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Experimental study of corrugated
tubes under lateral loading
A Eyvazian*, I Akbarzadeh, and M Shakeri
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
The manuscript was received on 21 January 2011 and was accepted after revision for publication on 31 October 2011.
DOI: 10.1177/1464420712437307
Abstract: Thin-walled tubes are widely used as energy absorbers in various vehicles and moving
parts. The objective of this study is to investigate the energy absorption characteristics of tubes
with corrugations in different geometries, under lateral loading. In order to produce corrugations,
an innovative solution is introduced. Quasi-static tests were conducted to study the effect of
changing the corrugation geometry (type and amplitude). The results show that tubes with corrugations have a higher mean crushing force which is directly proportional to the number of
corrugations and their amplitudes. Moreover, it was observed that corrugated tubes can absorb
approximately four times more energy than the tubes without corrugations in the same sizes and
weights. Finally, it was found that corrugated tubes are more effective in lateral direction as
energy absorbers, as they present suitable force–deflection responses.
Keywords: corrugated tubes, energy absorption, quasi-static loading, deformation mode, lateral crushing
1.
INTRODUCTION
Vehicle crashes are inevitable accidents for which
proper provisions must be taken. A popular measure
is the application of efficient energy absorbing
devices which have been proposed in different types
and varieties. Many of such devices take advantage of
thin metal tubes due to their various features, namely,
low cost, easy manufacturability and energy absorbing efficiency (which is the absorbed energy per unit
weight of the material).
Energy absorbing tubes can be loaded either axially
or laterally. Herein, laterally compressed tubes,
discarding the problems associated with axially
loaded tubes (such as an undesirable initial peak
load, low stroke efficiency (SE), and dependency to
axial alignment), are vastly used as energy absorbers.
They have a smooth load–displacement diagram and
the loading direction does not affect their efficiency.
*Corresponding author: Department of Mechanical Engineering,
Amirkabir University of Technology, PO Box 15875-4413, Tehran,
Iran
email: [email protected]
Furthermore, they are more easily manufactured and
installed on devices.
Many researchers have studied the effect of different parameters on the energy absorption properties
of the absorbers. In one of the primary works,
DeRuntz and Hodge [1] analytically studied the compression of a mild steel tube under quasi-static lateral
loading. Omission of plastic hardening in their work
imposed errors on prediction of load–displacement
characteristics. Later, Redwood [2] and Reid and
Reddy [3] tried to enhance the model through inclusion of the strain hardening ignored by DeRuntz.
Reddy and Reid [4] also studied the strain hardening
phenomenon in different metals and investigated the
plastic models proper for each group. The latter
researchers made further theoretical and experimental studies on lateral compression of metal tubes with
the inclusion of inertia effects [5–10]. The effect of
periodic processed grooves on absorption efficiency
was investigated by Carney and Sazinski [11]. Shrive
et al. [12] studied nested systems taking advantage of
metallic tubes with different configurations. Tubes
with non-circular cross-sections have also been subjected to studies. Gupta and Ray [13] experimentally
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Table 1
Tested specimens’ geometries
Type
Wall thickness (mm)
Diameter (mm)
Corrugation amplitude
Number of corrugations
Type of corrugation
S
CID1
CID2
CIS2
COD2
CIO3
2.5
2.5
2.5
2.5
2.5
2.5
79.5
79.5
79.5
79.5
79.5
79.5
—
3.9
3.9
1.9
3.9
4
—
1
2
2
2
3
—
Inner
Inner
Inner
Outer
Inner þ outer
and analytically studied the crushing of square tubes
under lateral loading, and proposed a model for
prediction of first peak load and post-collapse load–
compression curves. In another research, Jing and
Barton [14] performed numerical and experimental
studies on lateral crushing of square tubes, with a
focus on collapse mechanisms and the relationship
between energy absorption and tube deflection.
