Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide Ahmad Baroutaji, University of Wolverhampton, Telford, United Kingdom Mustafa Sajjia and Abdul-Ghani Olabi, Bernal Institute, University of Limerick, Limerick, Ireland and University of the West of Scotland, Paisley, United Kingdom r 2017 Elsevier Inc. All rights reserved.

1 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.7.1 2.7.2 2.7.3 3 4 5 6 7 7.1 7.2 7.3 8 References Further Reading

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Introduction Axial Crushing Circular Tubes Square Tubes Multi-Corner Tubes Triangular Tubes Global Bending Frusta and Tapered TW Tubes Advanced TW Tubes Multicell tubes Functionally graded thickness tubes Stiffened and corrugated tubes Oblique Loading Axial Inversion Axial Splitting/Tearing Lateral Bending Lateral Flattening Circular Tube Non-Circular Tube Nested Tube Conclusion Remarks

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Introduction

The demand for advanced transportation in modern society is increasing on a daily basis. This has led to continuously increasing numbers of vehicles on the roads. Inevitably, vehicular crash accidents have also increased and have become a major worldwide health problem. For better safety circumstances, vehicles’ structures should be able to protect occupants through converting most of the kinetic energy during a crash situation into other forms of energy in a predictable and controllable fashion. Thus, the demand for components and systems that can maintain the structural integrity as well as dissipate the kinetic energy during an impact has increased by engineers and researchers in the field of structures. The capability of a structure to manage and absorb the force of a serious crash and to reduce death and injury risk of the occupants is known as crashworthiness [1,2]. A crashworthy design has become the main safety criteria of the occupants-carrying vehicles such as aircraft and vehicles. The most popular form of collapsible energy absorbers, that are widely used to absorb the kinetic energy and to improve the crashworthiness behavior of a structure, is thin-walled (TW) components. The common use of TW components as energy absorbing devices is due to many important aspects including superior performance under dynamic loading, cost-effective, high efficiency, ease of manufacturing, and installation. TW energy absorbers were employed in many crashworthiness applications including aircraft subfloor structures [3], front structures of cars and trains [4], rollover protective structures (ROPS) of heavy equipment used in agriculture and construction, such as earthmoving machinery and tractors [5]. Basically, the energy absorption (EA) performance of TW components depends highly on the material properties, tube geometry, and deformation mode. The crash components of a road vehicle are mostly manufactured using a metallic material such as aluminum alloy and mild steel. The energy absorbing behavior of metallic TW tubes has received a significant amount of research in the last four decades. The main findings were reported in many review articles and books including those authored by Olabi et al. [6], Alghamdi [7], Abramowicz [8], Qiu and Yu [9], Lu and Yu [1], and Jones [2]. Generally, there are various crushing or loading situations through which metallic TW tubes can be deformed plastically and absorb kinetic energy; the most common situations include axial crushing [10], lateral indentation [11,12], lateral compression [13], tube inversion [14,15], and tube splitting [16,17]. Each one of these crushing situations is associated with one or more

Reference Module in Materials Science and Materials Engineering

doi:10.1016/B978-0-12-803581-8.09267-5

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Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

deformation modes that play a main role in the energy dissipation process and lead to various EA responses. In the recent years, researchers have developed many nontraditional shapes of TW tubes with aim to enhance the crashworthiness performance of structures. The goal of the present article is to review the energy absorbing and crush responses of the common and nontraditional TW components. The main focus of this article is on the energy absorbers that are made from a metallic material, mostly mild steel and/or aluminum. Those energy absorbers made from composite materials are considered to be beyond the scope of this article. The rest of the article is arranged based on the main deformation mechanisms used to deform the TW energy absorbers which include axial crushing, oblique loading, axial inversion, axial splitting, lateral bending, and lateral flattening.

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Axial Crushing

Axially loaded TW components are the most commonly used structures as energy absorbers. The axial crushing of tubes is characterized by a reasonably constant collapse load and a comparatively high energy absorbing capacity where the majority of the tube’s material deforms plastically to participate in the energy dissipating process. These energy absorbers have a huge variation in terms of geometric shape where they may be circular, square, triangle, or polygon in cross-section. Furthermore, they may be formed in a single or multicell configuration. Additionally, they may adopt a form that is straight or tapered in appearance.

