Experimental comparison of energy absorption characteristics of polyurethane foam-filled magnesium and steel beams in bending

Accepted Manuscript Title: Experimental comparison of energy absorption characteristics of polyurethane foam-filled magnesium and steel beams in bending Author: Ping Zhou, Elmar Beeh, Michael Kriescher, Horst E. Friedrich, Gundolf Kopp PII: DOI: Reference:

S0734-743X(16)30034-3 http://dx.doi.org/doi: 10.1016/j.ijimpeng.2016.02.006 IE 2650

To appear in:

International Journal of Impact Engineering

Received date: Revised date: Accepted date:

16-5-2015 16-11-2015 12-2-2016

Please cite this article as: Ping Zhou, Elmar Beeh, Michael Kriescher, Horst E. Friedrich, Gundolf Kopp, Experimental comparison of energy absorption characteristics of polyurethane foam-filled magnesium and steel beams in bending, International Journal of Impact Engineering (2016), http://dx.doi.org/doi: 10.1016/j.ijimpeng.2016.02.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

Experimental comparison of energy absorption characteristics of polyurethane foam-filled magnesium and steel beams in bending Ping Zhoua,*, Elmar Beeha, Michael Krieschera, Horst E. Friedricha, Gundolf Koppa a

German Aerospace Centre (DLR) - Institute of Vehicle Concepts, Pfaffenwaldring 38-40, 70569

Stuttgart, Germany

Highlights: • Empty and foam-filled AZ31B and DC04 beams were tested in three-point bending. • Both AZ31B and DC04 beams show an effect of strain rate on the energy absorption. • A higher density foam achieves higher bending resistance, but fractures earlier. • AZ31B significantly outperforms DC04 in terms of specific energy absorption. • AZ31B beams reach higher specific energy absorption than steel DC04 beam.

Abstract Lightweight magnesium alloys and polyurethane foams have attracted much attention in the automotive industry due to their potential to reduce vehicle weight. This study conducted quasi-static/dynamic three-point bending tests to investigate the energy absorption characteristics and deformation behaviour of empty and polyurethane foam-filled magnesium alloy AZ31B thin-walled beams, and to make comparisons with mild steel DC04 beams. The results showed that both deformation/fracture modes and energy absorption capacity of the thin-walled beams subjected to bending loads depend on the strain rate and other parameters, such as the beam material’s strength and ductility, foam density and wall thickness. Both the DC04 beams and AZ31B extruded beams showed a positive effect of strain rate on the energy absorption capacity. A beam filled with a higher density foam achieves higher bending resistance, but fractures at a smaller deflection. The experiments demonstrated that AZ31B significantly outperforms DC04 in terms of energy absorption and specific energy absorption for the foam-filled beams, when the *

Corresponding author Email address: [email protected] (Ping Zhou)

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beams are subjected to bending loads at a deflection of 250 mm. However, this gain could be weakened when the performance is assessed at a larger fracture deflection because the foam-filled AZ31B beams tend to fracture at smaller deflections. For applications which require limited deformation, there is a possibility to develop lightweight auto-body structures such as rocker rails by substituting foam-filled AZ31B structures for mild steel structures, while maintaining or exceeding their current crashworthiness and safety. Keywords: Magnesium alloy; Polyurethane foam; Thin-walled beam; Energy absorption; Bending collapse 1.

Introduction Driven by automotive lightweighting goals through multi-material design, the wide

applications of light metals (e.g. aluminium alloys, magnesium alloys and titanium alloys), advanced and ultra high-strength steels, composites (e.g. carbon and glass fibre reinforced plastics) and cellular solids (e.g. honeycombs, metallic and polymeric foams) become increasingly attractive in the automotive industry [1, 2]. Magnesium alloys have always been attractive to automotive manufacturers due to their low density (≈ 1.8 g/cm3), high strength-to-weight ratio, high damping resistance, easy recycling and so on. It is generally accepted that the expanded applications of magnesium alloy products on automotive structures should provide an effective way to reduce vehicle weight and thus improve energy efficiency and driving capability for electric vehicles. Up to now, the majority of the applications of magnesium alloys are limited to few high pressure die casting (HPDC) products, such as engine components, transmission cases, steering wheels and instrument panels, due to their inherent advantages such as excellent structural integrity and high pressure die castability [3, 4, 5]. Recently, there is a desire to employ magnesium alloys as crashworthy components in automotive body-in-white structures; therefore more attention has been paid to wrought magnesium alloys, i.e. rolled sheets and extrusions, which generally exhibit higher strength and ductility than HPDC magnesium alloys. For instance, the European collaborative R&D project “SuperLIGHT-CAR” [6] and Canada-China-USA collaborative R&D project “MFERD” [7] have already carried out a large amount of systematic research in this field. Generally, good crashworthiness, safety, structural integrity and corrosion resistance are required in such applications. However, overcoming wrought magnesium alloys’ disadvantages, such as inferior cold formability, corrosion resistance and joinability to dissimilar materials, is still a challenging task.