Morris et al. [15] performed a theoretical, numerical,
and experimental study on elliptical braced tubes
under lateral compression. This study indicates that
application of twofold absorbers allows for a higher
collapse load, while elliptical shaded tubes provide a
larger displacement stroke in comparison to circular
tubes. The latter authors in another experimental and
numerical work [16] studied circular and elliptical
nested tubes under lateral quasi-static loading.
Their latter study shows that nested elliptical tubes
present higher crushing efficiencies compared to
their circular counterparts. Gupta et al. [17] studied
mild steel and aluminum tubes with different diameter-to-thickness ratios subjected to quasi-static
lateral loading. This study provides a comprehensive
demonstration of the mechanisms contributing to
deformation of tubes between platens.
A deeper reflection on the literature reveals that the
corrugations studied are all generated in the same
sizes. In order to obtain a comprehensive understanding of lateral collapse characteristics associated
with circular cylinders with periodic corrugations, it
is essential to conduct investigations on the effects of
corrugation geometry. In this article, a comprehensive experimental work is performed to study the
response of aluminum corrugated tubes, with various
corrugation geometries, to quasi-static compressive
loading in the lateral direction.
2.
EXPERIMENTAL PROCEDURES
In this study, the quasi-static analysis of corrugated
circular energy absorbers under lateral loading is
examined using experimental techniques. Although
these devices are usually exposed to much higher
velocities, it is common to analyse the quasi-static
response first, since the same pre-dominant
geometrical effects will also occur under dynamic
loading conditions. In general, quasi-static tests are
representative for dynamic tests. It is to mean that if
specimens with corrugation have better energy
absorption characteristic under quasi-static loading,
the same fact applies to impact loading, and most of
the publications in this field are based on quasi-static
loading. On the other hand, measurement of load
response in quasi-static loading is more accurate in
comparison with dynamic impact loading, which
adds to the superiority of quasi-static loading.
Finally, the plasto-mechanics of large deformations
is often studied in detail in quasi-static experiments,
because their mode of deformation is generally found
to be similar in quasi-static and low-velocity impact
tests [18].
2.1 Specification of test specimens
Six types of specimens are studied. In order to investigate the effect of corrugations on the lateral loading
response, there are differences in the number of corrugations and their depths. Moreover, inner and
outer corrugations are considered. Here, the corrugation production method allows for the flexibility to
have a combination of corrugations. All the specimens are cut from one continuous tube, and
machined in both ends precisely. The specimens
have the same wall thickness of 2.5 mm and the
diameter of 79.5 mm. The initial undeformed length
of the test specimens is 70 mm. Details on the specimens’ geometries for lateral compression are given in
Table 1.
Figure 1 illustrates the six different specimens provided. The S-type is a tube without corrugations.
CID1 and CID2 were provided to investigate the
effect of corrugation number on the energy absorption characteristics. In order to study the effect of
corrugation amplitude and differences in the inner
and outer corrugations, samples CIS2 and COD2
were prepared, respectively. Finally, in view of the
corrugation production method used, CIO3 specimens, which bear both inner and outer corrugations,
were produced.
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Experimental study of corrugated tubes under lateral loading
Fig. 1
3
Types of tested specimens: (a) S, (b) CID1, (c) CID2, (d) CIS2, (e) COD2, and (f) CIO3
2.3 Preparation of test specimens
Fig. 2
Representative engineering stress–strain curves
of the tested tubes
2.2 Material properties
The corrugated tubes were made up of an aluminum
alloy (AA 6060, with no heat treatment). The material
properties were obtained through tensile testing of
the extruded wall material, parallel to the direction
of the tube axis. Representative engineering stress–
strain curves of all the tested tubes are given in
Figure 2.
Seamless aluminum alloy (AA 6060) tubes of 79.5 mm
nominal diameter and 2.5 mm thickness were
selected owing to their forming characteristics compared to other materials like mild steel. Besides, they
are affordable and easily obtainable. Straight tubes
were cut precisely with the ends machined carefully
in order to obtain flat and parallel ends, normal to the
longitudinal axis.
