The effect of inclination and stand-off on the dynamic response of beams impacted by slugs of a granular material

The dynamic response of end-clamped sandwich and monolithic beams to impact by highvelocity tungsten carbide (WC) particle columns (slugs) has been measured with the aim of developing an understanding of the interaction of ejecta from a shallow-buried explosion with structures. The monolithic beams were made from stainless steel, while the sandwich beams of equal areal mass comprised stainless steel face sheets and an aluminium honeycomb core. High-speed imaging was used to measure the transient transverse deflection of the beams, to record the dynamic modes of deformation, and to observe the flow of the WC particles upon impact. The experiments show that sandwich beams deflect less than the monolithic beams both in normal and inclined impact situations. Moreover, the deflections of all beams in the inclined orientation were less than their respective deflections in the normal orientation at the same slug velocity. Intriguingly, the ratio of the deflection of the sandwich to monolithic beams remains approximately constant with increasing slug velocity for inclined impact but increases for normal impact; i.e. inclined sandwich beams retain their advantage over monolithic beams with increasing slug velocity. Dynamic force measurements reveal that (i) the momentum transferred from the impacting slug to both monolithic and sandwich beams is the same, and (ii) the interaction between the impacting particles and the dynamic deformation of the inclined monolithic and sandwich beams results in a momentum transfer into these beams that is equal to or greater than the momentum of the slug. These experimental findings demonstrate that contrary to intuition and widespread belief, the performance enhancement obtained from employing beam inclination is not due to a reduction in transferred momentum. Finally, we show that increasing the stand-off distance decreases beam deflections. This is because the slugs lengthen as they traverse towards their target and thus the duration of loading is extended with increasing stand-off. However, combining increased stand-off with sandwich construction does not yield the synergistic benefits of sandwich construction combined with beam inclination.The work was supported by the Office of Naval Research Grant N00014-09-1-0573 (Program manager, Dr. David Shifler) and the Defense Advanced Projects Agency under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser).This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0020768314004466

Momentum transfer during the impact of granular matter with inclined sliding surfaces

© 2017 Elsevier Ltd Increasing the inclination of a rigid surface that is impacted by a collimated granular flow reduces the fraction of granular matter momentum transferred to the surface. Recent studies have shown that the momentum reduction depends upon a frictional interaction between the granular flow and the impacted surface. High coefficient of friction surfaces suffer significantly more momentum transfer than predicted by resolution of the incident momentum onto the inclined plane. This discovery has raised the possibility that inclined surfaces with very low friction coefficients might reduce the impulsive transferred by the impact of high velocity granular matter. Here the use of a lubricated sliding plate is investigated as a means for reducing interfacial friction and impulse transfer to an inclined surface. The study uses a combination of experimental testing and particle-based simulations to investigate impulse transfer to rigid aluminum surfaces inclined either perpendicular or at 53° to synthetic sand that was impulsively accelerated to a velocity of 350–500 m/s. The study shows that impact of this sand with lubricated plates attached to an inclined surface rapidly accelerates them to a velocity of about 55–70 m/s, and reduces the impulse transferred to the inclined surface below. The reduction of impulse by this approach is comparable to that achieved by changing the inclination of the surface.This research was funded by the Defense Advanced Research Projects Agency (DARPA) under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser)

Deep penetration of ultra-high molecular weight polyethylene composites by a sharp-tipped punch

The penetration of unidirectional (UD) and [0#/90#] cross-ply ultra-high molecular weight polyethylene fibre composites by sharp-tipped cylindrical punches has been investigated. While the measured penetration pressure for both composite types increased with decreasing punch diameter, the pressure was significantly higher for the cross-ply composites and increased with decreasing ply thickness. A combination of optical microscopy and X-ray tomography revealed that in both composites, the sharp-tipped punch penetrated without fibre fracture by the formation of mode-I cracks along the fibre directions, followed by the wedging open of the crack by the advancing punch. In the cross-ply composites, delamination between adjacent 0# and 90# plies also occurred to accommodate the incompatible deformation between plies containing orthogonal mode-I cracks. Micromechanical models for the steadystate penetration pressure were developed for both composites. To account for material anisotropy as well as the large shear strains and fibre rotations, the deformation of the composites was modelled via a pressure-dependent crystal plasticity framework. Intra and inter-ply fracture were accounted for via mode-I and delamination toughnesses respectively. These models account for the competition between deformation and fracture of the plies and accurately predict the measured steady-state penetration pressures over the wide range of punch diameters and ply thicknesses investigated here. Design maps for the penetration resistance of cross-ply composites were constructed using these models and subsequently used to infer composite designs that maximise the penetration resistance for a user prescribed value of fibre strength.DARP

Coupled discrete/continuum simulations of the impact of granular slugs with clamped beams: stand-off effects

