Size Reduction
Introduction
Upon IFPRI's request, this report contains a summary of the experimental and theoretical investigations on fracture and comminution at the Institute fiir Mechanische Verfahrenstechnik und Mechanik der Universitdt Karlsruhe.
In 1957, when Bans Rumpf started to build up the institute, comminution was a well established domain in engineering. Rumpf then had the idea to combine experience in engineering with the scientific methods of physics. This was the basis for a long period of successful research, lasting longer than Rumpf's life, which ended in 1976. In spite of comminution being only one of several quite different research activities in the institute, from 1957 to 1989 totaling 222 papers had been published on fracture and comminution. Most of the papers, however, are written in German and therefore widely unknown in Anglo-American countries.
Some of Rumpfs numerous PhD students were physicists. The first of them, Klaus Schbnert, initially assisted to realize Rumpfs ideas of a comminution science. Soon he became head of the fracture and comminution group which he directed for more than two decades. Under his influence most of the research in this field has been carried out at Karlsruhe. Since. 1981 Schijnert directs the Institute of Mineral Processing of the University of Clausthal.
To write this report, Klaus Schonert would have been the most appropriate person. Without his ideas and critic discussions, many of the highly complicated experiments in fragmentation and single particle comminution would not have been performed and many of the theoretical and experimental results would not have been found. It is difficult to distinguish today, which of some new ideas in fracture and comminution research were Rumpfs or Schdnerts ideas or the ideas of PhD students. Probably such a differentiation is unimportant. The period of successful research was not only the result of new ideas but even more a consequence of stimulation and leadership. Both, Rumpf and Schdnert highly motivated their co-workers.
Klaus Schlinert was not available, to write this report. The publications are available, however, and since I am knowing nearly all authors personally - some still from my time as undergraduate student - I have taken the risk to follow IFPRI's invitation to review three decades of comminution research in Karlsruhe.
This report is not a treatise on comminution. It will not describe and discuss the details of the various research projects. The objective of this review is the transfer of information about the activities of the comminution group at Karisruhe and their experimental and theoretical results. Detailed information can be found in the individual 222 papers.
In addition to the review, IFPRI wanted answers to some questions as well as recommendations for future research in comminution. These items are appended in this report.
Executive Summary
The attrition of particles of known properties has been studied in a number of pieces of testing equipment. The novel and most flexible of these, a cone cell, has permitted the breakage of particles in gaps of known width to be studied in a rational manner for the first time. It is found that a close-sized feed can suffer high breakage rates at two gap openings, with a minimum rate between these at an intermediate gap size. Negligible breakage rates are found for low, less than one half a particle diameter, and for high gap widths, say exceeding three particle diameters. For mixed particle feeds, segregation of material into the gap is of crucial significance. These findings are of broad relevance to a wide range of solids processing equipment.
Studies on an annular cell, used to simulate breakage in a failure zone within the bulk of a material, showed that the Gwyn kinetics applied over three orders of magnitude of stress. It was shown by use of a well characterised and specially prepared extrudate that there was a shift from bodily failure at high stresses to surface abrasion at low stresses. These extrudates could also be formed into particles of different shapes; it was found that one of the Gwyn parameters was independent of shape and size whereas the other was dependent upon both.
The potential to modify the annular cell to establish links with the results of the cone cell was demonstrated but much remains to be done to cement these. Nonetheless, a complete understanding of attrition due to mechanical means now seems to be within our grasp. An aim of future work is to form estimates of product size distribution from a knowledge of the breakage of single particles under a number of loading conditions and an appreciation of packing theory.
Summary
This report describes the work carried out in the year 1989 on the project ‘Impact Attrition of Particulate Solids’ supported by a grant from IFPRI. It contains a brief summary of our previous work outlining the features which require further investigation, a literature survey on the relation between fracture mechanics and attrition, and some preliminary work on the effect of hardness on the formation of cracks by quasi-static compression of a corner of cubic particles.
The main objective of this work is to investigate the mechanisms of attrition of particulate solids, and therefore particular attention is paid to the initiation and propagation of cracks and their morphology. Ionic crystals with cubic habit such as NaCl, KC1 and MgO have been used so far as model granular materials because their physical and structural properties are well-characterised. It has been shown previously that the impact attrition of these crystals takes place mainly through localised loading on the corners and edges. This leads to plastic deformation of the impact site, followed by the formation of diagonal cracks, and detachment of platelets from the face adjacent the impact site. It is the last feature which is particularly responsible for the formation of debris in the attrition process, and whose mechanism is under investigation in the current work.
To ascertain whether the formation of platelets in impact attrition of particulate solids is due to strain rate hardening, single melt-grown crystals of KCl, NaCl and MgO were subjected to quasi-static compression of their corners against a hard flat surface. These crystals have different values of hardness, so that the effect of hardness can be investigated independent of dynamic effects which may be present under High strain rates.
The results show that in all cases the material response is elastic/plastic; compression of a corner leads to plastic deformation followed by initiation and propagation of cracks from the plastic zone. The deformation stress is found to be lower than the Vickers hardness.
