Effects of triggering and polyurethane foam on energy absorption of thin-walled circular tubes under the inversion process

Journal of Energy Storage 27 (2020) 101071

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Effects of triggering and polyurethane foam on energy absorption of thinwalled circular tubes under the inversion process

T

Mohammad Javad Rezvani , Hamidreza Souzangarzadeh ⁎

Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran

ARTICLE INFO

ABSTRACT

Keywords: Trigger Inversion Polyurethane foam Energy absorption Initial peak load

In this article, an attempt has been made to increase energy absorption and control suddenly applied load in the inversion process of both empty and foam-filled circular tubes. For this purpose, rigid steel die as a triggering mechanism is installed on the shock absorber. When the circular tube is subjected to axial compression, it is driven into the trigger and the empty tube is expanded or polyurethane foam is compressed as much as the trigger's length. In this new innovation process, the effects of triggering and polyurethane foam are investigated on specific energy absorption (SEA), initial peak load and inversion mechanism. To do so, numerical simulation is carried out to evaluate the shock absorber performance. To verify the results of numerical simulation, some quasi-static experimental tests are conducted. In the light of the results, employing a trigger at the bottom of the foam-filled tubes causing an increase in the energy absorption in comparison with the empty ones. In addition, the presence of trigger prevents the suddenly applied load to occupants and the main part of structures. Therefore, this mechanism could be a palatable alternative as an energy absorption system in structural safety design.

1. Introduction Optimal design of thin-walled structures in the modern automotive industry has been considered due to their excellent crashworthiness, load-carrying capacity and low cost and light weight [1]. The deformation mechanism of these structures could be categorized according to the type of loading, geometric dimensions and supporting conditions as either progressive buckling [2], global bending [2], external [3, 4] and internal [5, 6] inversion, expansion [7-9] or splitting [10, 11]. One of the major shortcomings of thin-walled tubes is a sudden initial peak load transferred to the main structure and occupants. Therefore, to reduce the initial peak load, different strategies such as a triggering or initiator [12, 13], grooved or corrugated tubes [14-17], origami crash boxes [18], thin-walled structures with tailored properties and thicknesses [19, 20] and segmented tubes [21, 22] have been investigated. Triggering mechanisms or buckling initiators are often applied for two main reasons. One is that the initiator or the trigger is used to reduce the initial peak load in thin-walled tubes, and second, it used to initiate progressive folding of the tube. Ghani and Hassan studied the effect of the external tapered plunger as a triggering mechanism on crush performance of square columns [23]. They found that increasing the plunger angle leads to the reduction and increasing the initial peak load and crush force efficiency respectively. The effect of adding initiator was

⁎

studied for square and circular empty tubes [24, 25]. Those results indicated that by utilizing a buckling initiator, the initial peak load in circular and square tubes reduced effectively. Another approach is filling thin-walled energy absorbers with foams that would enrich the energy absorption capability. The researches have shown that the amount of absorbed energy in foam-filled tubes was greater than the empty ones [26-30]. An idea of installing the initiator was also proposed on the foam-filled circular tubes with stiffened annular rings to increase the energy absorption and to prevent the suddenly applied load to the main parts of the automotive and its occupants [31]. The inversion of thin-walled tubes is one of the deformation modes for energy-absorbing over an appropriate die of circular profile. Several researchers have been examined the circular tubes' crashworthiness parameters on external and internal inversion by theoretical, experimental and numerical simulation [32-39]. Leu analyzed the curling behavior on inside-out inversion in critical condition [40]. The results showed that the critical bending radius on a conical die was a function of geometric parameters and material properties. Sun and Yang studied the free deformation mechanism in tube inversion under conical die [41]. They found that there exists a critical conical angle in die, which the tube was curled to form a double-walled tube. Niknejad et al. investigated experimentally the effects of fillers on circular tubes during the inversion process [42]. The results showed a considerable increase

Corresponding author. E-mail addresses: [email protected], [email protected] (M.J. Rezvani).

https://doi.org/10.1016/j.est.2019.101071 Received 30 May 2019; Received in revised form 25 October 2019; Accepted 7 November 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 27 (2020) 101071

M.J. Rezvani and H. Souzangarzadeh

Fig. 1. Details of the specimens design with rigid steel die: a) External inversion, b) Internal inversion.

