Introduction
Attrition is a ubiquitous problem in processing and handling of particulate solids. It causes dust formation, and has a detrimental effect on product quality and the reliable operation of process equipment. The research coordination of IFPRI identified the need for a better understanding of the various mechanisms involved in attrition in order to provide a fundamental base on which to address the problem. The objective of our research programme is therefore to elucidate the mechanisms of attrition of particulate solids, and to relate the rate of attrition to the material properties and to the loading conditions to which the particles are subjected.
A predictive model of impact attrition of particulate solids having a semi-brittle failure mode was developed in the previous IFPRI research programme. The model has been applied to the analysis of attrition propensity for several species of ionic crystal. This report summarises the results obtained in the past year on the effect of particle size on the attrition rate. Furthermore, the approach developed for the analysis of impact attrition has been extended to modelling wear of single particles. A summary of the literature survey is also included in this report.
The mechanism of attrition considered here is a chipping process, where small quantities of material are removed from the surfaces around the comers and edges of the particle. Our previous work has shown this to be an important process in the impact attrition of ionic crystals with a semi-brittle failure mode in the velocity range up to about 40 m/s. Fragmentation of the whole particle occurs at higher impact velocities or for materials with a relatively low value of toughness. However, this mechanism has not been addressed so far in our work.
In the chipping process, material removal is caused by the initiation and propagation of sub- surface lateral cracks. These cracks form readily during the unloading stage of an elastic-plastic deformation, and are driven by the residual tensile stresses produced by the plastic flow. Therefore, the analysis of impact attrition is based on the fracture mechanics of sub-surface lateral cracks. A dimensionless parameter has been derived from this analysis, which represents the volume fraction of material lost from a single particle by the formation of such cracks:
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where H is the hardness, p is the density, U is the impact velocity, 1 is the linear dimension-of particle, Kc is the critical stress intensity factor, and + is the constraint factor defined as the ratio of the hardness to the yield stress. The parameter IJ quantifies the attrition propensity, and it includes all the relevant material properties and impact conditions. The fractional loss per impact 4 is considered to be some function of q. In the first instance the existence of a simple linear relationship has been explored:
where a is the proportionality constant.
To verify the theoretical predictions, ionic crystals with a cubic habit such as MgO, NaCl and KC1 have been used as model materials because their structure and properties are well- characterised. The dependence of fractional loss per impact on material properties and impact velocity was verified previously for 2 mm melt-grown crystals (Ghadiri and Zhang, 1992). A linear relationship between the fractional loss per impact and the particle size is expected, but this could not be shown unambiguously in the previous work. To examine the effect of particle size on attrition, it is necessary to measure the fractional loss per impact for several particle sizes while keeping other parameters constant. The earlier work on the size effect used commercial solution-grown PDV salt crystals in the size range of 355-500 pm. This material contains a large number of polycrystalline particles which split into individual crystals on impact, hence obscuring the mechanism of chipping under verification, To combat this problem, a special experimental procedure involving repeated impacts was developed in order to quantify an asymptotic value of fractional loss per impact. The asymptotic was considered to represent chipping, as at that stage all the polycrystalline particles had split into smaller individual crystals and been removed from the sample by sieving. This procedure has been reported in the Final Report (FRR 16-03) of the previous IFPRI project (Ghadiri and Zhang, 1992). The repeated impact technique was however considered unsatisfactory because the number of impacts could also influence the fractional loss due to work-hardening of the comers and edges of the crystals, or purely as a result of the gradual change in particle size as the test proceeds.
The choice of solution-grown crystals rather than large melt-grown crystals for the tests was at that time associated with the fact that the bore of the air-eductor used in our experimental device was too narrow to allow particles larger than 3 mm to pass through. Recently, a new attrition rig with a larger bore was constructed to overcome this shortcoming. The results of the experimental work investigating the effect of size on attrition rate for relatively perfect, large melt-grown crystals is described in this report.
In the past year some work has been carried out to verify the existing models of lateral crack formation in ionic crystals as well as other materials of interest. A new microscopic technique, the Confocal Laser Scanning Microscope has been used for this purpose, and the results are currently being analysed, This new technique is now available at the University of Surrey, and it will allow us to carry out further characterisation of sub-surface damage arising from impact or quasi-static contact.