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Magnesium alloys show different mechanical characteristics compared with steels and aluminium alloys. Due to their hexagonal close-packed (HCP) structure, magnesium alloys can only initiate limited crystallographic slips and twinning at room temperature, resulting in low ductility [8]; whereas much higher ductility can be achieved at warm temperatures because more deformation mechanisms can be activated [9]. Moreover, during traditional rolling and extrusion processes, the normal of the basal plane of the HCP crystal generally aligns perpendicular to the rolling and extrusion direction respectively. This not only forms strong texture and plastic anisotropy [10, 11, 12], but also leads to pronounced tension-compression asymmetry [9, 13] which is characterised as a large strength difference between tension and compression and a very high work hardening rate in compression. Pronounced strain rate sensitivity induced by different deformation mechanisms under different load rates is another major feature of magnesium wrought alloys, thus providing an advantage in energy absorption in crash scenarios. Comprehensive studies regarding the effect of strain rate sensitivity have been covered in the literature [12, 13, 14, 15]. Considerable effort has been devoted to improve the mechanical properties of wrought magnesium alloys through optimising forming processes or developing new alloys [16, 17, 18, 19, 20]. In terms of structural applications, much attention in recent ten years has been paid to the deformation mechanisms and mechanical behaviour of magnesium alloy thin-walled structures subjected to axial compressive loads. Dørum et al. [21, 22] studied the force-deformation characteristics and deformation modes including the fracture modes of HPDC magnesium AM60 single and double U-shaped thin-walled sections with or without interior reinforcing ribs in axial crushing. Later, they investigated several thin-walled magnesium HPDC components as energy absorber under axial compressive loads using a shear-bolt principle and achieved good energy absorption characteristics [23, 24]. In recent years, Wagner et al. [25, 26] studied the deformation characteristics of magnesium AM30 extruded beams and AZ31 sheet beams in axial crushing. In such cases, magnesium beams do not produce the so-called accordion shaped deformation mode [27] like steel and aluminium beams; instead, they crack and split into large fragments. Rossiter et al. [28, 29] performed finite element simulation utilising a material model considering tension-compression asymmetry and specific failure criteria. Beggs et al. [30] made a comparative study of the failure modes and energy absorption capacity of circular tubes subjected to axial compression and the experimental results demonstrated that magnesium AZ31

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extruded tube with thicker wall outperforms both steel and aluminium tubes in term of specific energy absorption because it fractures via fine sharding. Steglich et al. [?] assessed the crashworthiness of the rectangular tubes made of magnesium AZ31 and ZE10 sheet and extrusion under quasi-static axial crushing. It was observed that the higher work hardening rate in uniaxial compression tests contributes to higher energy absorption by the formation of multiple buckles. While considerable effort has been made to understand the deformation mechanisms of generic thin-walled structural members subjected to axial crushing, a previous study [31] on 81 real world vehicle crash scenarios showed that up to 90% involved structural members fail in bending collapse mode. Previous researchers [32, 33, 34, 35, 36] have thoroughly investigated the bending behaviour of different types of steel and aluminium thin-walled structures and developed a series of mathematical models to accurately describe or predict the folding behaviour and bending moment-rotation characteristics. Usually, only a small portion of an empty thin-walled beam undergoes plastic deformation because the bending collapse is localised at plastic hinges with the remaining portion rotating as rigid bodies. Due to the inward fold formation at the compression wall and consequently reduced cross sectional area at plastic hinges, the load carrying capacity drops significantly after the local sectional collapse occurs at a small rotation, resulting in low energy absorption efficiency. To improve the energy absorption efficiency of thin-walled beams, the concept of filling lightweight cellular materials such as metallic or polymeric foams into empty thin-walled beams has received increasing interest. In the past two decades, a number of researchers [37, 38, 39, 40, 41, 42] carried out extensive studies on the bending behaviour of steel and aluminium thin-walled beams filled with lightweight foams by using experimental, analytical and numerical methods. It was found that the internal lightweight foam filler is able to stabilise the cross section of thin-walled beam and retards the local sectional collapse at the compression wall, and therefore significantly improves the load carrying capacity and specific energy absorption. The lightweight foam filler not only absorbs kinetic energy by its own compressive plastic deformation, but also helps the surrounding metallic shell spread plastic deformation over a larger bending zone by its interaction with the beam walls. However, little attention has been paid to the bending collapse behaviour of empty and foam-filled thin-walled beams made of magnesium alloys. Dørum et al. [21, 22] studied the load

