Full length articleExperimental and numerical investigation on bending collapse of embedded multi-cell tubes
Introduction
In the past two decades, different approaches are employed to improve the crashworthiness performance of thin-walled energy absorbers, including adopting metallic foam fillers [1], [2], [3], [4], [5], multi-cell sections [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] and most recently variable wall thickness [23], [24], [25], [26], [27], [28]. Among these methods, adopting multi-cell tubes is the most promising one and has received enormous attention in the research community. The energy absorption capacity of them in various load cases was investigated, and in almost all cases the efficiency (SEA, specific energy absorption) of multi-cell tubes is very much higher than that of single cell tubes. The axial crush resistance of multi-cell tubes [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [18] attracted the most attention. In axial crushing, the SEA value of multi-cells was demonstrated [10] to be greatly (up to several times) higher than that of single cells. Theoretical models [6], [10], [14] were established to analyze the energy absorption mechanisms of the constituent elements and to predict the mean crushing force and energy absorption of multi-cell tubes. Comparatively speaking, the studies on multi-cells subjected to transverse [19], [20] or oblique loads [21], [22] are quite few and generally concentrate on numerical analysis. The reason for this is that theoretical analysis for bending or oblique collapse is much more complicated than that for axial crushing, while the experimental study is hampered by the inconvenient fabrication of multi-cell tubes.
In fact, multi-cell tubes with various sectional shapes can be produced by extrusion process. However, it is only suitable for large-scale manufacture. Specialized equipment is required for the production and any change in shape or dimension of the cross-section requires the production of a new mold. This leads to poor flexibility and low cost-effectiveness. To overcome this drawback, a novel type of embedded multi-cell (EMC) tube, which is highly cost-effective and easily available, was proposed recently by Zhang et al. [29]. The EMC tubes are constituted by a group of single tubes confined within a larger thin-walled envelope. On the basis of experimental tests and numerical investigations, the axial crush resistance of EMC tubes was analyzed by them [29], and the interaction effect between the inside and outside tube was reported to account for about 40% of total crush resistance of the whole structure.
In this paper, bending collapse responses of EMC tubes under three-point bending loads are investigated. Quasi-static loading tests of empty and EMC tubes are carried out first, and numerical analysis is then performed to simulate the experiment. The energy absorption characteristics of EMC tubes with various configurations are analyzed, and the energy absorption efficiency of EMC tubes is compared with that of traditional single cell and multi-cell tubes. The relative merits of EMC tubes are analyzed, and some conclusions are drawn for such structures subjected to transverse loading.
Section snippets
Specimen preparation
Aluminum alloy 6063O square tubes with different dimensions are employed to prepare the EMC specimens. Square tubes with the outer width C = 32 mm and the thickness t = 0.95 mm are served as outside envelopes, and two square tubes with C = 10 and 15 mm are used as the inside embedded tubes. The thickness of all the inside tubes is 1 mm. The specimens are shown in Fig. 1(a) and the cross-sectional shape is plotted in Fig. 1(b). Apparently, four cells of C10t1 and nine cells of C15t1 can be
Experimental setup
The quasi-static experimental setup for the three-point bending test is shown in Fig. 2(a) and the geometry of the test is plotted in Fig. 2(b). The head of the punch and the supports are cylindrical with a diameter of 24 mm. Two supports are spaced S = 180 mm apart. The punch velocity V is set to 1 mm/s during the loading process.
The properties of structural material AA6063 O have been obtained by Zhang et al. [29] by tensile tests based on the standard test methods in ASTM E8M-04. The tests
Finite element modeling
The explicit dynamic nonlinear finite element code LS-DYNA is employed to simulate the bending collapse of empty and EMC tubes numerically. All the specimens tested are simulated in the analysis, and a representative model is shown in Fig. 3. Belytschko-Tsay 4-node thin shell elements are used to model the wall of the tubes, the punch, and the cylindrical supports. The tube material AA6063 O is modeled by *MAT_024 piecewise linear plasticity model [30] with the hardening data given in Table 1.
Experimental and numerical results
The bending collapse of empty and EMC tubes is analyzed in this section concerning the deformation patterns and punch force responses. The influence of friction on the responses of EMC tubes is investigated by both experiment and numerical simulation. Furthermore, the performance of EMC tubes is compared with that of traditional empty and multi-cell tubes, and the relative merits of EMC tubes are demonstrated.
Dynamic loading
Beams are always subject to dynamic loads under impact events. The responses of beams under dynamic loading are different from those under quasi-static loading. The dynamic responses of EMC and TMC tubes are analyzed in this section. The dimensions of the tubes with 2 × 2 and 3 × 3 cells are the same as those in Section 5.4. Two velocities: 10 m/s and 20 m/s are employed, and the dynamic force response curves are shown in Fig. 20. It is noted that the major difference between dynamic and
Conclusion
The bending collapse of EMC tubes with various configurations is studied in the present work. Three-point bending tests are performed to investigate the influences of friction condition, end treatment and partially filling. Numerical simulations are also carried out to analyze the performance of EMC and TMC tubes under quasi-static and dynamic loads. The major results are summarized as follows:
- 1.
The bending resistance of EMC tubes is about 95–130% higher than the simple summation of the
Acknowledgements
The present work was supported by National Natural Science Foundation of China (Nos. 11672117, 11502177, 11372115).
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