Two types of crack morphology are observed: {110190 and subsurface lateral cracks. UO)90 cracks are found on all the three crystal types. These cracks are similar to both the quasi-static indentation fracture by a sharp indenter and impact fracture. This is expected as these cracks are formed by dislocation activity on {110145 slip planes, a common feature in all the three materials. Subsurface lateral cracks are found in MgO crystals only, i.e. in the hardest of the three materials tested. This supports the idea that the strain-rate hardening mechanism is responsible for the formation of the platelets as observed previously in the impact fracture of the softer NaCl crystals. It is therefore necessary to investigate the stress field in the region of the plastically deformed zone, with particular attention to the role of hoop tensile stresses in initiating the cracks. The most appropriate way to analyse the stress field in view of the anisotropy of the material is by Finite Element Analysis. Therefore our plan for the current year includes a theoretical analysis of the stress/strain state by the above numerical technique. This will be complemented by experimental work on quasi-static indentation, and on impact by a hard projectile in order to validate the theoretical work.
The Ultrafast Load Cell Device at the Comminution Center of the University of Utah was used for experiments on quartz (1400 pm - 1700 pm) with the density of 2.65 g/cm? The sieves used for preparing the sample were A.S.T.M.E square hole sieves of 12 and 10 mesh respectively.
The Ultrafast Load Cell Device (ULCD) has been used for impact comminution of defined particle beds. The energy consumed by the particles, the force applied to the particles and the deformation of the particle bed is being determined.
After the comminution test the broken mass as well as the particle size distribution are determined by sieve analysis.
The impact test parameters varied are:
- Number of particle layers (pl)
- Drop height of ball (h)
- Anvil geometry of ULCD so that a ball-flat anvil and
- ball-curved anvil (called ball-ball) impact can be simulated.
Scope of the Report
This report covers comminution by impact as obtained if solid particles moving freely in a static or moving gas, generally air, impinge or collide with one another or with grinding elements in an impact grinding machine.
H. Rumpf /l.l/ distinguished between four types of stress:
Therefore only the second type of stress (II) describes the type of impact grinding covered in this report. With this type of stress the energy available for comminution is defined by the kinetic energy of the particle immediately before impact, which includes its mass and the relative velocity between the particle and a second body, usually taken to be of infinite mass. The final result, for example the surface area produced during comminution, is independent of the fact, whether the relative movement is mainly obtained by a high speed second body or grinding element and a slowly moving particle, or a particle impinging at high speed on the surface of a stationary solid object. Depending on the angle of approach between the two bodies and the relative movement of their centres of gravity, impact and friction dependent attrition occur simultaneously. The velocities of impact applied vary between ten and several hundred meters per second.
The word "impact" is used in the Anglo-Saxon literature also for a special kind of the first type of stress (I). If stress is applied at a comparatively low rate between the surface of two rigid bodies one defines this type of stress as: low compression /1.2, 1.3/. If however, the grinding mechanism of stamp or ball mills had to be evaluated, for example with single particle crushing tests, different so-called "impact-tests" were used, which consisted of:
- drop weight methods, and
- pendulum impact devices.
A considerable number of different test machines have been developed and an enormous amount of data published, most of which seem to have escaped present knowledge. In order to distinguish these "impact-tests" from tests performed under type of stress II, they have often been called "double impact-tests", because two solid surfaces contact the particle to be comminuted during stress loading. The main difference to impact grinding (type of stress II) has therefore to be attributed to the following facts:
- comminution takes place with the stress being applied between two solid surfaces, and
- the energy available for comminution depends on the mass of the drop or pendulum weights and their height of fall.
Results obtained under these circumstances are not relevant in impact grinding as described in this report. Information on drop weight and pendulum comminution tests for a variety of materials may be obtained from references /1.2 - 1.16/.
The present report covers therefore those impact grinding processes where particles moving freely in a static or moving gas, impinge or collide with one another or with so-called grinding elements or targets ‘of' much higher mass.
The report deals in chapter 2 with basic theoretical considerations, for example the exchange of energy during impact, the frequency of occurrence of direct central impacts, the maximum stress applied during impact etc.
Chapter 3 covers the test machines and results obtained in single particle impact.
Chapter 4 concentrates on the design and the performance of different impact grinding machines, for example: high speed pin and hammer mills, and fluid energy mills.
Summary
An analysis of the stress distribution near the corners of particles loaded at that corner is presented and this is seen to be a basis for the rational treatment of attrition. Incorporation of a fracture criterion enables the effect of corner angle on loads to cause local chipping to be seen. Attrition is taken to be the result of such chipping. Fracture through the bulk of the material is thought to be unlikely and that the fracture reported by Vervoorn does not always conform to the definition presented here. Rather it is seen as a larger scale but still local effect. An explanation for some of Vervoorn’s results is offered but further work needs to be done to extend the explanations.
The significance of plastic deformation is briefly considered and the origin and importance of residual stresses is discussed.
