Fractal dimension as a characterization of free volume created during fracture in brittle materials

Abstract

Abstract Observations of characteristic markings on the fracture surface of brittle materials can be used to quantitatively describe non-equilibrium fracture. The relationship between quantitative fractography and fracture mechanics is first presented to describe the fracture of primary bonds as a fractal process. Next, molecular dynamics (MD) and molecular orbital (MO) modelling of the fracture in silicon single crystal and silica glass demonstrates that experimentally measurable quantities can be obtained from modelling. The fracture process is then described as a series of quantized, bond reconfiguration events related to the production of free volume at the crack tip. A series of these reconfigurations along the crack front, due to thermal vibrations and lowest energy configurations, develop into the mirror-mist-hackle and crack branching patterns often observed. The fractal dimensional increment, D*, is described as a scaling factor for both the fracture energy and the geometry of the fracture surface volume created. Fractal geometry, fracture mechanics, MD and MO calculations and fractographic observations can be used in concert to link the atomic bond-breaking process to the formation of the observed fracture surface topography.