CRUSHING SIMULATION OF SQUARE ALUMINIUM 6061-T6
POLYURETHANE FOAM-FILLED UNDER DYNAMIC LOADING
M. F. Basiran1,a, A.Othman1,b, S.M. Sharif1,c
Department of Mechanical Engineering, Polytechnic Port Dickson, Malaysia
a
fitri@polipd.edu.my, bakbar@polipd.edu.my, csuhaila@polipd.edu.my
1
Abstract - The paper present the numerical studies of
dynamic axial crushing of thin-walled metallic
aluminum 6061-T6 alloy extrusion empty and foamfilled tubes polyurethane foam-filled square sections.
Nonlinear dynamic simulations were performed on
empty as well on foam-filled modeling. The dynamics
non-linear finite element code ABAQUS standard and
explicit was used to simulate the buckling and
crushing of columns. The influence of fillers on energy
absorption and behavior of square thin-walled
metallic aluminum 6061-T6 alloy extrusion empty and
foam-filled tubes arrangements was examined. Three
main collapse modes were identified for the crushed
model, for example, compound diamond asymmetric,
concertina axisymmetric and mixed mode fold
formations. Three different arrangement of foamfilled tube inner column were examined and
investigated. The polyurethane foams turned out to be
a significant factor positively influencing the energy
absorption capability and so by application in the
longitudinal members of cars frame improving
passengers’ safety.
Keywords: Thin-Walled Structure, Finite Element
Modeling, Progressive Damage, Foam-Filled
I.
INTRODUCTION
Many types of device are employed to absorb high
energy releases in containment structures such as pressure
vessels and in transport systems such as cars, trains and
lifts which are subject to collisions or impacts. These
devices usually have the advantage of being cheap, light
weight, easy to construct and are able to sustain a high
energy absorption density with constant loading before
failure. They may take the form of groups of thin walled
tubes, of uniform or tapered wall thickness, with circular
or polygonal cross-sections under axial impact loading,
which have desirable stroke dependent characteristics.
The energy absorption capacity will depend on the degree
of plastic deformation which the device can sustain under
the prevailing loading regime. To fully understand and
appreciate the energy absorption behavior, a systematic
parametric study of the device should be undertaken with
special reference to the geometrical dimensions for
instance tube length, thickness, cross-sectional radius, die
geometry, and material properties. The derivation of a
design formula in terms of the influencing parameters
then becomes a practical tool for the design engineer. The
Finite Element Method (FEM) can be employed as a
useful tool in this regard.
Over the last decade Finite Element Analysis (FEA)
has become firmly established as a design method across
a wide range of engineering disciplines. The unique
insights that numerical techniques such as FEA can
afford make these methods very attractive to industry.
Furthermore, modeling and simulation techniques are
often significantly cheaper and more flexible than other
methods, which make them attractive as aids in
experimental testing and prototype development.
However, it should be stressed that although computer
modeling techniques in general and FEA in particular,
have become standard tools in design and manufacture,
experimental verification remains an important
requirement. There is a growing interest in the use of
thin-walled structures as a means of absorbing the kinetic
energy of a moving body. Thin-walled structures are
capable of carrying loads for deflections beyond that
corresponding to ultimate or nominal buckling load. They
are also known to accommodate very large deflections
through the formation of folds and wrinkles [3]. In
applications such as aerospace, weight is a critical factor
and must be minimized. With thin walls less material is
used, and the structural performance per unit weight, can
be improved. Thin-walled structures comprise of plates,
shells, and thin-walled components acting as beams,
columns and beam columns.
The purpose of this study is to explore the effect of
impact velocity on the peak load and energy absorption
for double square tubes empty and foam-filled. Figure 1
shows progressive buckling, for example the sequential
formation of adjacent local folding patterns of the
deferent specimens. The double cell arrangements were
shown to be particularly efficient crush elements, as long
as global failure (Euler buckling) could be avoided. The
study also showed that double cell arrangements may be
preferable to single tube based on energy absorption
because the inner tube is more mass efficient.