static free inversion of circular tubes. Li and You proposed corrugated tube for inversion [44]. They found that the corrugated tube has a stable inversing mechanism and it was not needed to lubricated contact. A new model on the free inversion of circular tubes introduced to overcome the drawbacks of the two traditional types of tube inversion [45]. The results showed that the efficiencies of the new tubes were significantly higher than the plain circular tubes. Li and You proposed the corrugated thin-walled tubes for external inversion [46]. They achieved that the thin-walled corrugated tubes could have a much more stable inversion in comparison with their circular counterparts. Rajabiehfard et al. studied geometrical parameters such as the tube thickness and die radius in internal inversion process experimentally, analytically and numerically under axial impact [47]. They concluded that increasing the tube wall thickness increased the inversion force which not only makes the tube poorly absorbent but also decreases the tube displacement. Magrinho et al. focused on the external thin-walled tube inversion using different die fillet radii. They analyzed formability limits by local buckling, necking and fracture in principal strain space. The results showed that the curling radius was important on the formability limits of external tube inversion [48]. Mohammadiha and Ghariblu investigated the crush response of variable thickness distribution tubes subjected to oblique loading for external inversion process. They concluded that the tube thickness distribution, die radius, and coefficient of friction between die and tube have great influence on the responses of inversion [49]. Also, Mohammadiha and Ghariblu studied the axial crushing of Functionally Graded Thickness (FGT) tubes under external inversion process [50] . In the Following research, Mohammadiha and Ghariblu evaluated the effect of the strain rate on dynamic external inversion loading of FGT tubes. They found that the concave distribution of thickness for FGT tubes improved the energy absorption more efficient than other geometries [51]. Then they studied the effect of foam filling on the dynamic response and energy absorption capability of free inversion [52]. The results showed that the optimal design of the foam-filled free inversion tube have a significant improvement in the crashworthiness.

Fig. 2. Engineering stress–strain curve for aluminum tube. Table 1 Mechanical properties for aluminum tube. Properties

Aluminum

Density(kg/m3) Young modulus (GPa) Poisson ratio Yield strength (MPa) Ultimate strength (MPa)

2700 69 0.33 185 214

in energy absorption comparing with the empty tubes. Qiu et al. carried out a theoretical model to improve the knuckle radius and the steady inversion load [43]. The model provided more accurate predictions on both the knuckle radius and the steady inversion load for the quasi-

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Table 2 Specimens dimensions and die. Group

Specimen

External inversion (Empty)

H0-E-I-E

External inversion (trigger and Foam-filled)

T-H23-E-I-E T-H23-E-I-F H23-E-I-F H0-I-I-E T-H23-I-I-E

Internal inversion

Die R(mm) 3 3.5 4 4.5 3 3 3 3.5 3.5

R ri

t ri

H(mm)

Tube ri(mm)

t(mm)

L(mm)

0.15 0.17 0.2 0.22 0.15 0.15 0.15 0.17 0.17

0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.06 0.06

0 0 0 0 23 23 23 0 23

20 20 20 20 20 20 20 20.3 20.3

1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.2 1.2

97 97 97 97 97 97 97 97 97

All dimensions are in millimeter.

Notwithstanding that the advantages of the inversion mechanism are the constant inversion load and lower initial peak load, only 50% of tube length contributed to energy absorption in the process of inversion as one of its disadvantages. Therefore, in this present study, to increase the energy absorption in inverted tubes, a trigger mechanism is pressfitted bottom of the empty and foam-filled circular tubes. Up until now, no model has been proposed for the inversion of empty or foam-filled circular tubes with a trigger. This method allows preventing a suddenly applied load to the main parts of the structure and passengers when an accident occurs. In this innovative idea, an experimental and numerical simulation study was carried out to determinate the effect of adding the trigger to the bottom of empty and foam-filled circular tubes on crashworthiness characteristics. 2. Experimental test 2.1. Design and materials In the present study, a series of experimental tests have been carried out for studying the effect of a rigid steel trigger on the crashworthiness of circular tubes under the inversion mechanism. Fig. 1 shows the details of tubes and the dies. The circular tubes were made of aluminum,

Fig. 3. The stress-strain curve of polyurethane foam for ρ=100 kg/m3.

Fig. 4. Details of the position of the specimens on the die: a) H0-E-I-E, b) T-H23-E-I-E, c) T-H23-E-I-F.

