Response of an Indented Square Tube under Impact Loading
The dynamic buckling of the square tube with a V-shape indent under impact loading was investigated by experimental and numerical methods. The collapse modes of square tubes with different locations of indentation points were obtained experimentally. Numerical calculations of each experimental load...
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Tan, Z.H. Liu, L.S. Sun, Y.S. Cho, C. 2020-11-28T15:37:43Z 2020-11-28T15:37:43Z 2015 Response of an Indented Square Tube under Impact Loading / Z.H. Tan, L.S. Liu, Y.S. Sun, C. Cho // Проблемы прочности. — 2015. — № 1. — С. 179-186. — Бібліогр.: 19 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173279 539.4 The dynamic buckling of the square tube with a V-shape indent under impact loading was investigated by experimental and numerical methods. The collapse modes of square tubes with different locations of indentation points were obtained experimentally. Numerical calculations of each experimental load case were conducted to analyze the effect of the indentation point location on the crush force and energy absorption of the tube. Numerical results agree well with the experimental ones. The results show that the indentation point location exerts a significant influence on the crush force and energy absorption. Compared to an indentation-free tube, the peak force of the indented tube is evidently reduced. The collapse process of the tube includes two buckling steps. The first one begins from the indentation either forward or backward with respect to the end until the folds are densified, then the second buckling starts backward or forward, which results in a second peak force in the collapse process. Динамическое коробление квадратной трубки с V-образным отпечатком в условиях ударного нагружения исследовано экспериментальными и численными методами. Режимы сплющивания квадратных трубок с различным расположением точек индентирования реализовывали экспериментально. Выполнены численные расчеты каждого случая экспериментального нагружения с целью анализа влияния месторасположения точки индентирования на разрушающее усилие и энергию поглощения квадратной трубки. Численные результаты хорошо согласуются с экспериментом. Установлено, что расположение точки индентирования оказывает значительное влияние на разрушающее усилие и энергию поглощения. По сравнению с неиндентированной трубкой максимальное усилие, действующее на индентированную трубку, явно уменьшается. Процесс сплющивания трубки включает два этапа коробления. Первый начинается с индентирования вперед или назад относительно конца до тех пор, пока не происходит уплотнения складок, второй осуществляется назад или вперед , что создает в результате второе максимальное усилие. This work was supported by the National Natural Science Foundation of China (No. 11202071) and the Fundamental Research Funds for the Central Universities, Wuhan University of Technology (WUT: 2013-IV-095). The financial contribution is gratefully acknowledged. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Response of an Indented Square Tube under Impact Loading Поведение индентированной квадратной трубки в условиях ударного нагружения Article published earlier |
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Response of an Indented Square Tube under Impact Loading |
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Response of an Indented Square Tube under Impact Loading Tan, Z.H. Liu, L.S. Sun, Y.S. Cho, C. Научно-технический раздел |
| title_short |
Response of an Indented Square Tube under Impact Loading |
| title_full |
Response of an Indented Square Tube under Impact Loading |
| title_fullStr |
Response of an Indented Square Tube under Impact Loading |
| title_full_unstemmed |
Response of an Indented Square Tube under Impact Loading |
| title_sort |
response of an indented square tube under impact loading |
| author |
Tan, Z.H. Liu, L.S. Sun, Y.S. Cho, C. |
| author_facet |
Tan, Z.H. Liu, L.S. Sun, Y.S. Cho, C. |
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Научно-технический раздел |
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Научно-технический раздел |
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2015 |
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Проблемы прочности |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Article |
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Поведение индентированной квадратной трубки в условиях ударного нагружения |
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The dynamic buckling of the square tube with a V-shape indent under impact loading was investigated by experimental and numerical methods. The collapse modes of square tubes with different locations of indentation points were obtained experimentally. Numerical calculations of each experimental load case were conducted to analyze the effect of the indentation point location on the crush force and energy absorption of the tube. Numerical results agree well with the experimental ones. The results show that the indentation point location exerts a significant influence on the crush force and energy absorption. Compared to an indentation-free tube, the peak force of the indented tube is evidently reduced. The collapse process of the tube includes two buckling steps. The first one begins from the indentation either forward or backward with respect to the end until the folds are densified, then the second buckling starts backward or forward, which results in a second peak force in the collapse process.
