Frontal Crash Worthiness Performance of Bi-Tubular Corrugated Conical.pdf

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Frontal Crash Worthiness Performance of Bi-Tubular Corrugated Conical:
Structures under Axial Loads at Low Velocity
Conference Paper · April 2020
DOI: 10.4271/2020-01-0983
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2020-01-0983 Published 14 Apr 2020
Frontal Crash Worthiness Performance of
Bi-Tubular Corrugated Conical: Structures under
Axial Loads at Low Velocity
Akash Porwal, Abhishek Tripathi, and Prabu Krishnasamy Vellore Institute of Technology
Citation: Porwal, A., Tripathi, A. and Krishnasamy, P., “Frontal Crash Worthiness Performance of Bi-Tubular Corrugated Conical:
Structures under Axial Loads at Low Velocity,” SAE Technical Paper 2020-01-0983, 2020, doi:10.4271/2020-01-0983.
Abstract
V
ehicle collisions are a major concern in the modern
automotive industry. To ensure the passenger safety,
major focus has been given on energy absorption
pattern on the crumple zone during collision, which lead to
the implementation of new design of the crash box for low
speed collision. The main aim of this research is optimization
of the conical shaped structure based on its mean diameter,
graded thickness and semi apical angle. Further, to decrease
initial peak load of the conical crash box, corrugations are
integrated on structure and optimized based on different
parameters, such as number of corrugations, pattern of corru-
gation relative to both tubes and amplitude of corrugation.
The concept of bi-tubular structure is proposed to improve
both specific energy absorption and initial peak load during
crash event. A finite element model is created to perform para-
metric study on corrugated conical tube based on axial load
conditions at low velocity. Optimization to maximize total
absorbed energy and minimize peak impact load on the crash
box within constraints is conducted. The result showed that
design of proposed crash box effectively performs as energy
absorbing structure and can be used in the future vehicle body.
Introduction
C
rash box is an energy absorbing component installed
in the front most portion of the vehicle to absorb
energy during frontal collision. It protects the parts
like fender, intercooler, and radiator from the serious damage
during frontal impact. It is mounted behind the bumper,
therefore during the frontal impact, first bumper of the vehicle
comes into the contact, then the crash box. In this way energy
transmission takes place from bumper to crash box, and then
to the side rails which then affects the safety of passenger. The
improved energy absorption characteristic of crash box
increases passenger’s safety, while energy transmission should
be minimized to side rail portions.
The dissipation of energy with plastic deformation is
paramount in relation with the safety of vehicles of all sorts.
As long as there is deformation, there is energy absorption in
structure. These deformations may be permanent or tempo-
rary. When the deformation is permanent, plastic strain is
produced, leading to plastic energy dissipation. The passive
safety load path can be classified into: low speed impact, high
speed impact, side impact, rear impacts, occupant and pedes-
trian protection. The occupant safety is ensured by proper
structural changes in the vehicle front structures. A robust
optimization should be performed to enhance the frontal
structure to meet various conditions and satisfy standard
crash tests.
At low speed, slight collision can damage the bumper
which requires huge repair cost, therefore bumper system
must be optimized at low velocity to reduce damages and car
reparationwhichreducesthecostofinsurance.Theresearchers
have used various optimization techniques to enrich the
frontal crashworthiness of the vehicle structure. Schwanitz
et al. [1] performed robust multi-parameter optimisation on
the crash box structure in terms of wave like surface contour,
the parameterization includes position and size of the holes
and welding seams, as well as material thickness. See Jung lee
et al. [2] proposed a new design to enhance the energy absorp-
tion characteristics of the crash box using the orthogonal array
method to compare standard sections like circular, polygons
and implemented topology optimization technique to deter-
mine the cross-section of crash box with maximum absorbed
strain energy. The proposed design offers better result at low
speed impact but fails to meet the high-speed impact because
of its different performance requirements.
Keywords
Frontal crashworthiness, conical bi-tubular structure, graded
thickness, semi apical angle, corrugations, axial load,
low speed collisions
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FRONTAL CRASH WORTHINESS PERFORMANCE OF BI-TUBULAR CORRUGATED CONICAL: STRUCTURES UNDER AXIAL
2
A crash analysis was performed to improve the vehicle
front structure through orthogonal design method and overall
balance method by [3] to optimise crash box based on trigger
depth, and its thickness for low speed impact. A crash system
was designed by [4] on the basis of the buckling modes.
Different designs were compared on the basis of load pattern
to reduce the load peaks during the crash conditions and
reduced load oscillations in the final design by about 5kN in
amplitude and wall thickness was optimised on the basis of
load patterns. Azimi et al. [5] worked on single and double
walled structures and proposed new bi-tubular structure
design based on inner conical and outer circular tubes which
resulted in improved energy absorption and reduced initial
peak load under oblique and axial loads. It was also shown
that use of foam filled structure does not always show better
crashworthiness characteristics. A. Baroutaji [6] presented
detailed review of various different thin walled tubes used for
crashworthiness performance including multi cell tubes,
functionally graded thickness tubes, hollow filled tubes, foam
filled tubes, different cross section tubes, laterally corrugated
tubes, linearly corrugated tubes, nested tubes, auxetic foam
filled tubes under lateral, axial, oblique and bending loading.