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under axial compression by using DARTEC 30 ton hydraulic press machines. After placing a specimen between steel die and top plate without any additional fixing, the plate with speed 10 mm/min moves downward. In order to reduce friction between the tube and the die, the PTFE powder is used. In addition, to ensure the repeatability of the experimental results, the tests were repeated three times for each of the tubes. The details of the position of the specimens on the steel die are shown in Fig. 4. 2.2. Criteria of energy absorber The desired criteria which are considered in assessing crashworthiness and the structure's safety enhancement are obtained from load-displacement curve [53].

Fig. 5. Typical load–displacement curve.

which absorbs the energy released during the process of the external or internal inversion. To obtain detailed information about the aluminum tube, the stress-strain curve according to ASTM B557M standard tensile test is plotted in Fig. 2. Moreover, the mechanical properties of the aluminum tube are given in table 1. According to Fig. 1, the circular tube has the outer radius ro, the inner radius ri, tube wall thickness t, die radius R, the trigger length H and the tube length L. Details of the specimens and steel die are listed in Table 2. In general, each specimen has a code: the first letter T in this code indicates the trigger, the second letter H with number denotes the amount of the trigger length, the third letter specify the external or internal inversion and the last letter shows the empty or polyurethane foam-filled tube. In this work, all of the geometrical parameters of tubes and dies are considered to be fixed and only the effect of adding a trigger on the empty and foam-filled tubes is investigated. The specimens are filled with polyurethane foam with a density of 100 kg/m3. Fig. 3 shows the stress–strain curve of the rigid PU foam. This curve is obtained by compressing a cubic foam sample according to the ASTM D1621-94 standard. To achieve the load-displacement curves, the specimens are placed

2.2.1. Absorbed energy The total energy absorbed, Eabsorbed, is equal to the area under the load–displacement curve, where:

Eabsorbed =

Pd

(1)

Where Pand δ are the crush force and crush distance, respectively. 2.2.2. Maximum crushing load According to Fig. 5, the maximum crushing load (Pmax) contributes to creating the first fold (which is what dictates the maximum compressive strength). An ideal absorber should have a low maximum crushing load and protect the entire structure. Therefore, provided that the shock absorber could be designed to have a mean crushing load equivalent to the maximum crushing load, it has the highest efficiency. 2.2.3. Specific energy absorption (SEA) SEA provides a way of comparing energy absorption capacity of structures with different masses. The SEA is calculated by the ratio of total absorbed energy to the tube mass:

Fig. 6. Finite element mesh and 3D view for the partially foam-filled rectangular tube with trigger.

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M.J. Rezvani and H. Souzangarzadeh

Table 3 Material parameters of crushable foam model considered for polyurethane foam Density. Density

Elastic parameters

SEA =

Young's modulus (MPa)

νf

Kf

100

21

0

1

(2)

Where m is total mass of the specimen undergoes deformation

Plastic parameters

ρf(kg/m3)

Eabs m

f p

3. Numerical simulation

0

In the present paper, the finite element models (FEM) of the empty and foam-filled circular tubes with a rigid steel triggering were modeled using explicit FE code ABAQUS/CAE version 6.5. The axisymmetric geometry of the model was created in part module. As shown in Fig. 6, the tube is assembled between the top plate and the rigid die. The top plate is free to move along the vertical axis with a constant velocity. The aluminum circular tubes and foam material were modeled with 4-node bilinear axisymmetric quadrilateral elements with reduced integration (CAX4R) and 2-node linear axisymmetric rigid link elements (RAX2) was used for the rigid die and the plate. After convergence of the solution, the optimum element size of 0.75 mm for the rectangular tubes and 3.5 mm for the foam filler were selected to produce acceptable results. The material properties of the aluminum tubes were defined as linear elastic and non-linear work hardening in the plastic region. The isotropic plasticity and crushable foam material models were used to model the circular tube and foam filler, respectively. The true stress-strain curves for both filler and aluminum materials were used in numerical simulations. Table 3 shows the material parameters for the polyurethane foam based on the crushable foam model. In these models, a self-contact interface was selected to prevent the interpenetration between each structure surface with itself. To define contact between the movable rigid plates, the foam and the trigger with the tube, "surface to surface" contacts were utilized. Since the simulation of the crushing tubes with test conditions in FE software takes a long time, it was necessary to find an economical solution for solving the problem. With knowledge of natural frequency, we can detect a down limit of time to consider the situation quasi-static. For choosing the load rating in the quasi-static situation, we started with the largest load rating which time is equal to the period of natural frequency. Then, by comparing the internal energy and kinetic energy, the best load rating scale was detected. In this paper, the actual crushing velocity of 10 mm/min was scaled up to 1 m/s. Fig. 7 reveals the total kinetic and the internal energy through the deformation process of the foam-filled circular tube under quasi-static loading. Such approaches have a negligible error under the crushing load. Hence, as shown in Fig. 8, the load-displacement curve obtained from the experimental test predicted the FE model with reasonable accuracy. It should be noted that the difference between simulation and experimental test at the beginning of the trigger movement might because of the displacement measured in the load cell, on the top of the tube in the first point of contact of the trigger and foam. The simulations of collapsed shapes after the axial crushing are illustrated in Fig. 9. Also, the crashworthiness parameters of the specimens are summarized in Table 4. The results show that there is an acceptable agreement between numerical simulations and experimental tests.