2.1

Circular Tubes

Circular tubes were frequently used in the axially loaded EA structures [18–21]. Basically, the axial crushing of a circular tube involves progressive folding or buckling of the tube with one or more of three main deformation modes: axisymmetric or concertina, non-symmetric or diamond, or a mixed mode, as shown in Fig. 1. This classification of deformation modes for a circular tube was given by Guillow et al. [10] who performed an experimental examination on axial compression of a circular aluminum tube under quasi-static conditions. Series of tubes with various ratios of diameter to thickness (D/t) were tested and a diagram which describes the various modes of deformation was created. The authors reported that the deformation mode of the circular tube depends significantly on the D/t ratio. Broadly speaking, the diamond mode occurs in tubes with D/t greater than 80 while the ring mode occurs when D/t is less than 50 and ratio of length to thickness (L/t) is less than 2. For tubes with D/t less than 50 and L/t bigger than 2, mixed mode is developed [1]. The influence of impact velocity on the deformation pattern of circular tubes was investigated by Wang and Lu [22]. A cylindrical shell was studied and exposed to axial impact with velocity values of up to 300 m/s. The authors found that high impact speeds produced a unique plastic deformation called “Mushrooming” which made the walls of the shell thicker. The authors reported that there are three modes of deformation, as shown in Fig. 2, depending on the velocity of impact and the thickness of the tubes as follows: (1) progressive deformation mode for tubes with small wall thickness at relatively low velocity, (2) mushrooming associated with folds for all tubes at medium velocity, (3) mushrooming associated with wrinkling for tubes with big wall thicknesses at high velocity.

2.2

Square Tubes

In practice, the use of circular components in the automobile structures met various difficulties associated with mounting to other structural members. Thus, for addressing the practical issues, square tubes have received a noticeable attention for fabrication of crashworthy components. However, the square tubes are less effective at absorption energy than circular tubes. Tang et al. [23] reported that the structural effectiveness of a square tube is about 0.7 of a circular tube. This could mainly be due to the fact that severe deformation in square tubes is concentrated in the zones near to the corner. The collapse mode of square tubes depends on the width to thickness ratio (b/t) and it could be either extensional mode, inextensional, or mixed [2], as shown in Fig. 3. A very thin square tube, typically with b/tE100, may adopt a non-compact deformation mode (Fig. 3(d)).

Fig. 1 Various deformation modes of axially loaded circular tubes: (a) axisymmetric mode; (b) non-symmetric mode; and (c) mixed deformation mode [10].

Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

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Fig. 2 Deformation states at velocities of 385, 277, 227, 173, and 0 m/s, respectively [22].

Fig. 3 Axial progressive deformation modes of square tubes: (a) extensional mode develops in tubes with b/to7.5; (b) inextenstional mode occurs in tubes with approximately b/t440.8; (c) asymmetric mixed mode occurs in tubes with 7.5rb/tr40.8 [2]; and (d) non-compact crushing mode occurs in very thin tube b/tE100 [24].

2.3

Multi-Corner Tubes

Multi-corner TW tubes, such as hexagonal and octagonal sections, have attracted increased attention and application in automobiles as EA components [25,26]. Such components have a greater number of corners in the cross-section than the square tube and thus they offer greater energy absorbing capacity [27]. The deformation modes of the regular multi-corner tube are the same as those reported for square tubes, i.e., inextensional, extensional, and mixed modes [28]. Although increasing the number of corners, as in multi-corner tubes, seems to be a promising approach to enhance the EA behavior, some researchers observed that EA improvement almost saturates beyond a certain number of corners [29]. This behavior was reported by Fan et al. [29] who conducted numerical and experimental investigations into the axial collapse and energy absorbing capability of low-carbon steel TW components with convex and concave polygonal sections including octagon, hexagon, 12-sided, and 16-sided star cross-sections. The authors noticed that the 12-sided star cross-section displayed the best EA performance with an increase of up to 48.5% in the specific energy absorption (SEA) compared with the hexagon cross-section of the same cross-sectional area. The EA capacity of 16-sided star crosssection was lower than that of 12-sided one which suggests that increasing the number of corners is not always effective.

2.4

Triangular Tubes

The axial crushing of tubes with an odd number of sides, such as triangular tubes, was also investigated by many researchers [30–32], but were less reported in the literature.

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Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

The triangular cross-section has only three corners (three sides) and hence it exhibited the least energy absorbing capacity among all other tubes. Its progressive folding is quite unique and different from those developed in the multi-corner tube [33]. The collapse mechanism of equilateral triangular structures under quasi-static axial loading was analyzed by Fan et al. [33]. Two main deformation modes were recognized for these structures based on their dimensions, named as rotational symmetrical mode observed in tubes with b/t460, and diamond mode, for tubes with b/tr55.3. Due to the fact that the energy absorbing capability of such tubes is quite low, they did not receive much application in the automotive industry.