Corrugations were fabricated through stamping
method. In this method, corrugations with different
geometries are easily made on the surface of the
straight aluminum tube. Dies used for this process
were made from steel, and had two separate parts
against each other. Special machinery was designed
to produce different types of corrugations. The dies
were installed on this machinery, and rotated in parallel axes but in inverse directions, by means of a special mechanism. The tubes were griped between the
two dies, and the two opposite dies gradually moved
toward each other during rotation. In this method,
corrugations with different amplitudes can be provided by choosing different distances between the
opposite dies. Furthermore, variation of corrugation
length is possible through application of different
dies. This method of corrugation production has
advantages in comparison with the hydro-forming
method. In this method, there is no need for expensive dies designed to resist pressure, which in return,
significantly reduces the cost of corrugated energy
absorber production. Moreover, this method is very
flexible and corrugations can be fabricated on the
tubes with different wall thicknesses and diameters.
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Figure 3 shows a corrugated tube and the die
assembly.
2.4 Testing procedure
Different quasi-static tests were performed on the
corrugated tubes in order to study their behavior
when subjected to lateral crushing. In each case, the
load–displacement curve is provided.
The specimens underwent quasi-static lateral loading between two dies (solid plates) which fixed the
two sides of the tubes after contact started. Instron
digital testing machine with a full-scale load of 500 kN
was employed. Load platens were set parallel to each
other before testing. To stimulate quasi-static
Fig.
3
Stamping method
corrugations
Fig. 4
for
fabrication
of
conditions and in order to ensure that no dynamic
effect was present, all the tubes were compressed at
a rate of 5 mm/min until limited crush, which implies
complete compaction of the tested tube with a sharp
increase in the recorded load. Loads and displacements were recorded by an automatic data acquisition system. Figure 4 presents a schematic of loading
procedure at the starting moment which resulted in a
distributed load throughout the contact interface line
(after formation of the hinges, there would be two
load lines; see Figure 11).
3.
RESULTS AND DISCUSSION
3.1 Crashworthiness of tubes
Figure 5 illustrates the load–displacement diagram
for all the specimens specified in ‘Experimental procedures’ section obtained through experimental
measurements.
In the above diagram, the load–displacement
curves have three stages. At first, the radial load sharply increases due to elastic changes. This initial stage
is followed by an approximately linear zone. This
stage continues as deformation proceeds up to the
full crushing of the tube. In the final stage, the load
response sharply rises up which indicates the end of
crushing zone.
As mentioned in Introduction, lateral crushing of
the tubes has the advantage of smooth load–displacement diagram. Moreover, there is no initial peak load
in the load–displacement characteristic, which is
usual in axial crushing of the tubes. The presence of
an initial peak load is dangerous for the system being
protected against crash, and is prone to cause great
damages.
Having acquired the above diagrams, it is possible
to make subsequent analyses on the crashworthiness
of the tubes. This feature has been compared for the
tubes through calculation of the parameters
expressed in Table 2. The parameters are described
in the rest of this section.
Schematic of loading procedure (at the starting moment)
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Fig. 5
5
Load–displacement diagram for the tested specimens
Table 2
Crashworthiness parameters of the tubes
Type
Total absorbed
energy (J)
Mean crushing
load (N)
Stroke
efficiency (%)
Specific absorbed
energy (kJ/kg)
S
CID1
CID2
CIS2
COD2
CIO3
61.79
121.55
139.00
88.54
156.64
202.77
809.15
1863.63
2298.07
1023.03
2408.91
3256.91
97.3
87.5
78.6
94.28
90.65
78.6
20.228
46.591
57.452
25.576
60.222
81.422
Fig. 6
Absorbed energy for different tested tubes as a function of displacement
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Fig. 7
Total absorbed energy of the six corrugated tubes subjected to lateral loading
Fig. 8
Mean crushing load of the tubes subjected to lateral loading
3.1.1 Total absorbed energy (Etot)
The energy absorbed, at any moment throughout
crushing, can be achieved through calculation of the
area under the load–displacement curve. In this
study, this parameter is calculated through numerical
integration of the load–displacement curve. Figure 6
displays the value of the absorbed energy for different
tubes as a function of displacement (the deformed
stroke). The final value for each curve, i.e. the value
at complete compaction of the tube, is denoted as
total absorbed energy. Figure 7 provides comparison
between the total absorbed energies of the
specimens.
