Crushing Analysis of Empty and Foam-Filled Cylindrical and Conical Corrugated Composite Tubes

Crushing Analysis of Empty and Foam-Filled Cylindrical and Conical Corrugated Composite Tubes

M. Mahbod, M. Asgari^*

Research Laboratory of Passive Saftey Systems, Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, P. O. Box: 19395-1999, Iran

1. Introduction

In recent years, the interest of using energy ab-sorber devices with higher crashworthiness capaci-ty has been increased [1]. Among various available models, thin-walled structures are known as the imperative components for energy absorption and therefore they play an important role in industrial transportation systems. The crush boxes are fabri-cated by a wide range of materials such as alumi-num, steel and composites which are utilized in different shapes such as circular, triangular, conical, squared and polygonal tubes [2-7]. The extensive studies concerning the crashworthiness of energy absorbers demonstrate that composite tubes are widespread structures used in various topologies due to their low density and high energy absorption capacity. Studies state that a composite structure can display higher energy absorption than that of a metal [8, 9]. However, the energy absorption of composite structures depends on a wide range of factors such as material characteristics, ply design, geometry, etc and a considerable amount of literature has been published on the energy absorption characteristics of composite structures affected by these factors [10-14]. Due to the recent developments of composite manufacturing methodologies, carbon fiber reinforced polymer (CFRP) components are widely used and fabricated in automotive and aerospace industries [10-13].

In a considerable number of papers related to composite materials crashworthiness, simple ax-isymmetric geometries were considered including revolutionary surfaces such as circular, elliptical, and conical surfaces, and flat surfaces such as square, rectangular, etc. Recently, the corrugations are introduced in the tube so as to force the plastic deformation to occur at pre-determined intervals along the tube generator as an effective and innovative solution [15-18]. The aims are to improve the uniformity of the load-displacement behavior of axially crushed tubes, predict and control the mode of collapse in each corrugation in order to optimize the energy absorption capacity of the tube. Eyvazian et al. [19] experimentally investigated the effect of corrugation on crushing behavior and energy absorption of aluminum circular tubes. The results indicate that tubes with corrugation have a uniform force-displacement curve without an initial peak load. Alkhatib et al. [20] numerically studied the crushing behavior and performance of corrugated tapered tubes (CTT) subject to oblique loading conditions.  It was found that some CTTs can achieve higher specific energy absorption relative to their tapered conventional counterparts and increasing the impact angles would lead to a reduction in performance. Elgalai et al. [21] experimentally analyzed crushing of composite corrugated tubes subjected to quasi-static loading. Results confirmed that changing the corrugation angle and fiber type would enhance the energy absorption performance of composite tube. Numerical study of energy absorption of cot-ton fibre/propylene corrugated tubes [22] also dis-plays that the tube energy absorption capability was affected significantly by varying the number of corrugation and aspect ratios. It is found that as the number of corrugations increases, the amount of absorbed energy significantly increases. Crushing behavior of corrugated metal-composite tube was examined experimentally under axial loading condi-tion by Eyvazian et al. [23].

In this work, a comprehensive numerical analy-sis of cylindrical and conical corrugated car-bon/Bismaleimide (BMI) tubes is performed under axial loadings. To do this, different tubes by varying the radius and number of curvatures are modeled and analyzed using LS-DYNA explicit dynamic code. These models are validated with appropriate experimental and analytical results. Performing a parametric study on geometrical corrugation parameters of tubes indicates that the energy absorption of the structures depends strongly on the corrugation parameters. Based on the obtained results, generating corrugated surfaces on tubes would improve the crush force efficiency significantly.

1. Numerical Modeling

2.1. Description of the Models

This study proposes corrugated cylindrical and conical composite tubes in order to offer better energy absorption in comparison with conventional straight tubes. It is interesting to note that corrugation is formed in rows of wavelike folds or basically shaped into a series of regular folds that look like waves [22]. In all cases, tubes have 110 mm length and 2-mm thickness. In cylindrical tubes, the diameter is 60 mm and the upper and lower diameters are 44 mm and 76 mm respectively in conical tubes. Corrugation is defined by the number of wave curvatures, n and the radius of curvatures, r. Each concave or convex of tube determines one curvature.

