EFFECT OF ALUMINUM FOAM AND FOAM DENSITY ON THE ENERGY
ABSORPTION CAPACITY OF 3D “S” SPACE FRAMES
a
R. Fragoudakis a and A. Saigal b
Graduate Student, [email protected]
b
Professor, [email protected]
Department of Mechanical Engineering
Tufts University, Medford, MA 02155
United States of America
ABSTRACT
Passenger safety during front collision depends to a great extent on the capability of the car’s front space frame structures to
absorb energy generated during the crash, while minimizing deformation. Finite element analysis (FEA) models of 3D S-shape
extruded aluminum frames were developed using the FEA simulation software ABAQUS/CAE and were evaluated for their
crashing behavior when loaded axially.
All models investigated possess an aluminum frame, 45o curvature angles and a square cross-section. All models were loaded
identically. One of the models tested was hollow inside, while the others were reinforced with aluminum foams of different
properties (density and modulus of elasticity). In addition, the Specific Energy Absorbed (SEA) was calculated for different
frames.
The aluminum frame with foam 10.8/40/L with the highest relative density (10.8%) and 40 cpi (cells per inch of foam), tested
longitudinally to the direction of solidification, revealed a structure (SSF-1-45-45-1) that can sustain great compression with the
least deformation and has the highest capacity to absorb energy during a collision.
Introduction
Passenger safety is one of the main target areas in automobile design. To reduce the risk to passengers during a front car
collision, it is necessary to examine the crashing behavior of the front members of the car’s frame and to find a way to increase
their energy absorption during a crash. Since the 1980s many researchers have indulged in the study and examination of such
space structures. These studies include energy absorption capacity of a square tube filled with foam under dynamic loading,
theoretical analysis of a foam-filled column during a collision and prismatic columns reinforced with aluminum foam undergoing
axial crushing [1-3].
Passenger security improvement can also be obtained by changing the geometry of the frame. A tube that is not straight but
possesses some curvature may prolong the deformation of the frame [4, 5]. Based on these studies, Zhang investigated the
crashing behavior of a 3D S-shape space frame [6]. After experimenting with a variety of different curvatures for the frame, it
was concluded that among the non-reinforced frames the one possessing curvature angles of 45 degrees, has the most
effective energy absorption capacity. This study deals with the examination of the crashing behavior of 3D S-shape space
o
frames with 45 curvature angles, reinforced with aluminum foams of different properties (density and modulus of elasticity).
Finite Element Model
Structure Nomenclature
The nomenclature used for each structure is SS (F)-1-α-β-#, where the variables represent:
SS
SSF
1
α
β
#
S-shape frame without foam filling
S-shape frame with foam filling
square cross-sectional area of the frame
angle of curvature α
angle of curvature β
number identifying the aluminum foam filling
The geometry of the frame resembles a hollow tube of square cross section. The frame has two curvature angles, α and β, of
45o each that give it its “S” shape. The straight end parts L1, shown in Figure 1b, are each 200 mm, while the total length L of
the frame is 780 mm.
The “S” configuration of the structure implies that the front and rear ends are not on the same axis but offset. In the x and y
directions the offset is D=D1=150 mm and in the z direction D2=212 mm (Fig. 1b). Since the two curvature angles are of the
same size, the radii of curvature, R, at these points of the frame are both 200 mm.
(a)
(b)
Figure1. (a) General geometry of “S” frame, and (b) Detail of frame geometry
Material Properties
Although the foam properties differed for the two reinforced models, the frame properties were kept identical in all models. The
frame is assumed of be made up of extruded aluminum AA 6063 T7 with density of 2770 kg/m3, modulus of elasticity of 69.0
GPa, Poisson’s ratio of 0.3 and yield stress of 86.94 MPa. The plastic stress-plastic strain data for AA 6063-T7 is shown in
Figures 2. As shown in Figure 3, the structures are axially loaded with a 500 kg mass at the rear end, to provide the
appropriate force during front end collisions. The frame possesses an initial velocity of 11.11m/s and the simulation time is
0.05 s, for a total displacement of approximately 0.51 m.
Figure 2. Plastic stress-strain properties of aluminum AA 6063-T7
(a)
(b)
Figure 3. (a) Geometric boundary conditions, and (b) Initial velocity field
Aluminum Foams
Table 1 lists the properties of the aluminum Al 6101 foams under compression used in this investigation, which were
developed by Nieh, et al [7]. These foams were used as reinforcements in the S-shape frames in the FEA models. The
compressive stress strain curve of each of the foams, together with their modulus of elasticity, density, yield strength ratio
(K=1.0) and tension yield strength ratio (Kt=0.1) constituted the input data for the models.
