Keywords: Thin-walled tubes, functionally graded thickness, axial impact loading, FEM.

Transcription

1 Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal July 2016 Editors J.F. Silva Gomes and S.A. Meguid Publ. INEGI/FEUP (2016) PAPER REF: 6334 A COMPARATIVE STUDY ON CRASHWORTHINESS CHARACTE- RISTICS OF THIN-WALLED TUBES WITH FUNCTIONALLY GRADED THICKNESS AND VARIOUS CROSS-SECTIONAL GEOMETRIES Cengiz Baykasoğlu (*), Merve Tunay Cetin Department of Mechanical Engineering, Hitit University, Corum, Turkey (*) cengizbaykasoglu@hitit.edu.tr ABSTRACT The present paper aims at investigating the effect of cross-section geometry on the crashworthiness characteristics of thin-walled aluminum tubes with functionally graded thickness (FGT). To achieve this aim, different thickness-gradient patterns and cross-section geometries (i.e. circular, square and hexagonal) are considered in analysis. The same height and average section area are selected for all kinds of tubes. In addition, the energy absorption performance of the FGT tubes having different section geometries are compared with their uniform thickness (UT) counterparts at the same weights. In most cases, it is seen that the FGT tubes having circular and hexagonal cross sections have more efficient crashworthiness performance in comparison with square one. The analysis results also show that the crashworthiness performances of FGT tubes are generally better than their UT counterparts. Keywords: Thin-walled tubes, functionally graded thickness, axial impact loading, FEM. INTRODUCTION Thin-walled structures are widely used as effective energy-absorbing devices in vehicle safety applications (Meran et al, 2016). Therefore, extensive research has been conducted to improve the energy absorption performance of thin-walled structures (Alghamdi, 2001; Abramowicz, 2003; Olabi et al., 2007; Mat et al., 2012). At this point, several thin-walled structure configurations such as circular, square, polygonal, tapered, straight and conical have been proposed in literature. The relevant literature indicates that the cross-section configuration parameter is very important in terms of energy absorption characteristics of thin-walled structures (Yuen and Nurick, 2008; Guler et al., 2010). As can be concluded from the literature, thin-walled structures having uniform thickness (UT) dominate the studies on the crashworthiness. However, the UT structures may not provide the best material usage and crashworthiness performance. On the other hand, more recent studies have confirmed that variable thickness is a crucial parameter to control energy absorption capabilities of energy absorbers due to their variable stiffness along the structure. Hence, a new structural configuration called functionally graded thickness (FGT) has been recently proposed to enhance the crashworthiness of thin-walled energy absorption. Sun et al. (2014) examined the effect of various wall thickness gradient patterns on crashworthiness of FGT structures under axial impact loading. Li et al. (2014) studied the energy absorption capabilities of the functionally graded foam-filled square tubes under several loading angles by using the nonlinear finite element method. In another study, An et al. (2015) investigated

2 Symposium_16: Crashworthiness and Dynamic Responses of Structures and Materials the energy absorption characteristics of foam filled thin-walled tubes with functionally lateral graded thickness under both axial and lateral bending loads. Li et al., (2015-a) compared numerically the crash behaviors of FGT square tubes, tapered square tubes, FGT circular tubes and tapered circular tubes with their UT counterparts under axial impact loading. Li et al. (2015-b) provided a comparative study on the energy absorption characteristics of different configurations (functionally graded thickness, tapered uniform thickness and straight uniform thickness) with the same weight. Li et al. (2015-c) also examined the crashworthiness of hollow functionally graded thickness tubes, foam-filled functionally graded thickness tubes, hollow uniform thickness tubes and foam-filled thickness tubes under multiple loading angles. Furthermore, Sun et al. (2015) investigated the effects of different parameters such as wall thickness range, the tube diameter, the gradient exponent and yielding stress on the energy absorption capabilities of FGT and UT tubes using nonlinear element code. Zhang and Zhang (2015) and Zhang et al. (2015) examined the energy absorption characteristics of straight and tapered circular FGT tubes with different impact velocities. Xu (2015) conducted a numerical study on the energy absorption capabilities of circular FGT tubes with various wall thickness and aspect ratios (D/l). Moreover, Baykasoglu and Tunay Cetin (2015) compared the energy absorption characteristics and collapse mechanisms of FGT aluminum circular thin-walled tubes with UT thin-walled tubes under axial loadings. All above mentioned studies showed that the energy absorption characteristics of FGT tubes have superiority over UT tubes with the same weight. It should be noted from above literature review, however, that limited studies are available on the crashworthiness of FGT tubes which have both cross-sections and gradient parameters as design variables. Motivate d by this fact, the effects of cross-section on the energy absorption performance of FGT tubes are investigated in this study. To achieve this aim, different crosssection geometries (i.e. circular, square and hexagonal) and different thickness-gradient patterns are considered in nonlinear explicit finite element (FE) analysis. The same crosssection area and length were chosen for all geometries (i.e. circular, square and hexagonal). Additionally, in order to compare the crashworthiness of FGT tubes with UT tubes, the designated indicators such as the specific energy absorption (SEA), the initial peak crash force (IPF) and the absorbed energy (AE) are considered. The results indicate that the circular and hexagonal FGT tubes have more efficient energy absorption capabilities than square one and crashworthiness of FGT tubes are generally better than their UT counterparts. FINITE ELEMENT MODEL DESCRIPTION Material Properties The material of energy absorbers is selected as aluminum alloy Al6063 T5. It has the mechanical properties: density ρ= 2700 kg/m 3, Young s Modulus E= GPa and Poisson ratio ν=0.33. The true stress-strain values of the aluminum alloy Al 6063 T5 is shown in Table 1. The strain rate effect is also included in simulations using Cowper-Symonds formulation. For the material used in this work, the strain rate parameters, D and n, are chosen s -1 and 4, respectively. Table 1 - True stress-strain values of aluminum alloy (Al 6063 T5) True stress (MPa) True strain