In order to analyze the effect of corrugation on crushing behavior of composite tubes, various types of corrugated composite carbon/BMI tubes have been compared with a non-corrugated one as a standard structure. The mentioned tubes are shown in Figs. 1 and 2 for cylindrical and conical models respectively. The number and also the radius of curvatures in tubes are introduced by a code as expressed in Table 1.

2.2. Finite Element Modeling

The present numerical investigation is performed using a non-linear explicit dynamic LS-DYNA code. As illustrated in Fig. 3 and Fig. 4, the FE model consists of three main parts as: 1) the corrugated composite tube, 2) aluminum foam and 3) the mass block. The mass block is modeled as a rigid body by 'RIGID_MAT' in LS-DYNA. It should be noted that the mass is considered 500 kg and also young's modulus is assigned as 200GPa. It is also worth mentioning that the mass block is allowed to move in the z-axis only. The material model MAT54, 'ENHANCED_COMPOSITE_DAMAGE,' progressive failure damage, is used to simulate the mechanical behavior of the composite tubes. The failure criterion of the mentioned material model is Chang-Chang [24].

Table 1. Number and radius of curvatures of corrugated models (b) to (e) in Figs. 1 and 2

All the composite tubes are modeled with Belytschko-Tsay shell element with five integration points through the thickness. Moreover, the aluminum foam is modeled by solid elements. A mesh convergence analysis for a foam-filled composite tube leads to considering the element size of 2 mm and 5 mm for shells and foam, respectively.

2.3. Material Properties of the Models

In the proposed structures, all the specimens consist of 16 plies of T700/QY8911 (carbon fiber T700 reinforced BMI resin QY8911) which are modeled by "COMPOSITE_PART" code in LS-DYNA. In order to simulate the aluminum foam, the material model MAT_154 "DESHPANDLE_FLECK_FOAM" is used in this paper. MAT_154 is an appropriate material model for simulation of aluminum foam that is used as the filler material in energy absorbers [6]. The effect of foam density was investigated by comparing the results of structures with different foam densities of 220 and 534 and 710 g⁄cm³. The mechanical properties of composite and foam filler which are used in simulation are summarized in Tables 2 and 3, respectively.

1. Crashworthiness Parameters

First of all, it is necessary to introduce the primary parameters used to evaluate the crushing behavior of energy absorber structures. The most important factor is the absorbed energy (EA) that is defined as below [26]:

                                                                (1)

where F, δ and δ_max represent crushing force, axial displacement and the maximum deflection of structure, respectively.

SEA (Specific Energy Absorption), defined as the ratio of the absorbed energy to the mass of the structure, is another vital factor which is applied for comparison among different specimens [26].

Table 2. Material properties of uni-directional carbon fiber/BMI resin lamina [25].

Table 3. The mechanical properties of aluminium foam [26].

                                                                    (2)

Furthermore, initial peak force, and mean force are the maximum force occurred during crushing and the ratio of absorbed energy to maximum deflection, respectively. Mean Force is calculated by the following equation [26]:

                                                                  (3)

Considering the mentioned parameters, Crushing Force Efficiency (CFE) is defined as the ratio of mean force to peak force [26]:

                                                               (4)

where  and  are the mean force and peak force, respectively. It should be demonstrated that the higher values of SEA and CFE would increase the energy absorption and safety of structures.

