A Method to Estimate the Energy Distribution During the Confined Comminution of Granular Materials
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During the confined comminution of granular materials, the work input is transformed into elastic energy stored in the grains, breakage energy used to generate new surfaces, energy dissipated by friction between grains in contact, and redistribution energy dissipated by the relative movement of crushed fragments. We assume that the expression of Particle Size Distribution (PSD) in a crushed sample is a function of a fractal distribution and a uniform distribution. This allows calculating the breakage parameter, the increase of surface energy, and finally the energy dissipated by breakage. By summing the contact energy at all the contacts within a sample, we calculate the elastic energy stored. The calculation of friction-dissipated energy requires calculating relative movements of contacts, which are highly unpredictable especially when crushing is involved. Thus we include the dissipation that results from the relative displacement of grains in contact (including both crushed fragments and surrounding intact grains) in the friction-dissipated energy. We obtain the friction-dissipated energy by subtracting the elastic energy stored in the grains and the breakage energy from the input energy. The results show that the energy distribution is stress sensitive and changes a lot with the increase of compressive stress. Energy dissipation by friction plays a major role during confined comminution.