Energy Absorption Analysis of Circular Tube of The Foam for High-
Speed Train
FAUZAN DJAMALUDDIN
Department of Mechanical Engineering,
Universitas Hasanuddin,
Poros Malino, Gowa, 92171,
INDONESIA
DANIEL SUSILO
Department of Research,
Universitas Multimedia Nusantara,
Tangerang, Banten,
INDONESIA
Abstract: - This paper discusses the outcomes concerning the crushing properties of aluminum foam–filled
tubes with a circular cross-section. The review assessed the impact of placing aluminum foam in single- and
double-walled circular. A parametric evaluation was performed concerning the circular with the single- and
double-walled variants. Validation results were contrasted against the documented experimental data, and a
noteworthy alignment was observed. The foam strain rate is vital in regulating the crushing properties of the
foam-loaded circular, and this factor must be considered. The outcomes also indicate the interaction between
the circular wall and foam core has a varying deformation category and specific energy absorption. Foam
loading had a similar effect concerning double-walled circular loads with foam. Moreover, evaluations were
performed to determine the impact of core thickness and impact velocity on the crashworthiness performance.
Further, it was discovered that a rise in core thickness for double-walled foam-loaded circular enhances
crushing characteristics until the walls still interact. Subsequently, any rise in core thickness leads to the
response aligning more with the single-walled circular energy absorber of a high-speed train
Key-Words: - Circular tube, foam, crashworthiness, impact, high-speed train, strain rate
Received: February 9, 2023. Revised: June 17, 2023. Accepted: July 23, 2023. Published: September 7, 2023.
1 Introduction
There has been a global interest in railway collision
studies due to the rising railway use for
transportation. High-speed collisions typically lead
to several deaths. The objective of evaluating such
collisions is to ensure passenger safety (Figure 1) by
improving design aspects to enhance train
crashworthiness. Positive results can be achieved by
evaluating dynamic structural properties like
acceleration, force on impact, deformation, and
energy absorption, [1], [2], [3], [4]. The most
accurate technique to examine a railway accident is
a full-scale train test, but its uses are few because of
its high cost and lack of suitable facilities.
Furthermore, accident scenarios in the actual world
would be different from laboratory prototype tests.
As a result, it is frequently beneficial to conduct
testing using miniature trains. To analyze the
dynamic response of train multi-body coupled
collision, the decrease in train collision incidents,
and the verification of the design parameters of train
crashworthiness, it is essential to create an efficient
train scaled model.
It is well-established that there are issues with
structure scaling for dynamic impact events, which
have made it difficult to use subsidized samples to
explain a variety of phenomena in engineering
structures under dynamic loads. In addition,
computational methods and outcome verification by
contrasting against experimental outcomes is a
common technique to evaluate railway vehicle
crashworthiness, [5], [6], [7], [8], [9]. Simulation
techniques are inadequate to assess the unavoidable
uncertainty due to input parameter dynamics;
furthermore, numerous complex limits concerning
structures cannot be exhibited, [10], [11].
Mathematical simulations can typically provide
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effective outcomes; however, they differ from the
fundamental aspects of accidents, [12], [13].
Fig. 1: Energy absorber of high-speed train
Vehicle impact safety has attracted more
attention as railway vehicles have developed. The
collisions between trains across the world result in
significant injury or death to passengers as well as
significant property loss. Thin-walled tubes, which
have been used in various applications, are
particularly effective at absorbing energy and have
been used to guard against car and train collisions.
Alghamdi assessed typical energy absorption
structures having varying cross sections and
presented deformation categories using numerous
literature reviews, [14]. In the study, [15], asserted
that extreme plastic deformations soak up most
kinetic energy from the impact. Further, studies on
corner cross sections suggested that 90° to 120°
angles are the most preferred for application studies.
Moreover, research, [16], [17], indicates that energy
absorption systems with multiple cells perform
superior to simple tubes. Further, cross sections
having octagonal or hexagonal shapes perform best.
Studies, [18], [19], [20], [21], [22], attempted to
optimise a structure’s energy absorption by
changing cross-corner angles and including shell
sheets.