Yang et. al [7] experimentally proved the new method of
designing crash box through section force evaluation by its
energy absorption ratio, considering engine bay package, car’s
styling and crash performance at both low and high velocity.
M.A. Guler [8] studied behavior of thin walled straight and
conical structures under axial impacts and showed that
circular cross section absorbers were more crush force efficient
compared to square and hexagonal cross section absorbers,
further he incorporated blanks and corrugations on walls of
absorber to reduce peak crush force, but no methods were
suggested to increase the SEA of corrugated structures. Yusof
et. al [9] gave a comprehensive review on design of geometry
profiles for crash box and advancement on use of materials
for crash box. Various metal matrix composites, high perfor-
mance thermoplastics, carbon fibre reinforced polymers and
glass fibre reinforced thermoplastics had been used to replace
metals for crash box performance enhancement [9]. In
addition,variousmetalssuchasAluminumalloys,Manganese,
Magnesium and High strength steels had been studied for
crash box. The numerical analysis performed by C. Kilicaslan
et. al [10] worked on foam-filled aluminum single and double
corrugated tubes for crash analysis which showed a drastic
decrease in peak force, but didn’t reflect any major increase
in SEA. Aluminum foam filling in the structure, helped
increasing the mean force and energy absorbed by the struc-
ture. SEA of foam filled double tubes were higher than single
tubes for higher corrugation length. A.A. Singace [11] showed
the different aspects of manufacturing of corrugated tubes,
further they did a detailed analysis of force versus displace-
ment curve of corrugated tubes with introduction of foam.
They proposed that the quantity, and quality of energy absorp-
tioncanbecontrolledbycorrugation.Furtheritwasconcluded
that there wasn’t any significant change in overall behavior
with introduction of foam.
Eyvazian et. al [12] worked on effect of axial and lateral
corrugation on crashworthy parameters and failure mode
in circular aluminum tubes. He concluded about the
controlled collapse mode of structure because of
corrugations, which is highly favorable for energy absorbers
design. Similar study was carried by [13] on sinusoidal corru-
gated tube which showed uniform load-displacement curve
and ring collapse mode of the structure which resulted in
40-80% decrease in peak crush force. The high energy
absorption of steel in compare to aluminum [13] indicated
the application where high energy absorption is required,
whereas in case of specific energy absorption, Aluminum 6
series dominated steel. Zhifang Liu et al [14], analyzed the
sinusoidal corrugated structure with varying radius-thick-
ness ratio, amplitude of corrugation and wavelength. The
three modes namely, dynamic asymptotic, buckling and
dynamic plastic buckling were calculated by finite element
method. The impact velocity and radius-thickness ratio were
the two main factor which determine the deformation
modes. They concluded that by increasing the radius-thick-
ness ratio, the energy absorption decreases.
Xiolin et. al [16] performed detailed comparative analysis
on multi-cell conical tube, multi-cell square tapered tube, and
fourfold-cell conical tube of same weight. The multi-cell
conical tube has better energy absorption capacity than multi-
cell square tapered tube and fourfold-cell conical tube and
proposed genetic algorithm procedure for final optimization
based on real conditions. Experiments were carried out by
[17] to prove high energy absorption capacity of foam filled
tri tubes compared to empty single tubes, foam-filled single
tubes, empty double tubes, foam-filled double tubes and
empty tri-tubes, they performed various parametric optimiza-
tion on foam filled tri tube to describe its complex behavior.
After undergoing detailed literature study on various crash
box structures, it was found that corrugated structures have
great potential to be used as highly efficient energy absorbers
under axial and oblique loads in vehicles. But many of studies
describe only about methods of decreasing initial peak crush
force of corrugated structure and not on how to enhance the
specific energy absorption of the structure. Therefore, outcome
of this paper will provide robust design process to enhance
crash performance based on specific energy absorption, peak
crush force and crush efficiency of the corrugated structure.
The proposed crash box design can then further be used in
future vehicle body for passenger’s safety.
The paper is subdivided into Geometrical description,
Material selection of the crash box, Material characterization
for finite element modelling, Finite element model and para-
metric optimization of design to obtain the require design of
crash box.
Numerical Modelling
Geometrical Description
The crash box is most crucial energy absorbing structure of
the vehicle for axial and oblique impacts. Its collapse mode
and energy absorbing capacity can greatly influence the full
vehicle’s crashworthiness and safety of the passengers. In
order to improve the energy absorbing characteristics, the
geometrical configuration of the crash box is optimized based
on overall dimensions of crash box, outer structural shape

3
and structural arrangement inside the crash box. Various
cross-sectional shapes are considered to analyze their energy
absorption capability. The overall length, perimeter and thick-
ness of tube is kept same in each case for analysis, as listed in
Table 1. In the entire paper, length of crash box is kept constant
as 180mm according to available installation space between
bumper and side rail in vehicle. Design flow in figure 3
explainsaboutdifferentgeometricvariationusedinsimulation.
Material Selection
Crash box is energy absorbing component installed in the
front most portion of the vehicle to absorb energy during
frontal collision. Two major aspects for selecting energy
absorbing material are:
1. The vehicle’s front sections should collapse due to
impact, to provide maximum absorption of the
kinetic energy during crash.
2. The passenger compartment should maintain its
structural integrity.
