Neil W. Page

The dynamic strength of partially saturated powder compacts: the effect of liquid properties

Abstract The flow stress of partially saturated pellets was measured at deformation velocities varying from 0.01 to 150 mm/s. The pellets, 20 mm in diameter and 25 mm high, were made with glass ballotini of a surface mean particle size, dp, of 35 μm. Water, glycerol and a series of silicone oils were used as the liquid binder, covering viscosities, μ, and surface tensions, γ, ranging from 0.001 to 60 Pa·s and 0.025 to 0.072 N/m, respectively. It was found that there was a critical strain rate (which was binder dependent) below which the peak flow stress, σpk, was independent of the strain rate, e. Above this critical strain rate, the flow stress increased with increasing strain rate. When plotted in terms of two dimensionless groups, the results collapsed onto one curve of the form: Str *=k 1 +k 2 Ca n where Str*=σpkdp/γcosθ is the dimensionless peak flow stress and Ca=μedp/γcosθ is the dimensionless capillary number, the ratio of viscous to capillary forces. θ is the contact angle (assumed zero in this work). The best fit values of the parameters were: k1=5.3±0.4, k2=280±40 and n=0.58±0.04. This result suggests that viscous forces are negligible at low strain rates, but become dominant at high strain rates. k1 is related to the static peak compressive strength of the pellets, k2 determines the critical Ca at which viscous effects become significant and n gives the power law dependence of viscous forces on the strain rate. This work is significant for granulation research since it highlights the fact that strengths measured under pseudo-static conditions may not be representative, even qualitatively, of how materials behave at the higher strain rates encountered in commercial granulators.

Quantitative comparison of three calibration techniques for the lateral force microscope

The quantitative use of atomic force microscopes in lateral mode for friction measurements has been limited by uncertainty about reliable calibration techniques. This article describes a comparison of three methods that have been proposed for the calibration of the lateral sensitivity of atomic force microscopes: (a) one based on movement of the photodiode assembly, (b) one based on the slope of the friction-loop while the contacting surfaces are in static contact, and (c) one based on a comparison of the lateral force signal on a surface with changing slopes of known orientation. All three methods gave comparable results thereby confirming their robust nature, and also confirming the validity of atomic force microscope methods for lateral force measurement. However, (b) indicated that for the commercial instrument used here, the lateral signal sensitivity is load dependent. A simple extension to (a) revealed the nature of this dependence: a misalignment of the four-quadrant photodiode detection system wi...

The importance of wet-powder dynamic mechanical properties in understanding granulation

Granule impact deformation has long been recognised as important in determining whether or not two colliding granules will coalesce. Work in the last 10 years has highlighted the fact that viscous effects are significant in granulation. The relative strengths of different formulations can vary with strain rate. Therefore, traditional strength measurements made at pseudo-static conditions give no indication, even qualitatively, of how materials will behave at high strain rates, and hence are actually misleading when used to model granule coalescence. This means that new standard methods need to be developed for determining the strain rates encountered by granules inside industrial equipment and also for measuring the mechanical properties of granules at these strain rates. The constitutive equations used in theoretical models of granule coalescence also need to be extended to include strain-rate dependent components.

Particle fractal and load effects on internal friction in powders

Abstract This paper describes a study of the influence of particle shape on internal friction. In this work, fractal measures of particle shape have been applied to a range of commercially available copper powders chosen for their contrasting particle shape but similar size ranges. The flow and packing properties of powders under gravity loading conditions were examined using flow time tests for known mass, apparent density and tap density. In addition to these tests, a ring shear cell provided the internal friction of the powders under applied load with applied normal stresses of approximately 0.35 MPa. Fractal measures have been found to be better discriminators of shape than conventional two-dimensional shape factors. There was good correlation between fractal measurement of particle shape complexity and the Hausner ratio, flow time and coefficient of internal friction.

Direct measurements of the adhesion between a glass particle and a glass surface in a humid atmosphere

An atomic force microscope has been used to measure the adhesion between individual silica-glass particles and a glass substrate in the presence of water vapour. It was found that the adhesion between the surfaces was not significantly altered, when compared with the dry case, at relative water vapour pressures of less than 0.6. Above this level of water vapour, the magnitude of the adhesion between the surfaces increased by approximately an order of magnitude. The transition of behaviour at a relative water vapour pressure of 0.6 corresponds to the formation of a capillary annulus having a critical Kelvin radius of approximately 2 nm. These findings are in good agreement with previous research data for the interaction of mica surfaces in water vapour. Force–distance data recorded as the particle and surface are separated from one another indicate the presence of a capillary neck between the surfaces. The form of these force–distance data indicates that the separation occurs under non-equilibrium conditions that more closely resemble the expected interaction under constant volume conditions (for the capillary neck). The results of this study also indicate the important role of equilibration time for the surfaces when not in contact. Successive force scans with only short equilibration times when the surfaces are separated result in the development of larger than expected capillary interaction forces. The results are relevant to the interactions between particles in a powder bed under flow.

