Optimal design on the high-temperature mechanical properties of porous alumina ceramics based on fractal dimension analysis

Fractal theory and regression analysis were employed for the first time to investigate the effect of pore size and pore distribution on high-temperature mechanical properties of porous alumina ceramics (PAC). In the present work, PAC with the comparable porosity, different pore sizes and pore distributions were prepared using carbon black as the pore-forming agent. Particular emphasis in this study was placed on the establishment of correlation between the thermal shock resistance and pore properties. The relationship between fractal dimension ( $D_{\text{f}}$) and thermal shock resistance parameter ( $R_{\text{st}}$) in specimens presented the negative power function, indicating that low $D_{\text{f}}$ could benefit the improvement of thermal shock resistance in specimens. The results showed that the increase of pore size and pore sphericity leads to a reduced $D_{\text{f}}$, the enhanced hot modulus of rupture (HMOR) and $R_{\text{st}}$. The decrease of proportion of micro-pores below 2 µm, the increase of mean pore size and pore sphericity could result in the decrease of $D_{\text{f}}$, and then improve $R_{\text{st}}$ and HMOR of specimens. Based on the correlation between $R_{\text{st}}$ and pore characteristics, PAC with improved thermal shock resistance could be achieved when their pore structure meets the above features.