Динамическое коробление квадратной трубки с V-образным отпечатком в условиях ударного нагружения исследовано экспериментальными и численными методами. Режимы сплющивания квадратных трубок с различным расположением точек индентирования реализовывали экспериментально. Выполнены численные расчеты каждого случая экспериментального нагружения с целью анализа влияния месторасположения точки индентирования на разрушающее усилие и энергию поглощения квадратной трубки. Численные результаты хорошо согласуются с экспериментом. Установлено, что расположение точки индентирования оказывает значительное влияние на разрушающее усилие и энергию поглощения. По сравнению с неиндентированной трубкой максимальное усилие, действующее на индентированную трубку, явно уменьшается. Процесс сплющивания трубки включает два этапа коробления. Первый начинается с индентирования вперед или назад относительно конца до тех пор, пока не происходит уплотнения складок, второй осуществляется назад или вперед , что создает в результате второе максимальное усилие.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173279 |
| citation_txt |
Response of an Indented Square Tube under Impact Loading / Z.H. Tan, L.S. Liu, Y.S. Sun, C. Cho // Проблемы прочности. — 2015. — № 1. — С. 179-186. — Бібліогр.: 19 назв. — англ. |
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| fulltext |
UDC 539.4
Response of an Indented Square Tube under Impact Loading
Z. H. Tan,
a,1
L. S. Liu,
a
Y. S. Sun,
b
and C. Cho
c
a Department of Structure Engineering and Mechanics, School of Science, Wuhan University of
Technology, Wuhan, China
b College of Mechanical and Vehicle, Hunan University, Changsha, China
c Department of Mechanical Engineering, College of Engineering, Inha University, Incheon, Republic
of Korea
1 zhtan@whut.edu.cn
The dynamic buckling of the square tube with a V-shape indent under impact loading was
investigated by experimental and numerical methods. The collapse modes of square tubes with
different locations of indentation points were obtained experimentally. Numerical calculations of
each experimental load case were conducted to analyze the effect of the indentation point location on
the crush force and energy absorption of the tube. Numerical results agree well with the experimental
ones. The results show that the indentation point location exerts a significant influence on the crush
force and energy absorption. Compared to an indentation-free tube, the peak force of the indented
tube is evidently reduced. The collapse process of the tube includes two buckling steps. The first one
begins from the indentation either forward or backward with respect to the end until the folds are
densified, then the second buckling starts backward or forward, which results in a second peak force
in the collapse process.
Keywords: square tube, indentation, collapse mode, crush force, energy absorption.
Introduction. Thin-walled structures have been widely used as energy absorbers and
lightweight components in civil engineering and military applications [1]. For example,
various thin-walled structures are designed to reduce the crash force and absorb the impact
energy during automobile crashes or spacecraft landings.
Numerous studies have been dedicated to the axial crush behavior and collapse
mechanisms of thin-walled tubes under quasi-static and impact loadings using various
theoretical, experimental, and numerical methods [2–9], which imly the impact energy
dissipation via reliable and stable collapse deformation modes. Some researchers report
that there is an extreme crush peak force during the initial buckling of the tube, which can
cause the excessive deceleration and severe injury to a protected person or object [10, 11].
In order to resolve this issue, the trigger configuration was designed to reduce the
initial crush peak force and achieve the stable collapse modes, such as the extensional or
inextensional ones [12]. Various types of triggers, such as corrugation [13, 14], groove
[15], dent [16], discontinuity [17], and buckling initiator [18] have been studied form the
viewpoint of the cylindrical or square tube buckling response. However, the dynamic
buckling behavior of an indented tube under impact loading remains an open problem.
In this study, the dynamic response of Q235 steel square tubes with a V-shape
indentation is investigated. The square tube is impacted by a cylindrical steel projectile at
the velocity in the range of 9.00 to 13.18 m/s. The dynamic deformation evolution is
recorded with a high-speed camera, and various collapse modes are revealed for the
different load cases. The numerical simulation of the impact test is also performed, in order
to analyze the crush force and energy absorption. A comparative analysis of the experimental
and numerical results is used to assess the collapse mechanism of an indented square tube
under impact loading conditions. In addition, the indentation location effects on the
collapse mode, crush force and energy absorption are discussed.
© Z. H. TAN, L. S. LIU, Y. S. SUN, C. CHO, 2015
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1 179
1. Experimental.
1.1. Specimen. The Q235 steel square tube dimensions are as follows: the square
cross section is of 20 20� mm, while the wall thickness (t) and length (L0) are 0.5 and 100
mm, respectively.
The V-shaped indentation is pressed into the two opposite faces of the specimen. Four
different indentation locations are designed in the specimens with the distances from the
impacted end to the indentation L of 12, 24, 36, and 64 mm, respectively. The V-shaped
indentation dimensions are: 2 mm in width (w) and 1 mm in depth (h), as shown in Fig. 1.
