Relationships between particle size and fracture energy or impact velocity required to fracture as estimated from single particle crushing

Abstract The relationships between fracture energy and compressive strength of sphere have been theoretically studied from the viewpoint of fracture mechanics using experimental results of crushing of spheres. Two kinds of glassy and five kinds of natural materials were examined. Specimen diameter ranged, from 0.5 to 3 cm. Combining the above with the size effect of strength reported in the previous papers, the authors obtained a new equation for the change in fracture energy with size. The specific fracture energy increased with a decrease in size and, with natural materials, when size was less than 500, μm, the specific fracture energy increased rapidly. Even if the kinetic energy of a particle with a size of 100 μm was converted completely into fracture energy, the impact velocities required to fracture were calculated to be 13 ∼ 225 m/s for the samples used in this report.