Modelling of thermal expansion of single- and two-phase ceramic polycrystals utilising synthetic 3D microstructures

Abstract

Determining effective properties of heterogeneous materials is interesting not only in the theoretical aspect but also in the practical one – engineering or technological. Therefore, steps allowing to obtain values of the effective coefficients of thermal expansion of single- and two-phase ceramic polycrystals, were described in the hereby work. At first, based on scanning electron microscope (SEM) images of materials used in the research, the basic microstructure parameters were determined. Then, by means of the Scheil-Schwartz-Saltykov method, the distributions of equivalent grain diameters (3D) were established. The obtained information on grains morphology were utilised in the reconstruction of three-dimensional microstructures of analysed polycrystals. Reconstructions were performed by means of the Laguerre tessellation. In the next step, on the basis of the proposed criterion, numbers of independent realisations – necessary to obtain effective coefficients of thermal expansion – were determined. Finally, the planned simulations (Finite Element Analysis – FEA) were performed and the obtained effective values were compared with the dilatometric measurements results. The path, presented in this work, leading from two-dimensional microstructure images via synthetic three-dimensional models of polycrystals to FEA models, allowed to obtain the effective coefficients of thermal expansion within the measurement error of experimental values.