Computer Simulation of Particle Breakage

Publication Reference: 
Author Last Name: 
C S Campbell A V Potapov
Report Type: 
Research Area: 
Size Reduction
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Publication Month: 
United States

This report concerns new work using a computer simulation of solid fracture. The details of the simulation technique were described in previous reports and wiIl not be repeated in detail here. For this model, rigid elements are assembled into a simulated elastic solid by “gluing” the elements together with compliant boundaries. The joints ticture when the tensile strength of the glued joints is exceeded, permitting a crack to propagate across the simulated solid. The great value of a computer simulation is that literally everything is known about the simulated system and is accessible to the computer experimenter. In addition the simulation allows the independent variation of material properties such as Young’s modulus, Poisson’s ratio and work of fracture - flexibility, that in the laboratory, is limited to the properties of available test materials. Consequently, a computer simulation offers the abiity to make investigations with a detail that is unthinkable to duplicate experimentally. As such simulation techniques are valuable is areas such as comminution and attrition, for which the actual problem is so complicated and so many events happen in so short a time, that experiments are historically limited to performing post-mortems on the fragments.

The first topic to be addresses in this year’s report finishes an investigation started in last year’s report. There we identified two breakage mechanisms that are responsible for the 16nal crack patterns observed in impact breakage. The frrst mechanism (Mechanism I) can be attributed to the stresses that develop in unbroken particles. These stresses are oriented azimuthally about the contact point and produces a series of fanlike cracks issuing outwards from the contact point. This is the only type of breakage occurs between the time that the particle fist makes contact with the wall and the time that the contact force has brought the center of mass to a halt (which is also roughly the point of maximum compression at the contact point). This type of cracking will continue as the particle rebounds, but will also develop cracks that are oriented perpendicular to the fanlike cracks. Such cracking cannot be accounted for by the stresses that develop within an unbroken particle and must be attributed to some other mechanism (Mechanism II) that in turn must be a byproduct of the Mechanism I cracks that have already developed in the particle. Making full use of the powers of a computer simulation, we were able to determine that buckling of the Mechanism I fragments was ultimately responsible for the Mechanism II breakage. From the way that this investigation utilizes the abilities of a computer simulation to control the simulated system and thus reveal the bending stresses that bring about the Mechanism II breakage, this investigation is an unusually good example of the utility of a computer simulation for studying this type of problem.

For the next topic, we returned to the Ball Drop simulations that were created long ago as examples of the simulation in action. These simulations were based on the IFPFU supported Ultra-Fast Load Cell experiments performed at the University of Utah. These are approximate experiments related to ball-milling that are tractable (i.e. involve relatively few particles) by the simulation (i.e. involve relatively few particles). Essentially they are 2-D simulations of a single large grinding ball dropped onto a static bed of breakable particles. As a result the particles in the bed are broken and/or scattered away from the grinding ball as it falls. Simulations were performed for 4 different bed depths and 3 diierent frictions. Generally, the deeper the bed, the less the total amount of breakage. The results show also show the dual role that friction plays in the breakage process. On the one hand, the majority of the grinding ball’s energy is lost to friction so that increasing the friction increases this energy loss. On the other hand, the friction holds the bed together and the larger the friction, i the longer the bed stays in place for the grinding ball to do its work. It appears that this latter effect is the stronger of the two in that increasing the particles’ coefficients of surface friction greatly increases the amount of breakage; that extra energy for breakage appears to come from a reduced kinetic energy of the scattered fragments.

Fiiy, to help address the interest expressed in the breakage of porous particles, we have performed some simulations of the effect of internal defects in the form of circular holes. The simulations show that the holes have two effects. First of all, they concentrate stress internally and are thus become the source of many of the cracks that form. Secondly, they act as internal free surfaces and thus attract propagating cracks. As a result, if the internal holes are regularly spaced the particle will break with a large number of fragments with sizes of the order of the hole spacing. Consequently, it were possible to create particles containing such holes, it would be possible to gain some control on the particle sizes generated by impact (and, as the mechanisms are much the same, presumably by crushing as well).