Three-dimensional fractal analysis of fracture surfaces in titanium–iron particulate reinforced hydroxyapatite composites: relationship between fracture toughness and fractal dimension

Fractal dimension has been considered as a measure of fracture surface roughness of materials. Three-dimensional (3D) surface analysis is anticipated to provide a better evaluation of fracture surface toughness and fractal dimension. The objective of this study was to quantify the fracture surfaces and identify a potential relationship between fracture toughness and fractal dimension in a new type of core–shell titanium–iron particulate reinforced hydroxyapatite matrix composites using SEM stereoscopy coupled with a 3D surface analysis. The obtained results showed that both fracture surface roughness and fractal dimension increased with increasing amount of core–shell Ti–Fe reinforcing particles. The fractal dimension was observed to be a direct measure of fracture surface roughness. The fracture toughness of the composites increased linearly with the square root of fractal dimensional increment (i.e., followed the Mecholsky–Mackin equation well) due to the presence of Ti–Fe particles along with the effect of porosity in brittle materials. The 3D fractal analysis was suggested to be a proper tool for quantifying the fracture surfaces and linking the microstructural parameter to fracture toughness.