As obvious in Figures 6 and 7, CIO3 with three
corrugations has the maximum total energy absorption. This type of corrugated tube has a capacity to
absorb 302 per cent more energy than the tube
without corrugation. All experimental results show
improvements in the crashworthiness characteristic
of corrugated tubes.
3.1.2 Mean crushing load (Pave)
Mean load is the average of the crushing load
response of the absorber through complete deformation. This parameter is useful for measurement of the
performance of the energy absorbers, and plays an
important role in their design. It can be calculated as
Pave ¼
Etot
Lc
ð1Þ
where Etot and Lc are the total absorbed energy and
the crush length, respectively. Figure 8 provides comparison between the different tubes’ mean crushing
loads.
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Fig. 9
Fig. 10
SE of the tubes subjected to lateral loading
Specific absorbed energy of the tubes subjected to lateral loading
3.1.3 Stroke efficiency SE
It can be inferred from this figure that higher SE
results in higher energy absorption capacity.
The relative crush length of a tube under compression
is an important factor in design of a tubular energy
absorber. This feature is known as the SE of the absorber which can be calculated as follows
SE ¼
Lc
D
7
ð2Þ
where Lc and D represent the crush length and the
diameter of the specimen (in lateral loading). Crush
length is the maximum displacement of the two
opposite dies at the moment the test is finished.
Test finish point refers to the moment when the
tubes are completely crushed, and reach to their
solid state, where the load–displacement curve sharply increases; this condition is called limited crush,
which implies complete compaction of the tested
tube with a sharp increase in the recorded load.
Figure 9 illustrates the SEs mentioned in Table 2.
3.1.4 Specific absorbed energy (etot)
Total absorbed energy is an important parameter in
selection of an absorber; yet, it is not a proper parameter for comparison between different materials and
geometries. For such comparison, specific energy
must be considered which is the energy absorbed
per unit weight of the absorber, and is calculated as
follows
etot ¼
Etot
M
ð3Þ
where Etot is the total absorbed energy and M the
mass of the tube. High values of etot indicate a lightweight absorber. Figure 10 compares the specific
absorbed energies associated with the tubes.
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Fig. 11
Deformation history of different corrugated tubes under lateral loading
3.2 Crushing mechanisms of different
corrugated tubes
The crushing mechanism has a close relation with the
number and the geometry of the specimen. Figure 11
exhibits the crushing of different samples under lateral loading. Here, two distinct types of failure are
distinguished: two-hinge failure and four-hinge failure. In the following section, it will be demonstrated
that energy absorption characteristic is related to
crushing mechanisms. In lateral crushing analysis of
tubes through theoretical viewpoint, it is common to
calculate the mean load by the number of failure
hinges at which plastic deformation occurs [1–3].
3.2.1 Two-hinge failure mechanism
In the two-hinge mode which took place for specimens S (without corrugation), CIS2 and COD2, two
longitudinal hinges are observed to have developed.
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Then, the tube begins to yield, and two hinges are
formed diametrically opposite to each other at an
angle of 180 , as depicted in Figure 11.
3.2.2 Four-hinge failure mechanism
The four-hinge mechanism happens only for tubes
with corrugations. In this mode, four longitudinal
hinges appear on the tube walls. These hinges form
diametrically at the angular distances of 90 , as
observed in Figure 11 for specimens with higher
amplitudes, CID1, CID2, and CIO3. Hinges horizontally located are formed earlier than vertical hinges.
