This report sums up 6 years of work performed for IFPRI involving the development and use of a unique discrete element type simulation for solid fracture. The technique, developed in the first years of this work issembles equivalent solids by “gluing” together discrete polygonal or polyhedral elements. If properly assembled, this resuhs in an approximately homogeneous linearly elastic solid with predictable elastic properties, The “glued” joints can only withstand a specified tensile stress until they break and allow a crack to cross the solid. Both two- dimensional and three-dimensional realisations of this idea have been developed. The three-dimensional simulation has been shown to be able to replicate detailed experiments of particle crushing. In addition a “hybrid” mode] has been developed which borrows from finite element techniques on the element level to allow the elements themselves to deform. This permits the simulation of systems that undergo large elastic or plastic deformations, As the simulation was developed from techniques developed to simulate the flow of unbroken particles, it is uniquely adapted to studying situations involving both flow and breakage.
This report will summarite the highlights of the work. As some of the annual reports are nearly as tong as this final report, it is impossible to provide much detail here and the reader is referred to the annual reports to fill in the gaps. In addition to the description of the simulation technique, four topics will be discussed in detail.
The first topic discussed in detail will be our simulations of single particle impact breakage, which probably revealed the most interesting results from these simulations. These showed that the observed breakage pattern resulted from two mechanisms. The first, “Mechanism I,” breakage results irom the stresses that are generated in an unbroken particle. In two-dimensions, this produces a fanlike pattern of cracks issuing from the contact point, while in three-dimensions this results in the breakage into orange-segment fragments. These are the first sets of cracks to appear during the impact. The second, “Mechanism II” cracks are oriented perpendicular to the Mechanism I fragments (and thus cannot be accounted for by the stresses that are generated in an unbroken particle); the cracks appear at the end of the impact and produce the region of finely broken material that surrounds the contact point. Using the power of computer simulation, we were able to determine that the Mechanism II breakage results from the buckling of the Mechanism I fragments. It is clear that these two mechanisms also act in compression breakage (and, in fact, can be seen in some of three-dimensional simulations of compression breakage) and other ways of loading a particle to failure.
The next topic, performed at the request of then TC chairman Tom Taylor, was an examination of the attrition shear-cell experiments that John Bridgwater had performed under an IFPRI contract in the 1,980’s. These showed some contradictory results that indicated that the eflicicncy of attrition changed (evidenced as a change in the slope of the Gwyn rate curve) as the prevalent breakage mechanism changed from pervasive fracture to corner chipping. This produced some controversy that we were asked to resolve by simulating those experiments. Using conditions as close to the Bridgwater experiments as we could perform, we were able to replicate his results about the change of breakage mechzinism and about the change in slope of the Gwyn rate curve when plotted against a parameter that was equivalent to that used by Bridgwater. This, however, was not a reflection of a change in fracture efficiency or other fracture properties, but was due to transient shear work that was not accounted for in Eridgwater’s parameter. When plotted against the true shear work performed on the system, all the Gwyn rate curves were found to overlap indicating that the efficiency of attrition was unchanged by the change in breakage mechanism.
Also based on previous IFPRI research performed at the University of Utah, were our ball-drop simulations performed to improve the understanding of ball milling. Like the Utah experiments, these simulated the flow and breakage that resulted from dropping a single grinding ball onto a bed of particles. The first such simulations were performed on randomly assembled beds. These indicated that the strength of the bed was the primary factor in determine the efficiency of breakage. In particular, the stronger the bed, the longer it held together and allowed the grinding ball to do its work. One conclusion that can be drawn from this work is that the breakage occurs more efficiently for shallow particle beds which implies that mightly loaded mills should be more efficient than heavily loaded. We then went on to study regularly assembled beds that should bound the strength of all possible randomly assembled beds. This led to a surprising additional observation that the presence of structures (in this case regular structures) within the bed could supersede simple bed strength as the determining factor for the breakage efficiency.
Finally, we studied the effect of preexisting damage on impact breakage. This consisted of three separate but related studies. First of all, in order to fulfil1 Hans de Jong’s interest in porous particles, we studied the breakage of particle containing regularly spaced circular defects. These defects had two interesting properties. First of all the holes are isotropic and act as stress concentrators which initiate cracks that follow the local prevailing stress field. Secondly, under large deformation, they developed a local stress field that attracted passing cracks, causing the cracks to close on neighboring holes and produce fragments with sizes on the order of the hole spacing. The resulting size distributions were therefore very steep in that range of fragment sizes. We then studied the effects of linear cracks which are (I) not isotropic and will only initiate larger cracks if the surrounding stress field roughly ~OIIOWS the path of the preexisting crack and (2) possess no mechanism of attracting passing cracks like their circular counterparts. AS a result, it was found that linear defects largely affected the energetics of the problem by decreasing the energy required to propagate a crack across a particle and seemed to have no significant other effects On the generated size distributions, unless the cracks were long enough, in which case they interfered with and enhanced the Mechanism II breakage and produced larger quantities of fines.
Other problems were examined that time did not permit to be completed and are not discussed in this report. These included studies on particle shape and impact geometry. Also we continued to perform unbreakable discrete particle simulations of hopper flows (to fulfil1 a promise in our first proposal) and developed an efficient technique for the simulation of non-round particles. For information on these, the reader is referred to the various annual reports.
The termination of the IFPRI grant brings these simulation studies to a close, as least for the near future. That’s unfortunate as the simulation technique has a bright future, especially if computers continue their exponential increases in power. Much of the work presented here, involves detailed looks at the breakage process that is of scientific interest and, because of the insights they provide into the size distributions that are produced, are of indirect engineering interest. In fact, the work has demonstrated two ways of tightening the size distribution, by using large impact velocity and by inserting holes into the particles before breakage, although it is unlikely that either could be practically implemented. But further insight gained from these simulations might result in just such a practical technique. We would also have liked to study compression breakage in greater detail to see if other breakage mechanisms and other ways of controlling the size distribution would make themselves apparent.
But soon it should be possible to model entire process systems such as ball mills which are only approximately modeled by the ball-drop simulations described above. While waiting for computers to improve to those levels , it should be possible to use the detailed information obtainable from the simulation to derive “filters,” through which data obtained from large unbreakable simulations might be passed to allow predictions of the breakage rates. For example, there are many unbreakable particle simulations of the flow in a ball mill, which only provide insight into the breakage process at the level of revealing the stress pattern inside the particle bed. A series of simulations of the breakage induced by various loadings on single particles and on particle beds would allow that stress information to be processed into predictions of breakage rates and size distributions; simulations similar to the shear-cell simulations presented herein, would be use to ascertain the effects of shear abrasion n the breakage process. (In fact, it should be able to derive preliminary estimeates from the data we already have.) That would allow the evaluation of the choice of operating paramctcrs, such as the dcgrcc of loading of the ball mill. Knowing the size distribution produce’d would help in the choice of separation devices. Another possible new direction would be to include interstitial fluid effects in the simulation in an attempt to model wet grinding. (We are in the early days of development of a multiphase flow simulation using a slightly different technique than used in Tsuji’s IFPRI work.) In short, there is still a great deal of information that this simulation technique could reveal about particle breakage and grinding processes that is both of scientific and direct engineering value.