Study Of Thermoelastic Crack Problems For Functionally Graded Materials

Functionally graded materials (FGMs) can be used to effectively reduce the high residual and thermal stresses caused by the mismatch in thermal expansion coefficients of different materials. Furthermore, they contribute to solve the problems such as instability and cracking raised by the interface discontinuity. Therefore, FGMs are always used as heat coatings and it is important to investigate the thermal fracture and thermoelastic problems of FGMs.The progress of fracture problems are reviewed in Chapter One, especially the research of functionally graded coating and substrate structure. In addition, the thermoelastic coupling behavior developments of FGMs are also commented in detail.The interface cracking problem for a functionally graded coating and finite substrate structure under thermo-mechanical loading is studied in Chapter Two. The interface heat conductivity index is introduced to describe the partial conduction of the crack surface. With the use of integration transform and introducing the dislocation density functions, the present problem is reduced to the solution of a system of singular integral equations which are solved numerically by Labtto-Chebshev method. The effects of interface heat conductivity index and material inhomogeneous parameters on the surface temperature field and strain energy release rate are discussed.In Chapter Three, firstly , the governing equations of the thermoelastic coupling theory are derived for isotropic material based on L-S model, which are suitable for both homogeneous materials and FGMs. Secondly, using the united form, the finite element format of different thermoelastic coupling models is obtained and the dimensionless form is deduced too. At last, the finite element programs are written in Fortran90 language and verified widely. The coupled thermoelastic problems of FGMs are investigated in Chapter Four, and the temperature and displacement fields are analyzed. The effects of thermoelastic coupling models,material parameters changing forms and relaxation times are discussed. Based on the conventional coupled thermoelastic model (CTE model), the influences of Poisson's ratio as an independent variable are also considered for FGMs.