The energy absorption depends on the flow stress and the
folding pattern of the structure. Flow stress is directly related
to plastic strain, greater the plastic strain in the body, more
will be the plastic energy dissipation resulting in good energy
absorbing capacity. Crash boxes are mostly made of steel and
aluminum with various compositions. In addition, weight
shouldbereducedwhileimprovingtheperformancecompared
to the current systems which majorly includes steel and
aluminum. Material selection involves deformation and
progressive failure behavior in terms of stiffness and strain
hardening. Deformation and strain throughout the process
are crucial to determine energy absorbing capacity of mate-
rials. The parameters considered for the material selection
are: - Density, Young’s Modulus, Yield Strength, Ultimate
strength, Percentage elongation, Specific strength, strain hard-
ening exponent and strain rate sensitivity. Based on these
properties, Al 7075-T6 alloy is selected compared to other Al
Alloys series and steel. Al 7075-T6 results in higher energy
absorption due to its higher strain hardening behavior and
strain rate effects. Greater the strain hardening exponent,
more will be the flow stress in the material. The effects of strain
rate can be compared based on true stress-strain curve of Al
alloys obtained from tensile test of each specimen (figure 1).
The response of tubes made of aluminum is strain rate
insensitive while that of steel is strain rate sensitive. Al 7075-T6
has advantage of high specific energy absorption and light-
weight as compared to steel. Therefore, Aluminum offers
better crash energy management efficiency than steel. It also
has better plastic energy dissipation properties than Al 6061.
Table 2 highlights mechanical properties of Aluminum alloys
and steel.
Material Characterization
High plastic strain on the material during crash leads to the
flow stress on the material. In this condition, material response
is dominated by the plastic material behavior. This plastic
deformation is described by the yield function, which defines
stress-state-dependent onset of the plasticity and gives the
direction of plastic flow by flow rule. Therefore elastic-plastic
material behavior with isotropic strain hardening was consid-
ered for the simulation of crash analysis. Aluminum alloy
7075-T6 was used for the thin walled columns with the
following mechanical properties: density = 2810 kg/m3
, Yield
Strength = 503MPa, Young’s Modulus = 71.7GPa and Poisson’s
ratio = 0.33.
TABLE 1 Different Cross-Sectional Shapes of Outer Structure
of Crash Box
Specimen
Shape Dimensions
Length(mm) Thickness
(mm)
Cylindrical 180 Diameter = 60mm 2.5
Hexagonal 180 Rib = 31.4mm 2.5
Square 180 Rib = 47mm 2.5
Rectangular 180 Cross Section = 31 x
62 mm2
2.5
Triangular 180 Rib = 62mm 2.5
Conical 180 Min Dia. = 45mm,
Max Dia. = 77mm
2.5
Pyramidal 180 Min cross section
= 40x42mm2
Max cross section
= 40 x 47mm2
2.5
©
SAE
International.
FIGURE 1 Stress Strain Curve for Aluminum Alloy Al
7075-T6 and Al 6061-T6
©
SAE
International.
TABLE 2 Comparison of Mechanical Properties of Al 6061, Al
7075 and AISI 304 [17]
Properties Al 6061 Al 7075 AISI 304
Density (kg/m3
) 2810 2810 8000
Young’s Modulus (GPa) 68.9 71.7 193
Yield Strength (MPa) 276 503 215
Ultimate Strength (MPa) 310 572 505
Poisson’s ratio 0.33 0.33 0.33
Elongation (%) 17 11 70
Strain Hardening Exponent 0.22 0.29 0.45
©
SAE
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4
The isotropic strain hardening was obtained from strain
stress curve data of tensile test as shown in Figure 1. As
Aluminum is insensitive to strain rate under low impact
velocity of 15km/h, strain rate dependency effect could
be ignored for quasi-static crushing. Geometric nonlinear
effects are significant for crash analysis, so geometric nonlin-
earity is included during deformation process.
In this model, a load curve is used to describe the initial
yield strength (σ0) as a function of effective strain rate. The
yield stress for this material model is defined as:
s s e e
Y h p
eff
E
= +
¢
0

where σ0 is the initial yield strength, ε.’
is the effective strain
rate, (εp)eff
is the effective plastic strain, and Eh is given by:
E
EE
E E
h =
-
tan
tan
Finite Element Modelling
In this study, three-dimensional finite element model (FEM)
was established using the explicit nonlinear solver in ABAQUS
for numerical simulation of low speed axial crushing of the
energy absorbing structures. Figure 2 shows the FEM model
of a conical structure, which consists of rigid fixed plate at
bottom and moving plate at the top. Therefore, bottom plate
is pinched and an initial velocity of 15 km/h is applied on the
moving plate to simulate low speed collisions.
Homogeneous Shell model of crash box tube is developed
with mesh size of 2mm to ensure that deformation process is
accurately captured. Top and Bottom plate are modelled as
Rigid elements with mesh size of 4mm. The entire model
consists of thin walled structures modelled by using 4 node
shell continuum (S4R) with 5 integration points along the
thickness direction under Simpson thickness integration rule.
The model uses penalty based isotropic frictional coefficient
of 0.3 for tangential contact behavior at all surface pair’s
location. The bottom surface of tube is tie constrained with
bottom plate through master and slave surface to make tube
stable in position during crash. The top plate is constrained
in all direction except its x axis translation motion downwards
with velocity of 15km/h and it is imparted a lumped mass to
simulate a head-on collision. There are two crash boxes in
frontal structure which are responsible for absorbing kinetic
energy of the vehicle. In these case, mass of an average sedan
car is assumed to be 1100kg.
