Size Reduction

CONCLUSIONS

Nine different test devices have been discussed in this report and beside them other designs are possible. Now the question arises which particular device should be selected? Obviously this depends on the objectives of the planned investigations. For this reason the following aspects have to be considered for a decision:

• Are the investigations focussed on the particle breakage behaviour and the primary breakage or on the secondary breakage?
• What kind of material should be tested: brittle materials as minerals and the like or ductile deforming materials such as polymers?
• Is it of interest to vary widely the particle size and what size range is to be investigated?

Each researcher has to decide what contribution to the comminution science or what improvement to the technology he wishes to perform. Nevertheless it seems reasonable to suggest two test devices for measuring the data for secondary breakage (fraction of broken particles, breakage function, increase of the specific surface and the liberation grade) for wide applicability.

1. A piston press with different working units for testing brittle particles in the single particle situation above 1 mm and for interparticle stressing above 10 pm. Special working units for different temperatures are possible, therefore also polymer particles could be stressed at low temperatures. The piston force should be at least 200 kN, but the hydraulic system has to be sufficiently sensitive that a force of only a couple of kN could be applied accurately. The advantages of such a device are the following:

The general aim of the work is to elucidate the mechanisms of attrition of particulate solids. The specific objective of the current work is to investigate various types of damage under impact and sliding conditions. In particular, the transition velocities involved in impact breakage, the relative importance of normal and tangential stresses, the size distribution of the impact product and the effect of load and displacement on the material removal in surface wear have been investigated.

High-speed digital video recording was used to observe fracture patterns of a range of materials with diverse properties and structures as a function of impact velocity. The video recordings clearly show the existence of three identifiable velocity ranges where materials exhibit plastic deformation only, chipping, and a combination of chipping and fragmentation. This information is essential for developing realistic models of particle breakage.

Single particle impact tests of porous silica particles were carried out to investigate the dependence of attrition rate on impact velocity and impact angle. There is a significant increase of the attrition rate with impact velocity, with a maximum level of approximately 4.5% at 20 m s-l, for the size range 2.00-2.36 mm. The attrition behaviour of the samples is relatively insensitive to the impact angle in the range 25”-65’. However, preliminary impact tests with silica particles of different shape and porosities show that there is a dependence of the attrition rate on impact angle, depending on particle structure. Further work is on-going in this area.

A full size analysis of the impact products of PMMA and porous silica particles after a single impact was carried out in order to investigate the change of the size distribution with impact velocity. The Gates-Gaudin-Schumann distribution describes very well the size distributions of the mother particles and debris. The power index of the distribution is nearly constant for PMMA, but it varies significantly for porous silica. The cause of this variation is currently under investigation.

Single particle wear tests were also performed with the aim of elucidating the mechanisms of particle failure under sliding conditions. This occurs by abrasive wear at relatively low loads and long sliding distances, by chipping at slightly higher loads and short sliding distances, and by fragmentation at high loads. The data in the abrasive-wear regime of silica particles with high porosity, and hence low strength, show that the material loss is linearly proportional to the sliding distance and hence corroborate the predictions of the model developed by Ghadiri et al. (1995) for the semi-brittle failure mode. However, the wear test method developed here can provide quantitative information only about the abrasive wear rate, and the impact testing method has to be used for investigating the chipping rate of particulate solids.

This report presents the work on cornmunition under the IFPRI grant since 1993. A literature review has already been produced together with a detailed presentation of the experimental methods used (see report AR 27.02). Complementary references can be obtained from the literature review on communition research at the university of Karlsruhe (report SAR 012-06).

The objective of this research is to advance understanding of the fundamentals of fragmentation behaviour and develop experimental techniques to predict communition behaviour from a universal test. An experimental rig has been built to reproduce single particle impacts on a target and study the influence of the material properties on breakdown in ultra-fme grinding. Another experimental rig has also been constructed to study the impact of two jets of particles, as in an air-jet mill. Further experiments concern grinding experiments in laboratory scale equipment in particular wet grinding with a stirred bead mill and dry grinding with an air jet mill. The develoment of methods for characterizing debris from fragmentation forms a link between these two experimental studies.

Part A

Part A of this report presents the results of the experiments performed with the single jet apparatus. Seven kinds of particles have been used showing different behaviour depending on the type material and the processing involved in its manufacture.

Part B

Part B gives the results of the study with the opposed jet rig. Three diffent powders have been used so far.

Part C

Part C presents the methods being developped for morphological analysis.

Part D

Part D describes a method developed for analysing fine grinding kinetics for determining breakage and selection functions.

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).

Executive Summary

This paper summarizes a variety of this author’s industrial experiences with various conditions in size reduction processes which can either positively or negatively influence the narrowness of the product size distributions that can be produced. There are a relatively large number of operating factors, which if not properly selected, can give non first order breakage which unnecessarily broadens the final product size distributions produced by most industrial grinding devices. Key among these types of factors are dry powder aggregation, slurries that exhibit a rheological yield value, mill underfilling or overfilling, non-optimal rotating speeds for certain types of mills, media sizes that are too small for the material size being ground, and performing too large a size reduction ratio with a single grinding device. It is important in any size reduction operation that these potentially negative factors be evaluated (checked) so as to give their best performance. In other words, the best place to start in narrowing particle size distributions at the industrial level is to avoid using non-optimal operating conditions.

