Finite element analysis of the fracture statistics of self-healing ceramics

Abstract

Self-healing materials have been recognized as a promising type of next-generation materials. Among them, self-healing ceramics play a particularly important role, and understanding them better is necessary. Therefore, in this study, we applied the oxidation kinetics-based constitutive model to finite element analysis of a series of damage-healing processes in self-healing ceramics (alumina/SiC composites). In the finite element analysis, the data on the microstructure distribution, such as relative density, size and aspect ratio of pores, and grain size, were taken as input values and reflected onto the parameters of a continuum damage model using a fracture mechanical model. We then performed a 3-point bending analysis, to consider both the self-healing effect under certain temperature and oxygen partial pressure conditions and scatter of the strength of the ceramics. Our results confirmed that the proposed methodology can reasonably reproduce both strength recovery and damage propagation behavior in selfhealing ceramics.

Finite element analysis of fracture behavior in ceramics: Prediction of strength distribution using microstructural features

“…In this study, we proposed the FEA methodology in which a cohesive-force embedded isotropic damage model was used to describe the stress-strain relationship. [19][20][21] Details regarding the formulation of the damage model is further discussed in reference. 27 The stress-strain relationship based on a typical isotropic damage model is given as where σ is the Cauchy stress tensor, ε is the strain tensor, c is the fourth-order elastic coefficient tensor, and D(0 ≤ 𝐷 ≤ 1)is the damage variable in which D = 0 and 1 are the non-damaged and perfectly damaged states, respectively.…”

“…where κ is the maximum value of the equivalent strain in the loading history, 𝜅 0 is the equivalent strain at the damage initiation, h e is the characteristic length that corresponds to the length of the element in FEA, 28 σ F is the fracture stress, and G F is the fracture energy. We adopted the following modified equivalent von Mises strain from previous studies, [19][20][21]27 which is a scalar value, for the evaluation of κ, which is expressed as…”

“…10,22,[29][30][31][32][33] Moreover, we assumed an ellipsoidal pore (rotational spheroidal pore) with a major axis radius R (=R a ) and a minor axis radius R b , as shown in Figure 1B. [19][20][21] In addition, the length of the circumferential initial crack is important in describing the dependence of the grain size on the strength. In previous studies, the initial crack length was the same order of magnitude as the grain size.…”

“…18 Moreover, the finite element analysis (FEA) methodology was proposed to predict the strength scatter of ceramics based on microstructural data, including the relative density, grain size distribution, and pore distribution. [19][20][21] In addition, this approach, which is within the framework of FEM, can examine the fracture probability of components with various shapes under various boundary conditions. Furthermore, it can also be applied to fiber-reinforced CMCs and self-healing ceramics.…”

“…Furthermore, it can also be applied to fiber-reinforced CMCs and self-healing ceramics. 21 The distribution data of the microstructure are expressed by appropriate probability density functions (PDFs) and reflected in the parameters of the damage model (stress-strain relationship) via a fracture mechanics model. In addition, the stochastic distribution of the microstructure in multiple FEA models (e.g., tens to hundreds of specimens of the same lot) can be naturally reproduced using random numbers, and the fracture strength that differs for each analysis model is evaluated.…”