Multi-objective optimization of energy absorbing behavior of foam-filled hybrid composite tubes
Introduction
With the development of logistics and transportation sectors, the number of vehicles used in land, air, and sea transportation is increasing day by day. In the accidents that occur due to this increase, besides the financial losses, deaths and injuries occur. Active and passive safety systems are developed in order to minimize the effects of adverse events arising as a result of accidents. Thin-walled tubes are the most common application forms of passive safety systems due to their lightness, high energy absorption capability, easy production and low cost.
In the literature, to examine the effects of cross-section geometry, [1], [2], filling material [3], [4], [5], [6], hierarchical honeycomb [7], [8], [9], grooving [10], [11], [12] and reinforcement [13], [14] on the energy absorption behavior of thin-walled tubes, besides experimental [15], [16], [17], analytical [18], and numerical studies [19], [20], optimization studies [21], [22] are also carried out. In their study investigating the energy absorption behavior of circular, square, rectangular, hexagonal, triangular, pyramidal, and conical tubes, Nia [23] et al. determined that circular cross-section tubes have the highest energy absorption capability and recommended conical and pyramidal tubes due to their reduction in peak force. Asanjarani [24] et al., in their study investigating the energy absorption behavior of corrugated tubes with different cross-section geometries, showed that cross-section geometry, conicity, and corrugation had significant effects on energy absorption behavior. Shokrieh [25] and his colleagues who numerically examined the effect of cross-section geometry in composite tubes determined that circular composite tubes absorb more energy than square-section composite tubes. Studies have been carried out on the effect of cross-section geometry on the energy absorption capability of nested tubes as well as single tubes. For example Pirmohammad et al. [26], [27] studied the behavior of nested interconnected tubes (ribs) in axial and oblique crashes. In a similar study, Li Yang [28] and coworkers have developed a theoretical equation with an error rate of less than 5% for the average force estimation of multi-cell and nested interconnected tubes. Duarete and his colleagues [29] investigated the energy-absorbing behavior of aluminum foam filled and empty tubes produced with powder compact foaming technique and found that foam filled tubes were deformed in the axisymmetric mode and the foam filling improved the energy-absorbing behavior. In another study, Duarete et al. [30] showed that foam-filled thin-walled tubes produced in-situ exhibit superior energy absorption ability.
Studies on energy-absorbing tubes in recent years have focused on metal / composite hybrid tubes created by combining metal and composite tubes in different ways. With hybridization, it is aimed to combine high specific strength in composite tubes with high strength in metal tubes. [31]. One of the first studies on hybrid tubes was conducted by Mamalis et al. [32] They showed that fiber-reinforced metal tubes have the advantages of both metals and reinforced composite material and that the theoretical model they proposed was in good agreement with the experiment. Bambach [33] and colleagues showed that the equation they developed for average force, peak force, and total energy absorbing of square-section tubes reinforced by externally wrapping CFRP is consistent with the experimental results. In another study on square tubes reinforced by externally wrapping CFRP, Zhang [34] and colleagues found that the number of CFRP layers wrapped in hybrid tubes, after reaching a certain value, increases energy-absorbing behavior compared to plain aluminum tube. Zhu [35] et al., in their studies on circular and conical tubes reinforced with fabric CFRP wrapped on aluminum tubes, showed that hybrid tubes exhibit 45% more specific energy absorption behavior than aluminum tubes. Cui [36] and colleagues investigated the energy absorption behavior of CFRP and GFRP hybrid tubes wrapped on the aluminum tube with filament wrapping method and they compared filament wrapping, vacuum bagging, and nested manufacturing methods. In their study, they found that the most suitable method in terms of energy absorption is filament wrapping and the CFRP-wrapped hybrid tube at a 45° angle had the highest energy absorption.
Studies using different filling materials (Polyurethane foam, metallic foam, etc.) and optimization analysis are carried out in order to improve the energy absorption behavior of hybrid tubes. Sun [37] et al., in their study investigating the energy absorption behavior of CFRP / Aluminum tubes under lateral loading with the optimization method, showed that the tube whose length, thickness, and fiber alignment were optimized absorbed more energy at 42.96%. Li [38] et al. experimentally investigated the semi-static crush behavior of foam-filled aluminum CFRP hybrid tube under transverse loading conditions and optimized the foam density, tube thickness, and CFRP fiber layer number in order to achieve the highest energy absorption. They determined that the optimized tube absorbs 213% more specific energy than the basic design.
In addition to nested hybrid tubes, metal / metal, metal / composite hybrid structures joined by end-to-end method were also studied. Gedikli [39] investigated the energy absorption of tubes made of different metallic materials joined with weld seams and found that with weld seam tubes of different thickness and material, the absorbed energy and crash force can be adjusted appropriately. In another article, Gedikli [40] tried to optimize the energy absorption behavior of hollow and foam-filled weld-seamed tubes according to specific energy absorption, peak force, and crash force ratio, and determined that weld-seamed tubes decrease the peak force, while foam-filled ones increase the absorbed energy value. Meric [41] and colleagues optimized the wall thickness and foam density of hollow and foam-filled conical welded tubes made of different materials. De Luca [42] and colleagues numerically studied the energy absorption behavior of hybrid tubes consisting of Al 6060 and CFRP tubes and aimed to improve crash performance simultaneously with weight reduction with the proposed new hybrid tube.
