The fractal evolution of particle fragmentation under different fracture energy

- Fractal model for the particle fragmentation
- Relation of the fragmentation fractal dimension to specific fracture energy
- Fragmentation fractal dimension determined from the fragment mass-size distribution

Brittle particles fragment when compressed or under impact. The particle fragmentation leads to a power-law relation of the number or mass of particles as a function of the particle size. The resulting power-law relation is accurately characterised by a fractal dimension of the particle fragmentation. The fractal dimension of particle fragmentation depends on the probability of particle failure, which correlates with the applied stress and fracture energy according to Weibull's statistics. Thus, the fractal dimension of particle fragmentation is related to the applied stress and fracture energy, and the relation of the fragmentation fractal dimension to the applied stress and fracture energy is proposed in this paper. It can be validated by the experimental data of marble particle fragmentation and brittle fracture data for rock particles published previously.

The fragmentation fractal dimension is positively related to the specific fracture energy in the logarithmic function.52