1. Numerical Results and Discussion

4.1. Validation

4.1.1. Validation of Composite Tube

In this paper, a circular composite tube that has been evaluated in [27] is validated based on the experimental test. In this test, uniform length of 125 mm and an internal diameter of 50 mm were considered for G803/5224 specimen. A triggered mechanism is also set up at the top of the structure. Figs. 5 and 6 compare the force-displacement curve and final deformation pattern of the specimen between FE simulation and experiment, respectively. According to Fig. 6, FE simulation can predict the final deformation pattern of the composite tubes. Also, Fig. 5 shows the suitable agreement between experimental and numerical curves.

4.1.2. Validation of Aluminium Foam

In this section, the proposed FE model of an aluminum tube filled with aluminum foam is compared with experimental and theoretical results indicated in [28, 29]. In order to validate the numerical results, the experiment test which is done in [27], and the related theoretical solution is applied. On the other hand, according to the above approach, mean force and peak force of the model is calculated theoretically.

Fig. 5. Force-displacement curves of the composite tube from numerical and experimental [27] results.

Table 4 shows a comparison between numerical, experimental and theoretical mean force and peak force of the model. Obviously, there is suitable agreement among numerical results and both the experimental and theoretical solutions.

4.2. Crashworthiness of empty corrugated tubes

Fig. 7 depicts the force-displacement curves for empty straight and corrugated cylindrical tubes subjected to axial crushing. As indicated in Fig. 7, the straight cylindrical tube experienced a sharp drop in force at the beginning of the crushing which leads to less CFE in comparison with corrugated ones. As shown in Fig. 7, peak force of straight tube is significantly higher than that of corrugated tubes. It is clear from Fig. 7 that the maximum deflection is about 65 mm for straight tube, while it is more than 80 mm for corrugated ones. Hence, corrugation improves the crushing behavior of tubes. On the other hand, a comparison of SEA between corrugated tubes and straight one, demonstrates that straight tube has the highest value of SEA. However, corrugation improves the CFE without an intense reduction in the SEA. Also, the crashworthiness parameters of empty straight and corrugated cylindrical tubes are described in Table 5. According to Table 5, peak force of the corrugated tubes varies between 74.07 kN for Cr3n20 and 113.74 kN for Cr18n8, while it is set to be 239.85 kN for the straight tube. Another imperative advantage of corrugation is the fact that these models have increased the crushing length. It is figured out that Cr5n16 presents the highest value of SEA of corrugated tubes while it has appropriate CFE. In comparison with the straight tube, this model improves 149.86% of CFE while their mean force is approximately the same, and SEA decreases 10.86%.

Fig. 8 indicates the force-displacement curves for empty straight and corrugated conical tubes subjected to axial crushing. As demonstrated in this figure, the maximum deflection is about 65 mm for straight tube, while it is more than 80 mm for corrugated ones in conical tubes.

The crashworthiness parameters of empty straight and corrugated conical tubes are described in Table 6. According to Table 6, the mean force and CFE have been improved significantly in corrugated tubes in comparison with straight conical one. On the other hand, a comparison of SEA between corrugated tubes and straight one reveals that the straight tube has the highest value of SEA. According to Table 6, SEA of corrugated tubes varies between 29.82 kJ/kg for CCr3n20 and 42.64 kJ/kg for CCr18n8, while it is set 45.91 kJ/kg for the straight conical tube. It is figured out that CCr18n8 presents the highest value of SEA of corrugated tubes. However, CCr3n20 presents the highest value of CFE for corrugated tubes which is 88.06% higher in comparison with the straight cylindrical tube. Furthermore, CCr5n16 improves CFE by about 70% in comparison with the straight tube without an intense reduction (about 12%) in the SEA.

In order to have better comparison between conical and cylindrical corrugated tubes, SEA and CFE of the proposed tubes are compared in Fig. 9 and Fig. 10, respectively. As indicated in these figures, the conical and cylindrical tubes show the same trend by variation of the number of corrugations. Moreover, in all models, the conical corrugated tubes have better performance than cylindrical ones in case of SEA and CFE. For instance, the SEA is improved by 27% in CCr18n8 in comparison with Cr18n8. Moreover, the CFE is improved by 21-34% in conical tubes compared to cylindrical ones.

