In the last report, we studied the breakage of particles with regularly spaced circular defects as a way of studying porous particles. Those simulations showed a significant effect on the size distribution which, in particular, showed a nearly vertical portion indicating that the size of a large fraction of the produced fragments was governed by the hole spacing. Most homogeneous solids are assumed to be filled with microcracks and we were curious whether they would demonstrate a similar effect on the final breakage results. Unlike the circular defects studied last year, small linear cracks concentrate more stress at the tip. But at the same time, unlike circular defects, linear cracks have a preferred direction and may only participate in the breakage if that direction coincides with the direction of the induced tensile stresses within the particle. As a result, the breakage behavior was nothing. like that for the circular defects. The major effect of the cracks was to increase the degree of Mechanism II breakage, thus increasing the percentage of fines within the system. No effect was seen on the Mechanism I breakage, which governed the sizes of the largest particles.
We are also continuing our ball drop simulations, in which a single grinding ball is dropped onto a bed of particles, as an approximation to ball milling. In last year’s report, we showed that the stronger the particle bed, the larger the degree of induced breakage. This occurred because the strong beds, held their constituent particles in position long enough, without scattering, for the grinding ball to induce breakage. This year’s results gave a great deal more insight into the manner in which the particle bed affected breakage. We became concerned that the random manner in which the beds were assembled might have a significant effect on the eventual breakage. Thus, we attempted to bound the effect of the bed packing by studying the breakage of the weakest and the strongest regularly packed beds. The strongest and also the densest twodimensional construction is a hexagonal packing in which each particle is in contact with six neighbors. The weakest, and likely the least dense stable bed, is a square packing in which particles are arranged on the corners of a square and each particle is in contact with only four neighbors. We hoped to bound the behavior of randomly packed beds between these two extremes as the strength all such beds must lie between these two. Surprisingly though, we found other effects arising from the regular nature of the packings. In particular, the square bed, which has the weakest packing and in the light of last year’s results, should exhibit the least breakage, actually demonstrated more breakage than the hexagonal packing. This was a result of the square packing presenting internal columnar structures to oppose the descent of the grinding ball; these columns underwent nearly complete breakage. The hexagonal bed, on the other hand, naturally spread the grinding ball’s energy throughout the bed, reducing the energy concentration in any given particle thus reducing the breakage, Further evidence of this can be seen in the fact that there was a small effect of inter-particle friction on the breakage in the square bed, (as least when compared to the hexagonal bed) as friction has little effect on the strength of these columnar structures. As a result, the internal order of the bed as well as the overall bed strength can strongly affect the degree of induced breakage.
Finally, we have developed this year, an algorithm for efficiently studying the mechanics of non-round particles. Most granular simulations study round particles as they are far more efficient to simulate. For example, the polygonal particle simulations that make up the heart of our breakage analyses, are approximately 10 times slower than an equivalent round particle simulation. However, most natural particles are not round and are not as likely to roll as non-round particles. This affects the overall mechanical properties of the system. For example, it is hard to get significant angles of repose for round particles as they simply roll away when the angle becomes marginally steep. This new simulation technique uses particle shapes composed of circular arcs and is only about half the speed of an equivalent round particle simulation. This allows a great variety of shapes to be studied at a relatively inexpensive price.