On the nature of dynamic cavity collapse using x-ray phase contrast imaging

The presence of cavities in materials under dynamic load significantly affects the way in which energy is distributed, by causing localised extrema of pressure and temperature when they collapse. There is interest in ‘cavity collapse’, as the phenomena has come to be known, from a wide range of fields, with the intention of either mitigating or harnessing the extraordinary conditions created. Most notably, there are applications in the medical sciences, in the development of energetic materials, and from research into nuclear fusion. A key aspect of understanding the phenomenon is to observe it directly, which allows comparison to numerical simulations of the process. This has been successfully achieved for cavities in fluids through established high-speed optical imaging techniques. However, capturing cavity collapse in solid media has remained elusive, due to the difficulties that even transparent solids pose in using visible light illumination. In this work cavities in the solid polymer poly[methyl methacrylate] (PMMA) – collapsed under shock loading – are captured with high-speed synchrotron X-ray imaging. The brilliant and hard X-rays delivered by beamline ID19’s undulator source, combined with the beam’s high level of spatial coherence, result in phase contrast enhanced radiographs that reveal details of the col- lapse process in new and exquisite detail. For this purpose, two separate gas gun systems are transported to the European Synchrotron Radiation Facility (ESRF), over multiple experimental campaigns, generating a wide range of pressure states. To image the experiments, a custom-made, multi-camera indirect X-ray imaging system is developed, capable of capturing 100 ps time resolved frames from individual X-ray pulses for 10s of μs at frame rates up to 5.68 Mfps.
The radiographic results show the impacted cavities exhibiting a wide range of behaviours as the shock loading pressure is increased. Strength-dominated col- lapse is observed at the lower pressures, with features like cracking and fragmentation cause by damage, and perturbations that form along the cavity interface, which indicate the presence of shear banding. The spacing between the bands is shown to decrease as the shock pressure increases, which indicates the in- creased proportion of melt within the PMMA medium. Above a threshold shock pressure, bulk melting is mostly complete and hydrodynamic modes of cavity collapse are seen, with jet formation, and, at the very highest pressures, the formation of a hot plasma inside toroidal vortices. A head-to-head comparison is performed between the experimental results and 2D/3D simulations run in the code SCIMITAR3D, with broad and close agreement with the experiments. This gives confidence in details from the simulations not available from the experiments, such as the local evolution of density, pressure, and most notably temperature during collapse. In the strength regime a network of high-temperature shear bands form, emanating from perturbations along the cavity interface, as are seen in the experimental radiographs. A re-shock generated by the collapse further heats the region, resulting in large temperature rises. At the highest shock pressures there is heating from the shock, followed by further heating during col- lapse and the mixing of material in toroidal vortices, resulting in a highly intense hot spot. Analysis of the collapse time vs. loading pressure, with additional simulations on aluminium, copper and stainless steel, reveal what appears to be a general scaling law for collapse time based solely on loading pressure, geometry and material stiffness.
This work represents a significant experimental advancement in research into cavity collapse, providing new insight into the transition between strength and hydrodynamic states during intense shock loading. As well as being relevant to the fields interested in the specific phenomenon, the results are relevant to areas beyond, such as shear banding, damage and crack formation, and jet instability formation. The results also showcase the capabilities of the high-speed imaging system used in the experiments, and the quality of radiographic imaging that can be obtained through synchrotron radiography, as well as the techniques necessary to analyse the results. This work lays the foundation for future work into cavity collapse, with many avenues left to explore, such as multiple interacting cavities collapsing in a solid, and further investigation into the precise role that strength plays in the collapse dynamics.

Keywords: adiabatic shear bands
two-stage gas gun
x-ray phase contrast imaging
cavity collapse
shockwaves
synchrotron radiation
MHz imaging
PMMA
hydrodynamic modelling