CFRP hybrid tubes

Journal Pre-proof Experimental and numerical studies on the bending collapse of multi-cell Aluminum/ CFRP hybrid tubes Zhixin Huang, Xiong Zhang, Chongyi Yang PII:

S1359-8368(19)32544-2

DOI:

https://doi.org/10.1016/j.compositesb.2019.107527

Reference:

JCOMB 107527

To appear in:

Composites Part B

Received Date: 3 June 2019 Revised Date:

16 September 2019

Accepted Date: 10 October 2019

Please cite this article as: Huang Z, Zhang X, Yang C, Experimental and numerical studies on the bending collapse of multi-cell Aluminum/CFRP hybrid tubes, Composites Part B (2019), doi: https:// doi.org/10.1016/j.compositesb.2019.107527. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

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Experimental and numerical studies on the bending collapse of

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multi-cell Aluminum/CFRP hybrid tubes

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Zhixin Huanga, Xiong Zhanga,b ∗ Chongyi Yanga

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a Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China

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b Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Luoyu Road 1037, Wuhan 430074, PR China

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Abstract: Wrapping the structures with composites and adopting multi-cell sections are two typical methods to

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improve the crashworthiness of thin-walled beams. However, the effects of combining these two methods on

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crashworthiness are not clear. This paper aims to investigate the bending collapse and crashworthiness of the multi-cell

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aluminum/carbon fiber reinforced plastic (Al/CFRP) hybrid tubes under quasi-static and dynamic loading. Three-point

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bending tests are firstly conducted for the CFRP, Al and Al/CFRP square tubes with single or multi-cell sections. The

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deformation characteristics and crushing force responses of the tubes are analyzed, and the energy absorption

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performances are evaluated. The bending resistance of the Al tubes is increased by up to 41% attributed to the CFRP

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enhancement. The non-linear finite element software ABAQUS/Explicit is then employed to simulate the tests and help

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analyze the deformation mechanisms. Parametric studies are performed to investigate the influence of the Al wall

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thickness, the number of CFRP plies, loading velocity, partial wrapping and sectional shape on the crashworthiness of

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Al/CFRP tubes. Results show that the Al wall thicknesses, partial wrapping, and sectional shapes have a significant

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influence on the deformation pattern and force response of Al/CFRP tubes, while the number of CFRP plies and the

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loading velocity have a relatively small influence. The specific energy absorption of Al/CFRP tubes can be increased

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by 11% by introducing partial CFRP wrapping, and in all cases, the multi-cell Al/CFRP tubes outperform the single-

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cell counterparts in crashworthiness performances.

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Key words: Bending collapse; Al/CRFP hybrid tubes; Multi-cell section; Impact loading; Crashworthiness.

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1. Introduction

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In the vehicle industry, thin-walled beams are widely used as energy absorption components to

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protect the occupants from injury [1-2]. The energy absorption performances of the beams under

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various loads have attracted great interests in the scientific community [3-15], and continuous efforts

∗

Corresponding author. Tel.: +86 2787543538; fax: +86 2787543501.

E-mail address: [email protected] (X. Zhang).

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are made by researchers to explore the collapse mechanisms and improve the crashworthiness of the

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thin-walled beams.

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Bending collapse is an important energy dissipation mechanism of thin-walled beams under

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lateral loads. A large number of studies were carried out on the bending collapse of thin-walled beams

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by researchers. In 1983, Kecman [16] firstly proposed a theoretical model to predict the pure bending

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response of thin-walled rectangular section tubes. Then, the pure bending collapse mechanisms were

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further studied by Wierzbicki et al. [17] and Kim and Reid [18], and closed-form solutions were

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derived for the moment-rotation response. Considering that pure bending is seldom encountered in

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real crash events, recently researchers exerted more efforts on the three-point bending collapse of thin-

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walled beams with various sectional shapes. The three-point bending collapse of thin-walled

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rectangular tubes was recently studied by Huang and Zhang [19-20]. Two typical deformation modes:

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bending collapse and bending with indentation were identified by them, and theoretical methods were

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proposed to predict the moment or force responses. The collapse of dual rectangle tubes under three-

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point bending was addressed by Bai et al. [21], and an analytical solution is also derived for the

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bending response. The collapse resistance of various multi-cell tubes under three-point bending was

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analyzed by Wang et al. [22], and the specific energy absorption (SEA) of the multi-cell sections was

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reported to be over 50% higher than that of the single-cell counterparts. However, all these studies

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only deal with the bending collapse of metallic beams.

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In recent years, composite structures have been increasingly applied to the vehicles to improve

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the fuel economy [23-24]. The composites have the advantages of high strength and lightweight, but

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the brittle fracture of composites may significantly impair the crashworthiness of the structures. This

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phenomenon was widely observed in the bending processes of composite structures. For example,

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Gliszczyński et al. [25] investigated the pure bending of glass fiber reinforced plastic (GFRP) channel

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section profiles, and the failure of fibers led to a significant decrease of the bending moment. The

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three-point bending of square and double hat-shaped carbon fiber reinforced plastic (CFRP) beams

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was studied by Liu et al. [26-27], and the fiber breakage resulted in sharp drops of the force responses

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and low energy absorption efficiency.

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The metal/composite hybrid beams have been recently adopted as an effective approach to

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achieve lighter weight and better crashworthiness [28-29]. The metal/composite hybrid beams

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combine the merits of both the metal and composite. The good plasticity of metal and high specific

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strength of the composite can bring a strong hybrid structure. In recent years, the crashworthiness of

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the hybrid structures under transverse loads has been addressed by many researchers. Shin et al. [30]

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studied the three-point bending collapse of Al/CFRP hybrid square tubes, and the bending resistance

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was greatly affected by the lay-up sequence of the laminates. The bending response of Al/GFRP tubes

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was investigated by Jung et al. [31], and the SEA of the hybrid tube was found 29% higher than that

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of the Al counterpart. The collapse characteristics of Al/CFRP circular beams under three-point

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bending were analyzed by Sun et al. [32], and the SEA value of the hybrid structure was increased by

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43% by structural optimization.

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It is noted that most of the current studies are concerned with the collapse of metallic profiles,

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pure composite structures, and single-cell metal/composite beams. Up to now, there are still no studies

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on the bending collapse of metal/composite beams with multi-cell sections. Since the metallic multi-

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cell sections exhibit high bending resistance and good energy absorption performances [21-22, 33],

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the crashworthiness and collapse mechanisms of multi-cell metal/composite hybrid tubes under three-

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point bending will be quite noteworthy and interesting.

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This paper aims to study the bending collapse of multi-cell Al/CFRP hybrid tubes. Quasi-static

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and dynamic three-point bending tests are first conducted for the pure CFRP, Al and Al/CFRP square

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tubes with single or multi-cell sections. The nonlinear finite element software ABAQUS/Explicit is

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then employed to simulate the tests and help analyze the collapse mechanisms. Finally, parametric

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studies are carried out to investigate the influences of the Al wall thickness, the number of composite

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layers, loading velocity, partial CFRP wrapping, and sectional shape on the bending responses and

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crashworthiness of Al/CFRP hybrid tubes.

