Morphology of particles
Many of the flow and packing properties of powders are dependent upon the sizes and morphologies of the constituent particles.
For example, a decrease in packing density and the flow rates of powders generally accompanies a decrease in the average particle size (and/or an increase in the irregularity of the particle morphology). These properties are important in real world scenarios such as the requirement to determine the mass of powder that can be stored in a silo of given dimensions, or the tooling fill depth to be employed in order to form a given part from powdered metals. Consequently, companies spend considerable time and resources on equipment that will allow them to measure, for example, the particle size distribution for the powders they employ.
Proprietary systems are available that measure particle size by employing a wide range of methodologies, such as 'laser diffraction' and 'time of flight' measurement. However, a fundamental limitation of these systems is the unrealistic assumption that the particles are spherical. In, for example, the powder metallurgy (PM) industry, the majority of powder tonnages employed is composed of particles that exhibit a random morphology such as those produced through water atomization of iron. The figure below shows a micrograph of such a particle.
Despite the important influence of morphology on powder behaviour, only a relatively small amount of simulation work has been reported in this area. This is perhaps due to the perceived difficulties associated with realistic simulation of irregular particle morphologies and their associated packing behaviours. The availability of techniques for accurate quantification of this morphology, along with measurements of particle sizes, would provide the information needed for useful prediction of powder behaviour. Vision systems can offer this functionality as a consequence of the large amount of information they can provide regarding particle characteristics.
Simulation of powder behaviour
The packing and flow behaviour of granular materials is critical to materials handling and processing in a number of industries. Examples include the food industry, mineral extraction, polymer manufacturers, and metal powder processors. In the latter case parts are often manufactured in a process where metal powder flows and packs into a die and then undergoes compaction at pressures of up to 1 GPa. Numerous studies have indicated that the density characteristics of the resultant compact have a significant effect on the dimensional variation and strength of the final part. This is a consequence of the influence of the compact density upon the degree of shrinkage during sintering, and ultimately the available load-bearing cross-section of the final part. Since the powder packing density is of primary importance in determining the final material density, significant benefits could be attained through realistic simulations of powder packing behaviour.
The simulations developed by the UWE team are of the Monte Carlo type, in that they are based on random placements and movements of particles. A specified number of particles are placed randomly within a square and then each is repeatedly moved in a random direction to ensure that no overlapping is occurring. The particles are then moved under the influence of a gravity field so that they are randomly packed into a funnel. The particles can be represented as two-dimensional disks, so that their maximum random packing density is 0.82 (in contrast to 0.64 for spheres). The main reason for employing 2D rather than 3D simulations is to reduce the computation involved, (however 3D simulations of the packing behaviour of spheres and irregular particles have been completed). The 2D simulations do however enable a number of interesting phenomena to be studied, such as the effects on flow of container geometry (caused by bottleneck or wall effects). Ultimately the aim is to provide a comprehensive 3D simulation that will enable accurate prediction of the effects on packing density of wall and inter-particle friction.
Modelling 3D Particle Morphology
Advanced 3D simulation of powder behaviour has also been undertaken by MVL staff. For example, it has been gratifying to find that a new research technique developed at UWE by Lyndon Smith in 1997 (published in Computational Materials Science) for modelling the packing of irregular particles, has been used by other researchers. This 1997 paper was the first to describe a technique that combines spheres of different sizes (typically a large one and several smaller ones) by overlapping them, in order to produce three dimensional (3D) models of real irregular particles, for use in Discrete Element Modelling where the 3D particles are moved in order to simulate the effects of gravity on particle assemblies.
Since this time, the UWE method has been employed by a number of researchers, who have published journal papers. For example, a Technical Note by Garcia et al. employing the technique appeared in Geotechnique in 2009. Garcia et al. also state in their 2009 paper that: "the algorithm has been shown to require only a modest number of spheres to produce clusters that closely resemble the original particle"; this was a finding also presented in our 1997 CMS paper, where a quantitative analysis was given of the effects of increasing the number of spheres in the modelled particle from 2 up to 15. The high-degree of similarity of the particle modelling methods presented in the two papers is also clearly illustrated in Fig. 2 of the CMS paper and Fig. 10 of the Geotechnique paper. In both cases the simulated particle consists of a large sphere with several smaller spheres located at its surface. The only difference between the two figures is the exact sizes of the spheres, the amount of overlap employed and the resolution of the renderer used to visualise the particles. The UWE approach was also employed in a 2010 Granular Matter paper by Ferellec and McDowell. Here, Ferellec and McDowell also state that: "Real particles can be modelled precisely in terms of shape using a reasonable number of spheres"; as mentioned, this was a finding also presented in the 1997 CMS paper.
Further illustration of the utility of the approach for modelling irregular particle morphologies for simulating packing behaviour is provided by the fact that in 2004 it was developed into a commercial package called "DigiPac" for simulating particle packings. In their 2004 paper, Gan et al. state that the method employed in DigiPac is similar to that described in the 1997 CMS paper (see www.kona.or.jp or www.structurevision.com).
Simulated model of an irregular particle, consiting of a large sphere with smaller spheres located at its surface.