Nevertheless, most of the referred works
concerning energy-absorbing structures are related
to automobiles rather than railways. Improving
metro vehicle crashworthiness requires novel
designs comprising gradual energy absorption, as
suggested by, [23]. The optimization was based on
response surface frameworks. In the study, [24],
designed circular tubes were incorporated with foam
to perform axial deformation studies. Their work
established efficient crash ability outcomes
concerning the devised structures. In the study, [25],
proposed a cutting-style structure to absorb energy,
and its mathematical and practical correlations
concerning the design variables and impact
outcomes were assessed. Lastly, optimization
outcomes indicated that the suggested structure
exhibited an appreciable crashworthiness
improvement.
Recent decades have witnessed the development
of extremely lightweight engineering materials like
aluminum foam. It has distinct mechanical
characteristics like retaining low constant stress
under extensive strain deformation before it
densifies. Energy absorption is a primary
application of this material. Incorporating the
circular with aluminum foam enhances energy
absorption properties, stabilizing the circular’s
buckling properties. In the study, [26], [27], [28],
mathematically evaluated metal foam core-based
thin-walled members and suggested extraordinary
weight efficiency. In the study, [29], contrasted
energy absorption for double- and single-walled
circular having distinct cross sections and axial
load-crushing aspects. The outcomes indicated that
a circular double–walled foam–filled circular
exhibited superior energy absorption ability
regardless of loading properties. Another reseacher
[30], evaluated foam–filled circular in single-,
double-, and multi-wall configurations, including
circular forms. The multi-walled foam-loaded
circular exhibited noticeable differences in energy
absorption and deformation characteristics.
Numerous studies and reports discuss aluminum
foam and its strain rate sensitivity, such as, [31],
asserting that closed foam cells are independent of
strain rate primarily due to gas dispersal across the
cells after the wall cracks. The study, [32], indicated
a remarkable impact of strain rate concerning peak
stress and densification strain. Moreover, a
mathematical assessment performed by, [33],
indicated that the cell geometry of aluminum foams
affects strain properties for higher strain values.
Recently, [34], assessed the dynamic and quasi–
static compressive crushing properties of circular
in–situ aluminum foam–filled circular. The
outcomes suggested that strain rate impacts circular
crushing characteristics. Therefore, to better
comprehend how single- and double-walled foam–
filled circulars respond to low-speed impact, this
work conducted a parametric assessment of such
structures where the foam core and impact velocity
are affected due to strain rate.
2 Materials and Methods
2.1 Finite Element Models of the Structures
To model energy absorbing structures, the
aluminum foam-filled double tubes of the length of
L = 210 mm and outer diameter do = 90 mm.
Moreover, a stroke efficiency of 0.5 as described
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thus for all tubes was assumed a maximum crash
distance of 100 mm.
Fig. 2: The schematic of the double circular tubes
The rigid wall impacted the top of the tubes at
an initial velocity of v = 10, 15.6, and 21.1 m/s
which is the speed obtained from the Railway
Assessment Program (Figure 2). The rigid
body as the mass block was modeled, all other
translational and rotational degrees of freedom were
fixed then only one allowable is translational
displacement. The mass block of 2000 kg is
attached to the top free end. This material structure
has a yield stress of aluminum thin-walled
tubes σy and density of foam filler ρf.. The cross-
section of the bitubal circular tubes were shown in
Figure 3. The outer diameter do and inner
diameter di of each tube, respectively. Moreover, the
outer and inner thickness (t) of the double tube wall
is 1.8 mm. The Parameters of the Geometrical and
impactor of the tube are presented in Table 1.
Table 1. Parameters of Geometrical and impactor of
the tube
To develop the models of aluminum foam-filled
tubular tubes and to predict the response of thin-
walled structures impacted by free-falling impinging
mass, the finite element (FE) code FE software was
used.
Fig. 3: Cross section of double circular tubes (a)
empty single-walled tube (SW), (b) foam-filled
double-walled tube (DWFF), and (c) foam-filled
single-walled tube (SWFF)
Four node shell continuum elements with five
integration points in the element thickness direction
were used to simulate the wall of tubular tubes.
Furthermore, the foam filled was modeled utilizing
eight-node continuum components, decreased
integration approaches, and the hourglass control.
Enhancement-based hourglass control and decreased
integration were used to prevent fake zero energy
deformation states and keep volumetric locking at a
distance. 2 mm element sizes were determined
based on mesh convergence research for the shells
and foam components. Mesh convergence is
addressed to achieve enough mesh density and
correct recording of the deformation process.