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2. Specimens and experimental setup

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2.1 Specimens preparation

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Aluminum multi-cell square profiles and WP-3011 plain woven carbon fiber/epoxy prepreg are

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employed to fabricate the Al, CFRP, and Al/CFRP hybrid specimens. The representative Al specimens

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are shown in Fig. 1(a), and two different sectional shapes: double-cell and quadruple-cell sections are

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adopted. The length of the Al tubes is 270 mm, and the outside sectional dimension is 32 mm × 32

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mm. The wall thicknesses of the outside and inside plates of the multi-cell sections are slightly

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different. As indicated in Fig. 1(b), the thicknesses of the outside plates and inside ribs are 0.95 and

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1.01 mm, respectively.

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In the fabrication of pure CFRP specimens, three layers of the prepregs are wrapped on the Al

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tubes with a layer of demolding film between them, and they are then enclosed and cured in a furnace.

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The curing temperature is controlled as follows: the temperature is linearly increased to 120 ℃ in 90

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minutes, and then kept constant for 90 minutes, and finally cooled down to the room temperature.

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After the curing process, the pure CFRP specimens can be taken out from the Al tubes by demolding.

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Due to the manual operation errors and spring back of the composite, small fillets are developed for

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the CFRP sections, and the fillet radius is measured to be 2 mm.

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During the fabrication of Al/CFRP hybrid specimens, the Al tubes are first treated by using a

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phosphoric acid anodizing method to achieve good adhesion with CFRP layers. The outside tube

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surfaces are then wrapped with three layers of prepregs, and finally, the hybrid beams are cured with

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the same process as the pure CFRP specimens.

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The representative CFRP and Al/CFRP tubes are also shown in Fig. 1(a). For the sake of

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convenience, the pure CFRP, double-cell and quadruple-cell Al specimens are denoted by CFRP, A2,

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and A4, respectively. The Al/CFRP hybrid tubes with double-cell and quadruple-cell sections are

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distinguished by CA2 and CA4, respectively.

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2.2 Material properties

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The material of the Al tubes is AA6063-O. According to ASTM E8M-04 [34], the constitutive

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relation of the material is obtained by performing uniaxial tensile tests on a 10 KN capacity Zwick

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Z010 universal test machine. The engineering stress-strain curves of AA6063-O are plotted in Fig. 2

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(a). The mechanical properties are as follows: density ρ = 2.7 g/cm3, Young's modulus E = 68.9 GPa,

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Poisson's ratio ν = 0.33, the initial yield stress σy = 30.1 MPa and the ultimate stress σu = 106.1 MPa.

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The WP-3011 plain woven carbon fiber/epoxy prepregs are manufactured by Weihai Guangwei

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Composite Company. The weight per square meters of the prepreg is 330 g/m2, and the resin content

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is 40%. The thickness of the carbon fiber woven fabric is 0.25 mm. In order to obtain the mechanical

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properties of composites, several experimental tests are conducted according to related test standards,

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including the tensile (ASTM D3039 [35]), compression (ASTM D695-10 [36]) and in-plane shear

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(ASTM D3518 [37]) tests. The stress-strain curves of CFRP under tensile, compression and in-plane

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shear tests are plotted in Fig 2. (b) - (d). Since the interfacial properties are critical for collapse

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responses, the bonding strengths between CFRP and CFRP or CFRP and Al in normal and shear

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directions are also tested, and the curves for bonding strength are given in Fig 2. (e) - (h).

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The damage initialization and evolution of composites are associated with the critical fracture

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energy. The related fracture energy for the same type of composite WP-3011 produced by the same

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company was tested by Sun et al. [14], although the strengths of the present material are slightly

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different. The fracture energy data measured by them are employed here. According to Sokolinsky et

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al. [38], the critical fracture energy is approximately linearly correlated to the strength [38]. The

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critical fracture energies for composite failure and interfacial damage are hence linearly adjusted

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accordingly. The detailed values of the CFRP mechanical properties are presented in Section 5 for the

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numerical study.

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2.3 Experimental setup

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Figure 3 illustrates the schematic diagram and experimental setups for the quasi-static and

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dynamic impact three-point bending tests. In the two loading cases, the radius of the cylindrical punch

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and supports is R=12 mm, and the span between the two supports is S=180 mm. Two repetitions are

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tested in each case.

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The quasi-static bending tests are performed on a 100 kN capacity universal testing machine with

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computer control and data acquisition system. The loading speed is kept constant to be 1 mm/s, and

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the stoke distance is set as δ=85 mm. For the pure CFRP tubes, the loading process is manually

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terminated, when the reaction force drops to almost zero.

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The dynamic impact tests are conducted on a drop-hammer test machine. The total mass of the

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hammer is 78.1 kg, and the release height is set as 1.35 m above the specimens. Due to the influence

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of friction, the impact velocity is measured to be 5.1 m/s before the hammer contacts with the

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specimens. The stroke distance in the impact tests is δ=87.5 mm, and two buffers are put below the

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hammer to terminate the impact process.

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3. Quasi-static tests

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3.1 Deformation process and force response

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In the quasi-static tests, the deformation processes of the specimens are recorded by a video

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camera. In all cases, the two repetitions of the specimens show almost the same deformation behavior.

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Figure 4 presents a typical deformation process of the pure CFRP tubes. When the punch is in contact

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with the CFRP, inter/intra-lamina cracks are first generated for the composites in the upper corners.

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With the ongoing of the loading, the cracks on the top flange propagate from the corners to the center,

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while those on the web plates spread from top to bottom. Finally, the fibers in the top flange and web

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plates are completely fractured, and asymmetric deformation is observed for the structures.

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The force-displacement curves of the pure CFRP tubes are shown in Fig. 5(a). The response

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curves can be generally divided into two stages. In the first stage, the crushing force increases to a

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peak rapidly, and it then drops gradually in the second stage. It is obvious that the pure CFRP tubes

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are not desirable for energy absorption since the fiber break significantly reduces the load bearing

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capability and load uniformity of the structure.

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The deformation processes of A2 and A4 in the quasi-static tests are presented in Fig. 6. The two

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Al multi-cell sections show similar deformation behavior. The plastic deformation is first formed in

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the areas beneath the punch, and it then expands to the adjacent regions. The punch indents into the

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tube and almost the whole cylindrical punch head is enclosed by the deformed flange and web plates.

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The force-displacement curves of the Al tubes are plotted in Fig 5(b) and (c). The two Al sections

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show different force response tendencies since the bending resistance of thin-walled beams is

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significantly affected by the sectional shape. For A2, the crushing force increases rapidly to an initial

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peak and then decreases to some extent. After that, the force rises again to a much higher second peak

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and finally drops again. As for A4, the crushing force increases fast to an initial peak and then keeps

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rising to a second peak, and finally declines gradually.

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Figure 7 presents the deformation behavior of CA2 and CA4. The collapse of these hybrid tubes

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is dominated by the plastic deformation of the Al multi-cell profiles and accompanied by the failure of

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the CFRP. The significant local indentation and global bending co-occur for the tubes in the

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deformation processes, and the CFRP in the center region is completely broken. Generally, the CFRP

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restrains the outward deformation of the Al walls, while the deformation of the Al walls and the

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compression of the punch lead to the failure of the CFRP.