Coupled discrete particle/continuum simulations of the normal (zero obliquity) impact of granular slugs against the centre of deformable, end-clamped beams are reported. The simulations analyse the experiments of Uth et al. (2015) enabling a detailed interpretation of their observations of temporal evolution of granular slug and a strong stand-off distance dependence of the structural response. The high velocity granular slugs were generated by the pushing action of a piston and develop a spatial velocity gradient due to elastic energy stored during the loading phase by the piston. The velocity gradient within the “stretching” slug is a strong function of the inter-particle contact stiffness and the time the piston takes to ramp up to its final velocity. Other inter-particle contact properties such as damping and friction are shown to have negligible effect on the evolution of the granular slug. The velocity gradients result in a slug density that decreases with increasing stand-off distance, and therefore the pressure imposed by the slug on the beams is reduced with increasing stand-off. This results in the stand-off dependence of the beam's deflection observed by Uth et al. (2015). The coupled simulations capture both the permanent deflections of the beams and their dynamic deformation modes with a high degree of fidelity. These simulations shed new light on the stand-off effect observed during the loading of structures by shallow-buried explosions

Effect of surface properties on momentum transfer to targets impacted by high-velocity sand slugs

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 show the show momentum transmitted from the slugs into the targets. The targets were coated with Alumina, PTFE, show Aluminium or sand-paper layers in order to investigate the effect of varying surface hardness and show surface show roughness. In all the cases, the fraction of the slug momentum transferred into the target was show equal show for dry and water saturated sand slugs and also independent of the slug velocity over the range 73ms−1−137ms−1that 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 sand-paper 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 sand-paper: 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.The work was supported by the Office of Naval Research Grant N00014-09-1-0573 (Program manager, Dr. David Shifler) and the Defense Advanced Projects Agency under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser)

Surface instabilities in shock loaded granular media

© 2017 Elsevier Ltd The initiation and growth of instabilities in granular materials loaded by air shock waves are investigated via shock-tube experiments and numerical calculations. Three types of granular media, dry sand, water-saturated sand and a granular solid comprising PTFE spheres were experimentally investigated by air shock loading slugs of these materials in a transparent shock tube. Under all shock pressures considered here, the free-standing dry sand slugs remained stable while the shock loaded surface of the water-saturated sand slug became unstable resulting in mixing of the shocked air and the granular material. By contrast, the PTFE slugs were stable at low pressures but displayed instabilities similar to the water-saturated sand slugs at higher shock pressures. The distal surfaces of the slugs remained stable under all conditions considered here. Eulerian fluid/solid interaction calculations, with the granular material modelled as a Drucker–Prager solid, reproduced the onset of the instabilities as seen in the experiments to a high level of accuracy. These calculations showed that the shock pressures to initiate instabilities increased with increasing material friction and decreasing yield strain. Moreover, the high Atwood number for this problem implied that fluid/solid interaction effects were small, and the initiation of the instability is adequately captured by directly applying a pressure on the slug surface. Lagrangian calculations with the directly applied pressures demonstrated that the instability was caused by spatial pressure gradients created by initial surface perturbations. Surface instabilities are also shown to exist in shock loaded rear-supported granular slugs: these experiments and calculations are used to infer the velocity that free-standing slugs need to acquire to initiate instabilities on their front surfaces. The results presented here, while in an idealised one-dimensional setting, provide physical understanding of the conditions required to initiate instabilities in a range of situations involving the explosive dispersion of particles.he work was supported by the Defense Advanced Projects Agency under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser)

Compressive response of a 3D non-woven carbon-fibre composite

The compressive response of a three-dimensional (3D) non-interlaced composite comprising three orthogonal sets of carbon fibre tows within an epoxy matrix is analysed. First, the compressive response is measured in three orthogonal directions and the deformation/failure modes analysed by a combination of X-ray tomography and optical microscopy. In contrast to traditional unidirectional and two-dimensional (2D) composites, stable and multiple kinks (some of which zig-zag) form in the tows that are aligned with the compression direction. This results in an overall composite compressive ductility of about 10% for compression in the low fibre volume fraction direction. While the stress for the formation of the first kink is well predicted by a usual micro-buckling analysis, the composite displays a subsequent hardening response associated with formation of multiple kinks. Finite element (FE) calculations are also reported to analyse the compressive response with the individual tows modelled as anisotropic continua via a Hill plasticity model. The FE calculations are in good agreement with the measurements including prediction of multiple kinks that reflect from the surfaces of the tows. The FE calculations demonstrate that the three-dimensionality of the microstructure constrains the kinks and this results in the stable compressive response. In fact, the hardening and peak strength of these composites is not set by the tows in direction of compression, but rather set by the out-of-plane compressive response of the tows perpendicular to the compression direction