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, a0. 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, b0. 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.