ABSTRACT
Ball mills, stirred-ball mills, jet mills and vibration mills are commonly used in preparing ultrafine powders in the chemical industries. The comminution behavior of these mills can only be understood by studying the microproces of particle breakage. For many years researchers studied single- particle breakage, but in actual mills beds of particles break between impacting surfaces. Therefore, in this work the break- age of particle layers between a moving ball and a stationary anvil is studied.
In grinding mills ball-to-ball collisions trap and fracture particles. Curved surfaces between balls trap the intervening particles and balls falling on the particles cause breakage. Similarly, particles are also trapped and broken between “curved” and “flat” surfaces (such as liners) within the mill.
Whenever the stress developed within an individual particle exceeds the compressive strength, the particle breaks. The stress applied to the particle depends on the assemblage of particles present in the zone of breakage. Therefore, a systematic study is needed to learn about fracture behavior of assemblage of particles under specific loads and specific geometry of the impacting bodies. Such a study has been carried out at the University of Utah using a device known as the ultrafast load cell.
These studies were conducted in dry systems only. It is found that, regardless of the number of layers of particles present between impacting balls, only the last two or three layers are broken, as long as the mill allows free movement of particles. The distribution of broken fragments gets finer as the energy of impact increases, but the amount of material broken in an assemblage is roughly the same for all energy inputs. The impacting balls consume some energy upon rebounding. For instance, balls falling through larger heights can carry with them 15% of the input energy during rebound. Another important aspect learned in this project, for which direct evidence is not shown in this series of experiments conducted for WPRI, is that the conversion of input energy into particle breakage is higher at low input energy. This means that balls falling through small heights, in the range of 5-20 cm, are very efficient in breaking particles. In the mill, particles break under compressive stress. Shearing stresses only help the particles to escape from the zone of breakage and may somewhat reduce their apparent strength. Therefore, a combination of compressive and shear stresses is ideal for breakage of particle assemblies.
There are two key features to be considered for any comminution device. First, what is the force or stress, produced by impacting surfaces, and second, what is the size distribution of fragments produced by the applied stress? This report details clearly the distribution of fragments produced upon application of a certain energy. What is needed is a study of forces produced by mass of colliding bodies in the mill. In the case of ball mills, the “lifter” lifts the ball, and as a result the falling ball exerts a force on the bed of particles. In the case of attrition mills, the impeller stirs the mass of ball, which in turn generates a distribution of forces within the ball mass, A study of the forces produced within the mills would complement the work reported here.
Summary
The purpose of this research project is to examine the existence of the grinding limit of fineness or the equilibrium size of product powder by in-liquid grinding using media mills, and to find the factors which determine the ultimate sizes. Furthermore, the rate of fine and ultrafine grinding in liquids by the media mills was investigated mainly from the viewpoints of the mechanical grinding conditions.
It was confirmed using a planetary ball mill with very high grinding rate that the equilibrium particle size and the negative grinding phenomena do exist even in in-liquid grinding, as far as the sizes are evaluated by laser scattering- diffraction method. The equilibrium size reduced with decreasing ball size (3mm to 0.5mm) and was well correlated with the force exerting on a single ball by the maximum centrifugal acceleration in the mill pot. On the other hand, the limit size determined in terms of absorption method was found independent of the grinding conditions within most of the present experimental range.
The particle size distributions of products ground in the specific surface area by BET gas water by the media mills were well presented by the Rosin- Rammler equation. Their distribution constants n showing the sharpness of distribution were considerably higher than those usually obtained by the dry grinding with larger balls and found dependent on the ball size.
It was made clear that there is an optimum size of balls for the grinding of certain feed particles and for other mill's conditions. The in-liquid grinding with the planetary mill at higher frequency with larger balls produced products with agglomerates, the amount of which was possibly evaluated by the deviation of size distribution from Rosin-Rammler distribution.
EXECUTIVE SUMMARY
We have developed a model of impact attrition of particulate solids with a semi-brittle failure mode. Observations of the impact damage by high speed photography show that attrition is caused by platelets chipping off from faces adjacent to the impact site. Detailed examinations by optical as well as scanning microscopy, and more recently by confocal laser scanning microscopy show that the platelets are produced by propagation of sub-surface lateral cracks. Therefore, the analysis of impact attrition is based on the fracture mechanics of sub-surface lateral cracks. A dimensionless parameter, representing the volume fraction of materials lost from a single particle by the formation of such cracks, is derived:
where p is the density, 1 is the linear dimension, v is the velocity, H is the hardness, Kc is the critical stress intensity factor, and 4 is the constraint factor given by the ratio of the hardness to the plastic yield stress. This parameter quantifies the attrition propensity, and it includes all the relevant material properties. The fractional loss per impact is considered to be function of Y/. In the first instance the existence of a simple linear relationship has been explored.
A series of tests on a number of model materials were carried out to verify the theoretical predictions, in particular for the effect of velocity, particle size, and material properties. It is shown that, overall as a first attempt, the trend of the data agrees reasonably well with the theory. However, there are intricacies in the experimental data, the description of which requires further refinement of the theoretical model.