The response of dry and water saturated sand slugs impacting normally oriented and inclined rigid-stationary targets with four different surface coatings is measured with an emphasis on the quantification of the momentum transmitted from the slugs into the targets. The targets were coated with Alumina, PTFE, Aluminium or sandpaper layers in order to investigate the effect of varying surface hardness and surface roughness. In all the cases, the fraction of the slug momentum transferred into the target was equal for dry and water saturated sand slugs and also independent of the slug velocity over the range that is investigated here. For normal impacts, the surface coatings had no measurable influence on the momentum transfer into the targets and this was attributed to the symmetry of the impact event. However, the break of symmetry in the inclined impact cases resulted in two non-zero components of the net transmitted momentum into the targets and a strong influence of the surface coatings. This is attributed to friction between the sand particles and the target surface with the resultant transmitted momentum increasing in the order Alumina to PTFE to Aluminium to sandpaper surface coatings. In all cases, the transmitted momentum was less than the corresponding value under normal impact. Coupled discrete particle/ Lagrangian simulations of these experiments with the sand particles modelled as spheres captured the normal impact measurements with a high degree of fidelity. However, the simulations underestimated the transmitted momentum for the inclined impacts especially for the rough surface coatings such as the sandpaper: increasing the friction coefficient between the particles and the target in the simulations did not improve the predictions. We demonstrate that this discrepancy is due to the spherical particle assumption: in the experiments the sand particles are sub-spherical and this reduces the tendency of particles to roll on the target surface and thereby increases frictional interactions. Increasing the radius of gyration of particles decreased the discrepancy between the measurements and the predictions but yet could not accurately predict all components of the transmitted momentum. Most numerical calculations tend to use spherical particles to represent the impacting granular media. However, this study demonstrates the need to appropriately parameterise particle shape in such discrete particle calculations to accurately capture the granular media/ structure interactions.

No abstract

The effect of grain shape and fracture on the interaction of high velocity granular slugs with rigid stationary targets is analysed for targets in normal and inclined orientations. The granular slugs comprise spherical, rod-shaped or cubic grains and are constructed by connecting together spherical sub-particles with either rigid or beam connectors. The case when grain fracture is suppressed (rigid connectors between sub-particles) is first analysed. With increasing grain aspect ratio, the grains tend to slide rather than roll on the target surface and this increases frictional interactions with the target surface. However, these enhanced frictional forces do not affect the momentum transmitted into normally oriented targets due to the symmetry of the problem. By contrast, the break in the symmetry for inclined targets results in the transmitted momentum increasing with grain aspect ratio. Fracture of the grains (as modelled by the fracture of the beam connectors between sub-particles) is shown to affect the momentum transmitted into the inclined targets. This is a consequence of fracture resulting in a change in grain shape. In this case the simulations show that the transmitted momentum is a function of the initial grain shape, the fracture properties of the grains and the impact velocity. In fact, grain fracture results in an enhanced transmitted momentum for initially cubic grains but fracture of grains with a high initial aspect ratio results in a reduction in transmitted momentum as these grains fragment into more spherically shaped grains.

The response of idealised cermets comprising approximately 60% by volume steel spheres in a Sn/Pb solder matrix is investigated under a range of axisymmetric compressive stress states. Digital volume correlation (DVC) analysis of X-ray microcomputed tomography scans (μ-CT), and the measured macroscopic stress-strain curves of the specimens revealed two deformation mechanisms. At low triaxialities the deformation is granular in nature, with dilation occurring within shear bands. Under higher imposed hydrostatic pressures, the deformation mechanism transitions to a more homogeneous incompressible mode. However, DVC analyses revealed that under all triaxialities there are regions with local dilatory and compaction responses, with the magnitude of dilation and the number of zones wherein dilation occurs decreasing with increasing triaxiality. Two numerical models are presented in order to clarify these mechanisms: (i) a periodic unit cell model comprising nearly rigid spherical particles in a porous metal matrix and (ii) a discrete element model comprising a large random aggregate of spheres connected by non-linear normal and tangential "springs". The periodic unit cell model captured the measured stress-strain response with reasonable accuracy but under-predicted the observed dilation at the lower triaxialities, because the kinematic constraints imposed by the skeleton of rigid particles were not accurately accounted for in this model. By contrast, the discrete element model captured the kinematics and predicted both the overall levels of dilation and the simultaneous presence of both local compaction and dilatory regions with the specimens. However, the levels of dilation in this model are dependent on the assumed contact law between the spheres. Moreover, since the matrix is not explicitly included in the analysis, this model cannot be used to predict the stress-strain responses. These analyses have revealed that the complete constitutive response of cermets depends both on the kinematic constraints imposed by the particle aggregate skeleton, and the constraints imposed by the metal matrix filling the interstitial spaces in that skeleton.

No abstract