Fig. 7. Kinetic and internal energy for T-H23-E-I-F specimen under quasi-static load.

Fig. 8. Comparison between load–displacement curves obtained from experimental test and numerical simulation for T-H23-E-I-E specimen.

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Fig. 9. Crushed shapes of empty and foam-filled circular specimens derived from numerical simulation along with the 3D illustrations (180°). Table 4 Experimental and numerical simulation results after axial deformation. Specimen

Simulation SEA (kJ/kg)

Pmax (kN)

E (kJ)

Experimental SEA (kJ/kg)

Pmax (kN)

E (kJ)

Error% SEA (kJ/kg)

Pmax (kN)

E (kJ)

H0-E-I-E (r = 3) T-H23-E-I-E T-H23-E-I-F H23-E-I-F H0-I-I-E T-H23-I-I-E

31.09 42.31 32.03 34.22 33.43 42.05

21.22 28.51 29.11 23.76 14.94 19.28

1.59 2.08 2.19 2.03 1.41 1.86

27.41 41.54 35.66 34.95 30.43 37.99

20.79 28.83 30.79 23.33 18.16 20.10

1.40 2.15 2.32 2.07 1.29 1.68

13.4 1.8 10.2 2.1 9.9 10.7

2.1 1.1 5.5 1.9 17.7 4.1

13.4 3.3 5.4 2.1 9.8 10.7

4. Results and discussion

shown in Fig. 10(b), the inversion is completely formed for a die radius of 3 mm and the die radius to tube radius ratio is R/ ri=0.15. At higher radii of 3 mm, the specimens tended to fold or split longitudinally during inversion. This is because the maximum magnitude of circumferential stress exceeds a critical value in tension. Therefore, all of the experimental tests were performed over the die with radius R=3 mm.

4.1. The effect of the die radius In this study, to design a desirable energy absorber based on the crashworthiness criteria and to create a complete inversion, choosing a certain range of the tube thickness to diameter ratios and the die radius to diameter ratios are essential. Therefore, a series experimental test is carried out over dies of different radii namely 3, 3.5, 4, 4.5 mm under quasi-static axial compression. Fig. 10 shows a comparison of the loaddisplacement curve and the deformed shapes with different radii. As

4.2. The collapse modes In the present work, to increase the efficiency of energy absorbing, the idea of using a trigger in a press-fitted manner on the bottom of a circular

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M.J. Rezvani and H. Souzangarzadeh

Fig. 10. A comparison between the specimens over dies with different radii: a) load-displacement curve, b) deformed shapes.

tube was applied. Fig. 11(b) and 11(d) show the deformation stages of the specimens with a trigger. As shown in the figure, the deformation mechanism occurs in two steps. The energy dissipation in this two-step occurs mainly by plastic expansion, circumferential stretching of the tube due to hoop tension, meridional bending of the tube, combined stretching and bending, and the frictional strain at the interface of the tube with the die. In the first step, the trigger is driven into the circular tube and expands its end area as much as the trigger length. In the second step, the tube's bottom slips over the die radius and the tube diameter increases by circumferential stretching. At this stage, the axial load increases and the initial peak load is created. When the tube's bottom reaches the end of the die radius, the meridional bending starts and a full plastic hinge forms, so that the axial load of the tube decreases until the meridional bending completes. Then, the axial load starts to increase again. Therefore, the tube edge starts curvature upward and the contact between the tube and the die loses and formation of a knuckle begins. The remaining part of the tube deforms by moving downward in a combined stretching and bending mode. When the compressive load continues, the knuckle size completed and, the axial load becomes steady.