Table 4. A comparison between numerical, experimental and theoretical mean force and peak force of the model.

Table 5. A comparison between crashworthiness parameters of empty straight and corrugated cylindrical tubes.

Fig. 8. Force-displacement curves for empty straight and corrugated conical tubes.

Table 6. A comparison between crashworthiness parameters of empty straight and corrugated conical tubes.

Fig. 9. A comparison of SEA between cylindrical and conical corrugated tubes.

4.3. Crashworthiness of foam-filled corrugated tubes

Based on the proposed parametric study, Cr5n16 presents the higher performance in case of the SEA, and CFE between cylindrical tubes. Hence, the proposed structure is considered to be filled with different aluminum foams in order to investigate the effect of foams on the crashworthiness of cylindrical corrugated composite tubes. Three different aluminum foams are applied in this paper. Fig. 11 indicates a comparison between force-displacement curves of empty and foam-filled cylindrical composite corrugated tube. As shown in Fig. 11, using foams improves the energy absorption of structures. However, SEA has been decreased significantly due to the considerable increase in mass.

According to Fig. 12 (which presents the effect of foam density on crashworthiness parameters of cylindrical corrugated tubes), utilizing the foam with a higher density would increase the mean force and SEA impressively. However, the peak force has increased undesirably during the deflection due to the fact that in higher densities, densification region accrues in fewer strains. As indicated in Fig. 11, structures with higher density foam represent unsuitable crushing behavior, and they are not appropriate for crashworthiness purposes. On the other hand, the tube which is filled with low-density foam, provides a smooth force-displacement curve, and therefore it has the highest value of CFE. However, the SEA of this model is unacceptable in comparison with the empty tube.

Fig. 10. A comparison of CFE between cylindrical and conical corrugated tubes.

Fig. 11. A comparison of force-displacement curves of empty and foam-filled cylindrical composite corrugated tubes.

Fig. 12. Effect of foam density on crashworthiness parameters of Cr5n16.

Similar to cylindrical tubes, CCr5n16 is considered to be filled with different aluminum foams in order to investigate the effect of foams on the crashworthiness of conical corrugated composite tubes. Fig. 13 indicates a comparison between force-displacement curves of empty and foam-filled conical composite corrugated tube. It is clear in this figure that by increasing the foam density, the absorbed energy would rise significantly.

Fig. 14 indicates the effect of foam density on crashworthiness parameters of conical corrugated tubes. It is demonstrated from Fig. 14, that the peak force increased by increasing the foam density. However, the highest value of CFE and mean force is achieved in the model filled with medium density foam. Hence, medium density foam has better performance in case of both SEA and CFE.

1. Conclusion

This study was carried out to investigate the crushing behavior of empty and foam-filled cylindrical and conical corrugated composite tubes under axial crushing. Different corrugated tubes have been compared with straight ones. Foam-filled structures with different foam densities are studied regarding the specific energy absorption and CFE. Based on the obtained results, the following points can be concluded:

• The numerical model in LS-DYNA software shows good agreement with experiment; however, some failure modes of composites including delamination could not be predicted with this model.
• Creating corrugated surfaces on tubes, have significantly improved the crush force efficiency in all models in comparison with the straight tubes.
• The corrugated cylindrical model (Cr5n16) was achieved that improves CFE by about 150% in comparison with the straight tube without an intense reduction (about 11%) in the SEA.
• The corrugated conical model (CCr5n16) was achieved that improves CFE by about 70% in comparison with the straight tube without an intense reduction (about 12%) in the SEA.
• Overally, the absorbed energy increased by applying foams in both conical and cylindrical tubes. In cylindrical tubes, by increasing the foam density, CFE considerably decresed due to to the fact that in higher densities, densification region accrues in fewer strains. Moreover, medium density foam has better performance in case of both SEA and CFE for conical corrugated tubes.

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