Review and Further Validation of a Practical Single-Particle Breakage Model

Abstract

Particle breakage occurs in comminution machines and, inadvertently, in other process equipment during handling as well as in geotechnical applications. For nearly a century, researchers have developed mathematical expressions to describe single-particle breakage having different levels of complexity and abilities to represent it. The work presents and analyses critically a breakage model that has been found to be suitable to describe breakage of brittle materials in association to the discrete element method, either embedded in it as part of particle replacement schemes or coupled to it in microscale population balance models. The energy-based model accounts for variability and size-dependency of fracture energy of particles, weakening when particles are stressed below this value, as well as energy and size-dependent fragment size distributions when particles are stressed beyond it, discriminating between surface and body breakage. The work then further validates the model on the basis of extensive data from impact load cell and drop weight tests. Finally, a discussion of challenges associated to fitting its parameters and on applications is presented.

Simulating breakage tests using the discrete element method with polyhedral particles

“…High values result in coarser size distributions, with the opposite being observed for lower values of bulk Young´s modulus. This is not surprising, given that the split of energy from a collision is dependent on the bulk Young´s moduli of the surfaces [27]. An additional simulation, carried out by reducing 10 times the bulk moduli of steel and copper ore in the simulations, resulted in finer size distributions 10 Comparison between experimental data (symbols) and simulations (lines) using different values of bulk Young´s modulus for granulite particles contained in the size range 31.5-26.5 mm for impacts at 1.0 kWh/t.…”

“…The relationship between particle size and median fracture energy, hereby called size function, is described using the expression [22,27]…”

“…More detailed comparisons of Eq. ( 3) to data are available elsewhere [22,27,28]. Rocky DEM considers that in a contact between particles or between a particle and surfaces of a device, the energy dissipated in the contact is split between the bodies, according to their stiffness [27,29], as well as the particle volume.…”

“…( 3) to data are available elsewhere [22,27,28]. Rocky DEM considers that in a contact between particles or between a particle and surfaces of a device, the energy dissipated in the contact is split between the bodies, according to their stiffness [27,29], as well as the particle volume. As such, from the values of stiffness and sizes of the bodies in contact, the specific energy actually dissipated in the particle during stressing is given by E k .…”

“…Equation ( 5) is implicit but can be easily solved iteratively with the initial guess D 0 [23]. Values of γ are material-specific and typically vary from 1.5 to 8 [24,27].…”