Figure 1: Empty, foam filled single tube and double
Square crushed specimens
II.
FINITE ELEMENT MODEL
It is well understood that numerical simulation using
finite element analysis allows wide variety of
optimization. Therefore, ABAQUS/EXPLICIT version
6.10 was used throughout the analysis. The simulation
processes have two differences composition of tubes,
which are empty tube (unfilled foam with double tubes),
and a double tube with filing foam into inner hollow
outer tube and outer surface inner tube. Shell elements
are used to model structures in which five integration
points were selected for each simulation analysis. The
two difference wall-thickness was analyzed significantly,
and the stresses in the thickness direction are negligible.
Generally three-dimensional shell elements are available
with three different formulations; general-purpose, thin
only and thick only. General-purpose shell elements are
valid for use with both thick and thin shell problems.
Furthermore, all general-purpose shell elements consider
finite membrane strains. All special-purpose shell
elements assume finite rotations; however, they assume
small strains.
crushing behavior and having of 60 x 60 mm outer tube
arrangement with inner tube were 50 x 50, 40 x 40, 30 x
30 mm and 1.0, and 2.0 mm wall-thickness. The foamfilled models were carried out from two tubes having
outer wall from the same material as empty tube profiles
as well as inner wall of tube. The inner tube has varied
with three different length width including 50 x 50, 40 x
40, 30 x 30 mm and 1.0 and 2.0 mm wall-thickness but
constrained at the same thickness as well as outer tube
thickness. All sections had a length of 150 mm. The
empty tube sections were tested as empty and foam-filled
tube profiles only with the foam in between inner and
outer tube wall. Figure 2 illustrates typical test model
geometry, whereas Table 3 presents tensile stress-strain
data curves of the used materials. In this study the
velocity dynamic of impact was applied at 20, 30 and 40
m/s axially onto the frontal crash flat plate analytical rigid
surface.
A. Crushing parameters
To represent real progressive collapse events, the
velocity and time need to be suitable. Taking a = 196.2
m/s2 as the benchmark since humans can only sustain 20
g of acceleration, value of sufficient crushing time can be
obtained. The initial velocity (V) of the tube is set to be 6
m/s, hence calculated value for crushing time; (t) was
found to be 0.02 s. The other important parameter of
representing crushing event is boundary condition. In
structural analyses, boundary conditions are applied to
those regions of the model where there displacements or
rotations are known. Such regions may be constrained to
remain fixed or may have specified nonzero
displacements or rotations. In this model the ENCASTRE
(V1 = V2 = V3 = VR1 = VR2 = VR3 = 0) condition has
been used where the top section of the tube is constrained
completely and thus, cannot move in any direction also.
The bottom section, however, is fixed in the horizontal
direction but is free to move in vertical direction (V1 =
V2 = VR1 = VR2 = VR3 = 0). The direction in which
motion is possible is called degree of freedom (dof),
hence this model only has a single degree of freedom. A
mechanical, concentrated force with a magnitude of 500
N was applied in order to initiate the crushing process.
The actual load magnitude is not critical because
ABAQUS will report buckling loads as a fraction of the
applied load.
B. Material models and properties
Two types of models were analyzed in this study which
is empty and foam-filled tubes. The empty square tube
models were arranged as double tubular ones, material of
aluminum 6061-T6 alloy was used to determine the
Figure 2: Test model geometry of type A, B and C
Table 1: Dimension of column finite element modeling
Table 2: Material Properties of Modeling
C. Crushing process
The simulation, which normally is run as a background
process, is a stage in which ABAQUS/Explicit solves the
numerical
problem
defined
in
the
model.
ABAQUS/Explicit is a special-purpose analysis product
that uses an explicit dynamic finite element formulation.