2.2 Material Properties
Extruded aluminum alloy circular tube (AA 6063
T1) packed with a closed-cell aluminum foam
(ALPORAS) block was employed in this research.
The mechanical characteristics of ALPORAS were
determined from, [24], [25], for different strain
rates, as shown in Figure 4a. According to, [24],
[25], ALPORAS with more than 15% relative
density will have a more pronounced strain-rate
impact. The kinetics of gas flow through the cell
structure is to blame for this. However, since, [24],
[25], did not include the densification section of the
stress-strain curves needed for numerical analysis,
some extra data were incorporated in this study
based on typical ALPORAS characteristics, as can
be seen in Figure 4(b). Young's modulus of solid
aluminum (E) was chosen as the second tangent
modulus. Since the aluminum foam would compact
and behave like solid aluminum during
densification, the final modified stress-strain curves
at a relative density of 16% are shown in Figure
4(c).
Young's modulus, plateau stress, first tangent
modulus, densification strain, and second tangent
modulus are typical characteristics that reflect the
behavior of aluminum foam. The material utilized
for the circular wall in this study is the 6063 T1
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densification strain. The constitutive behavior of the
foam model proposed by, [35], utilizing non-linear
FE software packages is based on an isotropic
uniform material. This study did not take into
account the effect of the manufacturing process on
the anisotropic behavior of aluminum foam.
Fig. 4: ALPORAS stress-strain curve with a relative
density of 16% at various strain rates, including (a)
original experimental data, (b) a typical ALPORAS
stress-strain curve used as a baseline for
modification, and (c) modified stress-strain curves
utilized in the current study, [36]
To gather precise material information and to
specify the input for material modeling in the
numerical simulations, two types of tensile tests
were performed: quasi-static (0.001 /s) and dynamic
(0.1, 1, 10, 100 /s). It was discovered that the
engineering stress-strain curve of aluminum alloys
is insensitive to strain rate, hence strain rate effects
do not need to be included in the material model.
Figure 3 depicts the true stress - true plastic strain
curve, [36]. AA6063-T1 true stress - true plastic
strain curve is presented in Figure 5.
Fig. 5: AA6063-T1 true stress - true plastic strain
curve, [36]
3 Result and Disscusion
3.1 Validation Data
To ensure finite element models are sufficiently
accurate for design structure, they should be
compared to experimental data, [37]. The difference
in the maximal crushing force between the
experiment test and the simulation is 1.42% (Table
2). The deformation patterns also indicate that the
model was quite similar (excellent agreement)
between the simulation and the test, as illustrated in
Figure 6.
Fig. 6a: Force displacement of simulation and
experiment test, [37]. 6b: Deformation mode (a)
simulation and (b) experiment test of DWFF
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Table 2. Difference between FEA and experiment
results, [37]
3.2 Plastic Deformation Modes
The SW1, SWFF, and DWFF1-DWFF10 circular
tubes undergo plastic folding distortions. It is
observed that frameworks that account for strain
rate align better with practical outcomes than those
that disregard it. Figure 7 depicts the initial
extensional folding of DWFF, which transitions to
in-extensional modes. It indicates that the fold count
concerning DWFF5 aligns well with the practical
outcomes. The DWFF5 foam core absorbed more
energy owing to superior peak stress at a higher
strain rate, as depicted in Figure 6. Strain rate
impact enhances corner-specific energy absorption
by enhancing local deformation in the circular of
aluminum. Consequently, there is a minor increase
in overall crushing force. Therefore, it can be
concluded that the foam core’s strain rate has a
meaningful impact on the crushing characteristics of
the foam-incorporated circular.
SW SWFF DWFF1
DWFF2 DWFF3 DWFF4
DWFF5 DWFF6 DWFF7
DWFF7 DWFF9 DWFF10
Fig. 7: Deformation mode of structures
3.3 Crushing Force Curve
Figure 8 depicts curves corresponding to SW,
SWFF1, and DWFF1-10 circular and presents the
instantaneous crushing force vs crushing length. It is
understood that the strain rate effect must be
accounted for in the material framework for finite
element simulations of the foam. Hence, a proper
and accurate estimate can be obtained concerning
the true physical and crushing characteristics of
axial dynamical loads placed on the circular. It can
also be seen that single-walled foam-filled circular
(SWFF) outperforms the responses of only circular
walls (SW) when loaded individually (Figure 8).
The interaction between the circular wall and the
foam will greatly improve the crushing resistance.
