2. By using the principle of superposition and Fourier transform, the singular integral equations are derived. There are some pole points in the integral path, an integral path in the complex plane consisting of four straight lines is adopted. The effects of the frequency of the incident wave, the incident direction of the wave, material gradient parameter and the crack configuration on the dynamic stress intensity factors (DSIF) are examined.In Chapter 3, the scattering of the plane incident wave (P wave, Sv wave) with arbitrary degree by the interface crack between the functionally graded coating and the homogeneous substrate is investigated. An integral path in the complex plane consisting of four straight lines is adopted to avoid singular points. Numerical results show the effects of the frequency of the incident wave, the type of incident wave, the incident direction of the wave, material gradient parameter and the crack configuration on the dynamic stress intensity factors (DSIF).The response of the functionally graded interlay with an interface crack subjected uniform heat flux is considered in Chapter 4. It is assumed that interface crack is partially insulated the temperature drop across the crack surfaces is the result of the thermal resistant due to the heat conduction through the crack region. Assuming no coupling between thermal and mechanical effects, the present problem consists of solving first the heat conduction and then the plane elasticity equations subjected to the appropriate boundary conditions. The asymptotic expressions with high order term for the singular integral kernel are obtained to improve the convergence efficiency of numerical integrals. The influences of material properties (i.e. the elastic module, the thermal expansion coefficient and the thermal conductivities) gradient parameters and dimensionless thermal resistant on the temperature distribution and the thermal stress intensity factors (TSIF) are figured.Because of the nature of the techniques used in processing, FGMs are seldom isotropic. Chapter 5 studied the interface crack problem of the orthotropic functionally graded coating-orthotropic homogeneous substrate structure under the loading of uniform heat flux. It is assumed the temperature drop across the crack surfaces is the result of the thermal resistant due to the heat conduction through the crack region. The governing equations of the temperature fields and displacement fields are converted into a system of singular integral equations and the asymptotic expressions with high order term for the singular integral kernel are considered. Numerical results are presented to show the influences of the orthotropic parameters and material properties (i.e. the elastic module, the thermal expansion coefficient and the thermal conductivities) nonhomogeneous parameters, crack position and dimensionless thermal resistant on the temperature distribution and the thermal stress intensity factors (TSIF).In Chapter 6, the transient response of the orthotropic functionally graded strip with a crack under convective heat transfer boundary is investigated. Laplace transform and Fourier transform are applied to reduce the mixed boundary value problems of the temperature fields and displacement fields to a system of singular integral equations in Laplace domain. In the numerical computation process, the asymptotic expressions with high order term for the singular integral kernel are considered. By using the numerical Laplace inversion method, the variations of the temperature distribution along the crack surface and extended line and transient thermal stress intensity factors are presented. The influences of the material nonhomogeneous parameters, the orthotropic parameters and dimensionless thermal resistant on the temperature distribution and the transient thermal stress intensity factors are analyzed.