1.2. Impact Test. A cylindrical steel projectile is launched via a gas gun and impacted
at the square tube, the impact velocity being measured by a laser velocimeter. The steel
square tube end is glued to the rigid wall, which is treated as a fixed constraint. The mass of
the steel projectile is 4.95 kg, while the motion velocity of the projectile ranges from 9.0 to
11.85 m/s, as is shown in Table 1. An FASTCAM-SA5 high-speed camera with the frame
rate set to 7,000 fps is used to record the deformation process of the square tubes in the
impact test. The experimental setup is shown in Fig. 2.
Z. H. Tan, L. S. Liu, Y. S. Sun, and C. Cho
180 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1
Fig. 1. The square tube with V-shape indentation.
T a b l e 1
Specimens and Experimental Load Cases
Case No. Indentation location (mm) Impact velocity (m/s)
1 0 10.17
2 12 9.85
3 24 10.05
4 36 9.83
5 64 10.20
Fig. 2. The impact device for the impact experiments.
2. Numerical Model. The numerical simulation of the experimental load case is
performed using the ANSYS LS-DYNA 970 commercial software. The square tube is
modeled using the Belytschko–Tsay 4-node shell elements with five integration points
through the thickness and one integration point within the element, while the projectile
FEM-mesh is constructed using 8-node solid elements. The shell element size for the
simulated square tube is about 1 mm. The clamped boundary condition is applied directly at
the square tube bottom to simulate the square tube fixation to the rigid wall. The projectile
velocities in calculations correspond to the experimental ones for various load cases under
study.
An automatic single-surface contact algorithm is applied in the simulation to account
for the contact between the tube walls throughout the deformation process, and an
automatically-adjusted node between the tube and the projectile is used in the surface
contact algorithm. The dynamic and static friction coefficients of 0.2 are used for the
self-contact of the square tube walls and for the tube-projectile contact.
A similar tube of the same material (Q235 steel) was also studied in [19], where the
material model #103 in the LS-DYNA code was applied. The respective parameters of this
model, which are used in the present study, are listed in Table 2.
3. Results and Discussion.
3.1. Buckling Process Results and Their Validation. The five load cases with different
indenation locations and impact velocities (Table 1) were experimentally investigated,
whereas each load case was tested twice to ensure the reliability of the results. The
respective numerical simulatons were also performed, and their results were compared with
respective experimental ones.
Figure 3 shows the deformation process of the tube without an indentation (Case 1).
The dynamic progressive buckling of the tube starts from the proximal end, while the
collapse mode is inextensional. The numerical results are in agreement with the experimental
data implying the final length of the deformed tube of 64 mm.
Figure 4 illustrates the results of Case 2. Here the numerical results also agree well
with the experimental datas. It is obvious that the onset of the collapse is at the indentation
position, which is followed by the progressive buckling from the indentation location
towards the proximal end. It is clear that the indentation efficiently induced the progressive
collapse, while the final length of the deformed tube is 44.8 mm.
Figures 5 and 6 show the collapse progress of the tube in Cases 3 and 4, respectively.
The deformation processes in these cases are similar: the tube is subdivided into the front
and rear parts by the indentation, while the total buckling process includes two steps. The
first step starts from the indentation location and proceeds backward to the proximal end, as
is shown in Figs. 5b–c and 6b–c. The first-step progressive buckling is terminated, when
the folds are densified, as shown in Figs. 5d and 6d, and the second step starts. The
second-step progressive buckling proceeds from the indentation location toward the distal
end. The experimental final length of the deformed tube is 49.2 mm.
Figure 7 presents the collapse process of Case 5, which is similar to those of Case 3
and 4, and includes the same two steps. The first-step progressive buckling proceeds from
the indentation location to the distal end until the folds are densified in the rear part of the
tube. Then the second-step progressive buckling starts from the indentation position and
proceeds to the proximal end. The experimental final length of the deformed tube is 69.3 mm.
Response of an Indented Square Tube under Impact Loading
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1 181
T a b l e 2
Parameters of #103 Material Model [19]
E, GPa � �Y , MPa �u , MPa C1 , MPa C2 , MPa Q1 , MPa Q2 , MPa
210 0.28 218 323.3 46.1 4.24 43.9 233.3
3.2. Crush Load. The numerical results exhibit a close correlation with the experimental
ones, which proves the validity of the applied numerical model. Therefore, this numerical
model was used to analyze the effect of indentation location on the crush load and energy
absorption values. Since the above effect should be assesed for the same impact velocities,
the models for Cases 1–5, which were used in the subsequent Sections, were modified to
simulate the projectile with the same impact velocity of 10 m/s compressing the tube until
the displacement of the projectile is 800 mm. Figure 8 presents the crush load values for the
tube in the different cases.