Tensile bond strength development between liquid-bound pellets during compression

Novel experiments have been performed to measure the tensile bond strength developed between two liquid-bound pellets when they are compressed together at low strain rates. Pellets 20 mm in diameter were made from 75-μm mass-mean sized glass ballotini with water and three different viscosity silicone oils (0.01, 1 and 60 Pa s). The water-bound pellets formed bonds which were brittle and ruptured quickly when strained in tension. The silicone oil-bound pellets were plastic and stretched back a significant fraction of their original length before the bond ruptured. The peak tensile strengths and rupture energies of the bonds were proportional to the radial strain in the bond zone. A model was developed based on a cold-welding analogy to predict the peak tensile strength of the bond as a function of the strength of the bulk pellets and the extent of radial strain in the bond region. There was good agreement between the model predictions and the experimental results for radial strains less than 7%. At higher radial strains, the bond strength appeared to level off, probably because the bonds began to fail by gradually peeling apart rather than by simultaneous rupture across the whole failure plane. This simple model should help in predicting the bond strength formed when two liquid-bound agglomerates collide, which will be important in understanding and modelling granule coalescence growth behaviour. It was also observed that the compressive strength of the pellets decreased with increasing liquid viscosity, probably due to a lubrication effect reducing inter-particle friction. This contrasts with the effect of liquid viscosity seen by other workers at high strain rates, and suggests that the strength ranking of formulations with viscous binders may be strain-rate dependent.

Brittle to Plastic Transition in the Dynamic Mechanical Behavior of Partially Saturated Granular Materials

The effect of liquid viscosity, surface tension and strain rate on the deformation behavior of partially saturated granular material was studied over a ten order of magnitude range of capillary number (the ratio of viscous to capillary forces). Glass spheres of average size 35 microns were used to make pellets of 35% porosity and 70% liquid saturation. As the capillary number increased, the failure mode changed from brittle cracking to ductile plastic flow. This change coincided will the transition from strain-rate independent flow stress to strain-rate dependent flow stress noted previously [Iveson, S. M. Beathe, J. A., and Page, N. W., 2002, The Dynamic Strength of Partially Saturated Powder Compacts: The Effect of Liquid Properties, Powder Technol., 127, pp. 149-161]. This change in failure mode is somewhat counter-intuitive, because it is the opposite of that observed for fully saturated slurries and pastes, which usually change from plastic to brittle with increasing strain rate. A model is proposed which predicts the functional dependence of flow stress on capillary number and also explains why the flow behavior changes. When capillary forces dominate, the material behaves like a dry powder: Strain occurs in localised shear planes resulting in brittle failure. However, when viscous forces dominate, the material behaves like a liquid: Shear strain becomes distributed over a finite shear zone, the size of which increases with strain rate. This results in less strain in each individual layer of material, which promotes plastic deformation without the formation of cracks. This model also explains why the power-law dependency of stress on strain rate was significantly less than the value of 1.0 that might have been expected given that the interstitial liquids used were Newtonian.

Strength and attrition resistance of agglomerates and particulate coatings

The mechanical properties of a range of agglomerates and particulate coatings have been measured using a nanoindenter. The effect of formulation properties such as powder and binder properties on coating hardness is described. An attempt is also made to measure the fracture hardness with the nanoindenter. The use of indentation technology to measure fundamental agglomerate properties is critically analysed. Based on the indentation measurements and standard attrition test results, the coating hardness is found closely related to the attrition rate under standard conditions and can be used to screen different powder/binder formulations

A velocity interferometer system for any reflector utilizing a short coherence length laser

A velocity interferometer system for any reflector, utilizing a laser of coherence length less than the optical path difference (OPD) between the two interferometer arms, is described and tested. In this instrument the laser beam is passed through the interferometer both before and after it is reflected from the target. As a result the coherence length of the laser need only be twice the relatively small distance traveled by the target in the time taken for light to traverse the OPD. Results are presented for a nonspecular target.