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The force response curves of CA2 and CA4 are plotted in Fig. 5(d) and (e), respectively. It is

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noted that the crushing force drops sharply at the approximate δ=45 mm due to the tensile fracture of

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fibers in the bottom flange in the center region. The force response curves can be divided into two

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stages by taking δ=45 mm as the boundary. In the earlier stage, the crushing force of the CA2 rises to

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the initial peak and then descends, and finally, it increases again, while that of the CA4 keeps

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increasing slowly after the initial peak. In the later stage, after the drastic drop, the force of the CA2

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keeps almost constant, while that of the CA4 increases gradually. Figure 5(f) compares the force

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responses of various specimens. Due to the CFRP enhancement, the Al/CFRP tubes get much higher

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crushing force than their Al counterparts.

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The final deformed shapes of the specimens in the quasi-static tests are presented in Fig. 8. For

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the pure CFRP tubes, the cracks are concentrated on the top flange and web plates, while the bottom

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flange is almost undamaged. The center part of one CFRP specimen breaks into fragments, and the

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fragments are not shown here. Furthermore, the CFRP tubes almost revert to the initial straight state

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after unloading due to the spring back of the material.

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As for the Al tubes, the top flange collapses inward, and multi-folds are formed on the top flange

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and web plates. The global bending is accompanied by the local indentation for these tubes. This

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deformation mode is attributed to the relatively lower indentation resistance and higher bending

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resistance of the beams, as addressed by Huang and Zhang [19-20]. The deformed shapes of the

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Al/CFRP tubes are similar to those of the Al tubes. The inner Al parts are bent with significant local

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indentation, and the CFRP around the punch is completely fractured.

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3.2 Energy absorption characteristics

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To better understand the influence of the composite wrapping on the energy absorption

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performance of the tubes, the energy absorption indices are calculated in two different displacement

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ranges. The first range is between 0 and 45 mm to exclude the complete fracture of composite, while

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the other covers the whole loading process.

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The energy absorption indices in these two ranges are summarized in Table 1. The indices

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include the energy absorption E, mean crushing force Pm, and specific energy absorption SEA (energy

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absorption per unit mass). Due to the brittle fracture of the composite, the Pm and SEA values of

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CFRP tubes are much lower than those of the Al and Al/CFRP tubes. By introducing the CFRP

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wrapping, the Pm values of A2 and A4 are increased by 27% and 41% in the first stage. Considering

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the mass increase due to CFRP wrapping, the SEA of A2 in the first range is decreased by 3%, while

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that of A4 is increased by 10%. In the whole range, the Pm values of CA2 and CA4 are 28% and 36%

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higher than those of their Al counterparts, respectively. In this case, the CFRP wrapping still almost

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has no improvement on the SEA of CA2, while the SEA of A4 is increased by 7%.

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The energy absorption of the Al/CFRP tubes is also affected by the interaction between Al and

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CFRP parts, just as addressed by Sun et al. [32]. To investigate the interaction effect, we compare the

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energy absorption E of the hybrid tubes with the sum of that of the corresponding Al and CFRP tubes.

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The total energy absorption E is calculated within the first 40 mm in the distance, since the pure CFRP

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tubes almost have no load carrying capacity when the crushing distance exceeds 40 mm. The sum of

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the energy absorption of A2 and CFRP is 89.17 J, and that of A4 and CFRP is 111.94 J. As for the

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hybrid tubes, the E values of CA2 and CA4 are 94.74 and 134.20 J, respectively. The relatively higher

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E values of the hybrid tubes indicate that the contribution of the interaction effect on energy

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absorption is 6.3% and 19.9% for the CA2 and CA4, respectively.

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4. Dynamic impact tests 8

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4.1 Deformation mode and force response

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Figure 9 shows the deformed shapes of the double-cell and quadruple-cell Al and Al/CFRP tubes

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in the dynamic impact tests. All the specimens exhibit global bending deformation with local

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indentation features, and the CFRP layers of the hybrid tubes are broken into two segments in the

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center areas. The deformed shapes of the specimens in quasi-static and dynamic tests are compared in

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Fig. 10. Generally, the deformation modes in the dynamic tests are similar to those in the quasi-static

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loading. However, obvious asymmetric deformation is observed for A2 and CA2 specimens in the

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dynamic loading, whose web plates tilt to one side in the lateral direction. Theoretically, the

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deformation of the middle rib breaks the balance of the stress distribution of the multi-cell sections

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and leads to the asymmetric deformation of the structures. This asymmetric deformation is aggravated

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in the dynamic loading and reduced to some extent by introducing the CFRP wrapping.

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The force-displacement curves of the specimens in the dynamic tests are plotted in Fig. 11. In all

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cases, the two repetitions give almost the same force responses, and the only small difference is

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observed for the curves of A2 in the later stage. This difference should be attributed to the slight

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difference in their asymmetric deformation processes. When compared with the quasi-static results,

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the dynamic force responses show four different features. Firstly, the crushing force in the dynamic

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loading fluctuates more violently than that in the quasi-static loading. Second, the initial peak force in

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the impact tests is much higher. The inertia effect in the dynamic loading should be the major reason

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for this. Third, the crushing force drops sharply at about δ=87.5 mm in the dynamic tests. This drop is

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due to the action of the buffers, and the loading process is then terminated. Fourth, in dynamic loading,

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the CFRP in the center area is wholly broken at δ=35 mm, which leads to the drastic drop of the

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crushing force. However, the CFRP is broken at δ=45 mm in the quasi-static tests. It seems that the

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CFRP is easier to fracture in the dynamic loading.

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4.2 Energy absorption indices

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In the dynamic loading, the energy absorption indices are also calculated in two different ranges,

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which is the same as done in quasi-static loading. The crashworthiness indices are listed in Table 2.

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Due to the CFRP enhancement, the mean crushing forces of A2 and A4 are increased by 12% and 24%

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in the first stage, while the increase rates are 21% and 28% in the whole stage. Due to different

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structural masses, the SEA values of CA2 are 16% and 9% lower than those of A2 in the first stage

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and whole process, respectively. For A4 and CA4, the calculated Pm and SEA values are almost the

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same in these two ranges.

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The energy absorption indices in quasi-static and dynamic tests are compared here to investigate

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the dynamic effect. For the first stage, the dynamic mean crushing forces of the Al tubes are 14%-16%

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higher than the quasi-static results, while the Pm values in the two load cases are identical for the

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Al/CFRP hybrid tubes. In the whole stage, compared with the quasi-static results, the dynamic Pm

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values of A4 and CA4 are increased by 14% and 7%, respectively. However, the dynamic mean

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crushing force of A2 is equal to the quasi-static one, while that of CA2 is even 5% lower than the

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quasi-static result in the whole process. The non-increase of Pm is due to the aggravated asymmetric

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deformation of the double-cell sections in dynamic loading (in Fig. 10), which decreases the structural

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collapse resistance. The index SEA shows a similar tendency as Pm in the two loading conditions.