3 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Structural Model The FE crash simulations are carried out by using the commercial FE code Abaqus/Explicit In FE model, the base of the circular tube having a 250 kg lumped mass (m) is attached to a moving rigid plate with a 10 m/s initial velocity (v 0 ) and the plate vertically crashed into a fixed rigid plate. Surface-to-surface and self-contact algorithms are implemented between tube and rigid plates and self-contact between walls of the tube, respectively. The friction between the tube s walls is determined by the finite penalty friction formulation. The friction coefficient value (µ) between rigid bodies and tube walls is chosen The standard convergence tests are performed and the global element size of 3 mm is considered in analyses. The proposed finite element model is validated using the experimental and numerical results in the literature. More detail information about the model validation can be found in (Baykasoglu and Tunay Cetin, 2015). Different cross- sections (i.e. circular, square and hexagonal) that have the same weight, length and cross-section area are considered in analyses. The circular, square and hexagonal tubes having the initial length 240 mm are used in analysis. In addition, the diameter of circular, the side lengths of square and hexagonal tubes are respectively selected as 80 mm, 71.5 mm and mm. The cross-section geometries are demonstrated in Fig. 1. Fig. 1 - The cross-section geometries of thin-walled tubes The configuration with functionally graded thickness is introduced similar to the functionally graded materials developed by previously study (Sun et al., 2010) by the following power law in the axial direction of tubes: (1) where t(x) is the thickness gradient function, n is the grading exponent of the wall thickness which is varied from 0.1 to 10, x is distance from the bottom end of the tube, t max and t min are the maximum and minimum wall thickness, respectively. The thickness gradient functions for various n values are demonstrated in Fig. 2. It can be observed that when the n values are less

4 Symposium_16: Crashworthiness and Dynamic Responses of Structures and Materials than 1, the gradient function shows a convex configuration and when the n values are greater than 1, it shows a concave configuration. Therefore, the weight of the circular tube increases with decreasing grading exponent n. Fig. 2 - Various thickness gradients for different n values. RESULTS In the present study, the crashworthiness of FGT and UT thin-walled tubes with different cross-sections and gradient exponents are investigated under axial impact loading. The initial peak force, specific energy absorption values and deformation modes for three cross-section geometries (i.e. circular, square and hexagonal) are obtained after the crash simulations. The formulations of these parameters can be found in (Baykasoglu and Tunay Cetin, 2015). The crashing force-displacement and absorbed energy-displacement curves of FGT tubes and equivalent UT tubes for selected n value (n=1) are presented in Figure 3. From the figure it can be seen that UT tubes have the maximum initial peak forces for all cross-section geometries. When the force-displacement curves are considered, the highest ending force is observed in circular FGT tubes. Furthermore, the force and absorbed energy values of hexagonal both FGT and UT tubes are generally higher than circular and square ones. There is a significant difference between FGT and UT force-displacement graphs, as follows, while the force values of UT tubes are almost stable fluctuated with increasing displacement, the force values of FGT tubes are gradually risen with increasing displacement. The reason for gradually risen graphs is the graded thickness of the FGT tubes. This situation indicates that the FGT tubes could provide more energy absorption and decrease the initial peak force. Figure 4 presents the specific energy absorption and initial peak force values of tubes. As shown in the figure, when the gradient exponent value increases from 0.2 to 10 there is a considerable decrease in the initial peak force for all cross-sections. Moreover, the initial peak force of FGT tubes for all cross-sections is lower than that of the UT counterparts. It is

