Relationship between Fractal Geometry and Fractography

Fractal geometry has been used to describe irregular fracture surfaces in a quantitative way. The fractal dimensional increment has been related to the fracture toughness of the material through the elastic modulus and a characteristic structure parameter, a ₀. The study of fractography has shown the relationship between the flaw/mirror size ratio and the fracture toughness. An experimental observation has shown that the fracture toughness is related to the elastic modulus through another structure parameter, b ₀. Combining all of these relationships leads to the conclusion that the fractal dimensional increment, D ^*, is directly related to the flaw/mirror size ratio. Experimental measurements of the fractal dimension and the flaw/mirror size ratio on glasses, a glass-ceramic, polycrystalline ceramics, and a single crystal all agree with the prediction. The implication of this finding is that there is a linear scaling law in operation at fracture between the energy of crack initiation and of microbranching and is reflected in the features on the fracture surface.