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5. Numerical simulation

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5.1 Finite element model

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The quasi-static and dynamic experimental tests are simulated by utilizing the commercial finite

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element software ABAQUS/Explicit. Figure 12(a) shows the finite element model for the impact test

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of quadruple-cell Al/CFRP tubes, which is a representative model for all the tests. The numerical

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model includes five parts: the punch, supports, the Al profile, CFRP plies, and the adhesive layers.

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The rigid element (R3D4) was employed to model the punch and supports. The Al and CFRP parts are

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discretized by conventional shell elements (S4R). The cohesive element (COH3D8) is used to model

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the adhesive layers. A mesh sensitivity analysis is performed to determine the mesh size. Three

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different mesh sizes: 0.5, 1.0, and 1.5 mm are adopted for the impact analysis of CA4, and the force-

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displacement curves are shown in Fig. 12(b). It is noted that the mesh size of 1.0 mm is fine enough to

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achieve good accuracy and is employed in the following analysis.

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In the numerical model, the surface to surface contact is defined to simulate the interaction

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between specimens and the punch or supports, and the general contact is applied to account for the

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self-contact of the specimens. Considering the different surface roughness, for the pure Al tubes, the

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friction coefficient for all the contacts is 0.3 [20], while for the pure CFRP and Al/CFRP tubes, it is

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set as 0.1 [30].

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For the quasi-static simulations, the loading speed has to be increased to complete the

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calculations in a reasonable time. According to the principles proposed by Santosa et al. [39], the

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loading speed is ramped to 1 m/s in the first 20 ms and then kept constant in the remaining process. In

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the simulation the impact tests, a point mass of 78.1 kg is applied in the center of the punch. The

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initial velocity of the punch is set as 5.1 m/s. The gravitational acceleration is defined as 9.81 m/s2 for

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all the parts.

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According to the ABAQUS documentation [40], the aluminum material is modeled by the elasto-

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plastic constitutive model, and the true stress-strain data converted from the engineering stress-strain

278

curves are used as input. The traction separation law is defined for the cohesive elements.

279

The thickness of these elements is specified as 0.1 mm and the related parameters are given in Table 3.

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The constitutive model of the CFRP plies is implemented by a user-defined material subroutine

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VUMAT. Detailed information about the traction-separation law and the VUMAT subroutine has

282

been introduced in references [38, 41-42], and it is hence not presented here. The mechanical

283

properties of the CFRP are listed in Table 4, and the related parameters for the plastic and failure

284

behaviors of CFRP under shear loading are summarized in Table 5.

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5.2 Numerical results

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According to the experimental results, the deformation and failures of the specimens are mainly

287

concentrated in the areas around the punch. In this subsection, the simulated deformation

288

characteristics in the center region of the specimens are compared with the experimental results. For

289

the pure CFRP and Al/CFRP tubes, the tensile damage statuses along the warp direction (SVD1) of

290

the CFRP are given in the numerical results. As for the pure Al tubes, the Von Mises stress of the

291

structures is plotted in the simulation results.

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The deformation processes of the pure CFRP, Al and Al/CFRP tubes in the quasi-static tests are

293

shown in Figs. 4, 6, and 7, respectively. It is noted that the deformation behaviors in simulations are in

11

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good agreement with those in the experiments. Figure 8 presents the final deformed shapes of the

295

tubes in the quasi-static loading, and the simulations give almost the same deformation patterns as the

296

experiment for the Al and Al/CFRP tubes. For the pure CFRP tubes, the simulated deformed shape is

297

different from the experiment, since the spring back of CFRP after unloading is not considered in the

298

simulation. The deformed shapes of tubes in the dynamic loading are presented in Fig. 9. The

299

simulation and experiment results compare fairly well.

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The force-displacement curves of the specimens in quasi-static and dynamic loading are plotted

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in Fig. 5 and 11, respectively. The simulated crushing force responses show good agreement with the

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experiment results. To further understand the differences between simulation and experimental results,

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the mean crushing forces in simulation (Pm-simu) are compared with the average mean forces in

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experiments (Pm-avg). As shown in Table 1 and 2, the error of the mean crushing force (Pm-simu/Pm-avg –

305

1) is 13.3% for the pure CFRP specimens, while it is less than 7.2% for the Al and Al/CFRP hybrid

306

tubes.

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Considering the high diversity of CFRP failure behavior, the present finite element model

308

simulates the three-point bending response of the thin-walled tubes with an excellent accuracy. The

309

numerical model is hence employed to perform the parametric study on the bending collapse

310

responses of the Al/CFRP hybrid tubes.

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6. Parametric study and discussion

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In this section, parametric studies are performed to investigate the influences of several critical

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factors on the bending responses of Al/CFRP tubes. These factors include the Al wall thickness, the

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number of CFRP plies, loading velocity, partial CFRP wrapping, and sectional shape. In the

315

parametric analyses, the dimensions of the square Al profiles are kept unvaried as the length L=270

316

mm and outside width b=32 mm. The numerical model validated in the previous section is adopted,

317

and the default parameters in the simulations are set as the Al wall thickness t=1.0 mm, the number of

318

CFRP plies n=3 and initial velocity V=5.1 m/s. When the effect of one factor is investigated, other

319

parameters are kept constant. The stroke distance is set to δ=80 mm, and the crashworthiness indices

12

320

are also calculated in two different ranges: the first one covers the first half stage 0-40 mm, and the

321

second one includes the whole process 0-80 mm.

322

6.1 Al wall thicknesses

323

The wall thickness of the Al profiles is a critical factor for the bending responses of the hybrid

324

tubes. Numerical simulations are performed for double-cell and quadruple-cell Al/CFRP tubes with

325

three different Al wall thicknesses: t=1.0, 1.5 and 2.0 mm to analyze its influence.

326

The deformed shapes of the Al/CFRP tubes are shown in Fig. 13. It is noted that the CFRP plies

327

in the center areas are wholly fractured, and the hybrid tubes show two different deformation modes:

328

bending with indentation and bending collapse. The deformation mode of a tube is determined by the

329

relative strength on the resistance of the bending collapse and local indentation. Due to the relatively

330

lower indentation resistance of thin Al sections, CA2 and CA4 with t=1.0 mm deform in the bending

331

with indentation mode. For t=1.5 and 2.0 mm, the bending collapse mode is developed for the hybrid

332

tubes.

333

Figure 14 presents the force-displacement curves of the Al/CFRP tubes with three different Al

334

wall thicknesses. In general, the increase of t results in higher crushing force and smaller distance for

335

the sharp drop of the force. However, the sharp drop is not significantly observed for CA2 with t=1.0

336

mm, which is similar to that of CA2 in the dynamic impact tests (in Fig. 11). This occurrence may be

337

associated with the severe asymmetric deformation of the relatively thin double-cell section. This

338

severe asymmetric deformation leads to the torsion and skew of the beam and primarily results in the

339

shear failure of the fibers in the bottom flange, instead of the tension fracture.

