Relationship of energy to geometry in brittle fracture
Nicholas Mecholsky2020, Journal of the European Ceramic Society
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Abstract
Numerous investigators have noticed that there is a relationship between the energy of branching and the energy of initiation during a fracture event in materials that fail in a brittle manner. Usually, this is measured in terms of the stress intensities, i.e., K B /K c. The ratio has been reported between 3 and 4, implying a constant value. However, data suggests that it is a constant for a material, but not a universal constant. The fractal dimension of the fracture surface is related to the critical stress intensity factor. It is a measure of the tortuosity of the fracture surface. We show that the K B /K C ratio is directly related to the square root of the fractal dimensional increment, indicating a relationship between the energy of crack propagation and the tortuosity of the fracture surface.
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