PSI - Issue 35

V.A. Zimina et al. / Procedia Structural Integrity 35 (2022) 188–195 V.A. Zimina, I.Yu. Smolin / Structural Integrity Procedia 00 (2021) 000–000

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their wide applications in various industries. For example, Al 2 O 3 –ZrB 2 –SiC composites are considered as one of the most promising materials for extreme environment applications. Zirconium diboride belongs to the class of ultra high temperature ceramics and is well known for its unique set of properties: high melting temperature, high thermal conductivity, oxidation resistance, high chemical stability, high hardness, and high strength (Fahrenholtz et al., 2007; Guo, 2009). There are also other examples that prove that three-phase composites provide better characteristics and even new properties as compared to two-phase composites. In this regard, it is of interest to study the mechanical properties and features of the fracture of three-phase composites under various external influences. These investigations are necessary to predict the strength and control the fracture of products made of such materials. It is common knowledge that composite materials have a heterogeneous microstructure that affects their elastic and strength properties, as well as the mechanical behavior of the materials in general. There are various analytical and numerical methods for predicting the effective properties of composites. Theoretical estimations for the upper and lower bounds for effective elastic moduli of multiphase materials stem from well-known pioneering works by Voigt and Reuss that were later improved by Hashin and Shtrikman. And numerous studies in this field of research are still in progress. Afonso and Ranalli (2005) introduced a new general model to calculate the elastic properties of three-phase composites by means of closed-form analytical solutions. The model is based on a combination of the modi fied shear-lag model and the method of cells. Lin and Ju (2009) presented micromechanical analytical framework to predict effective elastic moduli of three-phase composites containing randomly dispersed and pairwisely interacting spherical particles belonging to the two inhomogeneity phases that feature distinct elastic properties.. It is demonstrated that a significant improvement in the singular problem and accuracy is achieved by employing the proposed methodology. Liu (2010) considered the problem of characterizing the set of the effective tensors of multiphase composites. A novel derivation of the Hashin-Shtrikman bounds for multiphase composites and the associated attainment condition was presented. This condition asserts that the Hashin-Shtrikman bound is attainable if and only if there exists a second gradient field that is constant in all but the matrix phases. The fewer papers are devoted to the effective strength properties of multicomponent composites. Selezneva et al. (2016) proposed a stochastic 2D modeling technique for predicting the strength of randomly-oriented strand composites from the mechanical properties of the individual strands by using standard, easy to obtain mechanical properties from long fiber-reinforced composites and by employing simple analytical formulations. It should be mentioned that analytical methods allow us to consider only rather simple microstructure while numerical methods can take into account complex geometries. Thus, Young et al. (2016) used detailed three dimensional numerical simulations of elastic deformation to predict the effective Young’s modulus and Poisson’s ratio of spherical monodisperse and polydisperse core-shell particles variously distributed in a continuous matrix. The numerical results were compared with predictions of various effective medium approximations proposed in the literature that revealed their applicability bounds. Fedaoui et al. (2021) used a homogenization approach coupled to the finite element method for the investigation of the elastic properties of three-phase composites. They proposed a finite element model to predict the Young’s and shear modulus and studied few material configurations (properties, morphology, and volume fraction) using the finite element method to explore how the interface morphology and properties affect the material behavior. Numerical simulation offers as well certain advantages consisting in the fact that one can also mimic various loading conditions, including ones that can hardly be reproduced in experiments. Hence, many authors address the problem of the effective properties of multiphase composites but still, there is a lack in the studies of the fracture behavior of these materials at different scales. The purpose of this paper is to numerical estimate the elastic properties and the mechanical behavior of three phase ceramic composite Al 2 O 3 –ZrB 2 –SiC with taking into account the peculiarity of their structure. A novelty of this study lies in the simulation of the fracturing process in three-phase composite structure and computer models of the composite material structure build based on the microscopy experimental data. 2. Numerical model The mathematical model describing the mechanical behavior of ceramic composite contains the system of solid mechanics equations, including the following equations.