340

The energy absorption indices of the Al/CFRP tubes are calculated in Table 6. When t increases

341

from 1 mm to 2 mm, the Pm of CA2 and CA4 are increased by 153% and 140% in the first stage, and

342

by 108% and 113% in the whole process, respectively. The increments of SEA for CA2 and CA4 are

343

up to 43% and 34% in the first stage, and 17% and 18% in the whole stage. It can be concluded that

344

the increase of Al wall thickness is an effective approach to increase the crashworthiness of the

345

Al/CFRP tubes.

346

6.2 The number of CFRP plies

13

347

The influence of the number of CFRP plies on the collapse responses of the Al/CFRP tubes is

348

investigated here. Numerical simulations are carried out for CA2 and CA4 tubes with 3, 5 and 7 layers

349

of CFRP.

350

The deformed shapes of the Al/CFRP tubes are presented in Fig. 15. All these tubes develop the

351

bending with indentation mode, and the CFRP layers in the central region are completely broken. The

352

force-displacement curves of the tubes are plotted in Fig. 16. It is noted that the crushing force is

353

increased with the increase in the number of CFRP plies.

354

The energy absorption indices of the Al/CFRP tubes are listed in Table 7. Due to the

355

enhancement of CFRP, the Pm of CA2 and CA4 is increased by 23%-47% and 20%-35% in the first

356

stage, and 18%-40% and 16%-31% in the whole process. Considering the increase in structural mass,

357

the increase of CFRP layers has a slight improvement on the SEA of CA2 (6%-12%) and CA4 (5%-

358

6%) in the first stage, while it almost has no enhancement on SEA in the whole process.

359

6.3 Loading velocity

360

The influence of loading velocity on the crashworthiness of the Al/CFRP tubes is investigated in

361

this subsection. Numerical simulations are performed for Al/CFRP tubes loaded with three different

362

initial velocities V=5.1, 15 and 25 m/s.

363

The deformation patterns of the tubes are shown in Fig. 17. All these tubes deform in the bending

364

with indentation mode, and the CFRP in the center is completely fractured. The force response curves

365

of the tubes are plotted in Fig. 18. The increase of the initial loading velocity leads to much higher

366

force levels in the initial stage (δ < 10 mm), while it has a small influence on the crushing force in the

367

subsequent stages.

368

The energy absorption indices of the Al/CFRP tubes are summarized in Table 8. It is noted that

369

both Pm and SEA values are increased with the increase of the loading velocity. When the initial

370

loading velocity is increased from 5.1 m/s to 25 m/s, the Pm values of CA2 and CA4 are increased by

371

22% and 25% in the first stage, and 19% and 20% in the whole process, respectively. The SEA shows

372

a similar tendency as Pm when the loading velocity is varied.

373

6.4 Partial wrapping of CFRP

14

374

According to the previous analyses, the deformation is localized around the punch, and the CFRP

375

far from the center region is almost undamaged. To achieve higher energy absorption efficiency,

376

partial wrapping of CFRP on the Al tubes should be a quite promising method, since it can improve

377

the bending resistance of the beams with less mass. The effect of partial CFRP wrapping on the

378

crashworthiness of the Al/CFRP tubes is analyzed here. For simplicity, a parameter λ is defined as the

379

ratio of the length of the CFRP reinforced region to the whole tube length. Al/CFRP tubes with four

380

different λ=1.0, 0.75, 0.50 and 0.25 are analyzed.

381

Figure 19 shows the deformed shapes of the Al/CFRP tubes with partial CFRP wrapping. With

382

the decrease of λ, the deformation mode of CA2 switches from bending with indentation to bending

383

collapse. Nevertheless, the variation of λ almost does not affect the deformation mode of CA4, which

384

is bending with significant local indentation. For CA4 with λ=0.25, the CFRP wrapping region is

385

smaller than the plastic deformation area of Al tube, and the whole CFRP is debonded from the Al

386

profile.

387

Figure 20 plots the force-displacement curves of the tubes with partial CFRP wrapping. It is

388

noted that the force response curves for different λ values at λ>0.25 are almost overlapped for both

389

CA2 and CA4, while the reaction force level is much lower at λ=0.25. The lower crushing force of

390

CA2 at λ=0.25 is due to the switch of the deformation mode [19], while that of CA4 is attributed to the

391

debonding between the Al and CFRP.

392

The energy absorption indices of the Al/CFRP tubes are given in Table 9. For both CA2 and CA4,

393

the Pm values of λ=1.0, 0.75 and 0.5 show very slight difference in the collapse processes, while those

394

of λ=0.25 are much lower. With the decrease of λ, the SEA of CA2 is increased by 6%-11% in the first

395

stage. As for the entire process, the SEA of CA2 is increased by 5-8% at λ=0.75 and 0.50, while it

396

decreased by 16% at λ=0.25 due to the mode switch. When λ decreases from 1 to 0.25, the SEA of

397

CA4 is increased by up to 11% in both the first stage and whole process.

398

6.5 Sectional shapes

399

The sectional shape is a crucial factor for the crashworthiness of Al/CFRP tubes. To investigate

400

its influence, Al/CFRP tubes with single (CA1), double (CA2), quadruple (CA4) and nonuple (CA9)

15

401

cells are analyzed here. Two different cases are discussed: tubes with constant Al wall thickness (t=1.0

402

mm) and those with constant mass (m=170.85 g).

403

The deformation modes of the Al/CFRP tubes are plotted in Fig. 21. In the case of constant

404

thickness, all the tubes deform in the bending with indentation mode, while for the constant mass case,

405

CA1 and CA2 deform in the bending collapse mode, and CA4 and CA9 develop the bending with

406

indentation mode. In the later case, there is a shift of the deformation mode from bending collapse to

407

bending with indentation. This is reasonable since the wall thickness is decreased with the increase of

408

sectional cell number when the mass is kept unvaried, and thinner tubes are more ready to trigger local

409

indentation.

410

Figure 22 presents the force response curves of the tubes. In the case of constant thickness, the

411

increase of the sectional cell number results in a much higher crushing force, and the sharp drop in

412

crushing force is observed for CA4 and CA9. In the case of constant mass, the crushing force before

413

the sharp drop shows a comparable level for all sections. However, CA1 shows considerably lower

414

force level than other sections in the later stage. This is due to the fact that the resistance for bending

415

collapse mode is relatively low, and multi-cell sections achieve higher crushing force than the single-

416

cell counterpart at a relatively large loading distance [22].

417

Table 10 lists the energy absorption indices of the tubes. In the case of constant thickness, the Pm

418

and SEA are increasing with the increase in the number of sectional cells. When the cell number

419

increases from 1 to 9, the Pm values are increased by 125% and 127% in the first stage and the whole

420

process, respectively. At the same time, the SEA is increased by 31% and 32%, respectively. In the

421

case of constant mass, the energy absorption capacity and efficiency of the tubes are growing with the

422

increase of the number of sectional cells. Among these sections, CA9 achieve the highest Pm value,

423

which is 10% and 44% higher than that of CA1 in the first stage and the whole process. Due to the

424

constant mass, the influence of sectional shapes on SEA is the same as that on Pm.