In the literature, the energy-absorbing behavior of hybrid tubes formed by combining metal and composite tubes in radial direction has been studied. In this study, unlike the literature, the energy-absorbing behaviors of hybrid composite tubes (metal–metal and metal-composite) joined by the end-to-end method were investigated experimentally and numerically. The energy-absorbing behaviors of tubes made of Al 6063, St 52, and CFRP materials have been experimentally investigated and numerically modeled. Afterwards, single and double tubes were filled with aluminum foam of different density Foam 1 (500 kg / m)3), Foam 2 (750 kg / m3) and Foam 3 (1000 kg / m3) in the axial direction. After model verification, foam densities (500–1500 kg / m3) and wall thicknesses (1–4 mm, excluding composite tube) in foam-filled single and double tubes were optimized by the multi-objective optimization (MOO) method in order to determine the configuration with the highest specific energy absorption (SEA) and the lowest peak force.
Section snippets
Specimens description
In this study, the single and double hybrid tubes joined by the end-to-end method shown in Fig. 1 were used. The total length of the single and double hybrid tubes used is 80 mm and the wall thickness is 1.5 mm. Single tubes consist of aluminum (S_Al), steel (S_St), and CFRP (S_C) tubes, while the double tubes are formed by combining aluminum, steel, and CFRP tubes in pairs (D_St-Al, D_Al-C, and D_St-C) as given in Table 1. Composite tubes are made of unidirectional CFRP fabric with 6 layers
Modelling of metallic tubes
For the metallic tubes shown in Fig. 3, shell elements with Belytschko-Tsay element formulation with 5 integration points in thickness direction were used in the finite element model. For the accuracy of the finite element model, a mesh convergence study was performed and a mesh size of 2x2 mm was chosen. Hourglass control formation was used to prevent possible zero-energy modes. The AUTOMATIC_SINGLE_SURFACE contact card was used for the contact of the tubes in their internal nest, while the
Modeling of composite tubes
Damage mechanisms such as intralaminar shear, axial cracking, transverse ply failure, and delamination are observed in the deformation of composite tubes. A detailed numerical analysis methodology is required to adequately represent these failure mechanisms. The single-layer modeling approach is insufficient to demonstrate the effects of these damage mechanisms. It has been shown that the multi-layered shell modelling approach can represent many failure modes of an axially compressed composite
Modeling of aluminum foam
To improve energy-absorbing behavior in single and double tubes, as seen in Fig. 5, Foam 1, Foam 2, and Foam 3 metallic foam fillings were numerically filled in the tubes, having a density of 500 kg/m3, 750 kg/m3 and 1000 kg/m3, respectively. For the modeling of foam material, the smooth particle hydrodynamics (SPH) method and MAT_CRUSHABLE_FOAM material model were used in order to avoid convergence problems to large deformation cases [44 Kinematic constraints contact algorithm was defined
Accuracy of FEM, FNN and SPH model
The accuracy of the finite element model was tested by comparing force–displacement graphs and deformation images obtained from the experiments and numerical analysis for foamless S_Al, S_St, S_C, D_St-Al, D_Al-C, and D_St-C tubes. In Fig. 6 (a) and (b), it can be seen that the force in single metallic tubes increased until the first bulking started and decreased until the second bulking after reaching its maximum value. In the S_C tube, it increased until the first deformation started and then
Conclusion
In this study, the energy absorption behavior of single and double foam-filled tubes made of Al 6063, St 52, and CFRP tubes was investigated using the finite element method and MOO, and the results obtained are given below.
- 1.
As a result of the optimization process, an increase occurs in the absorbed energy values in all single and double tubes. For OPTIMUM S_Al, S_St, S_C, D_St-Al, D_Al-C and D_St-C tubes, the increments are 435%, 229%, 360%, 241%, 307%, and 255%, respectively, compared to
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (56)
- et al.
Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces
Thin-Walled Struct
(2013) - et al.
Dynamic and quasi-static bending behaviour of thin-walled aluminium tubes filled with aluminium foam
Compos Struct
(2014) - et al.
Manufacturing and bending behaviour of in situ foam-filled aluminium alloy tubes
Mater Des
(2015) - et al.
Bending performance evaluation of aluminium alloy tubes filled with different cellular metal cores
Compos Struct
(2020) - et al.
Energy absorption characteristics of three-layered sandwich panels with graded re-entrant hierarchical honeycombs cores
Aerosp Sci Technol
(2020) - et al.
In-plane crashworthiness of re-entrant hierarchical honeycombs with negative Poisson’s ratio
Compos Struct
(2019) - et al.
Crashworthiness analysis and optimization of sinusoidal corrugation tube
Thin-Walled Struct
(2016) - et al.
Behaviour of concrete-filled steel-tube columns strengthened with high-strength CFRP textile grid-reinforced high-ductility engineered cementitious composites
Constr Build Mater
(2021) - et al.
Experimental investigation of the crash energy absorption of 2.5D-braided thermoplastic composite tubes
Compos Struct
(2014) - et al.
Static and dynamic axial crush performance of in-situ foam-filled tubes
Compos Struct
(2015)