In this chapter, the results of compression tests are described for spheroidal materials demonstrating the different types of behavior—namely, (1) glass which is essentially elastic with brittle failure from microcracks, (2) PMMA which is elasto-plastic, (3) Aluminium oxide which is compactable, and (4) granules that display more complex behavior because of the interaction of the binder and the constituent particles. Discrete Element Method (DEM) simulations suggest that granule shape, and therefore structure, are important in determining the type and extent of breakage, particularly during processing, rather than the effects of particulate or binder properties. The significant plastic deformation found in PMMA in compression can be explained by its high-strain rate dependence. For aluminium oxide plastic deformation occurs without any change in the material in the contact area which suggests that densification may have occurred. The calcium carbonate granules fail by flattening of the contact area. This flattening may form a compacted cone followed by meridian cracks.

A numerical simulation of a particle in a horizontal pipe has been carried out, and the variation of aerodynamic forces is described. The major forces that control particle motion are drag in the axial direction, and lift due to air velocity gradient and due to spin in the transverse direction. An elastic contact model based on rigid body sliding has been incorporated, which avoids particle settlement without having to use any form of irregular bounce. The results from the simulation agree closely with experimental time-of-flight measurements.

Based on observations of single impact studies of spherical coherent and agglomerate particles made from a wide range of materials, a classification of failure modes is presented involving low, intermedite. It is based on low, intermediate, and high velocity regimes. The work allows a point of reference for the expected failure modes under impact conditions of spherical particles made from many different materials. Interestingly, there is considerably greater diversity of modes in the low compared with the high velocity regimes.

A study has been made of the damage caused by impact and compression in 8-mm-diameter polymethylmethacrylate (PMMA) spheres over a wide range of velocity and loading. Over 1000 single impact and 200 compression tests were conducted, with the form and mechanisms of damage being observed closely. Static indentation on PMMA material has also been carried out, with results found to be highly comparable with the literature. Five distinct forms of impact damage are described, with each one dominant over a certain range of velocity. This material has responded in a largely brittle–elastic manner on impact, in accordance with the known high strain rate properties of PMMA. In contrast, plastic deformation dominates in the static compression and indentation test.

Systematic data are presented for the single impact failure of 3.2, 5.3, and 7.2 turn fertiliser granules over a wide range of impact speeds and angles. The probability of failure was found to change only slowly between 90degrees (normal) impact and 50degrees, but decreased rapidly below 50degrees. The probability of failure increased with increasing size of granules. The effect of impact velocity on the mean, median and the proportion of the largest-sized fragments were examined. Two distinct forms of normal impact damage were identified, corresponding to low and high impact velocities, and the mechanisms of failure are discussed. (C) 2002 Elsevier Science B.V All rights reserved.

A study has been made of the damage caused by impact and compression in 8-mm-diameter polymethylmethacrylate (PMMA) spheres over a wide range of velocity and loading. Over 1000 single impact and 200 compression tests were conducted, with the form and mechanisms of damage being observed closely. Static indentation on PMMA material has also been carried out, with results found to be highly comparable with the literature. Five distinct forms of impact damage are described, with each one dominant over a certain range of velocity. This material has responded in a largely brittle–elastic manner on impact, in accordance with the known high strain rate properties of PMMA. In contrast, plastic deformation dominates in the static compression and indentation test.

The failure sequence of thick soda-lime glass plates under indentation from tungsten carbide spheres at high loads is described. Failure shows a combination of features normally associated with either blunt or sharp indentation. and most occurs during unloading. In particular the effects of irreversible processes of flow. densification, fracture and interfacial slip during loading on the initiation and propagation of failure during unloading are described and discussed.

Accurate measurements have been made of the impact and rebound behaviour of 5-mm aluminium oxide spheres impacting a thick soda–lime glass anvil, for impact angles from normal to very near glancing incidence. Speed, angle and rotation before and after impact have been measured with a strobe and single-frame digital camera. Reproducibility and precision are considerably better than in any previously published work, and have been achieved by careful attention to all aspects of the experiment, including the mechanical and optical systems, illumination, electronic control, computer-based image measurement, and the geometry and condition of the impacting surfaces. All aspects of the rebound dynamics of the elastic spheres, including the motion of the centre of mass and of the contact patch, the spin and the partition of energy, are fully described by the measured variation of the normal and tangential restitution coefficients over the range of impact angles. These measurements show very close agreement with the numerical work of Maw et al. which takes into account the effects of sticking, microslip and tangential compliance. For impacts with a greater obliqueness than about 30° from the normal, the results also agree closely with the classical theory of rigid body sliding.

Impact and compression tests have been carried out on soda-lime glass spheres in the diameter range of 0.4-12.7 mm. The paper describes the forms of failure and their variation with diameter and with impact velocity. At the lowest velocities, fractures are mainly due to a brittle-elastic response, with typical Hertzian ring and cone crack systems. At higher velocities or loads, inelastic deformation (densification, flow, or intense local fracturing and crushing) under the impact site leads to characteristic patterns of fragmentation arising from radial, lateral and median cracks.