The square tube buckling behavior for different load cases is shown in Table 3. As
compared to the peak force 19.1 kN of the tube without an indentation, the one of the tube
with an indentation exhibits a reduction by 14.1 to 25.7%. When the distance from the
proximal end to the indentation location is increased, the peak force of the tube with an
indentation also increases from 14.2 to 16.4 kN. Moreover, there is a second peak force in
182 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1
Fig. 3. The deformation process of Case 1. Fig. 4. The deformation process of Case 2.
Fig. 5. The deformation process of Case 3. Fig. 6. The deformation process of Case 4.
a
b
c
d
e
a
b
c
d
e
Z. H. Tan, L. S. Liu, Y. S. Sun, and C. Cho
Cases 3–5 (Fig. 8c–e), which is not observed in doesn’t occur in Cases 1 and 2 (Fig. 8a, b).
This can be explained as follows: when the first-step progressive buckling is terminated,
the folds are densified at the proximal (Cases 3 and 4) or distal (Case 5) ends, as is shown
in Fig. 8c–e. At this moment, the deformed tube can be considered as a new one with a
densified end. The tube starts to buckle again from the densified end, which results in the
second peak force appearance. This agrees well with the phenomenon observed in Figs. 5–
7. However, the progressive buckling is fully developed in Cases 1 and 2, in contrast to
Cases 3–5. Thus, there the second peak force is missing in Cases 1 and 2.
3.3. Energy Absorption. The energy absorption is defined as follows [19]:
E Fd� � �
�
,
0
where F and � are the crushing force and displacement, respectively. The mean crushing
force is one of the major parameters controlling the efficiency of the energy-absorbing
devices. The mean crushing force Fm is calculated as in [19]:
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1 183
Fig. 7. The deformation process of Case 5.
T a b l e 3
Performance of Square Tube for Different Load Cases
Case No. Peak force
(kN)
The second peak
force (kN)
Mean crushing
force (kN)
Energy absorption
(J)
1 19.1 – 39.00 312
2 14.2 – 42.38 339
3 14.3 8.49 41.38 331
4 15.1 9.24 40.62 325
5 16.4 7.43 42.13 337
Response of an Indented Square Tube under Impact Loading
F Fdm � �1
0
�
�
�
.
Figure 9 shows that there is no obvious difference in the energy absorption values of
the tube in various cases. The comparative analysis of the results listed in Table 3 and
depicted Fig. 9 reveals that the energy absorption of the tube without indentation (Case 1)
is the minimum. As compared to Case 1, the energy absorption in other cases is higher by
4.2 to 8.6%, which agrees well with the variation tendency of the mean force. This can be
184 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1
a b
c d
e
Fig. 8 Curves of crush force vs. displacement for different load cases at the velocity of 10 m/s:
(a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4; (e) Case 5.
Z. H. Tan, L. S. Liu, Y. S. Sun, and C. Cho
attributed to the following fact: although presence of the indentation decreases the initial
peak force, it also changes the fold wavelength. Moreover, the densification of the first-step
progressive buckling also contributes to the increase in energy absorption of a tube with an
indentation.
Conclusions. The dynamic response of the tube with an indentation was studied by
the experimental and numerical methods. The peak force and energy absorption values of
an indented tube were compared to those of a tube with no indentation. The performed
analysis of the deformation mechanism allow us to draw the following conclusions:
1. As compared to a tube with no indentation, the initial peak force of the indented
tube can be reduced by 14.1 to 25.7%, whereas the respective energy absorption can be
increased by 4.2 to 8.6%.
2. The indentation location has a strong effect on the peak force and energy absorption
values.
3. The progressive buckling of the indented tube in Cases 3 and 4 consists of two
buckling steps.
4. The densification of folds in the first buckling step results appearance of the second
peak crush force, which is considered as the additional contribution to the increase in the
energy absorption.
Acknowledgments. This work was supported by the National Natural Science
Foundation of China (No. 11202071) and the Fundamental Research Funds for the Central
Universities, Wuhan University of Technology (WUT: 2013-IV-095). The financial
contribution is gratefully acknowledged.
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Fig. 9. Energy absorption–displacement curves for different load cases.
Response of an Indented Square Tube under Impact Loading
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Received 20. 10. 2014
186 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 1
Z. H. Tan, L. S. Liu, Y. S. Sun, and C. Cho
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