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Impulse Loading of 3D Prismatic Cellular Structures

Holloman, Ryan
Thesis/Dissertation; Online
Holloman, Ryan
Wadley, Haydn
A novel light metal cellular structure has been designed and fabricated from assemblies of square cross section tubes oriented in a cross-ply 2D and orthogonal 3D arrangements tailored to support different combinations of through thickness and in-plane loads. A simple dip brazing approach is used to fabricate these structures from extruded 6061-T6 aluminum alloy tubes. By varying the tube wall thickness, the resulting 3D cellular structures had relative densities between 11 and 43%. Using a combination of experimental testing and finite element simulation of the through thickness compression, it was found that the 3D orthogonal structures have an approximately linear dependence of modulus upon relative density. However their strength had a power law dependence upon density with an exponent of approximately 5/3. These cellular structures exhibit almost ideal plastic energy absorption at pressures that could be selected by adjustment of the vertical and in-plane tube wall thicknesses. The dynamic compressive response of the 3D cellular structure, and the 2D [0º/90º]2 array and out-of-plane tubes from which they were constructed, have also been investigated using a combination of instrumented Hopkinson bar impact experiments, high speed video imaging and finite element analysis. It was found that the collapse strength was independent of compression rate for compression strain rates up to 2000 s-1, despite a transition to higher order buckling modes at high strain rates. The study identifies a synergistic interaction between the co-linear aligned and out-of-plane tubes, observed during quasi-static loading, extends into the dynamic regime. Finite element simulations, using a rate dependent, piecewise linear strain hardening model with a von Mises yield surface and an equivalent plastic strain failure criterion, successfully predicted the compressive stress- displacement relations and the buckling response of the structures, and confirmed the absence of strain rate hardening in the 3D cellular structure. The simulations also reveal that the ratio of impact to back face stress increased with compression strain rate and with sample relative density; a result with potentially significant implications for shock load mitigation applications of these structures. To investigate a shock loading application of the structure, a vertical pendulum apparatus has been developed and used to experimentally investigate the structures utility for impulse mitigation during explosive loading by wet sand. The test facility was used to measure the impulse and pressure applied by the impact of synthetic wet sand with an incident velocity of ~300 m/s to the flat surface of a back supported 3D cellular structure with thick (relatively rigid) and thin impact face sheets and was compared to that transferred by an incompressible solid aluminum test block of similar dimensions. By varying the distance between the sand layer and the impact face of the solid block, the transferred impulse and maximum pressure applied to the samples were both found to decrease with standoff distance. A particle based simulation method has been used to model the sand impact with the test structure and was able to successfully predict both the impulse and pressure transferred during the tests. The simulated results agreed well with experimental data, and both showed that the impulse transferred to a solid test structure was approximately the same as that of the sand that intercepted the sample front face, consistent with sand stagnation against its planar surface. The results are consistent with no strong sand reflection back towards the source. Experiments and simulations of the 3D cellular structures revealed that 10-15% less impulse was transferred to the cellular structures than was transferred to a solid block of similar dimensions. Analysis of experimentally validated simulations indicated that the decrease in transferred impulse with increasing standoff distance arises because of a small reduction in sand particle velocity (resulting from momentum transfer from sand to air particles) and an increase in lateral spreading of the sand particles as the standoff distance increased. This spreading resulted in a smaller fraction of the sand particles intercepting and impacting the finite area of the reference block impact face. Simulations of the sand interaction with the cellular structures revealed that a substantial part of the 10-15% impulse reduction for the 3D cellular structure was a result of a subtle interaction of the compressible sample and the aperture opening in the sand box lid within which the sand was accelerated. In solid samples, the sand stagnated against the bottom face of the sample and escaped though a gap between the sample bottom and the top of the sand box lid. This gap varied during the loading event because of elastic compression of the Hopkinson bars to which specimens were attached and flexure of the sand box lid due to sand impact on its underside. This gap remained small for the solid block and for cellular structures loaded to pressures less than their compressive strength. However, when the cellular structures were loaded above their crush strength, the rapid motion of the front face during core crushing opened the gap and relived the sand pressure applied to the sample front face. This effect was enhanced for thin front face sheet samples by deflection of the front face at the sides of the sample. This created a convex shaped sand impact surface and the subsequent sand particle impacts did not fully transfer their vertical momentum to the structure. To further investigate the sand structure interaction additional simulations were conducted with the (now well validated) simulation code in which the top lid of the sandbox was removed and the impact face sheet made rigid. As the core strength was reduced (by reducing the yield strength of the material used to make the core) the plastic collapse of the core was shown to lead to a ~5% reduction in transferred impulse compared to a solid (incompressible) structure and the loading rate (acceleration) also was significantly reduced. These results support recent calculations of sand particle impact by other groups and confirm that the sand-structure interaction for sand impacts in the ~300 m/s range is small.
University of Virginia, Department of Materials Science and Engineering, PHD, 2014
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