Bottom plate is constrained from all translational and
rotational displacement. Tubular structure in FE model is
modelled with material Al 7075 under elastic plastic model
to include strain rate effects and isotropic strain hardening as
explained in the previous section. The simulation is setup for
a time period of 0.038sec with very small stable time increment
(quasi static) such that total energy remains constant during
the crash event. The stable time increment estimate for each
element is based on linearization about the initial state
Crashworthiness Indicators
Initial Peak Load (IPL) - It measures the deceleration trans-
mitted to the vehicle occupant during crash and is also known
as initial crush force in the load displacement response. It is
the highest initial load point in the load displacement curve
during the beginning of crushing. It indicates the load needed
to initiate collapse and hence needs to be minimized.
Mean crush force (Pm) - it is the ratio of total energy
absorbed (Ea) to the axial displacement of component (L).
Pm
Ea
=
L
(eq. 1)
Total energy absorbed under axial deformation is the area
under load displacement curve of the deformed component.
Ea =
ò
0
lmax
Pdl (eq. 2)
Where P and L are crushing force and axial displace-
ment, respectively.
Specific Energy Absorption (SEA) - it is total energy
absorbed divided by mass of crushed component. It is particu-
larly important when weight reduction of structure is required.
SEA is not an intrinsic material property, it depends not only
on the material properties, but also on several other param-
eters, especially the specimen geometry.
SEA
Ea
m
= (eq. 3)
Where m is the mass of the component
Crush Force Efficiency (CFE) - it is the ratio of mean
crush force to the initial peak load. It defines the uniformity
of crush loads. It should be high for an energy absorber.
h
h = ´
Pm
P
100 (eq. 4)
Higher value of CFE has to be achieved for occupant’s
protection. SEA and CFE should be maximized while IPL
should be minimized to obtain highly efficient crash
box design.
FIGURE 2 Finite element model of the crash
box structure
©
SAE
International.

5
Design Process
Numerical Results
Parametric Optimization
The effect of crushing properties of tube on the outer geometry
is studied in this section. The optimization of the structure
begins with the basic cross-sectional shape of the crash box
considering square, hexagon, circular, triangular and conical
shape for which mean peak load and energy absorption is
determined. Table 1 describes about the geometrical proper-
ties of the different shapes used for the analysis. Conical and
Cylindrical tubes have almost similar energy absorption with
conical tubes having least mean peak load.
The peak force in conical and triangular structure is less,
this is due the decreasing moment of inertia of the frontal
cross section which results in decreasing flexural rigidity of
the structure and thus reducing buckling load. By the theory
of behavior of columns investigated by Leonhard Euler in
1757, the critical buckling load is directly proportional to
flexural rigidity, and here the structure deforms through
buckling. The smaller area in conical tube also helps to prevent
formation of plastic hinge. The largest advantage of tapered
circular tubes as compared to straight circular tubes is their
constant stability in progressive folding due to the axisym-
metric (concertina) mode of collapsing as shown in figure 4.
Further with the selection of conical shape crash box,
semi apical angle of the conical structure is optimized based
on the axial loading condition during crash situation to deter-
mine optimal angle with least peak load and high specific
energy absorption. The design of experiments is carried out
as listed in the table 4.
FIGURE 4 Progressive Folding (Concertina mode) of the
tapered circular tube
©
SAE
International.
FIGURE 3 Design procedure for crash box optimization
©
SAE
International.
TABLE 3 Crash Performance Characteristics of Different cross
section tubes
©
SAE
International.
TABLE 4 Geometrical Properties of Conical Tube with varying
semi apical angle
©
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6
Total length of the crash box is kept as 180mm with
maximum diameter having fixed value of 140mm and thick-
ness as 2.5mm, while semi apical angle of the conical tube
in varied
Figure 5 and Figure 6 depicts the response of load versus
displacement of different semi apical angles of conical tubes,
Peaks later in curve are higher than initial peak because of
increase in surface area, which in turn increases flexural
rigidity when moving from top to bottom of the cone.
Different peaks correspond to the axis-symmetric folding of
the conical tube during the quasi static analysis. Each peak
in the graph describes about the collapsing of the structure.
For each tube 5 progressive folds are formed during crash
analysis. Greater the number of progressive folds, more will
be plastic strain induced in the body and hence energy
absorbing capacity of the structure increases.
Initial Peak Load (IPL) decreases with the increase in the
semi-apical angle of the tube which is due to decrease in
frontal impact area. By Euler’s theory of columns, flexural
rigidity is directly proportional to the buckling load, reducing
the frontal area reduces flexural rigidity also known as
bending stiffness of the structure, which in turn reduces peak
load. As can be seen from figure 7, IPL of tube C8 is decreased
by 33% than that of tube C1. Also, crushing load efficiency of
the tube is greater for one with high semi-epical angle.
Energy absorbed by the conical tube decreases with
increase in semi-apical angle (SAA) due to less amount of
plastic strain produced in tube with higher SAA. However
there is very less difference in specific Energy Absorption
(SEA) for the structures from C1 to C5 with the change in
semi apical angle, but SEA value is lowered by greater extent
with the change in SAA from 13-15deg due to change in
collapse mode from concertina to diamond which reduces its
energy absorbing capacity. (Figure 8).
