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TECHNICAL PAPERS

On the Crush Worthiness of a Laterally Confined Bar Under Axial Compression

[+] Author and Article Information
Herzl Chai

Department of Solid Mechanics, Materials and Systems, Faculty of Engineering,  Tel-Aviv University, Tel Aviv 69978, Israel

The deformation of a bilaterally constrained column in the elastic range was studied in (18). It was found that the deformation is characterized by a sequential mode transition process that results from secondary buckling. The latter initiates at contact zones formed between the column and the confining walls. This process was found to be inherently asymmetric, which leads to significant scatter in the buckling mode transition loads. An extension of this study to laterally constrained plates (21-22) shows that once a number of buckles are initiated, the buckling pattern in this case tends to approach the 1-D configuration.

J. Appl. Mech 73(5), 834-841 (Mar 15, 2005) (8 pages) doi:10.1115/1.2047595 History: Received January 18, 2005; Revised March 15, 2005

Abstract

A combined experimental∕analytical work is carried out to elucidate the energy absorption potential of laterally confined bars under monotonically increasing edge displacement. The thickness $t$ and length $L$ of the bar, as well as the wall-to-wall separation distance, $h$, are systematically varied. Real-time observations show that the deformation of the bar is characterized by progressive buckling and folding, with the fully compacted material exhibiting repetitious cell unit whose wavelength approximately equals four times the bar thickness. The specific crush energy is little sensitive to the thickness of the bar but strongly varies with $t∕h$, the “volume fraction” of the structure, attaining a maximum when $t∕h≈0.5$. The main sources for energy dissipation are simple compression, plate folding and friction between the bar and the constraining walls, the latter of which dominates for $L∕t>10$. The experimental data are found to be well predicted by simple analytic expressions derived from limit plasticity analysis and incompressible material behavior. The simple configuration studied may shed light on the behavior of more complex structures such as honeycombs, foams, and thin-walled tubes, and may serve as a basis for multi-layer design possessing improved crush energy.

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Figures

Figure 1

Schematics of the test fixture and test specimen for a bar confined on all four sides and subject to axial compression

Figure 2

Video motion pictures showing the deformation of two different laterally confined PVC bars

Figure 3

Nominal stress vs. nominal strain for three different volume fractions, t=4mm, L∕t=20

Figure 4

Figure 5

Normalized cell length vs. volume fraction for a fixed value of L∕t(=26); symbols are test results, dashed line is a possible fit

Figure 6

The average number of folds in a unit cell vs. volume fraction, L∕t=26; symbols denote test results, dashed line is a possible fit

Figure 7

The specific energy delivered to the bar (i.e., energy per unit confinement volume, bhL) vs. volume fraction for three bar thicknesses, L∕t=26; the symbols and the curve denote test results and analytic prediction, respectively

Figure 8

Densification strain (i.e., end displacement at full stroke divided by the length of the bar) vs. volume fraction. The symbols correspond to the test data of Fig. 7, the solid line is analytic prediction derived based on material incompressibility.

Figure 9

Specific energy vs. normalized bar length for two different bar thicknesses such that h∕t=1.5; the symbols and the curve denote test results and analytical prediction, respectively

Figure 10

Deformation sequence used in the analytic model. Illustration is specified to n=3, where n is the total number of cells in the bar.

Figure 11

Illustration of the various modes of energy absorption used in the analytic model: (a) compression, (b) shearing, (c) bending, and (d) friction. The dark spots in (c) indicate the locations of folds while those in illustration (II) of print (d) indicate the assumed contact regions between the bar and the transverse walls.

Figure 12

Normalized specific energy vs. volume fraction for the four energy absorption models considered; dotted lines indicate a regions outside the nominally applicable range for each model. The frictional model is specified to L∕t=26 and μ=0.3.

Figure 13

Normalized mean stress vs. volume fraction for various cellular structures. The data for the circular and square tubes are constructed from results given in (23) and (7), respectively, while those for the honeycomb and foams are produced based on relations given in (1). The inserts for the square tube, the circular tube, and the honeycomb structure are taken from (7,3,16), in that order.

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