The response of DWFF is found to be much better
than the sum of the circular walls and the foam-
filled circular tube. For double-walled foam-filled
circular, indicating that in this model, the interaction
between the column walls and the foam also has a
significant effect on the crushing behavior of the
column, as shown in Figure 8. It can be seen also
that peak force increases significantly when
increasing the impact velocity of an impactor.
SW
SWFF
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DWFF1
DWFF2
DWFF3
DWFF4
DWFF5
DWFF6
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DWFF7
DWFF8
DWFF9
DWFF10
Fig. 8: Force response of structures with different
impact velocity
3.3 Foam–filled Circular Analysis
This portion discusses foam-loaded circular
crushing characteristics, energy absorption
properties, and specific energy absorption in Figure
8 and Figure 9. Initially, single- and double–walled
circular were evaluated concerning the impact of
aluminum foam insertion. Subsequently, the impact
of changing core thickness was evaluated. The
material framework of the foam considers the
effects of strain rate.
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Fig. 9: Energy Absorption responses of structures
with different impact velocity
This section assesses the crushing
characteristics of the DWFF circular at several core
thickness values (10 mm – 80 mm). The outcomes
are contrasted against the single–walled foam–filled
(SWF) circular. Instantaneous and mean-crushing
responses are depicted in Figure 10. The outcomes
indicate that the initial specific energy absorption
increase for a single foam-filled tube (SWFF). For
foam-filled double wall tubes (DWFF) it can be
seen that SEA increases from DWFF1 to DWFF7
and then reduces as the core thickness rises
(DWFF8-DWFF710), [37].
Fig. 10: Specific Energy Absorption responses of
structures with different impact velocity
3.4 Normalised Mean Crushing Force and
Structural Efficiency
Specific Energy Absorption (SEA) are critical
crashworthiness aspects to determine the energy
absorption efficiency of the elements, which are
defined as Figure 11 provides SEA values for SW,
DW, SWFF, and DWFF assessed in this portion.
Figure 11 depicts the SEA circular normalized about
the SW circular Therefore, the ability and efficacy
of several circulars having distinct geometries can
be contrasted directly concerning their energy
absorption characteristics. Figure 11 depicts the
normalized values of specific energy absorption
observed. Rising foam thickness leads to foam-
circular wall interactions, enhancing the circular’s
energy absorption ability until the inner wall is
minimal, and the characteristics of the double–
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walled foam–a filled circular approach that of the
single-walled equivalent, [38], [39].
Fig. 11: Normalised specific energy absorption of
structures with different impact velocity
4 Conclusions
This research presents a computational investigation
of aluminum foam-filled circular under dynamic
axial crushing force. The outcomes confirm that
adding foam to a column will enhance its capacity
to absorb energy. The outcome also demonstrates
predictions of the crushing behavior that may be
made using a numerical model that takes the strain
rate effect into account.
The interaction of the foam core with the tube
wall will change the mode of deformation from a
single localized fold to several propagating folds
and raise the column's mean total crushing force. In
double-walled foam-filled tubes, similar effects of
the filling are also seen. When compared to single-
walled circular tubes, the mean crushing force of a
foam-filled column is significantly enhanced,
however, when compared to a double-walled
circular tube, it is only slightly improved.
Increasing the core thickness will increase
the crushing force up to an indication where the
dimension of the inner wall tube is too small
and the behavior of the double-walled foam-
filled tube approaches that of the single-walled
foam-filled tube, according to analysis results of
the double-walled foam-filled tube with various
core thicknesses of the same outer wall
geometry. The findings demonstrate that the
double-walled foam-filled tube has a greater
mean crushing force than the single-walled
foam-filled tube.
Based on the above presented approach of
scaled train modeling, a similar scaled model of a
train may be created to offer a quick and effective
way to build the basic framework of a train in future
research. A scaled-down train model is essential for
understanding the development and energy
distribution during railway crashes since it can
accurately represent a full-size train collision and
offer a practical and affordable way to replicate
catastrophic incidents. The scaled modeling issues
for thin-walled structures in high-speed trains could
be effectively resolved by the scaled method
presented here. It is also suitable for the scaled
model design of other large prototypes composed of
thin-walled structures in engineering.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
-Fauzan Djamaluddin carried out the simulation,
the optimization and the methodology
-Daniel Susilo responsible for project administration
and methodology
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflict of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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