Tubes C1 to C5 undergo concertina collapse mode while
C6 to C8 undergo diamond collapse mode. Table 5 list the
values of crashworthy parameters to select the specific design.
Considering the advantage of Initial Peak Load, Specific
Energy Absorption and Crushing Load efficiency, conical tube
with semi apical angle of 12deg is chosen for further optimiza-
tion of the structure.
Thickness Optimization
The effect of thickness of the crash box on its crushing proper-
ties is described in this section. For this purpose, the conical
tube of semiepical angle 12deg and length of 180mm is analysed
with different thickness, the energy absorbed to weight ratio
of the structure is optimised by varying the thickness of the
FIGURE 5 Load v/s displacement curve of conical shape
with semi apical angle from 8 to 12mm
©
SAE
International.
FIGURE 6 Load v/s displacement curve of conical with
taper angle from 12 to 15 ©
SAE
International.
FIGURE 7 Initial Peak Load v/s semi apical angle curve
of conical tube
©
SAE
International.
FIGURE 8 Energy absorbed v/s axial displacement of
tubes with different SAA.
©
SAE
International.

7
crash box from 2.5mm to 1mm. The DOE is carried for deter-
mining optimal thickness between constant thickness structure
and graded thickness structure as shown in Table 6.
Figure 9 shows the load v/s displacement curves of
conical tubes with different thickness. As shown in the figure,
by decreasing value of thickness, the initial peak load
decreases. Tube T1 has maximum IPL while the tube T3 has
minimum IPL reduced by 58% due to decrease in effective
contact area during crash from T1 to T3. The energy absorp-
tion decreases from T1 to T4 due to decrease in the area under
curve of load displacement graph. It is mainly due to decrease
in plastic strain leading to lower value of plastic energy dissi-
pation. To optimise SEA, linearly graded thickness tube was
used and analysed in two different variants listed in Table 6.
Graded thickness tube has advantage of reduced IPL and
increase SEA.
From table 7, Energy absorbed decreases by large value
with decrease in thickness Tube T6 has highest specific energy
absorption increased by 3.5% compared to tube T1 while all
other tubes have lower value of SEA than T1. Tube T6 is
selected for further enhancing crash performance to improve
SEA and IPL.
Corrugated Structure
Optimisation
Corrugation pattern With the selection of conical tube
geometry with SAA of 12deg and graded thickness from
1.5 mm at the top increasing linearly to 2mm at the bottom,
corrugations were integrated into the structure to further
TABLE 5 Crushing Properties of Conical Tube with varying
semi apical angle
Tube
Code
Semi
Apical
Angle
Initial Peak
Load(kN)
Energy
Absorbed(kJ)
Specific Energy
Absorption
(kJ/kg)
C1 8 238.86 3.15 5.94
C2 9 237.50 3.013 5.827
C3 10 223.41 2.83 5.656
C4 11 217.53 2.75 5.612
C5 12 199.35 2.642 5.555
C6 13 184.77 2.28 4.78
C7 14 168.38 2.14 4.76
C8 15 160.05 2.02 4.44
©
SAE
International.
FIGURE 9 Dissymmetric folding (diamond mode) of
conical tube with conical angle 15deg
©
SAE
International.
TABLE 6 Geometrical Properties of Conical Tube with
different thickness
©
SAE
International.
FIGURE 10 Load v/s displacement curve of conical tube
with different thickness
©
SAE
International.
TABLE 7 Crushing Properties of Conical Tube with varying
thickness
©
SAE
International.
tubes with different thickness value
©
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8
improve SEA and IPL. Corrugated structure is optimised
based on the corrugation pattern, amplitude and number of
corrugations. Tube T6 is taken as standard to compare
different crashworthy parameters of corrugated structures.
Corrugation pattern were iterated based on inner config-
uration, outer configuration, inner-outer configuration (wave-
like) as shown in figure. During these study number of

corrugations is assumed to be 8 while amplitude as 5mm.
Corrugated structure with both inner outer configura-
tions is found to have least initial impact load of 8.7kN with
reduction of 88.3% than T6. Inner configuration and outer
configuration have almost similar initial peak load of about
28kN with reduction of 62.5%. All of three configurations
have low value of IPL as compared to simple conical tubes
without corrugation. This type of crash box act as efficient
trigger initiators that reduces the value of peak force
during collision.
Figure 13 shows the load v/s diaplacement curve of corru-
gated tubes with various configuration. These specimens
show more constant load-displacement curve providing a
constant amplitude of the load oscillation compared to simple
conical tubes due to controlled plastic deformation at the
corrugation. It is clear from figure that by implementing
corrugations, area under curve of load-displacement response
decreases resulting in lowered value of absorbed energy.
Furthermore, SEA value of O1, O2, O3 is decreased by 52%,
45% and 23% respectively as compared to tube T6, which are
listed in table 8
On the basis of SEA and IPL, Tube O3 is used to further
improve crash performance of corrugated structure
Corrugation Amplitude The effect of corrugation
amplitude of the crash box on its SEA and IPL during crash
is described in this section. The amplitude values used for the
analysis varies from 2 mm to 6 mm with inner-outer configu-
ration of the corrugated structure as illustrated in figure 14.
The number of corrugations is kept constant as 8.