Accurate measurements have been made of the rebound behaviour of 5 mm aluminium oxide spheres impacting a thick soda–lime glass anvil (fully elastic response) and an aluminium alloy anvil (involving some plastic deformation). Speed, angle and rotation before and after impact have been measured with a strobe and single-frame digital camera, for a range of impact angles from normal to very near glancing. High levels of reproducibility and precision have been achieved by careful attention to all aspects of the measurement, including the mechanical and optical systems, illumination, electronic control, and computer-based image measurement. Rebound parameters from the elastic and plastic impacts are analysed and compared in the context of the numerical work of Maw et al. for near-normal angles when sticking, micro-slip and tangential compliance are the major factors, and of rigid body sliding for more oblique angles.

The aim of this work is to provide useful quantitative support for theories of the restitution coefficient for normal impacts involving plastic: deformation, especially in the region close to the threshold at which plastic deformation begins. The impacts were from spheres of 5 mm diameter of aluminium oxide (which deformed elastically), dropped on to thick plates of mild steel or aluminium alloy. Very accurate measurements of impact and rebound velocities were made for drop heights from 1.75m down to 0.6mm, covering a range of velocities down to the yield threshold. Most of these results are in the elastic-plastic velocity range over which the indentation pressure varies from its value at initial yield of about 1.1 sigma(gamma), to the value when full plasticity is established of about 2.8(sigma gamma). The variation in the restitution coefficient with velocity in this range closely fits the rebound model of Tabor, which allows the indentation pressure to vary through the Meyer index II. The fitted values of n take into account these elastic-plastic effects as well as work hardening, demonstrating that a power-law compliance relationship is a very good model for the increase in indentation pressure as plasticity develops. Full plasticity only becomes established at impact velocities which are of the order of 100 times the velocity at which initial yield takes place. Models which assume a constant indentation pressure (perfect plasticity) are not a good match for the data in the elastic-plastic regime.

The aim of this paper is to describe an experimental facility to measure the low velocity impact behaviour of spherical particles with high accuracy. Measurements have been made of particle rotation, normal restitution coefficient to within of glancing incidence, and tangential restitution coefficient to within of normal impact, with very low scatter. The results are accurate enough to be used for quantitative comparison to theoretical studies. Achievement of a high level of precision and reproducibility has involved detailed attention to all aspects of the experiment design, construction, control and computer-based image measurement.

Blunt indentation experiments at high loads have been carried out on soda-lime glass plates using detailed in situ observation. The development of failure over a range of loads is described, showing a number of material removal mechanisms that arise from the propagation of primary and secondary cone cracks. Various inelastic deformation processes are also involved in the development of failure under these conditions. The observed mechanisms of material removal imply a velocity exponent in erosion tests that is rather higher than that seen when lateral cracks are the dominant cause of material loss.

The dispersion of longitudinal stress waves as they propagate in pressure bars distorts the shape of the pulse, and so can be a limitation to the accuracy of high strain rate tests such as the compressive split Hopkinson pressure bar (SHPB). The method of dispersion correction described in this paper is based on a bar phase characteristic which is derived entirely from measured stress pulses generated by the elastic impact of small spheres. This method does nor depend on any theoretical model of wave propagation, and automatically includes all distortions that could arise in mechanical or electronic aspects of the test. It is quick and convenient enough to be used on a routine basis to improve the accuracy of SHPB tests.

Soda-lime glass spheres in the diameter range of 4.7 mm to 12.7 mm have been impacted against ceramic anvils at velocities up to 100 ms(-1). The range of failure patterns found is described and analysed in the context of static indentation experiments on glass. At lower velocities, fractures are mainly due to a brittle-elastic response, with typical Hertzian ring and cone crack systems. At higher velocities, inelastic deformation (densification, flow, or intense local fracturing and crushing) under the impact site leads to the formation of radial, lateral and median cracks which then dominate the fragmentation process.

Abstracts are not published in this journal

The compressive split Hopkinson pressure bar (SHPB) technique allows the stresses on each end of the specimen to be measured individually. Results are presented showing a large difference between these end pressures, depending on specimen length and loading rate. The mechanisms responsible are shown to be a combination of inertial forces and non-uniform deformation due to wave propagation. Implications for the SHPB test are discussed.

The dispersion of stress waves in pressure bars distorts a propagating stress pulse, and hence limits the accuracy with which dynamic stress can be measured. This dispersion is caused by a frequency dependence of phase velocity, and previous methods of dispersion correction have adjusted the phase shift of dispersed frequency components using a theoretical bar characteristic. However, the effectiveness of these schemes with more than a small amount of dispersive distortion is very limited. A new method of dispersion correction described in this paper is based on a bar phase characteristic which is derived from measured stress pulses arising from the impact of very small spheres. Examples are given of reconstructing impact stress from a range of particle sizes, showing that the method is very effective even with large amounts of dispersive distortion.

Systematic data is presented on the failure probability of 5.15 mm aluminium oxide spheres over a wide range of impact speed and angle. The high number of tests made, with 100 particles individually tested per data point, was necessary to average out the variations in individual particle properties and to make the results consistent. This has enabled very close curve fits to be made to the data, and the parameters from these fits provide a comprehensive and reliable summary of the material performance. The results show that the probability of particle failure varies only slightly from normal impact to about 50°. Detailed examination of damaged particles has identified four primary forms of fracture which are common to normal impact and static compression. These fractures initiate from a subsurface cone of compression damage, and develop along meridian planes. An additional form of fracture found with oblique impact appears to be a result of tangential loading causing enhanced tension in the surface.