The Symmpact: A Direct-Impact Hopkinson Bar Setup Suitable for Investigating Dynamic Equilibrium in Low-Impedance Materials

Background Measuring the dynamic behavior of low-impedance materials such as foams is challenging. Their low acoustic impedance means that sensitive force measurement is required. The porous structure of foams also gives rise to dynamic compaction waves, which can result in unusual behavior, in particular if the foam material is so thick, that dynamic force equilibrium is not reached. Objective This work investigates comparatively large polyurethane foam specimens with densities in the range of 80 – 240 kg/m3 to deliberately achieve a state away from force equilibrium during high-rate compaction. The aim is to understand how an increase in strain rate leads to a reduction in strength for such materials. Methods A specialized direct-impact Hopkinson bar is employed. It uses polycarbonate bars to achieve the required long pulse duration of 2.6 ms to compress the large specimens into the densification regime. In contrast to existing setups, both striker and output bar are instrumented with strain gauges to monitor force equilibrium. The absence of an input bar allows monitoring force equilibrium more accurately. Special attention is paid to the calibration of strain gauges, taking non-linear effects, wave dispersion and attenuation into account. Digital Image Correlation is employed to analyze elastic and plastic compaction waves by means of Lagrange diagrams. Results Depending on density, the specimens show saturation of dynamic strength increase at high rates of strain $$\approx$$ ≈ 500 /s, or even negative strain rate sensitivity in case of the lowest density. The occurrence of apparent negative strain rate sensitivity is accompanied by a localized structural collapse front, moving at a low velocity of $$\approx$$ ≈ 10 m/s through the material. This apparent strain rate sensitivity is a structural effect which is related to the thickness of the specimen. Conclusions The primary aim of material characterization using Hopkinson bars is to achieve a state of force equilibrium. For this reason, very thin specimens are usually employed. However, data gathered in this way is not representative for thick foam layers. Here, an increase of strain rate can lead to a decrease of strength if homogeneous deformation is replaced by a dynamic compaction wave. This behavior can occur at strain rates encountered under conditions such as automotive crash.

Compaction Wave Propagation in Layered Cellular Materials Under Air-Blast

The propagation of compaction waves in layered cellular material subjected to air-blast is analyzed to examine the mechanism of compaction wave and reveal the phenomena that develop at the interface between the cellular layers. Similar to the previous studies of cellular materials under dynamic loading, the topology of cellular materials is neglected and homogeneous properties are assumed. The rigid-perfectly plastic-locking (R-PP-L) material idealization and the simple shock theory are employed to analyze the compaction situations. Analytical solutions for compaction wave propagation of double-layer cellular materials with two gradient-arrangements under air-blast loading have been worked out. The densification wave occurs at the blast end and then gradually propagates to the distal end for layers’ densities increase in the propagation direction (positive gradient). While compaction waves simultaneously form in both layers and propagate to the distal end in the same direction for the negative gradient. The finite element (FE) models using the Voronoi technique are carried out with practical aluminum foam to verify the predictions of the theoretical analysis. The potential of layered cellular materials to design efficient structural components under air-blast load is discussed, which would outperform their corresponding single counterpart with equal mass.

Multiscale Analysis of Particle Size-dependent Steady Compaction Waves in Granular Energetic Materials

A multiscale model is used to analyze the compaction processes in granular HMX beds composed of different particle sizes (coarse particles, d=40 μm and microfine particles, d=4 μm). The localization strategy of Gonthier is extended to include changes in thermal energy induced by compression. The variation in yield strength caused by solid-liquid phase change is also considered. Analysis of the steady-state wave structure indicates that the compaction behavior of a porous material is dependent on particle size. For solid volume fraction φs < 0.88, the fine particle beds provide greater resistance to compaction than the coarse particle beds, and they propagate compaction waves that travel at faster speeds. When φs > 0.88, the physical state of the compacted bed has become very similar for the two materials. For subsonic compaction waves, the evolution of the grain temperature shows that large particles lead to large hot spots and high temperature and coarse particles are more shock sensitive at low shock pressures. For supersonic compaction waves, compression induced changes in thermal energy play an important role in localization strategy. It increases the localization sphere center radius. The dissipated energy is deposited over a larger localization volume so that the grain temperature near the intergranular contact surface is reduced significantly. The localization center radius further increases because of the decrease in the yield strength caused by solid–liquid phase change. Consequently, the peak grain temperature is reduced further.