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carrying capacity and fracture behaviour of HPDC magnesium AM60 U-shaped thin-walled beams and found that the material’s inhomogeneous micro-mechanical properties in uniaxial tension and initial geometric imperfections of the profiles lead to a large scatter on the mechanical response of the beams. Easton et al. [43] made a comparative study on the energy absorption capacity of several HPDC magnesium alloys, wrought magnesium alloy AZ31, mild steel HA300 and aluminium alloy 6061-T6 plates in bending and buckling. The experimental investigation performed by Hilditch et al. [44] demonstrated that the magnesium alloy AZ31 extruded circular tube in three-point bending has higher load carrying capacity and energy absorption performance than an equivalent mass tube made of aluminium alloy with similar tensile yield strength. Wagner et al. [26] and Ali [45] studied the bending collapse and its numerical simulation method of thin-walled rectangular magnesium alloy AZ31 sheet beams. Results of these investigations show that some HPDC magnesium alloys and wrought alloy AZ31 thin-walled beams in bending and buckling significantly outperform steels and aluminium alloys with respect to specific energy absorption. This performance may be due to the following two inherent features. First, magnesium thin-walled beams have a higher moment of inertia due to the thicker cross section which is achieved by its lower density, while maintaining its mass. Second, due to the significantly higher work hardening rate in compression, a magnesium thin-walled beam shows a larger radius of curvature, and therefore more material is involved in plastic deformation. Nevertheless, a magnesium thin-walled beam is susceptible to fracture at plastic hinges at a relatively small rotation, which results in a rapid drop of load carrying capacity. The present study develops a foam-filled hybrid structure serving as an energy absorbing component subjected to bending loads. The hybrid structure is comprised of an outer rectangular thin-walled beam made of magnesium AZ31B sheet or extrusion, and a lightweight filler made of polyurethane foam. The main objective is to investigate the energy absorption characteristics and deformation behaviour including fracture modes of empty and polyurethane foam-filled magnesium AZ31B thin-walled beams in quasi-static and dynamic three-point bending tests, and to make a comparison with mild steel DC04 beams [46]. Load carrying capacity and deformation behaviour are discussed for steel sheet, magnesium extruded and sheet beams respectively. Different beams are examined to reveal the effect of strain rate, beam material’s strength and ductility, foam filler, foam density and wall thickness on deformation mode and energy

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absorption performance. 2.

Materials A commercial-grade magnesium alloy AZ31B (Mg-3Al-1Zn-0.3Mn, wt.%) in two

different forms was investigated in this study: extrusions with 3.0 mm nominal wall thickness and fully annealed (O-temper) sheets with 1.8 mm nominal thickness. The AZ31B sheets were produced by twin-roll cast and rolled processes in Thyssen Krupp MgF Magnesium Flachprodukte GmbH. The AZ31B seamless extrusions were fabricated by indirect extrusion process. Unfortunately, the detailed extrusion processing parameters such as extrusion speed, temperature and pressure were not provided to the authors. For comparison purposes, mild steel DC04 sheets with 2.0 mm nominal thickness were also investigated as a reference material. 2.1.

Beam details Rocker rails are primary energy absorption components in car side collision. In such

crash scenarios, these components absorb kinetic energy during bending collapse. As simplified models of typical rocker rails, rectangular thin-walled beams measuring 2000 mm long and 130 mm wide by 90 mm tall were constructed as shown in Fig. 1. For a steel DC04 sheet beam, its cross section was designed with 10.5 mm × 45° chamfers at four corners. The beam was comprised of two U-shaped profiles which were bent from sheets and then joined along the two flanges by resistance seam welding. For a magnesium AZ31B extruded beam, it was designed with the same cross sectional dimension as the steel beam and fabricated without weld seams. For a magnesium AZ31B sheet beam, a design of filleted corners with 20 mm radius was adopted to prevent severe initial damage in the bending zone, because magnesium AZ31B shows much lower ductility than steel DC04. The magnesium sheets were firstly bent into U-shape profiles at room temperature and then joined by tungsten inert gas welding. In the next step, the beams selected for foam-filling were treated by cathodic dip painting to get good interfacial bonding between the metallic shells and foam fillers. Finally, the beam cavities were fully filled with spray polyurethane pre-polymer foam with a nominal density of 0.05 g/cm3 or BETAFOAMTM polyurethane (PUR) foam with nominal density ranges of 0.20 g/cm3, 0.30 g/cm3 or 0.40 g/cm3. The BETAFOAMTM PUR foam produced by The Dow Chemical Company was formed when two chemical components were rapidly mixed together under high shear conditions. It was pumped from bulk containers into heated meter mix equipment. The proper mix ratio was in turn dispensed manually or robotically through an impingement mix gun. The

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foam was bonded to primed metal surfaces during its formation when the mixed components were injected into the beam cavity. The spray polyurethane pre-polymer foam was chosen to study the deformation behaviour of magnesium thin-walled beams filled with low density foam. 2.2.

Mechanical properties Quasi-static uniaxial tensile tests and compressive tests on dog-bone specimens, which

were cut along the rolling direction (RD) or extrusion direction (ED), diagonal direction (DD) and transverse direction (TD), were conducted at room temperature using a static universal material testing machine Zwick Roell Z250. For steel DC04 sheets, only quasi-static uniaxial tensile tests were conducted using the specimens cut along the rolling direction. For the uniaxial tensile tests, standard specimens with 50 mm gauge length and sub-size specimens with 25 mm gauge length outlined in testing standard ASTM E8 were used for sheets and extrusions respectively. The uniaxial compressive tests were conducted in accordance with the testing standard ASTM E9. The dog-boned specimens which were specially designed with 12 mm gauge length and 10 mm gauge width were tested. Flat anti-buckling plates were employed to suppress the buckling of the specimens. In order to prevent initial damage such as cracks or overheating zones on the cutting edges, all the specimens were cut by a water-jet cutting machine and then sanded with 400-grit sandpaper along the cutting edges. Testing speeds were adjusted to obtain nominal strain rates in the range from 0.001 - 0.1 s1. For each test case, at least five specimens were tested to confirm the variation in mechanical properties. Fig. 2 shows the measured average true stress-strain curves in the uniaxial tensile and compressive tests at a nominal strain rate of 0.001 s1 and the primary mechanical properties are summarized in Table. 1. Both the magnesium AZ31B extrusion and sheet exhibited slightly lower yield strength (0.2% YS) than the steel DC04 sheet, however their ultimate tensile strength (UTS) and uniform elongation (UE) and total elongation (TE) were much lower than the steel DC04 sheet. The magnesium AZ31B extrusion exhibited significant anisotropy of yield strength (≈ 120 MPa strength difference in tension) and total elongation (≈ 4% elongation difference in tension). By contrast, the magnesium AZ31B sheet exhibited lower anisotropy of yield strength in both tension and compression. Moreover, a pronounced tension-compression asymmetry was observed for both the magnesium AZ31B extrusion and sheet. The stress-strain curve shows a convex upward and concave downward shape in tension and compression respectively, and the tensile/compressive subsequent yield stress reached a same level at an elongation of