It is suitable for short, transient dynamic events, such as
impact and blast problems, and is also very efficient for
highly nonlinear problems involving changing contact
conditions, such as forming simulation. It is well known
that a nonlinear structural problem is one in which the
structure’s stiffness changes as it deforms. All physical
structures are nonlinear. In this simulation the stiffness is
fully dependent on the displacement; the initial flexibility
can no longer be multiplied by the applied load to
calculate the spring’s displacement for any load. Results
evaluation can be done once the simulation has been
completed and the reaction forces, displacements, energy
or other fundamental variables have been calculated. The
evaluation is generally done interactively using the
visualization module of ABAQUS/CAE.
The visualization module, which reads the neutral binary
output database file, has a variety of options for
displaying the results, including color contour plots,
animations, deformed shaped plots, and X–Y plots.
Figure 3: Verification of collapse modes foam filled
section, with the simulated on the left and experimental
on the right.
Table 3: Validation of experimental and numerical
analysis
Parameters
Experimental
Numerical
Error
(%)
Total compression
(mm)
Peak load (kN)
Mean load (kN)
Absorbed energy
(kJ)
150
85
65
21
168
96
50
19
10
11.4
23
9
D. Validation of the finite element model
Numerical simulation using finite element codes is
currently an important approach to learn in the crushing
behaviors of foam-filled columns. Some key issues in the
modeling, such as material model for aluminum foam,
contact definition; friction effect, boundary condition and
the bridge from dynamic to quasi-static were discussed.
In this work, nonlinear finite element ABAQUS/Explicit
version 6.10 package was employed to simulate the
crushing characteristics of foam-filled tube section. The
foam filler was modeled with 8-node solid element. The
model is highly dependent upon the mesh quality and
mesh size, due to the conditional stability characteristic
for an explicit finite element code. Strain–stress curve of
the foam obtained from the uniaxial compression
experiment was input into the model. Since the aluminum
foam filler would undergo extremely high local
compression and distortion, internal contact algorithm
must be applied to the solid elements to prevent negative
volume and numerical collapse. Rigid body property was
assigned to the shell elements, because no fracture or
failure or deformation was observed in the spot-weld in
the experiments. Only half of the specimen was modeled
due to the symmetry character. The load was applied at
the upper end of the specimen with a constant
displacement condition, through a rigid body which is
modeled with shell elements. Validation and verification
of the finite
element model is necessary before an effective partition
work could be carried out.
The validation work was carried out on the model of
foam-filled column to check if it could maintain
calculation stability while undergoing very high local
deformation and distortion in the filler, and check contact
conditions as well. Collapse mode and force history
depict a complete crushing process, therefore, both the
simulated collapse mode and force–displacement history
need to be verified with the experiments. Figure 3 give
the verification of these two main aspects and the
simulated collapse modes are compared with those from
experiments. For both empty and foam-filled columns,
the simulated and actual collapse modes are very much
alike, even in some detailed information, such as the
folding wavelength, the number of lobes, and the
effective crushing distance. The comparison of simulated
crushing force histories with the experiments also gives
good agreement, for each result of foam-filled. The
simulated mean crushing force is about 10% higher than
that measured from corresponding experiment, because
the loading rate in the model was increased to reduce the
solution time for a dynamic problem.
III.
RESULT AND DISCUSSION
With respect to the failure modes of test series empty
and polyurethane foam filled square extruded aluminum
6061 alloy profiles with small cross-sectional dimensions
the numerical revealed that progressive buckling could
almost exclusively be observed for some empty tubes and
the foam filled crush elements with square cross-sections
in Figure 4 to 7. All square empty and foam-filled tubes
profiles of this analysis test series having a foam density
than the square ones rather showed local progressive
damage, but not typically progressive, deformation
behavior, where the formation of folds began at different
locations, generally not in a sequential manner.
Furthermore, these element models buckled extensionally
with all folds moving outwards, which is obviously
caused by the presence of the foam core. The extensional
deformations are also evident from the dynamic load
compression displacement curves in Figure 4, because the
load fluctuations are much more pronounced. Filling
polystyrene foam inside of the tubes was in general
accompanied by shorter wavelengths of the individual
folds which is holds true for all element model test series.