2.5

Global Bending

In general, based on their dimensions, the TW tubes can undergo a global buckling or global bending deformation mode during their axial crushing. This mode is very inefficient and should be avoided when designing an EA structure because it is relatively unstable and can lead to a considerable decrease in the effectiveness of an energy absorber. The global bending deformation mode may occur in both square and circular tubes as shown in Fig. 4. The occurrence of global bending in axially loaded circular and square tubes depends on the D/t and length to diameter (L/D) ratios, as reported by Guillow et al. [10]. The experimental results obtained by Abramowicz and Jones [34], who investigated the transition of mild steel circular and square tubes from the inelastic global Euler buckling mode to the progressive folding mode, showed that there is a critical tube length (Lcr) where the tubes with lengths less than the critical value deform progressively while tubes longer than the critical length undergo a global bending mode. When the tube’s length is close to critical value, a mixed progressive deformation-global bending deformation mode was observed where the global bending mode developed at the later stages of the deformation. Generally, the transition criterion, i.e., the critical length, is believed to be influenced by the following factors: material properties including the yield stress and strain hardening behavior, impact velocity, and tube dimensions [34–38]. Abramowica and Jones [34] reported that square tubes with greater b/t or circular tubes with greater D/t have longer Lcr. Karagiozova and Alves [37] found that Lcr increases as the impact velocity increases.

2.6

Frusta and Tapered TW Tubes

Frusta and tapered TW tubes which include one or more inclined face to the longitudinal axis and may have circular, rectangular, or square cross-sectional shape were also considered as energy absorbing components by many researchers [39,40]. Generally

Fig. 4 Global bending deformation mode in (a) square tubes [8] and (b) circular tubes [10].

Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

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speaking, the tapered tubes are preferable to the straight (non-tapered) tubes due to their capability of absorbing the oblique impact loads effectively where they are less likely to undergo the global buckling mode. Also, the tapered tubes have more stable plastic behavior and lower initial peak force under axial loading than the non-tapered tubes. However, the SEA of a tapered tube is less than that of a straight tube [41]. Thus, in the applications where weight is important and reducing weight is a goal, straight tubes are favoured and represent the most effective structure for absorbing energy [41]. The deformation modes of tapered tubes are similar to those of straight tube where circular tubular cones usually deform in either the diamond mode or concertina mode, depending on the geometry of the tube [42].

2.7 2.7.1

Advanced TW Tubes Multicell tubes

In more recent times, multicell columns have been emerged as effective energy absorbing structures. The various configurations of the multicell columns include hexagonal [43], triangular [44], square [45,46], circular [23,47,48], octagonal [31], and tapered [49] tubes. These structures have received a considerable amount of studies due to their extraordinary EA capability. For example, Xiong and Hui [50] reported that multicell metal tubes, S4 and S5 in Fig. 5, are more efficient than single-cell tubes. An increase of 120 and 220% were recorded in the SEA for specimens S4 and S5, respectively. Zhang and Cheng [51] performed a comparative analysis of energy absorbing responses of multicell and foam-filled square tubes. The authors proved via numerical simulations that the multicell components are effective energy absorbers where their EA efficiency was about 50–100% larger than that of foam-filled tubes. Alavi Nia and Parsapour [31] presented an interesting investigation in which they compared the EA capacity of conventional and multicell TW tubes with octagonal, hexagonal, square, and triangular cross-sections. The authors proved that the tubes with multicell configuration have higher energy absorbing capacity than the tubes with standard sections. Furthermore, the multicell tubes with octagonal and hexagonal cross-sections were found to have the highest SEA.

2.7.2

Functionally graded thickness tubes

Functionally Graded Thickness (FGT) TW components have gained increasing attention recently as energy absorbing devices. The concept of FGT has been presented to various shapes of TW components such as square tubes [52], circular tubes [53], and frusta [54]. For circular tubes and frusta, the wall thickness was varied in the longitudinal direction, as shown in Fig. 6(a). The thickness in square tubes was varied in the transverse direction to allow more material to be placed in the corners of the square section and thus increase the wall thickness at these regions as the severe deformation occurred near these locations during the axial deformation, as demonstrated in Fig. 6(b). Generally, the FGT TW components have offered better crashworthiness behavior than their counterparts with a uniform thickness. As an example of the effectiveness of FGT energy absorbers, Xiong et al. [52] studied the crush and energy absorbing behavior of square tubes with a graded thickness. The authors reported that the specimen with graded thickness can absorb 30–35% more energy per unit mass than the normal specimen, i.e., specimen with uniform thickness, without increasing the initial peak force.

