When simulating particulate systems using the discrete element method (DEM), particle breakage can occur.
Sometimes the extent of this breakage is significant, such as in crushers and mills, which are designed to crush chunks of ore into smaller pieces.
Breakage is insignificant in cases when particles are subjected to handling, mixing, compaction and separation operations, where breakage is not desired.
However, in all cases, conducting DEM simulations without accounting for breakage can lead to biased results — sometimes even useless solutions.
Rocky DEM has always included capabilities for predicting particle breakage of non-round polyhedral particles, with mass and volume conservation based upon the stressing energy involved in the collisions.
The latest version of Rocky, release 4.1, incorporates a new, improved and validated model that extends the existing application range for modeling particle breakage. This model, called the Tavares Breakage Model (named for L.M. Tavares’ Ph.D. work at the University of Utah and further development with his group at the Federal University of Rio de Janeiro, Brazil), is also based on the Voronoi subdivision algorithm — which is well known for solving problems in the movie and gaming industry.
The Tavares model extends this functionality by adding capabilities (submodels) that can make breakage modeling quite realistic in a wide variety of situations. In particular, the model is useful in describing ore degradation during handling as well as size reduction in different types of crushers, providing greater confidence in predicting both the proportion of broken particles and product size distribution.
At the outset, the Tavares model accounts for variability in particle strength: Even when particles are the same size and material, each particle has a distinct strength or fracture energy. Strength varies with particle size so that as a particle becomes smaller, its strength increases — that is, the fracture energy per unit of material mass increases. This is described using the size-dependent breakage probability submodel.
The Tavares model predicts the outcome when particles are involved in a collision based on these tenets:
• If the energy involved in a collision is greater or equal to the particle’s fracture energy of the particle, the particle will break. The fineness of the fragments generated by this event depends on the stressing energy’s magnitude. At this point, a second submodel comes into play: the energy-dependent breakage submodel. Distribution of the fragments in size is then described using either one of the distribution functions, Gaudin-Schuhmann or incomplete beta function. The Voronoi subdivision algorithm is then used to reproduce this predicted distribution, generating the fragments that will appear in the Rocky DEM simulation.
• If the energy involved in a collision is lower than the particle’s fracture energy, the particle will not break. However, particle strength possibly will be reduced, making it more amenable to breakage in a future stressing event. This weakening is described using yet another submodel, the damage accumulation submodel, which was developed based on elements from continuum damage mechanics.
The Tavares breakage function extends the previous Rocky DEM model by considering particle properties that had not been covered in the earlier version.
Validity has been demonstrated via single-particle testing and documented in a number of peer-reviewed journal publications over the last 20 years. Indeed, model parameters for several materials are available in some of these publications.
Although users can take advantage of the published database on breakage properties¹, the best practice is to fit model parameters specific to their material of interest prior to conducting Rocky DEM simulations.
Single-particle breakage tests can be used in this task, including drop weight tests, impact load cell tests and repeated impact tests. Detailed technical information can be found at the footnoted scientific papers.
¹L.M. Tavares, R.P. King (1998). Int. J. Miner. Process. 54, 1-28.
L.M. Tavares, R.P. King (2002). Powder Technol. 123, 138-146.
L.M. Tavares (2009). Powder Technol. 190, 327-339.
L.M. Tavares, R.M. de Carvalho (2013). Miner. Eng. 43-44, 91-101.