Table 1. Properties of aluminum foams
Structure
Foam
Modulus of Elasticity / MPa
Density / kg.m-3
SSF-1-45-45-1
10.8/40/L
752
299
SSF-1-45-45-4
4.8/40/L
110
133
Results and Discussion
Deformed Frames
For each structure, the deformed contour plot of the S-shape frame was evaluated. These plots represent the way the
deformation of the frame progresses once the force induced from the collision impact overcomes the yield strength of the
frame material, and the frame starts folding.
Figures 4 – 6 show the deformed contour plots of the frame SS-1-45-45 without foam filling, frame SSF-1-45-45-4 reinforced
with foam 4.8/40/L and frame SSF-1-45-45-1 reinforced with foam 10.8/40/L, respectively. The goal of varying the foam
parameters is to evaluate the safest structure.
Figure 4. Deformed contour plot of structure SS-1-45-45 without foam filling
Figure 5. Deformed contour plot of structure SSF-1-45-45-4 reinforced with foam 4.8/40/L
Figure 6. Deformed contour plot of structure SSF-1-45-45-1 reinforced with foam 10.8/40/L
Although at first sight SSF-1-45-45-4 seems to maintain its original shape, a closer look at its contour plot reveals that it retains
most pressure (stress) at its curvature angles, and as a result is displaced backwards during the collision. This is not a
favorable deformation condition for the passengers, as it leaves no room between them and the collision point. On the contrary
SSF-1-45-45-1 retains all pressure in its front part preventing backward displacement. This helps keep the passengers away
from the collision spot. Thus, of the three structures analyzed, the aluminum frame with foam 10.8/40/L with the highest
relative density (10.8%) and 40 cpi (cells per inch of foam), tested longitudinally to the direction of solidification revealed a
structure (SSF-1-45-45-1) that can sustain great compression with the least deformation.
The question may arise: why the need for a reinforced frame? Why not an empty aluminum frame? When comparing any of
the reinforced models to the empty one, it is clear that the empty frame does not sustain much pressure at any of its ends. On
the contrary, as seen from the deformed contour plot (Fig. 4), its curvature points are under great compression. For these
reasons, the empty frame is not optimum as a model for improving passenger safety.
Impact Forces
Each frame structure undergoing collision is subjected to a force, which results from the collision and induces deformation to
the frame. Figure 7 shows the forces in the two reinforced structures as a function of displacement and shows that the peak
load and forces in general are higher for the structure SSF-1-45-45-1 filled with the higher density foam. Similar analysis
shows that the force on the empty structure SS-1-45-45 is the smallest in magnitude.
Figure 7. Force as a function of displacement for the two foam-filled structures
Energy Absorbed and the SEA
The area under each force curve gives the energy absorbed by each structure. Therefore, the higher the peak force curve the
greater the amount of energy absorbed by the frame. This is true and can be observed in Figure 8 which shows the energy
absorbed as a function of displacement for the two foam-filled structures.
Each of the structures has a different mass, as a result of the variation in density of the two different foams. The Specific
Energy Absorbed (SEA) is the ratio of the energy absorbed by the structure to the weight (in grams) of the structure. Using
SEA, a decision as to which frame is the most appropriate for the passenger’s safety is made not only on the basis of energy
absorption but also the relationship of this energy to the mass of the structure.
Table 2 shows the estimated peak force, energy absorbed and specific energy absorption for different structures. Based on
the discussions above and the numerical values in Table 2, it is clear that structure SSF-1-45-45-1 not only absorbs the
highest amount of energy but also has the highest SEA as well.
The total energy absorbed and the specific energy absorption of foam filled structures is significantly greater than empty
frames. Thus, aluminum foam is an efficient energy absorber, but higher density foam does not increase the Specific Energy
Absorption of the structure much as compared to lower density foam due to the overall increase in mass. In addition, the
increase in total energy absorption due to aluminum foam reinforcement is accompanied by an undesirable significant
increase in the peak force.
Figure 8. Energy absorbed as a function of displacement for the two foam-filled structures
Table 2. Energy Absorbed and Specific Energy Absorption as a function of
aluminum foam reinforcement
Structure
Foam
Mass / kg
Force / N
Energy / J
SEA / J.g-1
SSF-1-45-45-1
10.8/40/L
2.84
38987
8405
2.96
SSF-1-45-45-4
4.8/40/L
1.93
32014
5391
2.79
SS-1-45-45
EMPTY
1.20
16068
1675
1.40
Conclusions
Based on this study, it can be concluded that aluminum foam is an efficient energy absorber, but higher density foam does not
increase the Specific Energy Absorption of the structure much as compared to lower density foam due to the overall increased
mass. In addition, the increase in total energy absorption due to aluminum foam reinforcement is accompanied by an
undesirable significant increase in the peak force and the overall mass of the frame structure.
References
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Zhang, C., “Study of Crash Behavior of a 3-D S-Shape Space Frame Using Finite Element Method”, M.S. Thesis, Tufts
University, Medford, MA (2005).
7.
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