2.7.3

Stiffened and corrugated tubes

Stiffened tubes, in which external stiffeners is used with a circular tube, as shown in Fig. 7, were considered as efficient energy absorbers [55]. Such tubes have enhanced energy absorbing properties such as EA and SEA, improved crushing stability and less sensitive to loading characteristics such as direction and uniformity [55]. Most of these improvements were achieved through the capability of externally stiffened tubes to develop an axisymmetric deformation mode during the axial collapse where the plastic deformation occurred in the regions between the stiffeners and the stiffeners worked as a stabilization tool for the whole structure.

Fig. 5 Various configurations of multicell columns studied by Zhang and Zhang [50].

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Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

Fig. 6 Schematic diagram showing thickness grading patterns in (a) circular tubes and (b) square tubes.

Fig. 7 (a) Externally stiffened tube [55], (b) laterally corrugated tube [56], and (c) corrugated tube [56].

Similar to externally stiffened tubes, researchers also evaluated corrugated tubes as effective energy dissipating devices. Introducing corrugations in the axially loaded tubes forced the plastic deformation to take place at specific places along the length of the tube. This behavior enhanced the uniformity of the force-displacement response and allowed for predicting and controlling the collapse mode of the tubes [57]. Arameh et al. [56] conducted an experimental study into the EA performance of aluminum tubes with corrugations that were varied in geometries and directions. The authors observed that tubes with corrugations had better crashworthiness characteristics, uniform crush responses without high initial peak loads, and predictable collapse mode. They reported that corrugated tubes with their predictable EA performance can be considered as reliable energy absorbers.

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Oblique Loading

Since the axially loaded tubular structures can be used for vehicle crashworthiness applications in which the crush management system is frequently subjected to both oblique and straight loads, many investigations have been performed to analyze and evaluate the energy absorbing behavior of various TW components under oblique loads.

Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

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The early investigation presented in this regard was performed by Reid and Reddy [39]. Tapered rectangular tubes were subjected to oblique impact load with an angle of 10 degree to the tube’s longitudinal axis. The results showed that the energy absorbing effectiveness of tapered tubes were almost same for both oblique and axial loads. The previous work was expanded by Nagel and Thambiratnam [58] who examined the effects of loading parameters, including the impact velocity and the load angle, and the geometry variables, including the taper angle, number of tapered sides, wall thickness, web width, and tube length, on the behavior of tapered and straight TW rectangular tubes under oblique dynamic loading. The authors reported that the tapered tubes exhibited many important benefits over straight tubes including more stable mean load, greater energy absorbing capacity when the tube underwent a global bending deformation mode, and EA characterizations with less sensitive to load parameters. Reyes et al. [59,60] studied the energy absorbing behavior of aluminum square tubes under dynamic and quasi-static oblique loads. It was observed that the dominant deformation mode under the oblique loading was global bending which depended on both load angle and thickness. The authors also confirmed, through performing a parametric study, that the mean and peak loads decreased as the loading angles increased. Furthermore, the authors reported that there was no change in collapse mode between the quasi-static and dynamic cases. Børvik et al. [61] investigated the crush response of circular aluminum tubes under quasi-static oblique loading. It was also observed that both EA and peak force decreased with increasing the loading angle. The responses of other geometrical shapes of obliquely loaded TW energy absorbers were also reported in the literature. The studied cross-sections included multicell hexagonal columns [43], frusta [62,63], empty and foam-filled square tubes [64], multicell square tube [45,65], and tapered square tubes [58,66]. The main observation that was reported by the researchers is that the TW components under oblique loading are more likely to undergo the global bending deformation mode which may extremely reduce its EA effectiveness. The tendency of the tube to undergo a global bending mode increases with increasing the loading angle. Despite the aforementioned studies, the EA responses of TW tubes subjected to oblique loads have received relatively little attention compared to the number of studies conducted on the crush behavior of TW tubes under straight loads.