425

7. Conclusion

426

The quasi-static and dynamic three-point bending collapse of multi-cell Al/CFRP square tubes is

427

studied in this paper. The quasi-static and dynamic three-point bending tests are performed for the

16

428

CFRP, Al and Al/CFRP tubes with single, double-cell or quadruple-cell sections first. The deformation

429

characteristics and force responses are then analyzed. The non-linear finite element software

430

ABAQUS/Explicit is employed to simulate the tests and perform the parametric studies. The

431

influences of several critical factors on the bending responses of Al/CFRP tubes are discussed. The

432

major conclusions are summarized as follows:

433

(1) In the quasi-static and dynamic bending tests, all the Al and Al/CFRP specimens collapse in the

434

bending with indentation mode, and the complete fracture of composite in the center region leads

435

to sharp drops in the crushing force of Al/CFRP tubes.

436

(2) The pure CFRP tubes are not efficient for energy absorption due to the brittle fracture during the

437

loading. By introducing the CFRP wrapping, the Pm of the Al tubes is increased by 12%-41%,

438

while the SEA of the tubes is decreased or slightly improved due to the mass increase.

439

(3) The deformation mode and force responses of the tubes in the simulations compare well with the

440

experimental results. The error of Pm is 13.3% for the pure CFRP specimens, while it is less than

441

7.2% for the Al and Al/CFRP hybrid tubes.

442

(4) The deformation mode of the Al/CFRP tubes is determined by the relative strength on the

443

resistance of bending collapse and local indentation. The Al wall thickness, partial CFRP

444

wrapping, and sectional shape have a significant influence on the deformation mode, while the

445

number of CFRP plies and the initial loading velocity of the punch only have a small influence.

446

(5) The increase of the Al thickness can increase both the Pm and SEA of the Al/CFRP tubes.

447

Increasing the number of CFRP plies is also capable of enhancing the energy absorption capacity,

448

while it almost has no improvement on the SEA. The initial loading velocity of the punch

449

significantly affects the crushing force in the early stage, while it has a minor influence on the

450

force in the subsequent stages.

451

(6) Partial CFRP wrapping is an effective approach to increase the crashworthiness of the Al/CFRP

452

tubes. When the plastic deformation region of Al tubes is entirely wrapped by CFRP, the SEA of

453

the hybrid tubes can be increased by 11%. For both constant thickness and constant mass, the

454

multi-cell Al/CFRP tubes outperform their single-cell counterparts in crashworthiness.

17

455

Acknowledgements

456

The present work was supported by National Natural Science Foundation of China (Nos.

457

11672117, 11372115) and Natural Science Fund for Distinguished Young Scholars of Hubei Province.

458

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459

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23

Figure captions Fig. 1. (a) Representative specimens for the three-point bending tests and (b) dimensions of the sections (units: mm). Fig. 2. Stress-strain curves of: (a) AA6063-O, (b) CFRP in tensile tests, (c) CFRP in compression test, (d) CFRP in in-plane shear test; Test curves for bonding strength between CFRP and CFRP: (e) in normal direction, (f) in shear direction, and test curves for bonding strength between CFRP and Al: (g) in normal direction and (h) in shear direction. Fig. 3. (a) A schematic diagram and (b) the experimental setups for the quasi-static and dynamic impact bending tests. Fig. 4. Typical deformation behaviors of pure CFRP tubes in the quasi-static bending tests and simulations. Fig. 5. Force-displacement curves of the specimens in the quasi-static tests and simulations: (a) CFRP, (b) A2, (c) A4, (d) CA2, (e) CA4 and (f) various specimens. Fig. 6. Deformation processes of double-cell and quadruple-cell Al tubes in the quasi-static tests and simulations: (a) A2 and (b) A4. Fig. 7. Typical deformation behaviors of double-cell and quadruple-cell Al/CFRP tubes in the quasi-static bending tests and simulations: (a) CA2 and (b) CA4. Fig. 8. Final deformed shapes of the specimens in the quasi-static three-point bending tests and simulations: (a) CFRP, (b) A2, (c) A4, (d) CA2 and (e) CA4. Fig. 9. Deformed shapes of the specimens in the dynamic impact tests and simulations: (a) A2, (b) A4, (c) CA2 and (d) CA4. Fig. 10. Comparison of the deformed shapes of the specimens in quasi-static and dynamic impact tests. Fig. 11. Force-displacement curves of tubes in the dynamic three-point bending tests and simulations. Fig. 12. (a) The finite element model of quadruple-cell Al/CFRP tubes under dynamic three-point bending tests and (b) force-displacement curves for different mesh sizes. Fig. 13. Deformed shapes of Al/CFRP tubes with different Al wall thicknesses. Fig. 14. Force-displacement curves of Al/CFRP tubes with different Al wall thicknesses. Fig. 15. Deformed shapes of Al/CFRP tubes with different numbers of CFRP plies. Fig. 16. Force-displacement curves of Al/CFRP tubes with different numbers of CFRP layers. Fig. 17. Deformed shapes of Al/CFRP tubes subjected to different initial velocities. Fig. 18. Force-displacement curves of Al/CFRP tubes subjected to different initial velocities. Fig. 19. Deformed shapes of Al/CFRP tubes with partial CFRP wrapping. Fig. 20. Force-displacement curves of Al/CFRP tubes with partial CFRP wrapping. Fig. 21. Deformed shapes of Al/CFRP tubes with different sectional shapes. Fig. 22. Force-displacement curves of Al/CFRP tubes with different sectional shapes.

Tables Table 1 Energy absorption indices for the specimens under quasi-static three-point bending. Table 2 Energy absorption indices for the specimens under dynamic three-point bending. Table 3 Material properties describing the traction-separation law of cohesive elements. Table 4 Mechanical properties of the CFRP under tensile and compressive loading. Table 5 The parameters for the plastic and failure behaviors of CFRP under shear loading. Table 6 Energy absorption indices for the Al/CFRP tubes with different Al wall thicknesses. Table 7 Energy absorption indices for the Al/CFRP tubes with different numbers of CFRP layers. Table 8 Energy absorption indices for the Al/CFRP tubes under different loading velocity. Table 9 Energy absorption indices for the Al/CFRP tubes with partial CFRP wrapping. Table 10 Energy absorption indices for the Al/CFRP tubes with different sectional shapes.

1

32

1.01

0.95 32

1.01

0.95

(b)

(a)

Fig. 1. (a) Representative specimens for the three-point bending tests and (b) dimensions of the sections (units: mm).

2

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 2. Stress-strain curves of: (a) AA6063-O, (b) CFRP in tensile tests, (c) CFRP in compression test, (d) CFRP in in-plane shear test; Test curves for bonding strength between CFRP and CFRP: (e) in normal direction, (f) in shear direction, and test curves for bonding strength between CFRP and Al: (g) in normal direction and (h) in shear direction.

3

(a)

(b)

Quasi-static tests

Impact tests

Drop-hammer test machine

Fig. 3. (a) A schematic diagram and (b) the experimental setups for the quasi-static and dynamic impact bending tests.

