Investigation On Layered Model For Thermal Fracture Mechanics Problem Of Functionally Graded Material

Since the last half of the 20 th century,the composite materials have been developed significantly and applied widely.Engineers are able to design the composite material with particular performance according to engineering requirement by combining different materials.Nevertheless,stress concentration occurs on the interface bonding different materials due to the heterogeneity.The mismatch of material properties could be avoided by the continuous variation of material composition or micro structure at the bonding area between different parts.That was the initial concept of functionally graded materials(FGMs).In the application scenarios of FGMs,the damage and the initiation of cracks are inevitable due to the extreme mechanical environment.Therefore,the investigation about the fracture behaviors of FGMs is an important part of their evaluation of mechanical performance.In this thesis,a series of analytical methods for the fracture problems of FGM coating-homogenous substrate under various mechanical/thermal loading conditions are developed based on the piecewise-exponential model(PE model).After introducing the research background,purpose and significance of this thesis,the deficiencies of existing analytical models are extracted from the summary of the present research on the fracture problems of FGMs.Then the following works are conducted:Firstly,an analytical model is developed for the interface crack problem of FGM coating-substrate structure in which the coating mechanical properties are generally continuous.The continuous variation of coating mechanical property is characterized by a piecewise-exponential function.Through a series of mathematical manipulations,the fracture problem is reduced into a group of singular integral equations on the displacement field,which can be solved by numerical methods.Then,the influences of the geometric parameters and coating properties variations on the mixed-mode stress intensity factors(SIFs)and strain energy release rates(SERRs)of the interface crack are presented,and the relative conclusions could also be applied for reducing the risk of crack propagation.Based on the work of the second chapter,the PE model is developed further in the third chapter for the thermal fracture problem under steady heat flux,where the continuous variation of thermal conductivity and thermal expansion coefficient are taken into consideration.The thermal fracture problem is turned into solving the singular integral equations on the fields of temperature and displacement.The temperature and equivalent thermal stress distributions on crack surface and the thermal stress intensity factors(TSIFs)under different conditions,including thermal insulation of the crack,geometric parameters and coating properties variations,are calculated.Then the complicated influence of these factors on the thermal fracture behavior are analyzed.Based on the works mentioned above,the steady thermal fracture model is developed into a transient thermal fracture model in the fourth chapter,where the density and the specific heat capacity of the FGM coating are also described by the piecewise-exponential functions.For the transient problem,the mathematical manipulation and the calculation are conducted in Laplace space for convenience,and the required results in time domain are obtained after numerical Laplace inversion.The influences of thermal conductivity and thermal diffusivity on the magnitude and arriving time of the peak value of mode II TSIF are presented.The transient thermal fracture behavior of thermal barrier coating structure is also investigated.These analyses could benefit the designs and the manufactures of FGM coating-substrate structures.Based on the work of the fourth chapter,the hyperbolic heat conduction model(CV model)and the dual-phase-lag heat conduction model(DPL model),an analytical method,in which non-Fourier heat conduction is taken into consideration,for the fracture problem of FGM coating-substrate structure is developed.In this model,the variations of FGM coating’s phase lags of thermal flux and temperature gradient are characterized.The influences of the two phase lags,thermal conductivity and the geometric parameters on the transient thermal fracture behaviors are presented.According to the calculation results,the magnitude of the peak value of mode II TSIF becomes larger with the increase of thermal conductivity and phase lag of thermal flux,while the influence of phase lag of temperature gradient on TSIFs is pretty complicated.