Correlation between Agglomerates Hausdorff Dimension and Mechanical Properties of Denture Poly(methyl methacrylate)-Based Composites

The microstructure–property relationship in poly(methyl methacrylate) PMMA composites is very important for understanding interface phenomena and the future prediction of properties that further help in designing improved materials. In this research, field emission scanning electron microscopy (FESEM) images of denture PMMA composites with SrTiO₃, MnO₂ and SrTiO₃/MnO₂ were used for fractal reconstructions of particle agglomerates in the polymer matrix. Fractal analysis represents a valuable mathematical tool for the characterization of the microstructure and finding correlation between microstructural features and mechanical properties. Utilizing the mathematical affine fractal regression model, the <i>Fractal Real Finder</i> software was employed to reconstruct agglomerate shapes and estimate the Hausdorff dimensions (HD). Controlled energy impact and tensile tests were used to evaluate the mechanical performance of PMMA-MnO₂, PMMA-SrTiO₃ and PMMA-SrTiO₃/MnO₂ composites. It was determined that PMMA-SrTiO₃/MnO₂ had the highest total absorbed energy value (E_tot), corresponding to the lowest HD value of 1.03637 calculated for SrTiO₃/MnO₂ agglomerates. On the other hand, the highest HD value of 1.21521 was calculated for MnO₂ agglomerates, while the PMMA-MnO₂ showed the lowest E_tot. The linear correlation between the total absorbed impact energy of composites and the HD of the corresponding agglomerates was determined, with an R² value of 0.99486, showing the potential use of this approach in the optimization of composite materials’ microstructure–property relationship.