4

Fig. 4. Typical deformation behaviors of pure CFRP tubes in the quasi-static bending tests and simulations.

5

(b) A2

(a) CFRP

(c) A4

(d) CA2

(e) CA4

(f) Various specimens

Fig. 5. Force-displacement curves of the specimens in the quasi-static tests and simulations: (a) CFRP, (b) A2, (c) A4, (d) CA2, (e) CA4 and (f) Various specimens.

6

(a) A2

(b) A4

Fig. 6. Deformation processes of double-cell and quadruple-cell Al tubes in the quasi-static tests and simulations: (a) A2 and (b) A4.

7

(a) CA2

(b) CA4

Fig. 7. Typical deformation behaviors of double-cell and quadruple-cell Al/CFRP tubes in the quasi-static bending tests and simulations: (a) CA2 and (b) CA4.

8

(a) CFRP

(b) A2

Simulation

(c) A4

Partial view

Simulation

(d) CA2

Partial view

Simulation

Partial view

(e) CA4

Simulation

Partial view

Simulation

Fig. 8. Final deformed shapes of the specimens in the quasi-static three-point bending tests and simulations: (a) CFRP, (b) A2, (c) A4, (d) CA2 and (e) CA4.

9

(a) A2

Partial view

(b) A4

Simulation

(c) CA2

Partial view

Simulation

Partial view

(d) CA4

Partial view

Simulation

Simulation

Fig. 9. Deformed shapes of the specimens in the dynamic impact tests and simulations: (a) A2, (b) A4, (c) CA2 and (d) CA4.

10

Quasi-static

Dynamic

Quasi-static

Dynamic

Quasi-static

Dynamic

Quasi-static

Dynamic

Fig. 10. Comparison of the deformed shapes of the specimens in quasi-static and dynamic impact tests.

11

Fig. 11. Force-displacement curves of tubes in the dynamic three-point bending tests and simulations.

12

(a)

(b)

Fig. 12. (a) The finite element model of quadruple-cell Al/CFRP tubes under dynamic three-point bending tests and (b) force-displacement curves for different mesh sizes.

13

CA2

t=1.0 mm

CA2

t=1.5 mm

CA2

t=2.0 mm

CA4

t=1.0 mm

CA4

t=1.5 mm

CA4

t=2.0 mm

Fig. 13. Deformed shapes of Al/CFRP tubes with different Al wall thicknesses.

14

Fig. 14. Force-displacement curves of Al/CFRP tubes with different Al wall thicknesses.

15

CA2

layer=3

CA2

layer=5

CA2

layer=7

CA4

layer=3

CA4

layer=5

CA4

layer=7

Fig. 15. Deformed shapes of Al/CFRP tubes with different numbers of CFRP layers.

16

Fig. 16. Force-displacement curves of Al/CFRP tubes with different numbers of CFRP layers.

17

CA2

V=5.1 m/s

CA2

V=15 m/s

CA2

V=25 m/s

CA4

V=5.1 m/s

CA4

V=15 m/s

CA4

V=25 m/s

Fig. 17. Deformed shapes of Al/CFRP tubes subjected to different initial velocities.

18

Fig. 18. Force-displacement curves of Al/CFRP tubes subjected to different initial velocities.

19

CA2

λ=1.0

CA2

λ=0.75

CA2

λ=0.50

CA2

λ=0.25

CA4

λ=1.0

CA4

λ=0.75

CA4

λ=0.50

CA4

λ=0.25

Fig. 19. Deformed shapes of Al/CFRP tubes with partial CFRP wrapping.

20

Fig. 20. Force-displacement curves of Al/CFRP tubes with partial CFRP wrapping.

21

CA1

CA1

t=1.0 mm

m=170.85 g

CA2

CA2

CA4

t=1.0 mm

CA4

m=170.85 g

t=1.0 mm

m=170.85 g

CA9

CA9

Fig. 21. Deformed shapes of Al/CFRP tubes with different sectional shapes.

22

t=1.0 mm

m=170.85 g

Fig. 22. Force-displacement curves of Al/CFRP tubes with different sectional shapes.

23

Table 1 Energy absorption indices for the specimens under quasi-static three-point bending. Stage 1 Section

CFRP-1

Stage 1 + Stage 2

Mass

δ1

E

Pm

SEA

Pm-avg

Pm-simu

Error

δ2

E

Pm

SEA

Pm-avg

Pm-simu

Error

(g)

(mm)

(J)

(kN)

(J/g)

(kN)

(kN)

(%)

(mm)

(J)

(kN)

(J/g)

(kN)

(kN)

(%)

34.75

40.0

16.86

0.42

0.49

/

/

/

/

0.45

0.51

13.3

/

/

/

/

/

/

/

1.92

1.93

0.5

82.8

180.80

2.18

1.68

81.9

174.20

2.13

1.60

2.16

2.18

0.9

2.42

2.46

1.7

85.0

203.10

2.39

1.58

85.0

204.40

2.40

1.59

2.40

2.36

-1.7

85.0

235.10

2.77

1.65

2.45

2.48

1.2

85.0

233.70

2.75

1.64

2.76

2.71

-1.8

3.39

3.15

-7.1

85.0

278.60

3.28

1.70

85.0

275.60

3.24

1.68

3.26

3.10

-4.9

CFRP-2

35.23

40.0

19.19

0.48

0.54

A2-1

107.87

45.0

85.68

1.90

0.79

A2-2

108.76

45.0

87.32

1.94

0.80

A4-1

128.58

45.0

109.14

2.43

0.85

A4-2

128.70

45.0

107.99

2.40

0.84

CA2-1

142.78

45.0

112.71

2.50

0.79

CA2-2

142.90

45.0

107.79

2.40

0.75

CA4-1

164.01

45.0

157.05

3.49

0.96

CA4-2

164.31

45.0

148.23

3.29

0.90

24

Table 2 Energy absorption indices for the specimens under dynamic three-point bending. Stage 1 Section

A2-1

Mass

δ1

E

Pm

SEA

Pm-avg

Pm-simu

Error

δ2

E

Pm

SEA

Pm-avg

Pm-simu

Error

(g)

(mm)

(J)

(kN)

(J/g)

(kN)

(kN)

(%)

(mm)

(J)

(kN)

(J/g)

(kN)

(kN)

(%)

106.98

45.0

98.03

2.18

0.92

85.0

190.62

2.24

1.78

2.19

2.16

-1.4

85.0

175.68

2.07

1.63

2.16

2.23

3.2

2.79

2.81

0.7

85.0

229.49

2.71

1.78

85.0

232.64

2.76

1.80

2.74

2.90

5.8

2.45

2.66

8.6

85.0

226.60

2.67

1.59

85.0

218.17

2.57

1.52

2.62

2.71

3.4

85.0

296.65

3.49

1.80

3.47

3.29

-5.2

85.0

296.99

3.49

1.81

3.49

3.25

-6.9

A2-2

107.72

45.0

98.73

2.19

0.92

A4-1

129.07

45.0

126.18

2.80

0.98

A4-2

129.26

45.0

124.88

2.78

0.97

CA2-1

142.28

45.0

107.01

2.38

0.75

CA2-2

143.83

45.0

113.18

2.52

0.79

CA4-1

164.65

45.0

155.98

3.47

0.95

CA4-2

Stage 1 + Stage 2

164.50

45.0

155.93

3.47

0.95

25

Table 3 Material properties describing the traction separation law of cohesive elements.