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approximately 9%. It is noticeable that both the magnesium AZ31B extrusion and sheet exhibited very high work hardening rate in compression. In tension, the magnesium AZ31B sheet exhibits higher flow stress than the extrusion. BETAFOAMTM foam is a two-component blown rigid polyurethane foam. Fig. 1(d) shows a typical engineering stress-volumetric strain curve which was obtained by compressing or pulling a cubic specimen quasi-statically along one direction. Its mechanical behaviour in uniaxial compression can be characterised by three phases: linear elasticity, plateau stress and foam densification. During the stress plateau phase the foam experiences a large compressive strain and absorbs a considerable amount of energy. In uniaxial tension, however, the brittle fracture occurred at a small strain. It is known that the compressive strength of PUR foams increases with an increase of their density. Furthermore, the dynamic uniaxial compressive testing results show that PUR foam exhibits considerable strain rate sensitivity [47, 48]. 3.

Experimental procedures Quasi-static and dynamic three-point bending tests were performed at the DLR-Institute

of Vehicle Concepts. Fig. 3 shows a schematic view of the three-point bending test setup. The three-point bending test rig consists of two fixed supports and an indenter which is made of solid aluminium. The upper indenter was mounted to the actuator of the testing frame. The specimens were placed centrally between the two fixed lower supports. 3.1.

Quasi-static component three-point bending tests As shown in Fig. 4(a), the quasi-static three-point bending tests employed an MTS

horizontal servo-hydraulic testing machine with a 250 kN load cell and an internal displacement transducer. The bending force was recorded during the bending collapse, together with the cylinder displacement, giving a force-deflection curve of the bending process. The tests were conducted at a constant speed of 60 mm/s and terminated when reaching a prescribed deflection of 450 mm. 3.2.

Dynamic component three-point bending tests As shown in Fig. 4(a), dynamic three-point bending tests were performed on the

DLR-dynamic component testing system comprised of a pneumatic-cylinder actuator, a trigger block, a moving sled with a minimum mass of 767 kg, a fixed sled, two sliding rails, an acceleration sensor and three high speed cameras. The moving sled was initially locked mechanically by the trigger block which was connected to the pneumatic cylinder actuator. The

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trigger block stored required energy from the compressed air and triggered the motion of the moving sled. The force signal was calculated by the moving sled mass and its acceleration which was recorded by the acceleration sensor mounted on the moving sled. The three high speed cameras were used to not only monitor the deformation of the specimens at a frame rate of 1000 fps, but also measure the speed and displacement of the moving sled with a motion analysis software. To be noted, the system was designed to provide an initial speed up to 17.8 m/s; however, lower speeds were chosen to prevent potential risk of fixture damage due to dissipating remaining kinetic energy. Therefore, the dynamic bending tests were performed at an initial speed ranging from 2.0 - 6.0 m/s in this study. 3.3.

Experimental design

As shown in Table. 2, twelve different structures were investigated by using different combinations of the beam material, foam density and beam wall thickness. The specimens were identified by letters and numbers. The first letter “S” stands for a steel beam, “X” for a magnesium extruded beam and “M” for a magnesium sheet beam; the middle letter “E” stands for empty and middle number denotes the foam density; the last letter “S” stands for a quasi-static loading condition and “D” for a dynamic loading condition. Three to five repeat specimens were tested for each testing case. 4.

Results and discussion The experimental results of empty and foam-filled magnesium AZ31B thin-walled beams

and a wide range of comparisons with the results of steel DC04 sheet beams are reported. A good reproducibility of the experiments was obtained, although there were some minor differences among the repeat specimens that was attributed to variation in the material mechanical properties and the interfacial bond strength between the metallic shells and foam fillers. For simplicity, an average force-deflection curve for each testing case and representative deformation modes are shown in the following subsections. To monitor the status of the interfacial bonding between the metallic shells and foam fillers, two methods were employed: (i) drilling some very small holes on the metallic walls which were carefully designed, so that they didn’t affect the deformation behaviour of the beams. The foam inside at the holes was visible, so it was possible to capture the relative sliding between the metallic shells and foam fillers; (ii) cutting some sections on the beams after the testing. 4.1.