Within element model test series empty and foam-filled
square tubes, which were arranged in different ways,
empty, foam-filled tubes, and arrangement with
dimension of inner square tube profile, were analyzed.
foam-filled tube element model show a pronounced load
fluctuation during the load cycles, owing to the
extensional folding modes, which is followed by minor
differences between maximum and minimum loads due to
the inextensional buckling deformations of the extruded
aluminum 6061 alloy tubes.
Figure 5: Example deformation pattern of crushing
tube
Figure 4: Dynamic load (N) versus displacement ( m)
type of A foam-filled tube square profile (Wall-Thickness
= 1 mm: Velocity = 10 m/s)
The inner material profile in Figure 5 which is 50 x 50
mm was used inside the outer square filling with
polyurethane foam with 100 kg/m3 density. The typical
progressive buckling characteristics, which could be
observed in most numerical analysis of this test series of
wall thickness 1 and 2 mm as well as variable dynamic
impact loading of 20, 30 and 40 m/s, are evident from the
deformed elements shown in Figure 5 to 7. The type of A,
B and C foam-filled tube square profile also reveals the
higher densification in the outer region of the foam core
due to a multiaxial state of compression illustrated
resulting from foundation effects of the foam with respect
to the profile. Global failure was observed only for the
foam-filled tube foam filled elements. This can be traced
back to global buckling of the slender inner profiles,
leading to overall buckling of the whole arrangements.
All filled element modeling that deformed locally began
to buckle in an extensional mode, but after the formation
of some folds most switched to an inextensional mode,
which is typical for the empty profiles of this type of A, B
and C empty. The measured dynamic loads versus
displacement curves from Figure 4 also clearly display
the effects of the change of deformation modes. The
Furthermore, the dynamic load versus displacement
curves reveal a distinct quasi-steady progress of the
crushing forces which is fluctuating around a more or less
constant value, provided that the average foam density is
not too high. The ascending slope of the force level of
foam-filled tube type of B which square inner profile of
40 x 40 mm, however, is due to the foam behavior itself.
Example deformation pattern of crushing tube are shown
in Figure 5.
Figure 7 showed that the foam-filled tube type of C of
the sectioned inner square tube of 30 x 30 profile. Noted
that element model was crushed far beyond the stroke
length. Whereas the square inner and outer element
model rather tended to buckle inextensionally, a typical
extensional folding mode is apparent from the square
both of inner and outer crush elements of this test series.
Furthermore, many of the investigated elements started
with the simultaneous formation of folds at different
locations, and as a result a local, but not typically
progressive buckling behavior could be observed. For the
first stage this led in combination with breaking of the
global buckling of the tubes. The gluing between filler
and tubes of element model obviously caused the lobes to
be filled with polyurethane foam for the most part almost
of wall-thickness 1 and 2 mm square tube. However,
some breaking of the interface can also be observed for
these element models. It should be noted, however, that
the main reason for applying fiction coefficient for these
interaction surface of inner, outer and foam element
geometries model.
efficiencies can certainly be traced back to the foam
behavior. With filled with foam into the region of
densification, where the compressive dynamic load starts
to increase steeply and shifted to lower values of the
compressive strain.
Figure 6: Dynamic mean load (N) versus displacement
(m) empty tube square profile (Wall-Thickness = 1 and 2
mm: Velocity = 20 m/s)
IV.
