Fractal analysis on fracture surfaces of glass using replication techniques

Abstract

In order to understand the relationship between bond-breaking and the resulting topography on the fracture surface of brittle materials, a formal construct is needed. Fractal geometry offers a tool by which the fracture of brittle materials can be studied at the atomic and macroscopic levels using the same principles. In order to obviate the problems of anisotropy and microstructure, the ideal materials to study are glasses. Thus, the fracture surfaces of aluminosilicate and borosilicate glasses were analyzed using fractal geometric principles. Because the (slit island) technique employed required polishing of the embedded fracture surface and this process resulted in fragmentation of the surface, a replication procedure was developed whereby a plastic replica of the fracture surface was used in all analyses. The fractal dimensional increment, D *, of the glasses was determined for the borosilicate and aluminosilicate glasses to be 0.085±0.03 and 0.09±0.05, respectively. It was shown that the reciprocal of the fractal dimension increment is equal to the mirror-to-flaw size ratio for these glasses in agreement with theory and previous work on a single crystal, a glass-ceramic and polycrystalline materials. The implication of these findings is discussed in terms of the fracture process.