A novel numerical simulation method based on finite element analysis (FEA), which can evaluate the fracture probability caused by the characteristics of flaw distribution, is considered an effective tool to facilitate and increase the use of ceramics in components and members. In this study, we propose an FEA methodology to predict the scatter of ceramic strength. Specifically, the data on the microstructure distribution (i.e., relative density, size and aspect ratio of pore, and grain size) are taken as the input values and reflected onto the parameters of a continuum damage model via a fracture mechanical model based on the circumferential circular crack emanating from an oval spherical pore. In addition, we numerically create a Weibull distribution based on multiple FEA results of a three‐point bending test. Its validity is confirmed by a quantitative comparison with the actual test results. The results suggest that the proposed FEA methodology can be applied to the analysis of the fracture probability of ceramics.

The most prominent effect of the weakest link theory, which is used to derive the Weibull statistics of ceramic strength, is the size effect. In this study, we analyze the size effect on ceramic strength using the finite element analysis (FEA) methodology previously proposed by the authors. In the FEA methodology, the data of the microstructure distribution (i.e., relative density, size, and aspect ratio of the pore and the grain size) are considered as input parameters of a continuum damage model via a fracture mechanical model. Specifically, we examine five sizes of rectangular specimens under three types of loading conditions. Then, we simulate the fracture stresses of sets of 30 specimens under each size and loading condition and obtain the relationship between the scale parameter and effective volume using the Weibull distribution. The results suggest that the proposed FEA methodology can be applied to the analysis of the fracture probability of ceramics, including the size effect.

Among various ceramic matrix composites developed, self-healing ceramics have been studied as new functional materials. Self-healing occurs in such materials by high-temperature oxidation triggered by a micro-crack initiation on the surface, and the strength of the material autonomously recovers to its robust state since the micro-crack is re-bonded. To facilitate the use of self-healing ceramics in machines and equipment, a novel numerical simulation method based on finite element analysis (FEA) needs to be applied. In this study, we applied a previously proposed constitutive model to a series of self-healing and damage processes. In the constitutive model, the damage process is formulated on the basis of fracture mechanics, while the self-healing process is formulated on the basis of empirical oxidation kinetics. The FEA model implemented the constitutive model to simulate a series of experiments of the alumina/15 vol% SiC composites. The self-healing process was targeted to a prescribed damage by Vickers indentation. Thereafter, the self-healing behavior was quantitatively compared with that observed in the experiment. The results suggest that the proposed FEA approach can be applied to the analysis of ceramic matrix composites with self-healing properties.

Self-healing fiber-reinforced ceramic (shFRC) is a new functional material. When a microcrack propagates in this material, self-healing occurs owing to high-temperature oxidation. Then, the strength of the material recovers to its robust state since the microcrack is rebounded. However, to effectively demonstrate the self-healing function, a crack bifurcation, i.e., penetration/deflection, must be controlled. Therefore, the optimal composite design, in which the microcrack is induced in the interface along the fiber, is a key factor in developing shFRC. In this study, we investigate crack propagation using Finite Element Analysis (FEA). In FEA, the two-dimensional microscopic structure of shFRC with a three-layer construction is discretized. The three layers of construction are the matrix layer, the fiber bundle layer, and the non-oxide layer, called the self-healing agent. Using FEA, we examine ideal relationships of fracture stress and critical energy release rate between the fiber and interface layer considering the sintering characteristics. Furthermore, the relationship between fracture toughness, Young's modulus, and the relative density of the interlayer to induce a crack deflection at the interface is derived.

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