Abstract:

By controlling impact energy (E=6.27, 9.41, 12.54 J), number of impacts (n =1−15), and particle size (d =20, 30, 40 mm), this study systematically investigates the dynamic evolution of the fractal dimension D during the crushing of spherical particles. The experimental results demonstrate that D increases with n in a nonlinear, multi-stage manner. During the initial impact stage (n =1−5), brittle fracture is induced. For example, with d=30 mm and E=12.54J, ΔD/Δn reaches 0.062 per impact. In the subsequent stage (n＞5), the growth rate decreases to 0.015 per impact due to energy dissipation. A coupling mechanism exists among impact energy, particle size, and impact number. E dominates the initial crushing efficiency; increasing E from 6.27 J to 12.54 J enhances the final D by 13.5% for 40 mm particles. Smaller particles (20 mm) exhibit higher initial D due to stress concentration. The reinforcing effect of n on D decays as impacts accumulate. The basic model effectively characterizes the size effect, with errors ＜5% under most conditions. An extended model incorporating the fractal chaotic coefficient χ significantly improves prediction accuracy for fine particles. Both models capture the E-n-d coupling mechanism and provide an effective tool for quantitatively predicting particle crushing.

Key words: particle fragmentation, fractal dimension evolution, fractal chaotic coefficient, size effect, fragmentation dynamics model