A predictive model of the impact attrition of particulate solids was developed in the previous IFPRI programme (Ghadiri and Zhang, 1992):
where 5 is the fractional loss per impact, a is a proportionality constant, p is the particle density, U is the impact velocity, 1 is the particle size, H is the hardness, KC is the fracture toughness, and 4 is the constraint factor given by the ratio of the hardness to the yield stress. The model describes the chipping process and applies to materials that fail in the semi-brittle mode. The model predictions have been shown to agree reasonably well with the experimental results for ionic crystals that satisfy the semi-brittle failure conditions. In the current programme the work has been extended to glassy polymers, in order to assess the range of application of the model. The glassy polymers represent a category of materials that is completely different from ionic crystals in the material properties as well as structure. Poly-methylmethacrylate (PMMA) was selected as a model material because it is one of the most common glassy polymers and has a wide variety of applications.
Observations of the impact damage by high-speed photography showed that attrition was caused by chipping of comers and/or edges adjacent to the impact site at low impact velocities, and by fragmentation of the particle into relatively large fragments at high impact velocities. Detailed examination of the mother particles as well as debris by scanning electron microscopy and optical microscopy showed that chipping was produced by the propagation of sub-surface lateral cracks, and fragmentation by radial and median cracks. These mechanisms are associated with the semi-brittle failure mode.
A series of impact tests was carried out to quantify the extent of attrition. PMMA extrudates in the size range 2.36-2.80 mm were used. It was shown that these particles failed by chipping in the velocity range lo-30 m s-l and by fragmentation above 30 m s-l. The fractional loss per impact was measured as a function of impact velocity for 20 repeated impacts. In the chipping regime the fractional loss per impact was proportional to the impact velocity raised to the power 2.18, based on the first five impacts, and to the power 2.41, based on all the 20 impacts. The gradual increase in the power index indicates changes in the material properties with repeated impacts. However, these changes have not so far been quantified.
The effect of particle size was investigated on a theoretical basis. The limiting particle size below which fragmentation would not take place was estimated as about 300 urn for PMMA particles. Repeated impacts could reduce the limiting particle size due to fatigue effects or ductile shearing.
The conditions promoting the formation of lateral cracks were investigated by impacting rigid projectiles of various geometries on PMMA targets. It was shown that blunt projectiles were best as they induced a limited plastic deformation to initiate the cracks, and at the same time they could impart a significant amount of elastic strain energy to propagate the cracks. Further work is required to develop a mechanistic model of the fragmentation process.