4.3. Load-displacement curve Fig. 12 shows the load-displacement curve for external and internal inversion. In this figure, the effect of a trigger on the tube inversion is considered. As it is evident that from this figure, for the H0-E-I-E and H0-I-I-E specimens, the initial peak load is occurred immediately after applying load. While for the specimens of T-H23-E-I-E and T-H23-I-I-E, the initial peak load occurs after displacement of the tube as much as the trigger length (H = 23 mm). This design method can be used in an automotive bumper to prevent the applied load to the main parts of the structure and occupants. Furthermore, area under the load-displacement curve for the specimens of TH23-E-I-E and T-H23-I-I-E increases. Therefore, this model of design is a method to increase the energy absorption in the inversion process. 4.4. The effect of polyurethane foam on the tube inversion In this section, to evaluate the desirable energy absorber under inversion condition, a foam-filled circular tube is inverted under axial compression load. Fig. 13 shows the different stages of the inversion for

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M.J. Rezvani and H. Souzangarzadeh

Fig. 11. Different stages of internal and external inversion for the specimens: a) H0-E-I-E, b) T-H23-E-I-E, c) H0-I-I-E, d) T-H23-I-I-E.

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plastic expansion occurs, simultaneously. The second step, the tube's bottom reaches to the end of the die radius and the tube is inverted. Fig. 14 depicts the comparison between the load–displacement curve of the empty and foam-filled specimens with and without a trigger mechanism. In this figure, the effect of expanding the empty and foam-filled tubes have been considered. As shown in the figure, the initial peak load in the inversion process of the T-H23-E-I-F specimen is greater than the other specimens. This is due the fact that, the expanding of the tube and compressing of foam core by steel trigger leads to increase in the initial peak load. On the other hand, it can be seen that, for the empty specimen (H0-E-I-E), the initial peak load is occurred immediately after applying load. While for the foam-filled specimens or empty specimen under press fitting manner via a trigger (TH23-E-I-E, T-H23-E-I-F and H0-E-I-F), the initial peak load are created after deformation of the tube as much as the trigger length (H = 23 mm). Furthermore, the presence of polyurethane foam in the inversion process causes to increase the area under the load-displacement curve, when the foam core is compressed (Fig. 14). Therefore, this model of design is a method to increase the energy absorption and, it is recommended for use as an energy absorber in vehicle structures. Fig. 15 shows the comparison between the total energy absorbed of the internal and external inversion. It can be seen that the least value of absorbed energy in those specimens is 1.286 kJ belonging to internal inversion without a trigger (H0-I-I-E) with a decrease 44.5% respect to T-H23-E-I-F specimen. It is because of two reasons. One is due to the effect of press-fitted process via the trigger. In this stage, the energy is absorbed by the plastic expansion of the tube and the frictional energy at the contact interface between the die and deformable tube. The other one is due to the tube filled with polyurethane foam. When the axial compression is applied, the energy is dissipated by crushing of the foam core. In addition, as it is evident from the figure, the absorbed energy for the specimens with the internal inversion mechanism (H0-I-I-E and T-H23-I-I-E) is compared with the external ones. The dissipated energy in the external inversion mechanism is greater than the interval inversion. Generally, the expanding of tube wall and compression of the polyurethane foam in external and internal inversion process leads to increase the energy absorption. So, this type of design can be used in various industries as an energy absorber. Fig. 16 shows the comparison between the SEA of the internal and external inversion by considering the effects of triggering and polyurethane foam. Generally, the filled tube with foam and the expanding of tube wall in the inversion process by using a trigger leads to increase the SEA as compared with specimens without a trigger. As can be seen, the largest and lowest value of SEA are 41.53 kJ/kg and 27.40 kJ/kg belonging to specimens of T-H23-E-I-E and H0-I-I-E, respectively. Although the energy absorption in the tube filled with foam (T-H23-E-I-F specimen) is larger than the empty one (T-H23-E-I-E specimen), but the SEA for the empty tube is 14% higher respect to the foam-filled specimen. This is mainly due to the fact that the presence of foam leads to increase in the tube mass and therefore, the SEA decreases.