Figure 15 shows the load versus displacement response of
tubes with different corrugation amplitude. It can be seen that
each structure collapses in unfluctuating load oscillations. Also,
IPL decreases with increase in the corrugation amplitude. The
IPL of the tube A1 is decreased by 53.5% while that of tube A5
is decreased by 92% than that for T6. This effect is attributed
due to the increase in maximum plastic bending moment at
the corrugation places which collapses SEA and energy
FIGURE 12 Different variants of corrugation on the walls
of tube
©
SAE
International.
FIGURE 13 Load v/s axial displacement of corrugated
tubes with different configurations
©
SAE
International.
TABLE 8 Crushing Properties of Conical Tube with different
corrugation variant
Tube
Code
Mass
(kg)
Initial Peak
Load (kN)
Energy
absorbed
(kJ)
Specific Energy
Absorption
(kJ/kg)
O1 0.390 25.4 1.19 3.051
O2 0.392 28.3 1.36 3.469
O3 0.414 8.7 2.11 5.01
©
SAE
International.
FIGURE 14 Geometrical configuration of tubes with
different amplitudes
©
SAE
International.
tubes with different amplitudes
©
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International.

9
absorbed both increases with increase in amplitude because of
increase in amount of plastic strain which leads to better energy
dissipation. Though the SEA of Tube A4 and A5 is decreased
by 20% in compare to T6, they are more the other structures
in the same category by 40%. However, there is very less differ-
ence between SEA of tube A4 and A5 shown in figure 16
BasedonhighestSEAof5.096kJ/kg,tubeA4withamplitude
of 5mm is selected for further enhancing crash performance
Number of Corrugations In this section, the effect of
the corrugation geometry on the number of corrugations is
analyzed. During this study, inner-outer configuration with
corrugation amplitude of 5mm is selected as explained in
previous sections. The number of corrugations is varied from
6 to 12 for which shape of corrugation varies in each case. Tube
N2 has circular corrugation while all other tubes have elliptical
shape with semi-major axis perpendicular to axis of tube.
The crushing behavior of each case was obtained through
load v/s displacement graph shown in figure 17, where each
tube collapses in controlled progressive concertina mode. IPL
of Tube N1, N2, N3, N4 is decreased by 88%, 89%, 95%, 98%
and 98.5% respectively than that for T6. Therefore, IPL
decreases significantly by larger amount by increasing the
number of corrugations because of increase in number of
plastic hinge locations due to which structure collapses easily.
Energy absorbed increases with increase in number of
corrugations (Table 10). But SEA increase from N1 to N3 and
TABLE 9 Crushing Properties of corrugated tube with
varying amplitudes
Tube
Code
Mass
(kg)
Initial Peak
Load(kN)
Energy
absorbed
(kJ)
Specific
Energy
Absorption
(kJ/kg)
A1 0.312 34.7 1.13 3.62
A2 0.343 23.1 1.301 3.793
A3 0.376 11.09 1.81 4.813
A4 0.414 8.62 2.11 5.096
A5 0.44 5.747 2.157 5.09
©
SAE
International.
corrugated tubes with different amplitudes
©
SAE
International.
FIGURE 17 Geometrical configuration of tubes with
different number of corrugations
©
SAE
International.
tubes with different number of corrugations
©
SAE
International.
TABLE 10 Crushing Properties of corrugated tube with
different corrugation number
©
SAE
International.
corrugated tubes with different number of corrugations
©
SAE
International.

10
then decreases from N4 to N5 with N4 having highest SEA
(Figure 19), increased by 10% than that for tube A4. However,
SEA of N4 is still less by 0.7kJ/kg as compared to tube T6
The robust optimization of the single conical corrugated
structure is performed on the basis of corrugation shape,
amplitude and number of corrugation which lead to decrease
in initial peak load by 98.5% than that for tube T6 while SEA
offinalcorrugatedstructureis0.7kJ/kglessfromT6.Therefore,
to increase the SEA of structure, concentric conical structure
is used inside corrugated tube, explained in the next section.
It is clear from figure 20 that IPL of all corrugated tubes
is less than conical tube with tube A1 of corrugation amplitude
2mm having least difference of 53.5% while tube N5 having
maximum difference of 98% from tube T6. In terms of SEA,
Tube N4 has least difference of 12% and tube O1 has maximum
difference of 52% from tube T6 (Figure 21)
Corrugated Conical Bi-Tubular
Structure
With an aim to increase the SEA of the corrugated structure,
concept of bi-tubular corrugated conical design is proposed.
It is first optimized based on selection of simple conical tube
or corrugated conical tube as the inner structure. The outer
corrugated tube has specification of wave like corrugation,
amplitude of 5mm and number of corrugations as 12 based
on the analysis results in previous section. Figure 24 describes
the geometrical properties of bi-tubular outer corrugated-
inner conical tube and bi-tubular outer corrugated-inner
corrugated tube.
FIGURE 20 Comparison of Initial Peak loads of
corrugated tubes 9
©
SAE
International.
FIGURE 21 Comparison of Specific energy absorption of
corrugated tubes
©
SAE
International.
FIGURE 22 Deformation modes of tube O3 at different time intervals
©
SAE
International.
FIGURE 23 Deformation modes of tube N4 at different time intervals
©
SAE
International.

11
Figure 25 illustrates the load displacement response of
the inner corrugated structure and inner conical tube design.