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Axial Inversion

Tube inversion involves inverting a TW tube under axial compressive load. It can be classified into: free inversion using a suitable fixture and forced inversion using appropriately profiled die which turns the leading edge of the tube “inside out” [67–69], or “outside in” [70,71]. Generally, the EA performance through inversion process depends upon the mechanical properties of the tube, tube dimensions, inverting radius, and other operational problems such as friction between interfaces and surface quality of the die [14]. For external inversion the success of process depends on the ratio of fillet radius to tube’s diameter (r/D). The very small of this ratio (r/Dr0.03) may cause buckling deformation while large value could cause tearing for the tube instead of inversion [14]. Also, material properties and friction between the interfaces plays a key role in the success of the operation. Generally, the inversion becomes much easier by using a tube with ductile material over a die with low friction coefficient [69,72]. Miscow and Al-Qureshi [14] carried out experimental and theoretical investigations on external inversion of copper and brass tubes. The authors found that as received and/or partially work-hardened tubes are more suitable for the inversion than the tubes in annealed states, which generally showed premature buckling. The dynamic inversion of the tube was also investigated in literature. The strain rate and inertial effects in the free inversion of mild steel circular tubes were investigated by Colokoglu and Reddy [73]. It was found that the strain-rate sensitivity of mild steel increased the resistance to inversion, while the inertial effects played a role in both resisting and assisting the force needed for the inversion process. Reid and Harrigan [70] studied the internal inversion and nosing of mild steel circular tubes under quasi-static and dynamic loading. The authors reported that the steady-state inversion force is lower under dynamic loading conditions than under quasistatic loading and this was attributed to the role of inertia in assisting the inversion process. Harrigan et al. [71] expanded on this previous work by investigating the inertial effects caused by dynamic loading in the internal inversion of normal and tapered circular metal tubes. It was noticed that the inertial effects are more pronounced in the case of normal tube (tube with uniform thickness) because it generated a dynamic initial peak force in excess of the steadystate force.

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Axial Splitting/Tearing

The splitting of tubes can be seen as the intermediate between axial compression and axial inversion. It involves loading a tube onto a die with a relatively large radius than that used in tube’s inversion. Splitting deformation mode is efficient in terms of EA as the energy is dissipated via plastic bending, stretching and tearing of the metal into strips which can be subsequently curled, as shown in Fig. 8, to absorb further energy. Additionally, a splitting mode provide long crushing distance (up to 90% of the tube length), with an almost constant crush load.

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Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

Fig. 8 Final deformed profile of circular and square tubes under splitting mechanism [16,74].

Fig. 9 Deformation pattern of thin-walled tubes under lateral bending: (a) square tube [76] and (b) circular tube [77].

Reddy and Reid [75] conducted a number of static and dynamic experiments to inspect the deformation mode and the corresponding force-deflection curve for the splitting of circular metallic tubes. The authors reported that there are many parameters which have an effect on the splitting of tubes, including die radius and frictional effects, and the desired force-deflection response can be achieved by modifying these parameters. Also, it was noted that the mean crushing force of the axial splitting was lower than that noted in axial or inversion modes, but a higher crushing efficiency can be achieved. Huang et al. [16] expanded on previous work by providing more details on axial splitting and curling of circular metal tubes by using experimental and theoretical techniques. Various dies with different semi-angles were used to compress the mild steel and aluminum tubes axially. It was found that energy during the splitting process was dissipated by three mechanisms: bending, tearing, and friction. In addition to circular tube, square tubes were also considered for splitting deformation mode [74–79]. Lu et al. [79] performed an experimental study on splitting of square tubes. The aim of this investigation was to determine the energy associated with tube tearing for both steel and aluminum square tubes. It was found that the tearing energy per unit torn area can be related to ultimate tensile stress of the material and strain to fracture. Stronge et al. [78] and Huang et al. [74] examined the EA behavior of axially splitting square metal tubes. The authors explained that for this mode of deformation, the energy absorbing mechanisms are fracture energy due to splitting, plastic deformation as large deformations ensue, and frictional energy as the tube is passed over the mandrel.

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Lateral Bending

Since many of car components at the front, rear, and side, such as B-pillar, side-door beam, cross-beam of the bumper, may fail in bending mode during a crushing scenario, the bending behavior of TW tubes was the topic of many studies in literature [80,81], Generally, lateral bending of TW tubes involves applying a point load perpendicular to the longitudinal axis of the tube. The deformation of TW component under bending starts with a local indentation at the location of loading followed by a global bending of the tube due to significant reduction of the cross-section area at the loading location [80,81] (Fig. 9). The cross-sectional shape of the TW member influences its EA behavior under bending loading. Tang et al. [83] compared the EA behavior of different cross-sections, including circular, rectangle, ellipse, trapezoid, and hat section, under dynamic lateral bending. The results showed that the elliptical tube was harder to be deformed into a flat shape in the plastic hinge zone and thus it was considered as the most effective cross-section for bending loading. The EA through bending can be greatly enhanced by modifying the standard cross-section shape through incorporating reinforcing ribs [83], adopting multicell configuration [84] or using a FGT [76]. Wang et al. [84] investigated the bending collapse of multicell square tube. The multicell configuration of TW was introduced in the longitudinal direction and in the cross-section. The multicell configuration in the longitudinal direction was created using partition plates. These plates were found to be effective

Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

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when one plate was located beneath the loading punch. On the other side, the multicell configuration in the cross-section was also found to enhance the bending resistance. A tube with double-cell in the cross-section exhibited higher energy absorbing measurements than the other configurations and it was considered as the most effective multicell tube under bending loading. Zhang et al. [76] studied the bending response of FGT square tubes. The authors found that the FGT tube offers 40% increase in SEA than the uniform tube under bending loading. Sun et al. [85] analyzed the bending response of TW tube with a circular section and a thickness gradient along the longitudinal direction. It was proved that FGT provides better crashworthiness behavior than the uniform tube. Using ribs in the TW beam was also identified as an effective way to improve the bending response [83,86]. The ribs help in retarding the local deformation at the loading location resulting in improving the bending and energy absorbing performance [83].

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Lateral Flattening

The lateral flattening involves crushing the entire length of the tube parallel to its longitudinal axis. This deformation mode allows more material deformation than the lateral bending but not as much as in the axial crushing modes.

7.1

Circular Tube

The circular tube was the most investigated cross-section; its crush behavior and collapse mechanism under lateral compression has been well studied in the literature [13,87,88]. A detailed report on the responses of such tubes and their deformation mechanism was presented by Gupta et al. [13] who investigated the quasi-static lateral collapse of circular metallic TW tubes. Mild steel and aluminum tubes with different ratios of diameter to thickness were compressed in this study. It was found that each of the mean crush force and the energy absorbing capacity increased with decreasing the tube’s diameter and increasing the thickness. The behavior of a circular tube under dynamic lateral loading was studied by [88,89]. Under impact loading, the impact velocity is the dominant factor of the collapse pattern while tube dimensions have an insignificant effect on the deformation pattern [89]. In general, no change in the deformation mode or EA capability was reported for tube crushed under low impact velocity [90]. However, under high impact velocity, a laterally crushed circular tube shows a noticeable increase in the amount of absorbed energy and significant change in the deformation mode [90]. This behavior is mainly due to inertia effects which localize the plastic strains close to the striking side and increase the curvature of the segment subjected to deformation [90]. The collapse mode of the laterally loaded circular tubes, as shown in Fig. 10, is a plastic bending around the plastic hinges [90,91]. This deformation mode restricts the plastic strains near the plastic hinges and thus the amount of energy dissipated through the lateral collapse of a tube is limited and inefficient. Therefore, in order to increase the amount of energy absorbed by the laterally loaded tubes, the numbers of plastic hinges induced during the lateral collapse should be increased. For this reason, many researchers suggested using external constraints to create more plastic hinges during the compression [92,93]. Reddy and Reid [92] used side vertical constraints to prevent the horizontal diameter of a laterally loaded circular tube from becoming greater. It was found that side constraints increased the SEA capacity of the tube due to increasing number of plastic hinges during the plastic deformation. It was reported that constrained systems offer an EA capacity that is three times bigger than the normal system. On the other side, it was noticed that the maximum deflection of a constrained tube is less than the unconstrained tube. In addition to vertical constraints, inclined constraints were also employed as a tool to increase the energy absorbing capacity of laterally compressed tubes [94]. Reid [93] studied the effect of changing the inclination angle of the inclined constraints on the responses of a circular tube compressed by either point loading or a flat plate. It was found that the crush force increased as the inclination angle decreased. In general, it was concluded that using external constraints, either side vertical or inclined constraints, increase the EA efficiency of a laterally compressed TW tube. As an alternative of using external constraints to enhance the energy absorbing capacity, Reid et al. [95] suggested using of braced metal tubes in which the desired response of the system can be obtained by using tension members across the diameters of

Fig. 10 Deformed profiles of a mild steel tube at different stages of lateral compression [82].

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Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

a tube. The authors analyzed the collapse mechanism of two types of braced mild steel tubes; one with single braced tubes and the second with double braced tubes of different angles. It was reported that a noticeable enhancement in the energy absorbing responses can be achieved by using braced tubes but these systems are sensitive to the loading direction.

