International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 1442–1450, Article ID: IJCIET_10_04_151
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=4
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
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DEFORMATION STUDIES ON THE
SIGNIFICANCE OF COMBINED GEOMETRY
TUBES AS ENERGY ABSORBING STRUCTURES
A. Praveen Kumar
Department of Mechanical Engineering, CMR Technical Campus,
Hyderabad, Telengana, India.
D. Manieah
Department of Mechanical Engineering, CMR Technical Campus,
Hyderabad, Telengana, India.
ABSTRACT
The deformation behaviour of cylindrical tubes have attracted the attention of
researchers in recent years, due to their light weight, high energy absorption capacity
and ease of fabrication. Despite their excellent crash performance, high initial peak
force is a major shortcoming when they are subjected to axial impact. Though various
triggering methods have been examined in the previous literature with the aim of
reducing the initial peak forces, these kinds of geometrical discontinuities will
decrease the stiffness of the structure and also has a drawback of reduced energy
absorption capacity. Therefore, a tube configuration, which does not affect the
performance of the structure in normal use, whilst it could be improving its energy
absorbing characteristics and the level of deceleration pulse with delayed transfer of
impact crushing force is highly desired. This article aims to propose press-formed
combined geometry tubular structures which include cylindrical segment harnessed
with end-caps as a frontal crash safety element in automotive vehicles.
Key words: Combined geometry, Crashworthiness, End-capped tubes, Protective
structure, Thin-walled tubes.
Cite this Article: A. Praveen Kumar and D. Manieah, Deformation Studies on the
Significance of Combined Geometry Tubes as Energy Absorbing Structures,
International Journal of Civil Engineering and Technology 10(4), 2019, pp. 1442–
1450.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=4
1. INTRODUCTION
Crashworthiness design of thin-walled energy absorbing structures with low initial peak force
and superior energy absorption capability is a major concern in vehicle crash safety
applications due to the continually increasing demand for high speed with less weight [1].
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Deformation Studies on the Significance of Combined Geometry Tubes as Energy Absorbing
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Combined geometry tubular structures can meet requirements of these applications with
surplus features such as high strength to weight ratio, better stiffness, and tailored mechanical
properties. The combined geometry tubes manufactured with the combinations of profiles
such as cylindrical, conical and spherical are recently employed in aerospace protective
structures, due to the excellent energy absorption characteristics and uniform deformation
behavior of their constituents [2, 3]. These tubes deform mostly in stable and progressive
nature under static and impact loads, leading to relatively high efficacy of the transformation
of kinetic energy into irreversible plastic deformation energy. Investigations of the deforming
mechanisms and energy absorbing characteristics of these tubular structures are essential to
ensure the required protection level without causing any damage to the occupants and the
vehicle structures.
A sequence of analytical, experimental, and finite element investigations have been
conducted in the past decades to examine the deformation and energy absorption response of
thin-walled simple geometry tubes. These tubes comprise various profiles such as cylindrical,
conical, elliptical, square, hexagonal, triangular and S-shaped [4, 5]. Amongst these, extruded
cylindrical tubes have been widely used as a crashworthy element in vehicles owing to their
high strength, ease of manufacturing, lightweight, and outstanding crashworthiness
characteristics [6]. In spite of their excellent crash performance, high initial peak force is the
critical problem which has the potential to cause severe injury to the occupants. State-of-theart studies of cylindrical tubes reveal that numerous triggering techniques such as buckling
initiator, corrugation, diaphragms, holes, grooves, and patterns were investigated with the
intention of reducing the initial peak force [7-8].
Overall, the triggering method achieves stable deformation responses and might reduce
the initial peak force, but still, it has a drawback of poor energy absorbing capability through
reducing the stiffness of the tube. Crashworthy design engineers attempt to design ideal
energy absorbing elements with low initial peak force, stable deformation, and high energy
absorption characteristics. Aiming at this challenge, a novel hybrid concept called combined
geometry tubes has been proposed by Praveen Kumar et al. [9]. These tubes can resist applied
impact force by progressively deforming with the combination of their deformation behaviors
of geometries. The combined geometry has a good deformation behavior at different strain
rates due to their stable progressive deformation and representing various deformation types
of their different geometric segments.
In this article, several state-of-the-art studies that were performed earlier in order to
understand the axial deformation behaviour of conventional cylindrical tubes is described.
Those energy absorbing tubes made from the combined geometry structures are considered to
be beyond the scope of this article. Hence, the objective of the present article was to explore
the significance of press-formed combined geometry tubes that influences the crashworthiness
characteristics such as initial peak crushing force, energy absorption capability, and specific
energy absorption. A systematic study was further needed to understand the interaction
between the forming parameters and the subsequent crash performance of the proposed tube
configuration. The opportunities for future developments in the press-formed combined
geometry tubular structures are also reported.