Both of them have controlled progressive concertina mode
resulting in lower value of initial peak load. IPL of B2 is less
than B1 due to more corrugation locations in it resulting in
greater maximum plastic bending moment which collapses
structure easily. However, IPL of B2 is increased by 24% while
that of B1 is increased 57% compared to N4 due to the increase
in bending stiffness of the structure.
From figure 26, Energy absorbed and SEA of tube B1 is
greater than B2. Specific energy absorbed by B1 is increased
by 1%, and for B2 is decreased by 15% respectively from that
of tube N4. Thus, tube B1 with inner conical structure acts as
better energy absorber than tube B2 and N4.
From the above results listed in table 12, Outer corru-
gated - Inner conical structure acts as best energy absorber
even with low IPL of 4.1kN. Therefore, it is further iterated on
basis of minimum diameter of conical tube and its distance
from topmost point of corrugated tube, to maximize its SEA
value. The inner diameter of the conical tube is varied from
22mm to 30mm to understand its effect on IPL and SEA. The
distance of top of conical tube from topmost point of outer
structure is kept as 15mm. Table 12 describes the geometric
properties of variants of conical tube used for the analysis.
Load v/s displacement response of tubes from D1 to D6 is
almost similar (figure 27) with constant progressive plastic
folding of all tubes. IPL increases with the increase in minimum
diameter of conical tube due to decrease in plastic bending
momentwhichresultsinlargebucklingloadrequiredtocollapse
structure. IPL of D1, D2, D3, D4, D5, D6 is increased by 7%,
30%, 62%, 71%, 72%, 76%, 84% from that of tube B1. Conical
tube inside the corrugated structure have mixed collapse mode
(concertina and diamond) but the entire structure collapses in
controlled manner due to presence of outer corrugations.
From figure 28, there is very slight change in energy
absorbed by structure from D1 to D6 and does not follow any
particular trend with increase in minimum diameter of the
bi-tubular structure
©
SAE
International.
FIGURE 24 Geometrical properties of bi-tubular
structure design
©
SAE
International.
FIGURE 25 Load v/s displacement curve of
bi-tubular structures
©
SAE
International.
TABLE 11 Crushing Properties of different variants of
bi-tubular structure
© SAE International.
TABLE 12 Geometrical Properties of bi-tubular structure
S.No.
Tube
Code
Semi Apical
Angle
Min. Dia.
(mm)
Max Dia.
(mm)
1 D1 12 22 95.2
2 D2 12 24 97.2
3 D3 12 26 99.2
4 D4 12 28 101.2
5 D5 12 30 103.2
6 D6 12 32 105.2
©
SAE
International.

12
conical tube because of mixed collapse mode of inner conical
structure. SEA and Energy absorbed by D1 is maximum while
that of D2 is minimum. SEA of all tubes (D1to D6) is larger
than that of B1, T6 (Table 13) due to increase in plastic strain
energy during collision.
Specific Energy absorption of D1 is enhanced by 15%
from that of T6 and by 25% from that of B1. Hence, tube D1
possess advantage of both reduced peak load and increased
SEA compared to B1 and T6. Therefore, tube D1 performs as
potential energy absorber which requires less initial crush
force to buckle.
The geometry of tube D1 is further iterated based on its
top point distance from the topmost point of corrugated tube
(d), to analyze the effect of these parameter on SEA and IPL
of structure. Table 13 illustrates about various geometrical
configuration of inner conical tube used in the simulation
All of the structures from I1 to I5 collapses with unfluc-
tuating load oscillations in progressive manner with the inner
conical tube having mixed collapse mode. With the increase
in value of d, IPL increases and SEA decreases significantly,
leading to negative effect on crash performance in terms of
both SEA and IPL. This effect is attributed due to decrease in
cumulative plastic strain energy and increased bending
FIGURE 27 Load v/s displacement curve of bi-tubular
structures with different minimum diameter of inner
conical tube
©
SAE
International.
FIGURE 28 Energy absorbed v/s axial displacement
curve of bi-tubular structure with different minimum
diameter of inner conical tube
©
SAE
International.
FIGURE 29 Load v/s displacement curve of bi-tubular
structure with different variants of inner conical tube
©
SAE
International.
FIGURE 30 Energy absorbed v/s axial displacement curve
of bi-tubular structure with different variants of inner
conical tube
TABLE 13 Crushing Properties of bi-tubular structure with
different variants of inner conical tube
Tube
Code
Min Dia.
(mm)
Weight
(kg) IPL (kN)
Energy
absorbed
(kJ)
SEA
(kJ/kg)
D1 22 0.683 4.4 5.01 7.35
D2 24 0.688 5.607 4.37 6.35
D3 26 0.693 7.8 4.43 6.39
D4 28 0.698 8.738 4.74 6.79
D5 30 0.703 9.22 4.73 6.72
D6 32 0.708 10.1 4.8 6.77
TABLE 14 Geometrical Properties of inner conical structure
S.No.
Tube
Code
Semi
Apical
Angle
Min Dia.
(mm)
Distance from
Top of outer
structure (mm)
1 I1 12 22 15
2 I2 12 22 20
3 I3 12 22 25
4 I4 12 22 30
5 I5 12 22 35
©
SAE
International.
©
SAE
International.
©
SAE
International.