Steel DC04 sheet beams

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As reference structures, the empty and foam-filled steel DC04 sheet beams were studied first. The experimental force-deflection curves and final deformation modes under quasi-static and dynamic three-point bending conditions for these structures are given in Figs. 5, 6, 7, 8, 9. The results show that these curves have significant differences depending not only on the deformation modes, including fracture modes of different types of structures (i.e. w/o foam fillers), but also on the loading conditions. A significant global buckling mode was observed in SES in Fig. 6: an inward fold at the compression wall and two outward folds at the adjacent side walls, which formed a sectional crushing zone and several plastic hinges. The localised sectional crushing zone subsequently led to reduced cross sectional area, which was associated with the deceasing load carrying capacity after local sectional collapse occurred at a small deflection. As might be expected, no cracks were observed in SES due to its superior ductility. On the other hand, the results from the foam-filled steel sheet beams in Figs. 7, 8, 9 show that the foam fillers stabilised the cross sections of the thin-walled beams and retarded the local sectional collapse. There is a clear tendency showing that a foam-filled beam with a higher foam density achieves a stronger stabilisation of the cross section during the bending process. For example, in the case of S40S and S40D as shown in Figs. 8, 9 respectively, the foam fillers provided the thin-walled beams with lateral support to force the plastic deformation to propagate toward adjacent sections. Therefore, multiple plastic hinges were formed instead of a single large inward fold, resulting in higher load carrying capacity than SES. In the subsequent loading stages, multiple cracks occurred at the tension side of the foam fillers due to the brittle fracture behaviour of the PUR foam in tension [46]. Then, the plastic deformation tended to concentrate just underneath the indenter and slight buckling appeared, leading to a slow load drop as shown in Fig. 5. Eventually, the shell material at the tension wall cracked in the vicinity of the foam cracks, leading to a rapid load drop. However, a significant buckling mode was observed in S20S as shown in Fig. 7. A small inward fold was formed at the compression wall and intruded into the foam filler at the beginning of the bending process, which was mirrored by a slow drop of load carrying capacity at a small deflection of about 20 mm. In the subsequent loading stages, the foam filler inhibited the development of the inward fold and another inward fold was developed due to the jamming of the first inward fold, and therefore the bending force started to slowly climb up to a plateau. No cracks in the foam filler were detected in S20S. It indicates that the

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global buckling mode occurs at a smaller deflection, if the compressive strength of the foam filler is decreased in relation to the strength of the steel shell. Furthermore, comparing Fig. 8 and Fig. 9 shows that the deformation mode that was observed for the foam-filled steel beam subjected to dynamic loading condition was almost identical to that subjected to quasi-static loading condition. It is noted that in most cases, no relative movement between the foam filler and the tension/compression walls of the steel beams was detected in the early and middle stages of the bending process, although adhesion failure was detected in the late stage. This indicates that there is good interfacial bonding between the steel beam walls and foam fillers. The quantitative comparison between the empty and foam-filled steel sheet beams clearly indicates that the load carrying capacity of the thin-walled steel beams can be significantly improved by foam filling. Moreover, it is evident that the foam density significantly affects load carrying capacity, which means that the load carrying capacity increases with the foam density. For example, S40S and S20S respectively reached nearly 3.2 and 1.9 times higher peak bending forces than SES respectively. The effect of strain rate on the load carrying capacity was also observed. S40D has a slightly higher force-deflection curve than S40S. 4.2.

Magnesium AZ31B extruded beams The empty and foam-filled magnesium AZ31B extruded beams were tested under both

quasi-static and dynamic three-point bending conditions. Compared with the results from steel DC04 sheet beams, the present results as can be seen in Figs. 10, 11, 12, 13, 14 show that there are some similarities and some differences with respect to the shapes of force-deflection curves, deformation modes and fracture modes. XES in Fig. 11 and XED in Fig. 12 exhibited a similar global buckling mode to SES, when subjected to both quasi-static and dynamic bending conditions. Nevertheless, several cracks initiated at the outward folds and started to propagate along the longitudinal and transverse directions of the extruded beams at a small deflection. On the other hand, a significant stabilisation of the cross section was observed as well in X30S and X30D as shown in Figs. 13, 14 respectively. Moreover, the plastic deformation in X30S propagated to farther cross sections and six distinct folds and bulges were developed at the compression wall and the adjacent side walls respectively. This evidence indicates that more material in X30S is involved in the plastic deformation compared with the foam-filled steel sheet beams. Due to stress concentration, the

