Temperature-Dependent Thermoelastic Analysis of Multi-Dimensional Functionally Graded Materials

Functionally graded materials (FGMs) are advanced composites with material compositions varying continuously as a function of spatial position. The gradual change of material properties can be tailored to meet special requirements of different working environments. One of the main applications of FGMs is as thermal barrier coatings (TBCs) at high temperatures. Functionally graded TBCs are usually made with a mixture of ceramic at the top surface and metal at the bottom. The compositions of these one-dimensional FGMs are varied through the thickness with an optimized variation of volume fractions.\ud Under some practical conditions, such as the outer surface of an airplane, temperature changes drastically in two or three directions. Conventional one-dimensional FGMs have been shown to likely fail under these extreme circumstances. Therefore, it is necessary to develop FGMs with material properties varying in other dimensions to achieve multi-directional high-temperature resistance. However, this type of FGMs is not well studied due to their computational and experimental complexities. Based on such facts, we propose to study the thermoelastic behaviors of multi-dimensional FGMs. Most of the current researches assume temperature-independent material properties and uses simple rule of mixtures to estimate material properties at different positons, in order to simplify their calculations, but these assumptions ignore temperature effects as well as microscopic particle interactions and thus can be unrealistic. So we choose to include temperature dependent material properties to achieve better accuracy. Also, a self-consistent mean-field micromechanics Wakashima-Tsukamoto (WT) model is used in this analysis to estimate physical properties of the FGM, which has been proved to produce more accurate results. \ud We propose to study a multi-dimensional FGM plate, composed of ZrO2, Ti-6Al-4V and Al2O3. Finite element method is used to analyze temperature distributions, thermal stresses and failure criteria of the plate under steady state, heating and sudden cooling conditions. Simply supported and clamped boundary conditions are applied in the analysis. We also studied the influences of volume fraction laws and plate shape on the thermoelastic performance of FGMs. As a result, we obtained an optimal FGM structure by analyzing failure criteria