FRACTOGRAPHY AND FRACTAL GEOMETRY: WHAT CAN WE LEARN?

摘要

Fracture surface features contain quantitative information about the stress and energy associated with a specific fracture event. The approach presented here is predicated upon the fact that fracture is a fractal process. It is hypothesized that the fundamental unit of fracture at the appropriate length scale is a quantity known as a{sub}0. In turn, a{sub}0 can be related to the fracture energy, γ, and the elastic modulus, E, and through a scaling parameter, the fractal dimensional increment, D{sup}*, i.e., γ = 1/2 a{sub}0 ED{sup}*. The characteristic markings of mirror, mist and hackle observed on the fracture surfaces of glasses, ceramics and polymers are related to the fractal dimensional increment: (Y/Y{sub}j){sup}(1/2) c/r{sub}j = D{sup}*, where c is the crack size, r{sub}j, is either the mirror-mist radius (j = 1), mist-hackle radius (j = 2) or crack branching boundary (j = 3), Y and Y{sub}j are constants related to the initial and propagating crack geometry, respectively. The combination of atomistic modeling, experimental measurements and the application of fracture mechanics and fractal geometry leads to a suggested sequence and organization of the brittle fracture process. By applying fractographic principles combined with fractal analysis and fracture mechanics, several different types of problems can be solved. The combined analyses can be used to determine whether a product has been manufactured properly, to identify toughening mechanisms in composites and to identify the type of loading during fracture. Examples of each application are discussed in terms of fracture surface analysis and microstructural characterization.