2. DEFORMATION BRHAVIOUR OF CYLINDRICAL TUBE
Thin-walled aluminium tubes can have different geometry profiles, such as cylindrical [10],
square [11], hat-type [12], corrugated [13], and tapered [14] tubes. Many researchers have
made great efforts to examine the deformation behaviour and energy absorption
characteristics of all these energy absorbing structures. Among these, extruded cylindrical
tubes have been used widely as a crashworthy element in vehicles and are most popular
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studied by researchers owing to their high strength, ease of manufacturing, lightweight, and
outstanding crashworthiness characteristics [15]. One of the earlier deformation studies on the
cylindrical tubes was performed by Alexander in 1960‘s [16]. He proposed a theoretical
model for calculating the mean crushing forces of axisymmetric deformation mode of
cylindrical tubes. The cylindrical tubes with low D/t ratios (diameter/thickness) tend to show
concertina (axisymmetric) mode of deformation, while the tubes with high D/t ratios show
diamond (asymmetric mode) of deformation. The axial deformation of a cylindrical tube
involves progressive folding of the tube with one or more of three main deformation modes:
concertina, diamond, or a mixed mode under static and impact loading as displayed in Figure
1.
Figure 1 Various deformation modes of axially loaded cylindrical tubes
2.1. Triggering methods
A lot of previous literature show that, in spite of the superior impact performance of thinwalled cylindrical tubes, high initial peak force is the major problem which has the potential
to cause severe damage to the occupants and the vehicle. With the aim of reducing the initial
peak forces, triggering methods such as holes, patterns, grooves, corrugation, and chamfer
were introduced by numerous researchers in the past [17-19]. Figure 2 summarizes some of
the studies on the various triggering methods applied to the thin-walled cylindrical tubes. For
instance, Daneshi et al. [20] experimentally investigated the effect of circumferential grooving
on the deformation behavior of cylindrical tubes under axial loading and their results showed
that the grooves provided uniform crushing responses with decreased energy absorption
capacity. A variety of trigger types was generated including notches, holes and plastic folds. It
was concluded that the initial peak crushing force could be reduced by using these triggers.
However, no optimal solution was known among all the alternatives.
Figure 2 (a) triggered tube (b) corrugated tube (c) grooved tube
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Deformation Studies on the Significance of Combined Geometry Tubes as Energy Absorbing
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Overall, the triggering methods can reduce the initial peak crushing force, increase
stability and achieve uniform crushing responses but still, it has a disadvantage of reduced
energy absorption capacity through reducing the stiffness of the energy absorbing tube.
3. DEFORMATION BEHAVIOUR OF SPHERICAL SHELLS
Thin-walled spherical shells have been widely used for many engineering applications such as
nose cone of aircraft, rockets, ballistic missiles, pressure vessels, and gas tanks as these
provide excellent energy absorption. Experiments have shown that spherical shells deform
with an initial flattening followed by inward dimpling when they are compressed between two
rigid plates. Thick shells deform axisymmetrically and major load is absorbed by the rolling
plastic hinges. When the thickness of the shell is reduced considerably, the inward dimpling is
followed by non-symmetric multiple lobes which are caused by the development of stationary
hinges. The radius, thickness and height are essential geometrical parameters influencing the
crushing force of the structure.
For instance, Leinster et al. [21] explored the deformation response of a ductile spherical
shell subjected to rigid wall analytically and experimentally. An analytical method was
divided into two parts in terms of deformation mode of spherical shell as pre-dimpling
behavior mode and dimpling behavior mode. Gupta & Venkatesh [22] investigated the
dynamic deformation characteristics of thin-walled spherical aluminium shells. It was
illustrated that force-compression histories, mean crushing forces and energy absorbing
capacity were examined using finite element code. Gupta et al. [23] examined the impact
characteristics of the aluminium hemi and shallow spherical thin-walled shells under impact
loading. The deformation modes were obtained as local flattening, inward dimpling and
formation of axisymmetric and asymmetric folds at various velocities. Furthermore, the mean
crushing force increased as the radius and thickness increased. The numbers of folds
formation were varied depending on the R/t values and velocities, as shown in Figure 3. It
was reported that the mean crushing force and energy absorption capacity of hemi and
shallow spherical shells were a function of radius, thickness, and deformation rates.
Figure 3 Impact crush response of spherical shells [23]
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4. DEFORMATION CHARACTERISTICS OF COMBINED GEOMETRY
TUBES
The structures consisting of two or more geometric segments were termed as combined
geometry and this kind of structures absorbs higher energies and lower transmitted crushing
forces. The combined geometry which consists of spherical, conical or cylindrical geometric
shape can be used in many applications which include rocket warhead, radome of aircraft,
fuel tank, projectiles and crush boxes [24, 25]. The combined geometry has a good
deformation behavior at various strain rates due to their progressive buckling without any
discontinuity and representing various deformation types of their different geometric
segments. The combined geometry consisting of spherical and cone segments could be the
best example as shown in Figure 4. In this regard, Sheriff et al. [26] examined the quasi-static
and impact response of combined geometry shells which comprises conical frusta and shallow
spherical caps with many thicknesses 0.7, 0.9, 1.2 and 1.6 mm. It was reported that the
deformation of combined geometry shells occurred progressively. At first, dimpling of a
spherical cap and further deformation of conical frusta were observed. Three different
deformation modes were observed during deformation: Flattening, inversion of a cone, and
formation of folds.