13
stiffness from I1 to I5. IPL of I2, I3, I4, I5, I6 is increased by
45%, 100%, 102%, 115%, 169% compared to D1 (Table 14).
From figure 30, energy absorbed also decreases because
of poor folding of conical tube with the increase in top distance
leading to lower value of plastic strain and hence lowered
plastic energy dissipation. However, SEA and energy absorbed
by bi-tubular corrugated conical structure (I1 to I5) is greater
that single conical structure (T6) and single corrugated struc-
ture (N4), behaving as good energy absorber.
After robust optimization, bi-tubular outer corrugated
and inner conical shaped crash box (I1) is selected as final
design which has SEA enhanced by 15%, and IPL reduced by
95% from conical crash box T6. Figure 31 gives an insight
comparison for SEA, IPL of tube T6 (single conical), N4 (single
corrugated), I1 (bi-tubular conical corrugated). Thus, an
optimal design of bi-tubular crash box is proposed for low
speed collisions to enhance passenger’s safety and reduced
reparation cost. In addition, the proposed design absorbs more
than 50% of the kinetic energy during the collision
Conclusion
Robust optimization of the crash box structure is performed
on the basis of cross-sectional shape selection as circular
tapered tube. Further, conical structure was optimized based
on its semi apical angle, thickness and mean diameter.
For conical tube, IPL decreases with increase in SAA
while there is very slight change in SEA with increase in SAA.
IPL and SEA decreases by larger extent with decrease in thick-
ness. The concept of graded thickness structure was proposed
in order to increase its SEA. As a result, structure with graded
thickness have greater crash performance than one with
constant thickness.
Energy absorbing capacity of structure collapsing with
concertina mode is greater than the structure collapsing with
diamond mode due to its constant progressive folding and
high induced plastic strain in the structure.
IPL decreases significantly for the corrugated structures,
but its SEA value also decreases. Corrugated structure design
was enhanced based on corrugation configuration, amplitude,
radius and number of corrugations. Wave shaped like corruga-
tions have better crash performance than inner or outer
shaped corrugations. In addition, IPL decreases with increase
in amplitude due to increase in maximum plastic bending
moment while SEA also increases but tends to decrease after
certain point.
IPL decreases radically with increase in number of corru-
gations because of increase in corrugation places where
maximum bending moment occurs. In addition, SEA also
increases but tends to decrease after certain point.
TABLE 15 Crushing Properties of bi-tubular structure with
different variants of inner conical tube
©
SAE
International.
FIGURE 31 Comparison of crashworthiness parameters
of designs T6, N4, I1
©
SAE
International.
FIGURE 32 Deformation modes of tube B1 at different time intervals (sectional view)
©
SAE
International.

14
After performing various iteration on corrugated struc-
tures, IPL of corrugated design is decreased by 98% (tube N4)
compared to single conical design (tube T6). However, SEA
of corrugated design was still less than conical design (T6) by
11%. Due to this, idea of bi-tubular corrugated design was
proposed to enhance SEA value of crash box (I1) where SEA
was increased by 15% compared to conical design (T6).
Single Conical Structure can collapse in either diamond
or concertina depending on geometry of structure, while all
single and bi-tubular corrugated structures collapse in
controlled progressive concertina mode due to maximum
plastic bending moment at corrugation location and makes
the structure to collapse easily at corrugated place.
Bi-tubular structure with inner conical and outer corru-
gated structures performs as better energy absorber compared
to single corrugated and double corrugated tubes structure.
Inner conical structure collapses in the mixed mode (diamond
and concertina).
Minimum diameter of inner conical tube and its distance
from top affects crash properties of entire bi-tubular structure
as the bending stiffness increases with increase in minimum
diameter and hence, requires large buckling load to collapse.
Increment in value of parameter “d” results in negative effect
on SEA and IPL of bi-tubular structure, therefore it is kept
minimum in the final design.
The optimization process used in this study can be applied
on any corrugated structure design to achieve good balance
between SEA and IPL. Proposed Design of crash box (I1) gives
an insight of high crashworthiness and improved trade-off
between SEA and IPL. Therefore, it has a great potential of its
application to enhance passive safety in future automotive
vehicles and reduce the reparation cost.
Contact Information
Akash Porwal
Vellore Institute of Technology, Vellore, Tamil Nadu,
632014, India
akash_porwal@outlook.com
Mobile No. -7354568827
Abhishek Tripathi
Vellore Institute of Technology, Vellore, Tamil Nadu,
632014, India
abhiabhi454@gmail.com
Mobile No. -7905335805
FIGURE 33 Deformation modes of tube B2 at different time intervals (sectional view)
©
SAE
International.
FIGURE 34 Deformation modes of tube I1 at different time intervals (sectional view)
©
SAE
International.

© 2020 SAE International. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE International.
Positions and opinions advanced in this work are those of the author(s) and not necessarily those of SAE International. Responsibility for the content of the work lies
solely with the author(s).
ISSN 0148-7191
15
Acknowledgement
We are extremely thankful to the Dean, School of Mechanical
Engineering, VIT Vellore for providing invaluable support
for the research work.
Abbreviations
SAA - Semi Apical Angle
SEA - Specific Energy Absorption
IPL - Initial Peak Load
EA - Energy Absorbed
CFE - Crushing Force Efficiency MCF - Mean Crush Force
MCF - Mean Crush Force
DOE - Design of Experiments
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