7.2

Non-Circular Tube

In addition to circular tubes, tubes with various cross-sectional shapes such as elliptical [96,97], rectangular [98,99], hexagonal [100], oblong [101], and triangular [102,103] were also investigated under lateral loading in the literature. Generally, a square tube absorbs more energy than a rectangular tube with the same cross-sectional area [98]. The deformation mechanism of a square tube under lateral loading, as shown in Fig. 11, involves generating three pairs of plastic hinges two pairs are formed at junctions of vertical and horizontal sides while the last pair is formed at the mid-height of the vertical sides of the tube [98,104]. Similar to the circular tube, the geometrical parameters of a square tube are the main factors which influence its EA behavior. The results obtained by Niknejad et al. [104] who investigated the lateral collapse of rectangular brazen and aluminum columns under quasi-static loading, revealed that the specific absorbed energy by a rectangular column increases as the column thickness increases and width decreases. Niknejad and Rahmani [100] studied the lateral crushing of hexagonal columns under quasi-static loading. It was found that lateral load of the tube is proportional to the width and thickness of the tube. Wu and Carney [105] investigated the lateral compression of elliptical tubes. It was found that the crush efficiency and energy absorbing capacity of an elliptical tube is greater than those of the circular tube. Baroutaji et al. [101] reported on the lateral compression of oblong tubes. An oblong structure was formed by elongating the standard circular tube plastically in the diametrical direction as shown in Fig. 12. The results of this investigation showed that an oblong tube exhibited more stable crush response and greater energy absorbing capacity than a circular tube of equivalent mass. Wang et al. [103] examined the lateral crushing and EA behavior of triangular tubes under quasi-static lateral loading. The results demonstrated three main crushing styles of such tubes based on the base angle. Tubes with small base angle, less than 45.6 degree, crushed without folds, as depicted in Fig. 13(a), while tubes with big base angle, greater than 72.6 degree, were folded, as illustrated in Fig. 13(c). Tubes with a base angle between 45.6 and 72.6 degrees have the crushing pattern as illustrated in Fig. 13(b). A plastic hinges mechanism was adopted to derive the mean crushing force of these tubes. It should be noted that the available data in the literature do not allow comparing the EA behavior of the various structures under lateral loading. Also, the research work that reports on the mean crush force of such structures is very rare and thus more theoretical and comparative analysis is required for these structures.

Fig. 11 Progressive crushing mode of a square tube under lateral loading [99].

Fig. 12 Preparation procedure of an oblong tube: (a) initial circular tube and (b) final oblong tube [101].

Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

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Fig. 13 Various collapse patterns and plastic hinges model for triangular tube under lateral loading [103].

Fig. 14 Various nested tube systems under lateral loading: (a) standard nested tubes [107]; (b) optimized nested tubes [108,109]; (c) nested tubes investigated by Baroutaji et al. [91]; and (d) nested systems with external constraints [94].

7.3

Nested Tube

As mentioned before, the EA capacity is limited in a laterally loaded tube. Thus, in order to meet the design requirement of some applications which require larger energy absorbing capacity. Many researchers [91,94,106,107] suggested that the tubes can be

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Metallic Thin-Walled Tubes for Crashworthiness Applications: A Reference Guide

stacked together to form a tubular system with desirable EA behavior. The nested systems are of particular importance for applications with limited crush zone as they have more than one crushable element in the same space and thus they can absorb higher energy per unit length than a single tube [91]. Among the early investigations in this regards, Morris et al. [107] proposed nested tube systems in which circular or oblong tubes of different diameters were assembled and compressed by rigid platen under quasi-static lateral loading as shown in Fig. 14 (a). As it can be seen from the figure, these nested systems contain gaps between their components which caused sequential deformations for their components which in turn caused a non-monotonic rise in force throughout the deformation distance. An attempt was made by Olabi et al. [108,109] to optimize the responses of the previous systems by inserting two small bars in the space between the nested tubes, as shown in Fig. 14(b). The authors pointed out that using the small bars in the optimized configuration of nested systems was able to eliminate a non-monotonic increase in the force-displacement response that was noticed during the crush of the standard nested systems. It was found that the optimized nested system displayed a more desirable crush response than the normal system. Another attempt to improve the response of the nested tube system was introduced by Baroutaji et al. [91], who arranged the components of nested systems in particular ways, as shown in Fig. 14(c), so that they deformed synchronously upon loading in order to achieve the desirable force-deflection response. The authors reported that a nested tube system with two identical inner tubes (middle system in Fig. 14(c)) exhibited the best EA performance. The EA capability of the nested system can be enhanced significantly by applying the concept of external constraints as demonstrated by Morris et al. [94] who analyzed the responses of constrained nested systems, as shown in Fig. 14(d). It was found that the nested systems with external constraints absorbed more energy than those without external constraints.