3.3 Discussion on the effect of corrugation
As the experimental results showed us in the previous
parts, introduction of corrugations has different
effects on different crashworthiness parameters and
failure mechanisms of the tubes. In this study, the
effect of different aspects of corrugations have been
investigated and summarized as follows.
3.3.1 Effect of corrugation number
The two specimens CID1 and CID2 are provided to
study the effect of corrugation number on the load
response of this type of energy absorbers. As presented in Figure 11, the rise in the number of corrugations does not affect the failure mechanism.
However based on the results obtained, both the
total absorbed energy and mean crushing load are
increased by 23 per cent and 14 per cent, respectively,
as one more corrugation is fabricated on the tube.
Similarly, the specific absorbed energy increases by
23 per cent. However, the SE decreases by 9 per cent.
3.3.2 Effect of corrugation amplitude
In order to investigate the effect of corrugation depth
on crashworthiness characteristics of corrugated tube
specimens, types CID2 and CIS2 are compared to
each other. As illustrated in Table 1, CID2 specimens
have the corrugation depth of 3.9 mm, and CIS2s have
the corrugation depth of 1.9 mm. The deformation
history (Figure 11) shows that the reduction of the
corrugation depth affects the deformation mechanism in such a way that the tubes with higher corrugation amplitudes deform in four-hinge mechanism.
However, the tubes with lower amplitudes tend to
deform in the two-hinge mode. As a result, tubes
with higher corrugation amplitudes have higher
mean crushing loads, total energy absorptions, and
specific absorbed energies. In this study, deeper
corrugation (increasing the depth as much as
9
2 mm/100 per cent) increased the mean crushing
load, total absorbed energy, and specific absorbed
energy by 57 per cent, 124 per cent, and 125 per
cent, respectively. However as mentioned previously,
the rise in these parameters was accompanied by a
reduction in the SE – as much as 16 per cent.
3.3.3 Effect of corrugation alignment
In the experimental test program, two specimens
were provided to study how inner corrugation differs
from outer corrugation in the crush response. CID2
and COD2 are fabricated by stamping method
through changing the die position. The comparison
between these two specimens reveals that there is not
a significant difference between the mean crushing
loads, total absorbed energies, and specific absorbed
energies, and these parameters are higher in the outer
corrugation specimen as much as only 4.5 per cent
and 12.7 per cent and 5.2 per cent compared to the
inner corrugation. However, there is a significant difference in the SEs as much as 12 per cent for the outer
corrugation. Therefore, on the contrary to the previous, all the crashworthiness parameters are improved
by forming outer corrugations instead of inner ones.
Furthermore, it must be noted that outer corrugation
tends to deform in the two-hinge mechanism,
whereas inner one is inclined to the four-hinge mode.
3.3.4 Effect of combined corrugation
Specimen type CIO3 is provided in order to find the
effect of combined corrugations on the crashworthiness of corrugated tubes. Experimental test results
show that there is a significant increase in both
mean crushing load and total absorbed energy. In
comparison with the tubes without corrugation,
mean crushing load increases by 302 per cent, and
the total energy absorbed increases by 228 per cent.
4.
CONCLUSIONS
The objective of this article is to experimentally study
the effect of corrugation on the crushing behavior and
energy absorption of aluminum circular tubes. Six
types of circular corrugated tubes were prepared
and tasted under the same quasi-static lateral compressive loading conditions in order to provide a
means for comparison. Based on the results obtained,
the main conclusions can be summarized as follows.
1. Aluminum corrugated tubes exhibit an effective
and stable energy absorption phenomenon
under lateral compression.
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2. Fabricating corrugations on the tubes improves
both the mean crushing load and total absorbed
energy of the absorber.
3. The amplitude of corrugation plays an important
role in the crashworthiness characteristic of this
type of energy absorbers.
4. Energy absorption parameters of corrugated tubes
are dependent upon the failure mode, and the
four-hinge failure mode provides a higher value
of crashworthiness.