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largest fold cracked at its corner instead of intruding into the foam filler, which led to an abrupt load drop as shown in Fig. 10. Then, the crack propagated along the transverse direction towards the tension wall. In the subsequent loading stage, another crack initiated near the middle of the tension wall and rapidly propagated towards the compression wall. Eventually, the two cracks intersected near the neutral layer of the beam, leading to a complete fracture. It is also evident that there is an effect of strain rate on the deformation modes of the foam-filled magnesium extruded beams. In X30D, only slight folds and bulges were developed during dynamic bending. Moreover, only a single crack occurred at the tension wall and led to a complete fracture. Unlike the foam-filled steel beams, it was observed that a relative sliding between the foam filler and magnesium extruded beam walls occurred near the centre of the beam after the presence of the folds and bulges in all cases, which indicates that the interfacial bonding failed during the formation of the folds and bulges. A previous study [38] using analytical and numerical methods indicated that good interfacial bonding between an aluminium foam filler and aluminium extruded beam walls significantly improves the load carrying capacity in bending collapse. Future work will be taken to study the effect of interfacial bonding on the load carrying capacity and optimise the manufacturing process to improve the quality of interfacial bonding between the PUR foam and magnesium extruded alloy. A significant strengthening effect of the PUR foam filler was also observed. The peak bending force of X30S was nearly 3.8 times higher than that of XES. Moreover, the effect of strain rate on the bending resistance was captured. XED has a moderately higher force-deflection curve than XES. It was expected that the foam-filled beams should exhibit relatively higher strain rate sensitivity than the empty beams since both magnesium AZ31B and PUR foams exhibited positive strain rate sensitivity. However, X30D has just a slightly higher force-deflection curve than X30S. The relatively lower strain rate sensitivity of the foam-filled beams may be caused by the complex contact and interaction between the foam filler and magnesium extruded beam walls. This phenomenon was also mirrored by the strain rate-dependent deformation modes of the foam-filled magnesium extruded beams. 4.3.

Magnesium AZ31B sheet beams The representative force-deflection curves and final deformation modes of magnesium

AZ31B sheet beams subjected to dynamic bending condition are shown in Figs. 15, 16, 17, 18, 19. Compared with the magnesium extruded beams, the magnesium sheet beams exhibited

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similar characteristics, such as the shapes of the force-deflection curves, buckling modes of the empty beams, fracture modes of both the empty and foam-filled beams and strengthening effects of the PUR foam fillers. However, some differences were also observed for the foam-filled beams. First, no visible folds and bulges were observed in M20D and M30D. Second, good interfacial bonding between the magnesium sheet beam walls and foam fillers was detected before the presence of cracks. The force-deflection curve of MED in Fig. 15 has the same characteristics with that of XED in Fig. 10. Likewise, the curves of M20D and M30D have the same characteristics with X30S and X30D respectively. As can be seen in Fig. 17, M05D failed by global buckling, which indicates that the spray polyurethane pre-polymer foam filler with the low foam density of 0.05 g/cm3 is not strong enough to stabilise the cross section and therefore the characteristics of the force-deflection curve of M05D are similar to that of MED. M30D achieved moderately higher load carrying capacity than M20D, but M30D fractured at a considerably smaller deflection (175 mm vs 285 mm). These results indicate that the foam density significantly affects not only the load carrying capacity but also the fracture deflection. Higher load carrying capacity is obtained by increasing the foam density. Nevertheless, the increase of the foam density leads to a smaller fracture deflection. 4.4.

Comparisons of energy absorption capacity The energy absorption capacity of all the tested beams was evaluated by the energy

absorption (EA) and specific energy absorption (SEA), as illustrated in Figs. 20, 21. The EA was calculated by integrating the area under the experimental force-deflection curve. The SEA was calculated by dividing the EA by the mass of the structure. The EA and SEA at a deflection of 450 mm is summarised in Fig. 20. For steel DC04 sheet beams, it is evident that the capacity of these beams in both the EA and SEA can be significantly improved by PUR foam filling. For example, the EA of S40S was nearly 6 times higher than that of SES; although the mass itself increased by a factor of 1.7 (see Table. 2). Consequently, an increase of the SEA by a factor of nearly 3.5 was achieved. A 7% higher value of SEA was also obtained in S40D. S20S achieved nearly 3 times higher EA and nearly 2.2 times higher SEA than SES. It indicates that the EA and SEA of the foam-filled steel beams are significantly affected by the foam density. A foam-filled steel beam with a higher foam density tends to absorb more energy and reach higher SEA than that with a lower foam density.

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For magnesium AZ31B extruded beams, X30S achieved nearly 5 times higher EA than XES, although the mass itself increased by a factor of nearly 2.6. Consequently, an increase of the SEA by a factor of nearly 1.9 was achieved. Moreover, it was observed that the EA of the empty beams has a higher strain rate dependency than that of the foam-filled beams. XED achieved about 11% higher EA than XES; however, X30D achieved only about 3% higher EA than X30S. For magnesium AZ31B sheet beams, the results illustrate that the foam density has a complex relationship with the EA, SEA and fracture deflection. M20D achieved nearly 5.4 times higher EA than MED, although the mass itself increased by a factor of 2.8. Consequently, M20D reached 1.9 times higher SEA than MED. In the case of the low and high foam densities (0.05 and 0.30 g/cm3), the SEA was almost identical to that of MED because the EA and mass itself increased simultaneously by an almost identical factor. Due to the considerably smaller fracture deflection, M30D unexpectedly absorbed less energy than M20D, even though M30D has higher mass. It implies that the EA and SEA have a nonlinear non-monotonic relationship with the foam density in the range of 0.05 - 0.30 g/cm3. It is known that the EA and SEA of a thin-walled beam depend not only on its material properties but also on the structural design, such as the cross section geometry and wall thickness. As shown in Fig. 1, two different cross sections with the chamfered/filleted corners were examined. The corner type may affect the fracture behaviour in some cases since large plastic deformation may localised at the corners. For the current loading and boundary conditions, none of the tested beams exhibited fracture initiation at the corners, but at the tension/compression walls or the transition region between the fillets and side walls. Therefore, the geometric effect of corner type was ignored and the experimental results from the beams with different corner types are comparable. MED achieved nearly 2.2 times higher SEA than SES. This indicates that magnesium alloy AZ31B outperforms steel DC04 in terms of the SEA for empty thin-walled beams subjected to bending loads. Both M20D and S20S were filled with the 0.20 g/cm3 foam and M20D was 55% lighter than S20S. However, M20D reached 2.4 times higher SEA than S20S, although M20D absorbed about 11% less energy. Both X30D and M30D were filled with the 0.30 g/cm3 foam. X30D achieved nearly 2.2 times higher EA and 1.8 times higher SEA than M30D, although the wall thickness of X30D was