8

Conclusion Remarks

The vehicle’s crashworthiness has gained more attention in academic design research and the automotive industry to prevent injury and ensure the safety of occupants in an event of a collision. The TW tubes are the main elements that can improve the crashworthiness performance through plastic deformation. The main plastic deformation mechanisms in TW tubes used for crashworthiness applications are axial crushing, axial inversion, axial splitting, lateral flattening, and lateral bending. The axial collapse of TW components provides higher EA than the other deformations modes. This is mainly due to the fact that under axial loading most of the tube’s volume reach the plasticity limit and participate in the EA process. However, the axially loaded tubes might adopt an undesirable deformation mode, termed global bending, which is unstable and causes an extreme reduction in the energy absorbing capacity. Global bending mode is most likely to appear in the long tubes and under oblique loading situation. Axial inversion and axial splitting of TW tubes provide some advantages over other deformation mechanisms including higher crushing distance and relative steady crush force. However, successful inversion/splitting process require a suitable combination between different factors including tube geometry, die dimension, and friction between tube and die. Therefore, the inversion and splitting processes are considered as complex deformation methods. The energy absorbing capacity of laterally flattened tubes is greater than that of lateral indentation, but less than axial deformation modes. However, the absorbed energy through the lateral collapse of the tubes can be effectively increased by incorporating simple techniques such as using internal bracing or external constraints. With aim to achieve a better crashworthiness behavior, new unconventional configurations of TW tubes, such as multicell components and FGT tubes, have been recently developed as a new generation of energy absorbers. The goal of multicell configuration is to improve the EA behavior of TW tube by controlling the number and shape of angle elements in the crosssection. FGT configuration aims to increase the amount of material at the locations that suffer from a serious deformation while reducing the amount of material at less important zones and hence it allows for better distribution of tube’s material. Both configurations of TW components exhibited greater crashworthiness measurements and enhanced EA behavior than the conventional tubes for all loading situations. However, the multicell tubes are not widely used in practice due to high manufacturing cost and high peak crush force of such structures.

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Further Reading Alghamdi, A.A.A., 2002. Reinversion of aluminum frustra. Thin-Walled Structures 40 (12), 1037–1049. Alghamdi, A.A.A., 2010. Folding-crumpling of thin-walled aluminum frusta. International Journal of Crashworthiness 7, 67–78. Alghamdi, A.A.A., Aljawi, A.A.N., Abu-Mansour, T.M.-N., 2002. Modes of axial collapse of unconstrained capped frusta. International Journal of Mechanical Sciences 44 (6), 1145–1161. Avalle, M., Goglio, L., 1997. Static lateral compression of aluminum tubes: Strain gage measurements and discussion of theoretical models. The Journal of Strain Analysis for Engineering Design 32 (5), 335–343. Chen, W., Wierzbicki, T., 2001. Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Thin-Walled Structures 39 (4), 287–306. Jiang, P., Wang, W., Zhang, G.J., 2006. Size effects in the axial tearing of circular tubes during quasi-static and impact loadings. International Journal of Impact Engineering 32 (12), 2048–2065. Liu, W., Lin, Z., Wang, N., Deng, X., 2016. Dynamic performances of thin-walled tubes with star-shaped cross section under axial impact. Thin-Walled Structures 100, 25–37. Mamalis, A.G., Manolakos, D.E., Saigal, S., Viegelahn, G., Johnson, W., 1986. Extensible plastic collapse of thin-wall frusta as energy absorbers. International Journal of Mechanical Sciences 28 (4), 219–229. Nagel, G.M., Thambiratnam, D.P., 2004. A numerical study on the impact response and energy absorption of tapered thin-walled tubes. International Journal of Mechanical Sciences 46 (2), 201–216. Niknejad, A., Moeinifard, M., 2012. Theoretical and experimental studies of the external inversion process in the circular metal tubes. Materials and Design 40, 324–330. Reddy, T.Y., Reid, S.R., 1980. Phenomena associated with the crushing of metal tubes between rigid plates. International Journal of Solids Structures 16 (6), 545–562. Redwood, R.G., 1963. Discussion: Crushing of a tube between rigid plates. Journal of Applied Mechanics 31 (2), 357–358. (DeRuntz, Jr., John A., and Hodge, Jr., P.G., 1963. Journal of Applied Mechanics, 31(2), 391–395, 1964). Reid, S.R., Reddy, T.Y., 1978. Effect of strain hardening on the lateral compression of tubes between rigid plates. International Journal of Solids Structures 14 (3), 213–225. Rossi, A., Fawaz, Z., Behdinan, K., 2005. Numerical simulation of the axial collapse of thin-walled polygonal section tubes. Thin-Walled Structures 43 (10), 1646–1661. Zhang, X., Cheng, G., Zhang, H., 2009. Numerical investigations on a new type of energy-absorbing structure based on free inversion of tubes. International Journal of Mechanical Sciences 51 (1), 64–76.