5 Proceedings of the 5th International Conference on Integrity-Reliability-Failure apparent from this IPF-gradient exponent values that the circular FGT tube has relatively lower IPF values for all cases FGT, Circular FGT, Square FGT, Hexagonal UT, Circular UT, Square UT, Hexagonal Force (kn) Force (kn) Displacement (mm) Displacement (mm) Absorbed Energy (kj) FGT, Circular FGT, Square FGT, Hexagonal Absorbed Energy (kj) UT, Circular UT, Square UT, Hexagonal Displacement (mm) Displacement (mm) Fig. 3 - Force-displacement and absorbed energy-displacement curves for FGT and UT tubes. Similar to the IPF trends the SEA trends for all cross-sections generally decrease when the gradient exponent value increases from 0.2 to 10. All SEA values of square FGT and UT tubes except for n=0.2 are smaller than those of circular and hexagonal. There is a slight alteration in the SEA values of circular and hexagonal FGT tubes for 2 n 10. When the greatest difference is considered, the SEA value of square FGT tube is higher than approximately %24 of square UT tube with exponent 6. It can be also seen from the trends in Fig.4 that the SEA values of FGT tubes are higher than that of equivalent UT tubes for all cross-sections and also the SEA values of square tubes are less than that of circular and

6 Symposium_16: Crashworthiness and Dynamic Responses of Structures and Materials hexagonal tubes for all cases. Overall, these results indicate that the energy absorption capabilities of circular and hexagonal FGT tubes are superior to square tubes. IPF (kn) FGT, Circular UT, Circular FGT, Square UT, Square FGT, Hexagonal UT, Hexagonal SEA (kj/kg) ,2 0,4 0,6 0, Gradient exponent (n) FGT, Circular UT, Circular FGT, Square UT, Square FGT, Hexagonal Ut, Hexagonal ,2 0,4 0,6 0, Gradient exponent (n) Fig. 4 - The SEA and IPF values of FGT and equivalent UT tubes for different exponents n Figure 5 depicts the deformation modes of FGT and UT tubes at various gradient exponents n at the time frames of 15 ms and 20 ms. From the figure, it is clearly apparent that both FGT and UT tubes with all cross-section geometries have generally mixed deformation modes. The FGT tubes seem to be more advantageous than UT counterparts because of the FGT tubes have more stable folding than its uniform counterparts. Additionally, the circular and hexagonal tubes are exposed to more displacement than the square ones at the same time frames. Taken together, these results suggest that the circular and hexagonal FGT tubes have better energy absorption capability than square and UT counterparts

7 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig. 5 - Deformation modes of FGT tubes and corresponding UT tubes with various gradient exponents n at crash time of 15 ms and 20 ms

8 Symposium_16: Crashworthiness and Dynamic Responses of Structures and Materials CONCLUSION The main goal of the current study is to determine crashworthiness performances of FGT and UT tubes with different geometrical configurations. To this end, various thickness gradient patterns are modeled using gradient function and then are impacted on a rigid wall in the axial direction by using the nonlinear explicit FE method. The specific energy absorption, the initial peak crash force, the absorbed energy values and deformation modes are figured out to compare the energy absorption capabilities of thin-walled tubes. The main finding can be summarized as follows: In general, hexagonal and circular thin-walled structures have much better crashworthiness capability than square thin-walled structures. FGT tubes are able to control the crash behavior performances more effectively than their UT counterparts due to their variable thickness of the axial direction. The simulation results show that force and absorbed energy values of hexagonal both FGT and UT tubes are generally higher than circular and square ones. The initial peak force is an important parameter to enhance crashworthiness performances and control the sudden acceleration affecting passenger at the time of accident. The circular FGT tube has relatively lower IPF values for all cases so crashworthiness performances of circular FGT tubes are better than square and hexagonal ones. For all cases, the SEA values of square tubes are less than that of circular and hexagonal ones. These results show that the circular and hexagonal tubes have overall better crashworthiness performance than square tubes. REFERENCES [1]-Abramowicz W. Thin-walled structures as impact energy absorbers. Thin-Walled Structures, 2003, 41(2), pp [2]-Alghamdi AAA. Collapsible impact energy absorbers: an overview. Thin-walled structures, 2001,39(2), pp [3]-An X, Gao Y, Fang J, Sun G, Li Q. Crashworthiness design for foam-filled thin-walled structures with functionally lateral graded thickness sheets. Thin-Walled Structures, 2015, 91, p

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