Fig. 12. Comparison of the load-displacement curve between specimens by considering a trigger mechanism and without trigger: a) External inversion, b) Internal inversion.

the T-H23-E-I-F specimen by experimental test and numerical simulation. As shown in this figure, the trigger is press-fitted on the bottom of the foam-filled tube. The energy dissipation occurs simultaneously by crushing of the foam core, expanding of the tube as much as the trigger length (H = 23 mm) and the inversion process of the tube. As it is evident from Fig. 13, the process of deformation is carried out in two steps. The first step, the foam compressed as much as the trigger length and

5. Comparison of inversion mechanism with collapse mechanism In this section, to determine the relative performance of energy absorption in the inverted specimen, the deformation process of this study model is compared with that of tubes with different shapes from the

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M.J. Rezvani and H. Souzangarzadeh

Fig. 13. Different stages of external inversion for the T-H23-E-I-F specimen.

Fig. 14. Comparison of the load-displacement curve between empty and foamfilled tubes with external inverted specimen.

Fig. 15. Comparison of the energy absorption between the specimens with external and internal inversion.

previous studies [21, 54]. Therefore, the load-displacement curve and the final shape of a specimen of foam-filled aluminium rectangular tube [54] and a specimen of end-capped multi-component conical tube [21] are compared with the T-H23-E-I-F specimen (Fig. 17). The deformation process of the specimens of prior studies (S-60–20I and C-MT-E-4) are

completely different from that of present study, since the basis of energy absorption in specimens of the prior studies are folding and creating plastic hinges: the specimens are placed under axial compression; load

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M.J. Rezvani and H. Souzangarzadeh

Table 5 Comparison of the experimental results between the inversion and collapse mechanisms. Specimen

E(kJ)

Pmax (kN)

Pm (kN)

SEA (kJ/kg)

C-MT-E-4 [21] S-60-20I [54] T-H23-E-I-F

1.25 2.20 2.32

9.59 54.78 30.79

13.88 24.44 27.29

9.68 18.96 35.66

6. Conclusion A new type of method based on the external and internal inversion of circular tubes was introduced in the present work to increase the energy absorption and control the suddenly applied load on occupants and the main structures. To do so, a rigid steel trigger was placed on the bottom of the empty and foam-filled circular tubes with a press-fitting manner. In this study, quasi-static numerical simulations were performed to explain the crashworthiness characteristics in the process of inversion via a trigger. To verify the numerical simulations, several experimental tests were carried out. The main conclusions were outlined as follows:

• The inversion mechanism along with a trigger, which was press-

Fig. 16. Comparison of the SEA between the specimens with external and internal inversion.

increases during the plastic deformation due to strain hardening process; and the load declines dramatically while a plastic fold shapes completely. By increasing the crush force, second fold is created and the procedure is repeated until the specimen is completely crumpled. The load fluctuations during deformation of the prior studies models are undesirable for an energy efficient absorption device. However in the inversion mechanism the load is constant and it is favourable in the design of shock absorber. In addition, according to the values of crashworthiness parameters (table 5) the performance of the T-H23-E-I-F specimen is higher than the other specimens altogether. Thus, the investigations' results can assist automotive industry to optimal design of an absorber based on the inversion of the foam-filled tubes via a trigger.

•

•

fitted on the bottom of the empty and foam-filled tubes was completely different. The deformation process occurred in two stages. In the first one, the foam was compressed as much as the trigger length and plastic expansion occurred simultaneously. In the second stage, the tube's bottom reached the end of the die radius and then the tube was inverted. Comparing the trend of the load–displacement curve of the specimens with and without a trigger, shows that the maximum crushing load for the specimens without triggering (H0-E-I-E and H0-I-I-E) was immediately created at the beginning of inversion. While, in specimens with triggering, the maximum crushing load occurred after moving the trigger length. Therefore, by placing the trigger at the bottom of the circular tube, the intensity of the suddenly applied load is prevented to the main parts of the structures and occupants. The energy absorption and SEA increased by installing a trigger in a press-fitting manner on the bottom of the empty and foam-filled

Fig. 17. Comparison of the load-displacement curve between the inversion and collapse mechanisms. 11

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•

tubes, so that the increase of absorbed energy of the foam-filled tubes was more than the empty ones. Comparing the energy absorption of the external and internal inversion mechanism shows that the absorbed energy at external inversion was greater than the internal one.

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