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only nearly 1.7 times larger than that of M30D. Furthermore, the magnesium extrusions exhibited lower strength than the rolled sheets, as discussed in subsection 2.2. This indicates that the energy absorption capacity of a foam-filled magnesium AZ31B beam has a strong dependency on the wall thickness. Similar results were also observed for the foam-filled steel beams in previous work [46]. M20D reached the highest SEA which was about 13% higher than that of S40D; however, this outperformance is limited due to the fact that M20D fractured at a smaller deflection. Actually, in many real-world applications in bending, there is a limitation of deflection due to space protection constraints. In such circumstances, the beam generally works in cooperation with surrounding components to absorb sufficient energy during bending collapse. Generally, the fracture deflection of rocker rails in automotive side impact scenarios is limited to about 250 mm to protect passenger safety. Therefore, another comparison of the EA and SEA at a medium deflection of 250 mm is summarised in Fig. 21. Based on such a criterion, X30D and M20D reached nearly 1.6 times and 1.5 times higher SEA respectively than S40D. M20D achieved nearly 33% higher EA and 2.9 times higher SEA than S20S, although M20D was 54% lighter than S20S and even 38% lighter than SES. X30D absorbed nearly 16% less energy than S40D, but X30D reached 1.6 times higher SEA than S40D; moreover, X30D was 46% lighter than S40D and even 8% lighter than SES. These results indicate that magnesium alloy AZ31B significantly outperforms steel DC04 in terms of EA and SEA for foam-filled thin-walled beams in bending application which just require a relatively small deflection. If a larger fracture deflection is required, possible solutions to overcome the problem of premature fracturing and make further improvement on the SEA include improving the material ductility under both tensile and compressive loads, or using a material such as steel or aluminium alloy with higher ductility at the tension wall instead if suitable joining and corrosion protection methods can be developed. The analysis above indicates that the energy absorption capacity of foam-filled thin-walled beams depends on the strain rate and other parameters, such as the beam material strength and ductility, foam density and wall thickness. S40D, X30D and M20D reached the highest SEA from each group respectively. This study is not aimed to find the optimal structural design in terms of SEA, but there are four principles to reach the optimal SEA: •

The foam density should be sufficient to suppress the buckling/folding tendency

Page 15 of 25

of the wall strength/thickness combination. •

The foam density should not be too high to avoid the premature fracture of the

foam and shell material. •

A relatively smaller wall thickness and higher foam density should be used for a

shell material with higher strength and ductility, e.g. steel DC04. •

A relatively larger wall thickness and lower foam density should be used for a

shell material with lower strength and ductility, e.g. magnesium AZ31B. 5.

Conclusions The energy absorption capacity and deformation/fracture modes of the empty and

foam-filled thin-walled magnesium AZ31B and steel DC04 beams in three-point bending have been experimentally investigated in this study. The main conclusions are listed as follow: (1)

Both deformation/fracture modes and energy absorption capacity depend on the

strain rate and other parameters, such as the beam material strength and ductility, foam density and wall thickness. (2)

Both the DC04 beams and AZ31B extruded beams showed a positive effect of

strain rate on the energy absorption capacity. Moreover, an effect of strain rate on the deformation mode was observed for the foam-filled AZ31B extruded beams. The foam-filled AZ31B extruded beams developed six distinct folds and bulges in quasi-static bending, while only slight folds and bulges were formed during dynamic bending. (3)

The PUR foam filling stabilises the deformation of the thin-wall beams;

accordingly, it improves the energy absorption capacity. (4)

A thin-walled beam filled with a higher density foam achieves higher bending

resistance, but fractures at a smaller deflection. (5)

At a deflection of 250 mm, the AZ31B sheet beam filled with 0.20 g/cm3 foam

achieved nearly 33% higher energy absorption and 2.9 times higher specific energy absorption than the DC04 sheet beam filled with 0.20 g/cm3 foam, although the former was 54% lighter than the later and even 38% lighter than the empty DC04 beam. It indicates that the foam-filled AZ31B beam can absorb more energy and reach higher specific energy absorption than the foam-filled DC04 beam, while achieving an even lighter structure than the empty DC04 beam. However, this gain could be weakened when the performance is assessed at a larger fracture deflection, because the foam-filled AZ31B beam tends to fracture at smaller deflections.

Page 16 of 25

(6)

To optimise the energy absorption performance, the foam density should be

sufficient to suppress the buckling/folding tendency of the wall strength/thickness combination. Moreover, the foam density should not be too high to avoid the premature fracture of the foam and shell material. (7)

For applications which require limited deformation, there is a possibility to

develop lightweight auto-body structures such as rocker rails by substituting foam-filled AZ31B structures for mild steel structures, while maintaining or exceeding their current crashworthiness and safety. 6.

