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Particle Fragmentation

Fragmentation is the fundamental underlying process in many industrial comminution applications (e.g. milling, crushing). To simulate such processes the Discrete Element Method (DEM) has to be expanded to take into account the breakage of particles.

To this end many DEM implementations describing fragmentation adopt an agglomeration framework, where each parent particle is constructed from a number of smaller child particles. In the course of a simulation, child particles can be separated from the parent particle to form a fragment. A major disadvantage of this approach is the large number of particles required to model all fragments.

Alternatively, fragmentation processes may be described according to a probability distribution as a function of impact energy, local pressure or any other suitable breakage criterion. To this effect Weichert introduced the versatile Weibull distribution to the field of comminution.

In this approach the conditions for fragmentation are checked at each simulation time step. In the case of a breakage event the number and size of the progeny is derived from a probability distribution as well. The hereby generated fragments replace the original particle as shown in Fig. 1.

Fig. 1: A brittle particle (blue) breaks after collision with an unbreakable particle (red).

More precisely, the breakage index t - described via the Weibull 10 distribution - denotes the cumulative mass fraction of the progeny that is
smaller than 1 10 of the parent particle size. The parameter t is uniquely 10 related to other points on a family of size distribution curves t , defined as n the cumulative percentage passing a given fraction of the initial size (Fig.2).

Fig. 2: Determination of size distribution parameters tn from n the breakage index t10 .

In this way the particle size distribution is uniquely defined and the fragments thus obtained are randomly packed into the volume of the original particle (Fig. 3). However, assuming volume conservation, this leads to a compression of the particles and in further consequence to an unphysical repulsive normal force between the fragments. Our model resolves this problem by limiting these forces by the actually available elastic energy of the particles.

Fig. 3: Fragments created for t10 = 0.2 (left) and t10 = 0.5 (right).

(Daniel Queteschiner)