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.

Pochhammer–Chree equation solver for dispersion correction of elastic waves in a (split) Hopkinson bar

A robust algorithm for solving the Bancroft version of the Pochhammer–Chree (PC) equation is developed based on the iterative root-finding process. The formulated solver not only obtains the conventional n-series solutions but also derives a new series of solutions, named m-series solutions. The n-series solutions are located on the PC function surface that relatively gradually varies in the vicinity of the roots, whereas the m-series solutions are located between two PC function surfaces with (nearly) positive and negative infinity values. The proposed solver obtains a series of sound speeds at exactly the frequencies necessary for dispersion correction, and the derived solutions are accurate to the ninth decimal place. The solver is capable of solving the PC equation up to n = 20 and m = 20 in the ranges of Poisson’s ratio ( ν) of 0.02 [Formula: see text] ν [Formula: see text] 0.48, normalised frequency ( F) of F [Formula: see text] 30, and normalised sound speed ( C) of C [Formula: see text] 300. The developed algorithm was implemented in MATLAB®, which is available in the Supplemental Material (accessible online).

A numerical study of the impact perforation of sandwich panels with graded hollow sphere cores

In this study, we numerically investigate the impact perforation of sandwich panels made of 0.8 mm 2024-T3 aluminum alloy skin sheets and graded polymeric hollow sphere cores with four different gradient profiles. A suitable numerical model was conducted using the LS-DYNA code, calibrated with an inverse perforation test, instrumented with a Hopkinson bar, and validated using experimental data from the literature. Moreover, the effects of quasi-static loading, landing rates, and boundary conditions on the perforation resistance of the studied graded core sandwich panels were discussed. The simulation results showed that the piercing force–displacement response of the graded core sandwich panels is affected by the core density gradient profiles. Besides, the energy absorption capability can be effectively enhanced by modifying the arrangement of the core layers with unclumping boundary conditions in the graded core sandwich panel, which is rather too hard to achieve with clumping boundary conditions.