This paper examines three apparently disparate views of fracture in brittle materials with the purpose of showing the interrelationship of the fracture process at different length scales. Quantitative fractographic analysis of brittle fracture surfaces shows that there are characteristic markings on the surfaces that are self-similar and scale invariant, implying that fractal analysis is a reasonable approach to analyzing these surfaces. The fractal dimension is directly proportional to the fracture energy, #gamma#, during fracture for many brittle materials, i.e., #gamma# = 1/2 Ea_0D~* where E is the elastic modulus, a_0 a structural parameter and D~* is the fractal dimensional increment. Analysis of previous results of molecular dynamics modeling shows that the fractal nature of the fracture surface is consistent with the predicted surface produced during simulated fracture. The fractal dimensional increment, D~*, of the simulated fracture surface in a silica glass and silicon single crystal over a single order of magnitude matched well with those values measured on fracture surfaces of beams fractured in flexure for the same materials at length scales 1000-100 000 times larger. Finally, a ring contraction mechanism, modeled using semi-empirical quantum mechanical molecular orbital methods, is shown to be a likely step in the fracture of silica tetrahedra along the crack front. The geometry of the structure formed at the atomic scale from identified a reasonable atomic level foundation for the structural parameter, a_0. Based on a comparison of atomic and molecular modeling with macroscopically measured values of D~* and a_0, we suggest that the fracture process is a percolation of a series of ring contractions along the crack front, which result in the observed fracture surfaces for several brittle materials.
展开▼
