- Axial crushing analysis of end-capped circular tubes
（A Ghamarian，MT Abadi .Thin-Walled Structures, 2011, 49(6):743-752）
1.1 Abstract:
The paper investigates collapse mechanisms and energy absorption capacity during the axial compression of the end-capped thin-walled circular aluminum tubes which are hollow or filled with polyurethane foam.An experimental technique is used to evaluate the crushing behavior of the circular tubes under compressive quasi-static strain rate. A numerical model is presented based on finite element analysis to simulate the crushing of circular tubes considering nonlinear response due to material behavior, contact boundary conditions and large deformation. The validated model using existing experimental results is used to evaluate the dynamic response in order to determine the dynamic amplification factor relating the quasi-static results to dynamic response. The experimental and numerical results are used to determine energy absorption capacity due to the plastic deformation of thin-wall tube and crushable foam. The performance of end-capped tubes is compared with non-capped tubes and it is found that maximum initial peak load can be controlled and convenient crash protection systems can be obtained using end-capped circular tubes.
1.2 Introduction:
Thin-walled tubular structures are the most common elements used as crash protection systems which convert kinetic energy into irreversible plastic deformation energy. Such shock absorbers are light with simple geometries and can easily be attached to devices. The compressive axial load causes the initial and progressive buckling of thin-walled tubes. The load variations during the axial crushing determine the deceleration pulse during impact. The geometric parameters and material properties of the shock absorbers should be determined based on the allowable deceleration value as well as the initial kinetic energy of the impacting devices. The level of deceleration pulse is controlled by extending the time period required to dissipate kinetic energy due to the collision of shock absorber [1]. Experimental results [2,3] have shown that three modes of deformation may occur in axial loading of thin-walled circular tubes including axisymmetric concertina, non-axisymmetric diamond and a mixed mode and it depends on the ratios of diameter to thickness and diameter to height. The energy absorption capacity is more in the axisymmetric mode than the diamond mode of deformation. Energy absorption normally takes place by progressive buckling of tubes and the corresponding post-buckling load has an oscillatory nature.
The crushing response of the hollow and foam-filled thinwalled tubes under axial impact loading has received increased attention. Torigopala et al. [4] carried out some experiments to study the axial crushing of thin-walled high-strength sections subjected to the impact of a mass with prescribed velocity. Jensen et al. [5] performed some parametric studies to evaluate the effects of geometry, material properties, boundary conditions, impact velocity and imperfections on the axial crushing of thin-walled extrusion. The crushing behavior of tubular structures is reviewed in detail by Alghamdi [6].
The presence of the porous materials in thin-walled tubes improves crush stability and collapse mode [7–11]. The foams as porous materials are indeed ideal energy absorbers because they can undergo large deformation at nearly constant load before the porous volume is reduced up to a critical value and densification occurs for strain in the range of 60–90% [7]. The overall characteristics of foam materials are typically assumed to be isotropic and homogenous, namely uniform foam materials. Seitzberger et al. [11] carried out the experimental study of the mild steel
tubes with aluminum foam filler for circular and square cross sections. It was shown that thin-walled circular tube filled with high-density foam led to global buckling. The interaction at the foam–wall interface decreases the folding length, and therefore increases the crushing force. Experimental observation [10]shows that average crushing load of foam filled thin-walled tubes is greater than the empty tube and alone foam material. Hanssen et al. [12,13] developed some empirical formulas describing mean crushing loads for foam-filled circular and square columns. Reyes et al. [14] found that high-density aluminum foam could increase the energy absorption of thin-walled square tubes considerably,
but the specific energy absorption can be lowered compared with the hollow tubes. It was observed that the filling of thin-wall circular and square tubes with high-density foam may cause a reduction in specific energy absorption [15]. Therefore, selection of tube geometry and appropriate foam density are crucial in order to optimize the crashworthiness of such structures. Hou et al. [16] utilized single and multiple crashworthiness criteria to optimize the square thin-walled column with aluminum foam filler. Zarei and Kroger [17,18] used multi criteria design optimization technique to maximize energy absorption and minimize the weight of the foam-filled aluminum tubes. Nariman-Zadeh
et al. [19] adopted multi objective genetic algorithms to obtain optimum square aluminum column filled with aluminum foam.
The present research work concerns with the response of end capped circular tubes in axial compressive load to determine the effects of end cap on the crushing mechanism, crushing load and
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