Evaluation of local mechanical properties of SiO$_{2}$-based ceramic refractories using microscale modeling

The development of multiscale mechanical models of promising refractory materials is an urgent problem in the mechanics of solids. One of the reasons is the applicability of these models when creating digital twins of advanced refractories. The authors of this paper recently developed and validated a mesoscopic model of the SiO$_2$-based refractory material that is widely used in metallurgy. This model takes into account the characteristic structural features of SiO$_2$ refractory in the scale range of 10$^{-5}$–10$^{-2}$ m and the mechanical behavior features in a wide range of strain rates. However, the full use of the model requires knowledge of local mechanical properties of mesoscopic structural elements, in particular, the highly porous regions, which are formed by fine grains less than 10$^{2}$ pm in size. An experimental study of effective mechanical characteristics of such regions is an extremely difficult task. Therefore, the purpose of this work is to obtain the theoretical estimate using the microscale numerical simulation of highly porous regions of SiO$_{2}$ refractory material and to determine their integral mechanical characteristics. To study this problem, the two-dimensional model samples are developed that simulate fine-grained regions of the refractory and are characterized by different porosity and pore structure types (channel-like or closed type). The intervals of the variation of Young's modulus and strength characteristics of the samples are obtained depending on the porosity and morphology of the pore space. The contribution of the closed-type porosity to the integral mechanical characteristics of the refractory is determined; though, the volume fraction of such pores is low as compared to that of the channel-like pores. The obtained data will be used as input parameters of mesoscale refractory models for solving the urgent problems related to the study of the effect of microstructure parameters on the macroscopic mechanical and thermomechanical properties of SiO$_2$-based refractories.