5. Tubes with inner and outer corrugations exhibit a
high energy absorption capacity under lateral
loading.
FUNDING
This work was supported by Mechanical Engineering
Department of Amirkabir University of Technology.
ACKNOWLEDGMENT
The authors express their gratitude toward the
Strength of Materials Laboratory of Amirkabir
University of Technology for cooperation.
ß IMechE 2012
REFERENCES
1 DeRuntz, J. and Hodge, P. Crushing of a tube between
rigid plates. J. Appl. Mech., 1963, 30, 391–395.
2 Redwood, R. Crushing of a tube between rigid plates.
J. Appl. Mech., 1964, 31, 357–358.
3 Reid, S. and Reddy, T. Effect of strain hardening on
the lateral compression of tubes between rigid plates.
Int. J. Solids Struct., 1978, 14, 213–225.
4 Reddy, T. and Reid, S. Phenomena associated with
the lateral crushing of metal tubes between rigid
plates. Int. J. Solids Struct., 1980, 16, 545–562.
5 Reddy, T. and Reid, S. Lateral compression of tubes
and tube-systems with side constraints. Int. J. Mech.
Sci., 1979, 21(3), 187–199.
6 Reddy, T. and Reid, S. On obtaining material properties from the ring compression test. Nucl. Eng. Des.,
1979, 52, 257–263.
7 Reid, S. and Reddy, T. Large deformation behavior of
thick rings under lateral compression. In
Proceedings of the Symposium on Large deformation, Delhi, 17–19 December 1979, pp.108–121
(South Asian Publishers PVT Ltd, New Delhi).
8 Reid, S. and Reddy, T. Effects of strain rate on the
dynamic lateral compression of tubes. In
Proceedings Conference on Mechanical properties
of materials at high rates of strain, Oxford, 20–30
March 1979, ch. 3, Series no. 47, pp.288–298
(Institute of Physics Conference, Oxford).
9 Reid, S. and Reddy, T. Experimental investigation of
inertia effects in one-dimensional metal ring systems subjected to end impact–I. Fixed-ended systems. Int. J. Impact Eng., 1983, 1(1), 85–106.
10 Reddy, T., Reid, S., and Barr, R. Experimental investigation of inertia effects in one-dimensional metal
ring systems subjected to end impact–II. Free-ended
systems. Int. J. Impact Eng., 1991, 11(4), 463–480.
11 Carney, J. F. and Sazinski, R. J. Portable energy
absorbing system for highway service vehicles.
J. Transp. Eng., 1978, 4, 407–421.
12 Shrive, N., Andrews, K., and England, G. The impact
energy dissipation of cylindrical systems. In
Structural impact and crashworthiness (Ed. J.
Morton), 1984, Vol. 2, pp.544–554, (Elsevier Applied
Science Publishers. England).
13 Gupta, N. K. and Ray, P. Collapse of thin-walled
empty and filled square tubes under lateral loading
between rigid plates. Int. J. Crashworthiness, 1998,
3(3), 265–285.
14 Jing, Y. Y. and Barton, D. C. The response of square
cross-section tubes under lateral impact loading. Int.
J. Crashworthiness, 1998, 3(4), 359–378.
15 Morris, E., Olabi, A., and Hashmi, S. Experimental
and numerical analysis of the static lateral compression of tube type energy absorbers with different
indenters. Eng. J., 2005, 59(8), 505–510.
16 Morris, E., Olabi, A., and Hashmi, S. Lateral crushing of circular and non-circular tube systems under
quasi-static conditions. J. Mater Process Technol.,
2007, 191, 132–135.
17 Gupta, N., Sekhon, G., and Gupta, P. Study of lateral
compression of round metallic tubes. J. Thin Walled
Struct., 2005, 43(6), 895–922.
18 Gupta, N. K. and Abbas, H. Lateral collapse of composite cylindrical tubes between flat platens. Int. J.
Impact Eng., 2000, 24(4), 329–346.
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