For design of multi-layered environmental barrier coatings (EBCs), it is essential to assure mechanical reliability against interface crack initiation and propagation induced by thermal stress owing to a misfit of the coefficients of thermal expansion between the coating layers and SiC/SiC substrate. We conducted finite element method (FEM) analyses to evaluate energy release rate (ERR) for interface cracks and performed experiment to obtain interface fracture toughness to assess mechanical reliability of an EBC with a function of thermal barrier (T/EBC; SiC/SiAlON/mullite/Yb-silicate gradient composition layer/Yb₂SiO₅ with porous segment structure) on an SiC/SiC substrate under thermal stress due to cooling in fabrication process. Our FEM analysis revealed that a thinner SiAlON layer and a thicker mullite layer are most suitable to reduce ERRs for crack initiation at the SiC/SiAlON, SiAlON/mullite and mullite/Yb₂Si₂O₇ interfaces. Interface fracture tests of the T/EBC with layer thicknesses within the proposed range exhibited fracture at the SiC/SiAlON and SiAlON/mullite interfaces. We also estimated the approximate fracture toughness for the SiC/SiAlON and SiAlON/mullite interfaces and lower limit of fracture toughness for the mullite/Yb₂Si₂O₇ interface. Comparison between ERR and fracture toughness indicates that the fabricated T/EBC possesses sufficient mechanical reliability against interface crack initiation and propagation.

The reaction–diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction–diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls ($p_2$), and the average width of the walls ($p_3$). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in $p_2$ and $p_3$ for test data having 10% deviation from the training data were within 7% of the average magnitude of $p_2$ and $p_3$. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework.

Controlling the complex nanostructures that often form in cation-deficient oxides may provide an effective way to tailor their thermophysical properties, but this remains a challenging task. We report a study of un-doped and Hf-doped YTa3O9 with a Y-deficient double-perovskite structure using high-temperature X-ray diffraction, electron diffraction, and small-angle X-ray scattering. Undoped YTa3O9 has an orthorhombic structure with 90° and 180° domain walls and stacking faults observed at the micro and nano levels at room temperature. It undergoes a phase transition to a tetragonal phase, with an associated volume change, at around 700K. Doping of the materials with Hf successfully stabilizes a tetragonal phase that includes a superstructure with periodic distances of a few nanometers at room temperature. The thermal conductivity of Hf-doped YTa3O9 is lower than that of the undoped material, suggesting that the interfaces between nanodomains interfere with diffusive thermal transport.

As weight reduction of turbines for aircraft engines is demanded to improve fuel consumption and curb emission of carbon dioxide, silicon carbide (SiC) fiber reinforced SiC matrix composites (SiC/SiC) are drawing enormous attention as high-pressure turbine materials. For preventing degradation of SiC/SiC, environmental barrier coatings (EBC) for ceramics are deposited on the composites. The purpose of this study is to establish theoretical guidelines for structural design which ensures the mechanical reliability of EBC. We conducted finite element method (FEM) analysis to calculate energy release rates (ERRs) for interface crack initiation due to thermal stress in EBC consisting of Si-based bond coat, Mullite and Ytterbium (Yb)-silicate layers on a SiC/SiC substrate. In the FEM analysis, the thickness of one EBC layer was changed from 25 μm to 200 μm while the thicknesses of the other layers were fixed at 25 μm, 50 μm and 100 μm. We compared ERRs obtained by the FEM analysis and a simple theory for interface crack in a single-layered structure where ERR is estimated as nominal strain energy in the coating layers multiplied by a constant factor (independent of layer thicknesses). We found that, unlike the case of single-layered structures, the multiplication factor is no longer a constant but is determined by the combination of consisting coating layer thicknesses.