The Geometric Influence of the TubularHat Tube on Its Energy Absorption Capacity in Axial Load
Hung Anh Ly, Thanh Tien Pham
Department of Aerospace Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam
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To cite this article:
Hung Anh Ly, Thanh Tien Pham. The Geometric Influence of the TubularHat Tube on Its Energy Absorption Capacity in Axial Load. International Journal of Transportation Engineering and Technology. Special Issue: Experiments Researches in Aeronautical Engineering. Vol. 2, No. 51, 2016, pp. 1217. doi: 10.11648/j.ijtet.s.2016020501.13
Received: August 12, 2016; Accepted: October 9, 2016; Published: November 22, 2016
Abstract: Crashworthiness is an important criterion in vehicle design. In fact, a crashworthy design will reduce the terrible accidents that happen everyday. Normally, tube structures are used for this task by dissipating the impact energy on the folding waves formed during the crushing progress. This study continues the previous studies, focuses on analyzing the behavior of tubularhat subjected to axial collision. Because of the limitations on the experimental conditions, and by the finite element method, this study only concentrates on the tube section. There are two main objectives in this thesis. Firstly, we consider the difference between the behaviors of the tophat tube and of the doublehat tube with the same axial load. Then, the geometric influence of flange on the deformation of the tubularhat is investigated.
Keywords: Crashworthiness, TopHat, DoubleHat, Impact, Optimization
1. Introduction
Background
Crashworthiness is an important criterion for the vehicle choice. It is the ability to protect the passengers in the case of collision. A crashworthy design will ensure the safety for passengers. For example, in spite of a car impacts at a high speed, the driver is still safe thanks to the seatbelts. Besides, the car structure absorbs and dissipates the impact energy.
In the structure design, crashworthiness relates to the energy absorption of the structure. The impact energy is absorbed on the folding wave of the thinwalled structure. To make the design process easier, these structure behaviors have been studied for many years.
This study continues some previous works and focuses on analyzing the behavior of tubularhat subjected to axial collision. Objectives in this paper: the influence of the flange geometry on the deformation of the tubularhat is investigated.
Method of approach
Due to the limitations in terms of experimental conditions, this study focuses on analyzing the behaviors of the tophat and doublehat sections by the theoretical analysis and the simulation with the Finite Element Method (FEM). Thus, the explicit finite element software LSDYNA is used
2. Theoretical Background
The theoretical analysis of M. White, N. Jones and W. Abramowicz [2] [3]
Analytical solution for the quasistatic axial crushing force of tophat and doublehat sections
Tophat section
Crosssection of a tophat tube
(1)
Simplified solution for strain hardening materials
(2)
(3)
(4)
Doublehat section
Simplified solution for strain hardening materials
(5)
(6)
(7)
Analytical solution for the dynamic axial crushing of tophat and doublehat thinwalled sections
Tophat section
(8)
Doublehat section
(9)
3. Influence of Flange Location to TubularHat
Geometric
In this research, the behavior of tubularhat structure is studied. The configuration of tubular–hat section is demonstrated in Figure 5. a=50mm, t=1.1mm. The flange width f is chosen as 15 mm. The other dimensions, h and b, are listed in Table 1.
No.  ^{h}/_{b}  h(mm)  b(mm) 
1  0.0  0  50 
2  0.1  5  50 
3  0.2  10  50 
4  0.3  15  50 
5  0.4  20  50 
6  0.5  25  50 
Mesh size
The BelytschkoTsay 4node shell elements with 5 integration points are used to model column wall with the finer mesh size (2×2 mm).
Boundary and condition contact
In this study, we just examine the case of axial loading. Therefore, the indenter is only permitted to displace in zaxis. For the tube, the nodes in the lowest cross section are clamped. The indenter is set initial velocity V=8m/s.
The spotweld is a rigid 4solid that connects the nodal pairs between two sheets as shown in Figure 6. Spotweld is assumed that can not be broken, and the spotweld pitch is equaled to the meshsize (2 mm). The distance between the two surface is the thickness of plate.
