Prediction Of Fragment Size Distribution From Calculations Of Internal Stress In Spheres And Discs

Although industrial size reduction methods have an energy efficiency of only about 1 percent, methods of size reduction have not changed much for many years. One reason for slow progress has been the oversimple viewpoint that a single law should exist to relate size reduction to energy input. Modern simulation methods decompose the grinding process into a grinding rate function (selection function) and a breakage function. The breakage function is difficult to measure, and it usually requires tracers if it is determined from milling experiments. Prediction of breakage functions from basic principles is one objective of this paper. In this study we focus attention not on the gross energy input to the experiment, but on the spatial distribution of stress energy within the particle. We are led to this viewpoint by experimental observations of a few previous investigators (Bergstrom2, Rumpf3, Axelson4) and our own observations. Oka and Hiramatsu recently used their calculations of stress within particles for prediction of breakage, but again they tried to correlate the size of the fragments with the total stress energy, rather than the approach we propose. We assume that the stress energy is stored in the interior of the particle as the load is increased, until the particle breaks. We assume that each element of the particle breaks into fragments of a mean size that depends on the locally-stored stress energy. The size distribution of fragments is the computed from maps of the stress-