Gupta & Gupta [27] investigated the deformation response of combined geometry metallic
shells consisting tube and cone geometries at quasi-static strain rate. The tube samples were
manufactured from aluminum sheet between 1 and 5 mm by the conventional spinning
process and were annealed at 3000° C and cooled for 24 hours in a muffle furnace. Najibi et
al. [28] examined the energy absorption responses and the crushing force carrying capacity of
combined geometry metallic shells comprising 90 x 90 mm of square and 57 mm radius of
cylindrical tubes at quasi-static loading. The initial peak force value of cylindrical tube was
found 26.4% more than that of square during deformation; however, the energy absorbing
capability of the cylindrical tube was higher (22.8%) than that of the square tube as shown in
Figure 5.
Figure 4 Space capsule (ISRO 2007)
It was determined from the results that, utilizing the combined geometry metallic shells
resulted in 4.6% and 31% lower initial peak force than the simple cylindrical and square tube.
The energy absorption capacity of combined geometry shell was 18.1% higher than the square
tube and 4.7% lesser than the cylindrical tube.
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Deformation Studies on the Significance of Combined Geometry Tubes as Energy Absorbing
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Figure 5 Comparative numerical results of combined geometry tube [28]
The major findings of the literature review revealed that there is a substantial amount of
published information on the cylindrical thin-walled tubes with various configuration methods
to improve the energy absorption characteristics under axial loading such as filling with foam
material, stiffeners, stacking layers, varying thickness, and nested tubes. The literature
analysis also shows that triggering methods were introduced on the cylindrical thin-walled
tubes such as holes, patterns, grooves, corrugation, diaphragms, saw cutting, and buckling
initiator with the aim of reducing the initial peak force. However, both the methods have some
advantages and disadvantages. Therefore, the current study proposes press-formed combined
geometry tubes comprised of a cylindrical segment harnessed with plain end-capped tubes,
shallow spherical capped tubes, and hemispherical capped tubes for designing an efficient
energy absorbing structure applicable to wide range impact velocities as illustrated in Figure
6. For the occupant safety in automotive vehicles, a detailed study relating to crushing and
energy absorption characteristics of the capped cylindrical tube is needed. Though many
researchers reported an experimental and numerical analysis of the influence of the forming
history on the crashing characteristics of simple geometry like hat section, similar kind of
work has not been available for combined geometry cylindrical tubes.
Figure 6 Proposed combined geometry tubes
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In general, crushing force should be low in the beginning of an impact incident to reduce
the deceleration and avoid occupant injuries. But to the end of the impact event, a high
crushing force would be estimated to increase energy absorbing capability. Obviously, the
initial portion should have a thin wall to produce a low initial peak force, while the end
portion must have a thick wall to absorb additional impact energy. The combined geometry
tubes manufactured by forming process experience lowest plastic strain (thin wall) in the
initial portion and highest plastic strain (thick wall) in the end portion [29, 30]. The effective
plastic strain will make the tubular structure stiffer and is desirable to ensure that the onset of
yielding in the structural design is correct.
5. CONCLUSIONS AND FUTURE WORK
The present review article outlines the major trends in research and development of pressformed combined geometry tubular structures concentrating on the most recent work. The
major conclusions the authors draw from the reviewed studies are:

The review revealed that there was abundant volume of published data on theoretical,
experimental and numerical methods for determining the energy absorber response of various
simple geometries. Among these geometries, cylindrical tube cross-section had better energy
absorption due to its progressive folding nature.

The review of various triggering methods to reduce the peak force highlighted the importance
of minimum peak force to safeguard the occupants and the vehicle. However, the findings of
these study also indicated that these kinds of geometrical discontinuities decrease the stiffness
of the structure with reduced energy absorption capacity.

The literature on the deformation response of various spherical geometries emphasized the
importance of the local flattening, inward dimpling and formation of lobes for extending the
pulse duration with reduced peak force for better crashworthiness.

The review on combined geometry highlighted the importance of harnessing the end-caps with
cylindrical tubes for better energy absorption with reduced peak force.
In conclusion, in spite of advanced and comprehensive analytical and design methods
pertinent to combined geometry tubular structures, the ever-increasing range of applications,
different loadings and hybrid materials will continue to motivate experimental and numerical
research studies in the future.
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