The models in this study use two contact algorithms. The contact between the indenter and the tube is AUTOMATIC_NODES_ TO_SURFACE. Its static coefficient and dynamic coefficient of friction are 0.4 and 0.3. The contact AUTOMATIC_ SINGLE_SURFACE is used for the tube wall to avoid interpenetration of tube wall other.
Characteristics of materials
In this study, the wall tube material is mild steel RSt37 which was used by S. P. Santosa et al. [4] in the studies about foamfilled thinwalled column with mechanical properties: Young’s modulus E, initial yield stress σ_{y}=251MPa, ultimate stress σ_{u} =339MPa, Poisson’s ratio ν=0.3, density ρ=7830kg/m^{3}, and the power law exponent n=0.12. The empirical CowperSymonds uniaxial constitutive equation constants D=6844s^{1} and =3.91. The material model used to simulate mild steel is Type 24 MAT_PIECEWISE_ LINEAR_PLASTICITY – an elastoplastic material with an arbitrary stress versus strain curve and arbitrary strain rate dependency. The true stress – effective plastic strain curve of RSt37 steel was calculated by H. A. Ly. [5] from the engineering stressstrain curve of Santosa and was given in Table 2. The material model used for indenter is ρ=1.4e4kg/mm^{3}, mass is 114,2kg with Young’s modulus E=200GPa and Poisson’s ratio ν=0.3.
The material model used for spotweld is mild steel Rst37
Mild steel RSt37  
Effective plastic strain (%)  True plastic stress (MPa) 
0.0  251 
2.0  270 
3.9  309 
5.8  339 
7.7  358 
9.6  375 
11.4  386 
13.2  398 
Result of simulation using LSDYNA
No.  ^{h}/_{b}  Displacement(mm)  
1  0.0  23.85  153.78 
2  0.1  28.37  129.09 
3  0.2  33.80  108.41 
4  0.3  34.93  104.92 
5  0.4  35.57  104.82 
6  0.5  37.64  105.08 
The ratio h/b increases, the instantaneous force, mean force increase and displacement decrease. The ratio of h/b=0.5 gives the highest values of instantaneous force and mean force.
4. Influence of Flange Length to TubularHat Tube
Geometric of models
• Model (M1) Perimeter 300mm
The values of a, b, t and f are given in Table 4. The length of models is 270mm. The perimeter of top hat tube is 300mm.
No.  a (mm)  b (mm)  t (mm)  f (mm) 
1  65  65  1.5  10 
2  63  63  1.5  12 
3  62  62  1.5  13 
4  61  61  1.5  14 
5  60  60  1.5  15 
6  59  59  1.5  16 
7  57  57  1.5  18 
8  55  55  1.5  20 
9  53  53  1.5  22 
• Model (M2) Perimeter 350mm
The values of a, b, t and f are given in Table 5. The length of models is 270mm. The perimeter of top hat is 350mm.
No.  a (mm)  b (mm)  t (mm)  f (mm) 
11  73.5  73.5  1.5  14 
12  71.5  71.5  1.5  16 
13  69.5  69.5  1.5  18 
14  67.5  67.5  1.5  20 
15  65.5  65.5  1.5  22 
16  63.5  63.5  1.5  24 
Materials
The material parameter used for the indenter in model (M1) is ρ=1.84e4kg/mm^{3}, the mass is 151.13kg with the Young’s modulus E=200GPa and the Poisson’s ratio ν=0.3.
The material parameter used for indenter in model (M2) is ρ=2.16e4kg/mm^{3}, the mass is 176.24kg with the Young’s modulus E=200GPa and the Poisson’s ratio ν=0.3.