Elastic properties (MPa)

Variable

Delamination

Debonding

Kn

1000

1000

Ks

1000

1000

Kt

1000

1000

0

4.8

3.4

0

14.8

9.4

tt0

tn Damage initiation (MPa)

ts

14.8

9.4

c

202

143

c

891

566

Gtc

891

566

η

2.284

2.284

Gn 2

Fracture energies (J/m )

BK

Gs

26

Table 4 Mechanical properties of the CFRP under tensile, compressive and in-plane loading.

3

Density (kg/m )

Elastic properties (GPa)

Damage initiation (MPa)

2

Fracture energies (kJ/m )

27

Variable

Value

ρ

1320

E1

42.7

E2

42.7

G12

4.4

v12

0.05

X1+

643

X1-

267

X2+

643

X2-

267

S

37

Gfc1+

83

Gfc1-

72

Gfc2+

83

Gfc2-

72

Table 5 The parameters for the plastic and failure behaviors of CFRP under shear loading. Coefficient in the shear damage variable Maximum value of shear damage variable

β12

0.18

d12max

0.99

^

Initial effective shear yield stress (MPa)

σy0

58

Power term in the hardening equation

C

1053

Coefficient in the hardening equation

P

0.41

28

Table 6 Energy absorption indices for the Al/CFRP tubes with different Al wall thicknesses. Stage 1 Section

Stage 1 + Stage 2

t

Mass

δ1

E

Pm

SEA

δ2

E

Pm

SEA

(mm)

(g)

(mm)

(J)

(kN)

(J/g)

(mm)

(J)

(kN)

(J/g)

CA2

1.0

148.25

40

113.93

2.85

0.77

80

223.15

2.79

1.51

CA2

1.5

204.75

40

174.33

4.36

0.85

80

319.13

3.99

1.56

CA2

2.0

261.25

40

287.91

7.19

1.10

80

464.07

5.80

1.76

CA4

1.0

170.85

40

133.42

3.34

0.78

80

257.17

3.21

1.51

CA4

1.5

238.65

40

222.59

5.56

0.93

80

376.26

4.70

1.58

CA4

2.0

306.45

40

320.78

8.02

1.05

80

548.17

6.85

1.78

29

Table 7 Energy absorption indices for the Al/CFRP tubes with different numbers of CFRP plies. Stage 1 Section

Layer

Stage 1 + Stage 2

Mass

δ1

E

Pm

SEA

δ2

E

Pm

SEA

(g)

(mm)

(J)

(kN)

(J/g)

(mm)

(J)

(kN)

(J/g)

CA2

3

148.25

40

113.93

2.85

0.77

80

223.15

2.79

1.51

CA2

5

171.75

40

140.12

3.50

0.82

80

262.86

3.28

1.53

CA2

7

195.25

40

167.75

4.19

0.86

80

311.46

3.89

1.60

CA4

3

170.85

40

133.42

3.34

0.78

80

257.17

3.21

1.51

CA4

5

194.35

40

159.67

3.99

0.82

80

297.05

3.71

1.53

CA4

7

217.85

40

180.39

4.51

0.83

80

337.38

4.22

1.55

30

Table 8 Energy absorption indices for the Al/CFRP tubes under different loading velocity. Stage 1 Section

Stage 1 + Stage 2

V

Mass

δ1

E

Pm

SEA

δ2

E

Pm

SEA

(mm)

(g)

(mm)

(J)

(kN)

(J/g)

(mm)

(J)

(kN)

(J/g)

CA2

5.1

148.25

40

113.93

2.85

0.77

80

223.15

2.79

1.51

CA2

15

148.25

40

131.63

3.28

0.89

80

247.89

3.10

1.67

CA2

25

148.25

40

139.11

3.48

0.94

80

266.52

3.33

1.80

CA4

5.1

170.85

40

133.42

3.34

0.78

80

257.17

3.21

1.51

CA4

15

170.85

40

152.36

3.80

0.89

80

293.13

3.66

1.72

CA4

25

170.85

40

166.26

4.15

0.97

80

307.51

3.84

1.80

31

Table 9 Energy absorption indices for the Al/CFRP tubes with partial CFRP wrapping. Stage 1 Section

λ

Stage 1 + Stage 2

Mass

δ1

E

Pm

SEA

δ2

E

Pm

SEA

(g)

(mm)

(J)

(kN)

(J/g)

(mm)

(J)

(kN)

(J/g)

CA2

1.00

148.25

40

113.93

2.85

0.77

80

223.15

2.79

1.51

CA2

0.75

139.44

40

113.61

2.84

0.81

80

220.21

2.75

1.58

CA2

0.50

130.63

40

111.88

2.80

0.86

80

213.29

2.67

1.63

CA2

0.25

121.81

40

99.07

2.47

0.81

80

154.69

1.93

1.27

CA4

1.00

170.85

40

133.42

3.34

0.78

80

257.17

3.21

1.51

CA4

0.75

162.04

40

132.87

3.32

0.82

80

257.05

3.21

1.59

CA4

0.50

153.23

40

132.41

3.31

0.87

80

256.42

3.20

1.67

CA4

0.25

144.41

40

121.04

3.02

0.84

80

220.67

2.76

1.53

32

Table 10 Energy absorption indices for the Al/CFRP tubes with different sectional shapes. Stage 1 Section

Stage 1 + Stage 2

t

Mass

δ1

E

Pm

SEA

δ2

E

Pm

SEA

(mm)

(g)

(mm)

(J)

(kN)

(J/g)

(mm)

(J)

(kN)

(J/g)

CA1

1.00

125.65

40

89.03

2.23

0.71

80

174.78

2.18

1.39

CA2

1.00

148.25

40

113.93

2.85

0.77

80

223.15

2.79

1.51

CA4

1.00

170.85

40

133.42

3.34

0.78

80

257.17

3.21

1.51

CA9

1.00

216.05

40

200.85

5.02

0.93

80

397.09

4.96

1.84

CA1

1.48

170.85

40

134.37

3.36

0.79

80

212.06

2.65

1.24

CA2

1.19

170.85

40

125.94

3.15

0.74

80

244.97

3.06

1.43

CA4

1.00

170.85

40

133.42

3.34

0.78

80

257.17

3.21

1.51

CA9

0.76

170.85

40

147.69

3.69

0.86

80

304.53

3.81

1.78

33

Highlights (1) Quasi-static and dynamic three-point bending tests are conducted for Al/CFRP tubes; (2) Numerical analyses are performed to simulate the tests and analyze the mechanisms; (3) The bending responses and energy absorption performances of tubes are analyzed; (4) The influences of various factors on the bending responses of tubes are investigated; (5) The multi-cell Al/CFRP tubes outperform the single-cell counterparts in crashworthiness.

Declaration of interests

☐√ 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.