On the other hand, there are a number of factors which, when aggressively optimized, can give steeper (narrower) size distributions in a more proactive manner. Chief among these factors are the proper selection of staged grinding devices, the incorporation of appropriate classification, and, when possible, deliberate material selection (including modification in some cases) so as to promote the ability to produce steeper size distribution. The typical response of closed circuits involving classifiers are described in some detail. Also, a useful limiting case analysis method is presented which indicates the most narrow possible size distribution that can be produced with any material when all conditions are ideal. From an experimental viewpoint, the author also strongly recommends and describes a standard test sequence to be routinely run on each new material that an engineer might have to work with in a size reduction process. This rather minimal level of simple laboratory testing can give information which really helps to signal what types of operating responses might be possible on larger equipment with the material in hand.

Introduction

It is important to recall that the initial objectives of the research are to develop fundamental understanding and techniques to predict cornmunition behaviour from a universal test based on an experimental rig that reproduces single impact on a target in an air jet mill. The influence of the material properties on breakage in ultra-fine grinding are investigated. In Previous reports gave results for the impact of seven kinds of particles on a target and showed different types of behaviour. A classification was obtained (see report AR 27.03). A second rig has been built to study another impact configuration namely that of the impact between two jets of particles. Experiments are also performed with other types of mill and in particular an Alpine 100 AFG air jet mill. Morphological analysis is developed to study the shape of particles, debris and the action of the mills. In addition progress in the development of a model of an air jet mill is presented.

Part A

Part A of this report presents the results of the experiments performed with the single jet apparatus. Eight kinds of alumina particles impacted on a target are studied: three hydrargillites and five calcined hydrargillites. The influences of the material processing, the structure, and the calcination on the behaviour at impact are highlighted.

Part B

Part B presents the methods being developed for morphological analysis and gives results from the experimental impact rig and other methods of particle breakage.

Part C

Part C presents results towards the modelling of an air jet mill. In particular measurements and analysis of pseudo batch grinding experiments leading to the first determination of breakage and selection matrices for an air jet mill.

The general objective of the work at Surrey has been to elucidate the mechanisms of particle breakage under impact and sliding conditions. Predictive models, describing the chipping under impact and sliding conditions, have been developed based on indentation fracture mechanics. The specific objectives of the current work are to investigate the mechanism of particle fragmentation under impact and to characterise the mechanical properties of porous materials.

The study of fragmentation involved single particle impact tests in a range of impact velocities and feed particle sizes. The test materials covered a wide range of diverse mechanical properties and structures. The effect of impact velocity and feed particle size on breakage was evaluated using the full size distribution of the impact product. The analysis of the experimental results was by recourse to the Gates-Gaudin-Schumann distribution. The cumulative size distribution of the complement, i.e. the size range where fine debris and fragments arc expected, is shown to be a function of the group U’l . This conclusion is qualitatively similar to that applying to the chipping of particulate solids.

In an effort to incorporate the influence of material properties on the extent of fragmentation, the fracture toughness of spherical porous silica particles was measured using quasi-static Vickers indentation. The values of fracture toughness were found to be independent of the applied load and to fit well the expressions proposed in the literature. Fracture toughness is the most appropriate parameter for the characterisation of the resistance of materials to breakage, and the current work aims at establishing a relationship between porosity and fracture toughness by carrying out measurements on a single test material at different levels of porosity. The mechanical characterisation is expected to provide valuable information in the analysis of the effect of material properties on the fragmentation of particulate solids.

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.

The objective of this part of the report is to present the lastest results on cornmunition under the IFPRI grant that started in 1993. We recall that the objectives of the research are to develop fundamental understanding and techniques to predict communition behaviour from a universal test. An experimental rig was built up to reproduce single impact on a target in an air jet mill. The influence of the material properties on breakdown was investigated in ultra- fine grinding.

Section 1

Section 1 presents the results of the single particle impact experiments performed with the single jet apparatus. The influence of the size of particle is shown with glass beads and two polymers.

Section 2

Section 2 gives the results of the study of repeated impacts. Two approaches are used to compare the efficiency with a single impact.

Section 3

Section 3 studies the influence of the process of different hydrargillites on their behaviour at impact.

Morphological analysis tools are used in relation with the classical study (fragmentation profiles).

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 assembles equivalent solids by “gluing” together discrete polygonal or polyhedral elements. If properly assembled, this results 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 realizations 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” model 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 summarize the highlights of the work. As some of the annual reports are nearly as long 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

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 from 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

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 1980’s. These showed some contradictory results that indicated that the efficiency 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 mechanism 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 Bridgwater’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.

Ball-drop simulations

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 determining 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 lightly 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.

Preexisting damage on impact breakage

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 fulfill Hans de Jong’s interest in porous particles, we studied the breakage of particles 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 (1) not isotropic and will only initiate larger cracks if the surrounding stress field roughly follows 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 fulfill 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, at 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 used to ascertain the effects of shear abrasion on the breakage process. (In fact, it should be able to derive preliminary estimates from the data we already have.) That would allow the evaluation of the choice of operating parameters, such as the degree of loading of the ball mill. Knowing the size distribution produced 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.