Acknowledgements This work is supported by the DLR project “Next Generation Car”. The authors would

like to thank Mr. Philipp Strassburger, Cedric Rieger and Thomas Grünheid (DLR-Institute of Vehicle Concepts) for their kind assistance in conducting the component three-point bending tests. The authors also would like to thank Martin Holzapfel and Harald Kraft (DLR-Institute of Structures and Design) for theirs kind assistance in material coupon tests. The authors wish to acknowledge Katja Oswald and Jan Roettger (The Dow Chemical Company), who provided the BETAFOAMTM PUR foam filling for the PUR foams.

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Fig 1: Cross section of magnesium AZ31B empty extruded beams (a) and empty sheet beams (b) and foam-filled extruded beams (c). Note: all dimensions in millimetres.

Fig 2: The measured true stress-strain curves for the steel DC04 sheet (a), magnesium AZ31B extrusion (b), magnesium AZ31B sheet (c) and a typical engineering stress-volumetric strain curve for polyurethane foams (d) in uniaxial tensile or compressive tests at a nominal strain rate

Page 21 of 25

of 0.001 s1, and all tests were conducted at room temperature.

Fig 3: A schematic view of the three-point bending test setup. Note: all dimensions in millimetres.

Fig 4: Testing facilities: (a) MTS horizontal servo-hydraulic testing system for quasi-static tests and (b) DLR-dynamic component testing system.

Fig 5: Force-deflection curves for empty and foam-filled steel sheet beams [46]

Fig 6: Final deformation mode of empty steel sheet beam in quasi-static bending [46] Fig 7: Final deformation mode of foam-filled (density = 0.20 g/cm3) steel sheet beam in quasi-static bending [46] Fig 8: Final deformation mode of foam-filled (density = 0.40 g/cm3) steel sheet beam in quasi-static bending [46] Fig 9: Final deformation mode of foam-filled (density = 0.40 g/cm3) steel sheet beam in dynamic bending [46]

Fig 10: Force-deflection curves for empty and foam-filled magnesium extruded beams

Fig 11: Final deformation mode of empty magnesium extruded beam in quasi-static bending

Fig 12: Final deformation mode of empty magnesium extruded beam in dynamic bending Fig 13: Final deformation mode of foam-filled (density = 0.30 g/cm3) magnesium extruded beam in quasi-static bending Fig 14: Final deformation mode of foam-filled (density = 0.30 g/cm3) magnesium extruded beam

Page 22 of 25

in dynamic bending

Fig 15: Force-deflection curves for empty and foam-filled magnesium sheet beams

Fig 16: Final deformation mode of empty magnesium sheet beam in dynamic bending Fig 17: Final deformation mode of foam-filled (density = 0.05 g/cm3) magnesium sheet beam in dynamic bending Fig 18: Final deformation mode of foam-filled (density = 0.20 g/cm3) magnesium sheet beam in dynamic bending Fig 19: Final deformation mode of foam-filled (density = 0.30 g/cm3) magnesium sheet beam in dynamic bending

Fig 20: Energy absorption performance for different structures at a deflection of 450 mm

Fig 21: Energy absorption performance for different structures at a deflection of 250 mm

Table 1: Measured average mechanical properties of steel DC04 sheet, magnesium AZ31B extrusion and sheet in the rolling or extrusion direction at room temperature and a nominal strain rate of 0.001 s1 0.2% YS (MPa) Material

Thickness E (mm)

Compression Tension

modulus

UTS

UE (%)

TE (%)

(MPa)

(GPa) DC04

2.0

210.0

-

211

353

26.4

45.8

3.0

43.5

84

184

231

14.3

15.3

1.8

43.5

105

181

263

13.8

20.7

sheet AZ31B extrusion AZ31B

Page 23 of 25

sheet

Table 2: Summary of test matrix and specimen details Specimen

Shell

Foam

Mass (kg)

Speed (m/s)

Empty

12.35

0.06

0.20 g/cm3

16.92

0.06

0.40 g/cm3

21.15

0.06

0.40 g/cm3

21.15

6.0

material Empty and foam-filled steel beams SES

Steel DC04, T2.0

S20S

Steel DC04, T2.0

S40S

Steel DC04, T2.0

S40D

Steel DC04, T2.0

Empty and foam-filled magnesium extruded beams XES

Mg

Empty

4.32

0.06

Empty

4.32

2.0

0.30 g/cm3

11.35

0.06

0.30 g/cm3

11.35

4.5

AZ31B-F, T3.0 XED

Mg AZ31B-F, T3.0

X30S

Mg AZ31B-F, T3.0

X30D

Mg AZ31B-F, T3.0

Empty and foam-filled magnesium sheet beams MED

Mg

Empty

2.73

2.0

AZ31B-O,

Page 24 of 25

T1.8 M05D

Mg

0.05g/cm3

3.75

2.0

0.20g/cm3

7.70

3.5

0.30g/cm3

9.58

3.5

AZ31B-O, T1.8 M20D

Mg AZ31B-O, T1.8

M30D

Mg AZ31B-O, T1.8

Page 25 of 25