Nummerical results
• Model (M1) Perimeter 300mm
The simulation results of the tophat specimen with the geometric dimensions given in Table 4 include the displacement in Table 6 and Figure 9 and the crushing force in Table 7 and Figure 10. In Figure 10, the analytical mean crushing force (White & Jones) line is predicted by using Eqs.(2) and (8)
No.  4f/L  f (mm)  Displacement (mm) 
1  13.33  10  120.27 
2  16  12  119.26 
3  17.33  13  119.76 
4  18.67  14  112.97 
5  20  15  116.17 
6  21.33  16  120.76 
7  24  18  123.48 
8  26.67  20  127.61 
9  29.33  22  129.78 
We found that the displacement is shortest if , . Whenincreases, the deformation increases
No.  4f/L  f (mm)  Crushing force (kN) 
1  13.33  10  41.06 
2  16  12  41.39 
3  17.33  13  41.20 
4  18.67  14  43.78 
5  20  15  42.53 
6  21.33  16  40.86 
7  24  18  39.93 
8  26.67  20  38.64 
9  29.33  22  37.98 
The analytical mean crushing force is(White & Jones) P_{m}=39.279kN 
• Model (M2) Perimeter 350mm
The simulation results of the tophat specimen with the geometric dimensions given in Table 4 include the displacement in Table 8 and Figure 11 and the crushing force in Table 9 and Figure 12.
No.  4f/L  f (mm)  Displacement (mm) 
11  16  14  134.48 
12  18.29  16  131.63 
13  20.57  18  134.12 
14  22.86  20  112.97 
15  25.14  22  116.17 
16  27.43  24  120.76 
No.  4f/L  f (mm)  Crushing force (kN) 
11  16  14  42.98 
12  18.29  16  43.97 
13  20.57  18  43.09 
14  22.86  20  41.69 
15  25.14  22  41.53 
16  27.43  24  39.95 
The analytical mean crushing force (White & Jones) 
We found that the tube displacement is minimal when , or . If increases, the deformation increases.
5. Conclusion
When the ratio of h/b increases, the maximum of instantaneous force is increases. The ratio of h/b=0.5 gives the highest value of instantaneous force and mean force. By comparing a tophat tube and a doublehat tube with the same boundary condition and perimeter. We found that the crushing force of double  hat tube is higher than top – hat section. When displacement is same, if , the energy absorption capacity of tophat tube is the highest.
Achievement and Limitation
When the ratio of h/b increases, the maximum of instantaneous force is increases. The ratio of h/b=0.5 gives the highest value of instantaneous force and mean force. If , the energy absorption capacity of tophat tube is the highest.
In this research, the mechanical properties of the spotweld material is not considered because of the lack of experimental data. The results of the ratio are not tested experimentally
Nomenclature
 Width of a tophat or doublehat section  m 
 Depth of a tophat or doublehat section  m 
 CowperSymonds coefficients  s^{1},  
 Young’s modulus  Pa 
 Width of flange  m 
 Perimeter of a tophat or doublehat section  m 

 N 
 Mean static crushing force for a strain hardening material  N 
 Mean dynamic crushing force  N 
 Rolling radius of toroidal surface  m 
 Thickness of section  m 
 Density of material  kg/m^{3} 
 Yield stress  Pa 
 Ultimate stress  Pa 
 Poisson’s ratio   
Acknowledgments
The authors acknowledge the support from the Ho Chi Minh city University of Technology for provision of research grants.
References
Biography
Hung Anh LY is a Lecturer in the Department of Aerospace Engineering – Faculty of Transport Engineering at Ho Chi Minh City University of Technology (HCMUT). He received his BEng in Aerospace Engineering from HCMUT in 2005, his MEng in Aeronautics and Astronautics Engineering from Bandung Institute of Technology  Indonesia (ITB) in 2007 and his DEng in Mechanical and Control Engineering from Tokyo Institute of Technology – Japan (Tokyo Tech) in 2012. He stayed at ITB and Tokyo Tech for one month as a researcher in 2012 and 2013. He is a member of the New Car Assessment Program for Southeast Asia (ASEAN NCAP). His main research interests include strength of structure analysis, impact energy absorbing structures and materials. 
Thanh Tien PHAM is currently a finalyear student at the Department of Aerospace Engineering, Faculty of Transportation Engineering, Ho Chi Minh City University of Technology (HCMUT), Vietnam. He is going to receive the Bachelor’s degree in Aerospace Engineering from HCMUT in April, 2016. His research interests include the areas of structural impact and finite element methods. 