Deformation, energy absorption and crushing behavior of single-, double- and multi-wall foam filled square and circular tubes
Introduction
In the case of vehicle crash, the occupant safety is of the prime concern and this demands that the vehicle structure should be designed to withstand high impact forces. This demand is even further supplemented with the use of lightweight structure for higher fuel economy wherein the working stress reaches closer to the ultimate strength of materials [1]. In the case of impact/crash, the requirement is achieved through properly designed high energy absorption system. In the past, many energy absorbers had been developed which dissipate energy by crushing, cyclic plastic deformation, friction and fracture, bending etc. with variety of materials ranging from wood to metals and advanced fiber composites [2]. An ideal energy absorber should be of light weight and maintain the maximum allowable retarding force throughout the maximum possible displacement i.e. stroke length and should have maximum stroke efficiency [2]. In the case of ideal energy absorbers, the first requirement is that they should exhibit the long, flat load–displacement curve in which the plateau force is kept just below the damage force. Tubular structure is one of the most commonly used energy absorption system and in impact situations, the axial compression ability of the tubular structures deforming in a progressive manner is used [2].
In the past, several researchers studied different types of energy absorber systems such as frusta [3], [4], [5], circular tubes [6], [7], [8], square tubes [9], [10], [11], multi-corner metal columns [12], [13], and rods [14] for their application in impact and crash and presented the comprehensive results [15], [16], [17], [18], [19], [20], [21]. Further, thin-walled tubular structures had been used in the structural crashworthiness and their static and dynamic behavior had been studied both theoretically and experimentally in terms of the critical forces, types and modes of buckling, and the energy absorbing properties by several researchers [22], [23], [24], [25]. The energy absorption characteristic of tubular structures can be improved by filling them with light weight materials such as foams. The filling of foam in the tubes influences the buckling modes which in turn caused higher plastic deformation and higher energy absorption [26]. In the recent years, aluminum foam has shown very high potential in energy management because of its high energy absorption characteristic depicted by long plateau stress region at constant stress, moisture independent, high temperature and recyclable properties [27]. Chen and Wierzbicki analytically and numerically investigated the axial crushing of hollow multi-cell columns. They derived closed-form solutions to compute the mean crushing strength of such sections and also concluded that considering interaction between foam core and column wall significantly enhances the energy absorption [28]. Najafi and Rais-Rohani presented the axial crushing of multi-cell, multi-corner thin-walled aluminum tubes using LS-Dyna. They proposed an analytical formula based on super folding element theory for computing the mean crush force [29]. Abedi et al. investigated the empty and polyurethane foam-filled square and rectangular section under axial compression by considering the interaction effects between column wall and foam. Based on this investigation, they proposed relationship to compute the maximum axial force [30]. Tang et al. simulated the energy absorption capacity of cylindrical multi-cell columns using LS-Dyna. They concluded that wall thickness and number of cells considerably affect the energy absorption capacity [31]. Song and Guo numerically investigated the performance of windowed and multi-cell square tubes of the same weight under axial and oblique loading using Abaqus and concluded the effectiveness of multi-cell structure [32]. Nia and Parsapour investigated the energy absorption characteristics of multi-cell square tubes and found that addition of the partitions at corners increases energy absorption capacity of the tubes. Further they said that multi-cell square section absorb 227% higher energy than that of simple section [33]. Hong et al. studied the crushing behaviors of multi-cell tubes with triangular and Kagome lattices. They suggested the classical plastic models to predict the mean crushing forces of multi-cell tubes and claimed that these tubes has higher energy absorption efficiency [34]. Zhang and Zhang studied the axial compression of four different multi-cell column configurations experimentally, numerically and theoretically without considering the geometrical compatibility between different constituent elements. They used LS-Dyna for numerical simulation of multi-cell columns under axial loading and proposed a constituent element method to predict the mean crushing force of the multi-cell specimens. Based on this investigation they found that quad-cell configuration results in increased specific energy up to 30% [35]. Nia and Parsapour studied energy absorption capacity of simple and multi-cell thin-walled tubes with triangular, square, hexagonal and octagonal sections under quasi-static load. They used LS-Dyna for numerical simulation and compared the results with the experiments. They found that hexagonal and octagonal sections absorb highest amount of energy per unit mass of sections among the sections considered [36]. Recently, Jusuf et al. investigated the multi-cell columns in comparison with single-walled and double-walled columns under dynamic loading. They used LS-Dyna for numerical simulation and showed that energy absorption efficiency is improved by incorporating the internal ribs in multi-cell tubes [37]. Tehrani and Ferestadeh studied the energy absorption in tapered thick walled tubes using the finite element method and presented the analytical solutions [38].
It is well known that tubes deform in compression generally by four mechanisms as (i) tube inversion/tube splitting, (ii) progressive crushing, (iii) axis-symmetric buckling, and (iv) diamond shape buckling. Based on the review of the past investigations, it is observed that several researchers in the past carried out theoretical and experiment research on the foam filled tubular structures of different cross-section, arrangements, and different loading conditions, but still there exist a wide scope of research to optimize the foam filled tubular structure for wide practical applications. Hence, in the present investigation, the results from the numerical simulations are reported for compression of aluminum square tubes under impact loading. Three different configurations of square and circular tubes with same length and properties are analyzed for examining their effectiveness in crashworthiness. The present investigation is carried out with an aim to study (a) effect of foam filler in comparison with empty tube and (b) effect of concentric tube configurations.
Section snippets
Foam and tube material
The tubes are filled with the closed cell aluminum foam made through liquid metallurgy route at Council of Scientific and Industrial Research (CSIR)-Advanced Materials and Processes Research Institute (AMPRI), Bhopal, India. Aluminum foams are developed through liquid metallurgy route which involves number of steps as (i) melting of the alloy, (ii) followed by dispersion of calcium hydride (CaH2) particles in the melt, (iii) allowing the melt for short duration in the foaming temperature for
Numerical modeling/FEM simulations
The finite element simulation is carried out using the commercial code Altair® RADIOSSTM version 10.0 [41]. A total of three square and three circular tube configurations are modeled under axial impact loading with single, bi-tubular, and multi-tube structure with and without aluminum foam cores for both types of tubes. Each tube has a wall thickness of 2 mm and a length of 300 mm. The size of square configuration is 50 mm×50 mm with 5 mm clearance in the case of bi-tubular and tri-tubular
Validation of numerical modeling
The validation of the finite element model is carried out by modeling the geometry and comparing the experimental results of the square tube subjected to quasi-static axial compression as reported by Aljawi et al. [42]. The structural geometry of the tube and the properties used for the validation are exactly same as those reported by Aljawi et al. [42]. Fig. 7 shows the load vs. displacement curve of experimental results of Aljawi et al. and numerical results obtained using present FE
Simulation results and discussions
In the present investigation two types of tube shape (i.e. square and circular) as crash absorber are considered. Table 1 shows details of all the tube configurations and their nomenclature considered in the present investigation. The circular tubes has area equivalent to the corresponding square tubes for all tube configurations considered in the present investigation.
Conclusions
The present investigation is carried out with an aim to study (a) effect of foam filler in comparison with empty tube and (b) type of concentric tube configurations. Based on this numerical simulation behavior of concentric bi-tubular and tri-tubular empty and foam filled configuration are compared with single empty and foam filled deformations in terms of deformation modes and energy absorptions. This investigation demonstrates that the by arranging the tubes concentrically the deformation and
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