MEAN LOAD EFFICIENCY
Regarding the mean load efficiency, distinct
enhancements due to foam filling are shown in Figure 6
for all investigated crush elements. The filled tubes of
element model test series deliver improvements of up to
40 ± 50% for all cross-sectional shapes. Even higher
absolute values for empty and foam-filled tube can be
observed for the corresponding crush elements model,
mainly owing to the higher mean force efficiencies of the
inner with respect to the combination of tube and foam to
build up mass efficient energy absorption devices it has to
be taken into account that the mean load efficiencies of
the constituents should not differ much. The lower mean
load efficiency for the tubular member will be
advantageous. The filling foam density leads to:
(1)
An increased tendency for the outer tubes to
buckle extensionally,
(2)
An increased tendency towards global failure,
(3)
But also to the activation of higher interaction
effect
The results obtained for the different efficiency
parameters, which is showed in Figure 6, are presented
for all 3 different types of element model test series in
dynamic mean load versus displacement curve form in
Figure 6. For the empty square profile (empty) and filled
profile (foam-filled tube) of element model test series
where an increasing the wall-thickness of square inner
and outer profile the dynamic mean load will increase
opposite of displacement curves. The axial compression
load capacities were crushed progressively when square
profile increases a thickness. The reduction of the stroke
Figure 7: Dynamic absorbed energy versus type of tube
profile empty and foam-filled tube Cross-Section
As a result, from Figure 7, the element model analysis
apparent foam density of 100 kg/m3, a regular progressive
buckling behavior, dominated by inextensional folding
modes and, hence, with not too large energy fluctuations,
while retaining marked efficiency improvements with
respect to the mean load. Because the stroke efficiency
should also remain high for such densities, distinct
improvements of the whole energy absorption capacity
can be expected. To our experience this does not only
apply to empty crush elements with square cross-section
although the improvements are most pronounced in this
case of foam-filled tube profile. It can be seen in the
Figure 7; the velocity increase when a crush faster and
progressively even on empty absolutely in foam-filled
tube. It can be seen that the type of C apparent the highest
performance of energy absorption capability. However
the cross-sectional dimensions have to be selected
carefully in order to avoid global failure of one of the
tubes. Such metallic structures are, therefore, expected to
be of advantage mainly in structures that have to resist
considerable compressive load, so that larger crosssectional dimensions have to be applied in any case.
V.
SUMMARY AND CONCLUSIONS
The test element results model presented here confirm
that the mass related mean load level may considerably
be improved by filling tubular members with
polyurethane foam. Provided that the plastic buckling
behavior remains characterized by local modes, essential
enhancements were obtained for all investigated shapes
and dimensions. These improvements may partly be
traced back to the axial compression of the foam cores
themselves, but interaction efficiency is also play a
substantial role that the simple estimates.
With respect to the total energy absorption capacity of
a given crush element, however, improvements are less
pronounced. The reason for this is that the maximal
crushing distances, which may be utilized for energy
dissipation, reduce with increasing foam densities.
Nevertheless, improvements of the mass the investigation
of foam-filled tube arrangements revealed that these may
be preferable to empty analysis. It could be shown that
improvements are mainly due to the presence of the inner
profiles, which are in general more mass efficient than
the outer ones. Interaction effects are somewhat less
pronounced that for empty tubes. An analysis of
interaction effects was performed, which not only
allowed to determine the relative c influences of such
effects onto the mean load levels but also to and some
explanations concerning the differences between crosssectional shapes and mono-and foam-filled tube
arrangements, respectively. Furthermore, some basic
conditions for the appropriate choice of tube filler
combinations could be obtained this way. Design
considerations, pointing out the essential constraints for
the appropriate choice of foam densities for the
construction of mass efficient crush elements, have been
summarized. However, all considerations stated therein
are restricted to the behavior of dynamically loaded crush
elements, which are filled with polyurethane foam.
Furthermore, influences of gluing have to be investigated
in more detail, because they are expected to markedly
influence the energy absorption capacity of filled crush
elements. With respect to the design of `optimally tuned'
composite crush elements, numerical methods could also
turn to account, which allow to gain more insight into the
mechanics of such complex plastic deformation
processes.
ACKNOWLEDGMENT
We would like to thank the members of the Mechanical
Engineering Department, Polytechnic of Port Dickson for
their constructive comments, encouragement, and support
the commercial finite element software ABAQUS 6.10
theory and user’s manual.
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