Application of the fractal theory in fracture behavior of ceramics

In this paper, the application of the fractal theory in fracture behavior and mechanism of ceramics has been reviewed, mainly including the origin of the fractal theory, the fractal character of ceramic fracture and the calculation methods of fractal dimension, a variety of fractal models and the relationship between the fractal dimension and properties of ceramics. By analyzing the geometrical features of crack profiles and calculating the fractal dimensions of Al2O3-TiC(AT) and Al2O3-TiC-4%Co (ATC), the important information on the fracture behavior of the composites can be attained. The results show that the toughness and strength of the ATC composites became higher than before. As compared to the AT composites, ATC composites show a change of fracture mode from intergranular to a mixture of transgranular and intergranular type. Quantitative evaluation by fractal analysis of crack paths in both composites indicates that ATC composites present higher fractal dimension (or irregularity) than that of AT composites, which is positively proportional to the higher fracture toughness.