Self-similarity and energy-size relationship of coarse particles comminuted in single particle mode

"Self-similarity is proofed to be a common feature when brittle material is comminuted, either in particle bed or single particle mode. Appropriate test work is well documented for particle sizes less than 7 mm in several publications. In contrast, almost no research has been done for coarser particles. The aim of this paper is to show that the fracture pattern of coarser material also tends to be self-similar. Hence, single particles of quartzite, granodiorite and dolomite were comminuted under compressive load. The focus was set on three different size fractions -3.15 +2.5 mm, -31.5 +25 mm and lumps -300 mm. According to the wide range of particle sizes, three different piston-die presses were used with a maximum compressive force ranging from 5 kN to 4000 kN. The force-displacement curves were recorded in order to calculate the specific comminution energy. Additionally, the -31.5 +25 mm size fraction was crushed in a laboratory scale jaw crusher and a roll crusher. Some authors report that the energy-size-reduction relationship of self-similar materials can be approximated by a linear function, which is independent of the comminution equipment. In their charts the slope can be seen as a product-size-independent grindability measure. Our tests show a self-similar breakage behavior when particles in a range of -300 +3 mm are comminuted in single particle mode. Furthermore, the products of the piston-die-presses and the roll crusher are similar to each other in a self-similar representation of the particle size distribution. The jaw crusher product, however, is not self-similar compared to the piston-die-press products. Finally, the linear energy-size-reduction relationships are confirmed for each fraction, but show size dependent slopes."