Experimental and theoretical study of the influence of the addition of alumina powder

INTERNATIONAL Mechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME
AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
IJMET
Volume 3, Issue 3, September - December (2012), pp. 412-428
© IAEME: www.iaeme.com/ijmet.asp ©IAEME
Journal Impact Factor (2012): 3.8071 (Calculated by GISI)
www.jifactor.com

EXPERIMENTAL AND THEORETICAL STUDY OF THE INFLUENCE
OF THE ADDITION OF ALUMINA POWDER TO 7020 ALUMINUM
ALLOY FOAM ON THE MECHANICAL BEHAVIOR UNDER IMPACT
LOADING
ArkanJawdat Abassa1, DhaferSadeq Al-Fatal2
1
(Department of machines and equipment Engineering/ University of Technology, Baghdad,
Iraq, arkan_abassa@yahoo.com).
2
(Department of machines and equipment Engineering/ University of Technology, Baghdad,
Iraq, alfattal40@yahoo.com).

ABSTRACT

Aluminum foams are new materials mainly produced by expansion in proper chambers. A
relevant quantity of voids is generated in the metallic matrix during manufacturing, resulting
in a low material density. Aluminum foams are strongly affected by cells size, cells shape,
foam density, weight fraction and types of additives to aluminum foam. In this paper, the
influence of particle size, and weight fraction of Al2O3 particles on impact behavior of 7020
aluminum alloy foam was investigated, and then modeled using ANSYS12 software. Three-
dimensional models are suggested to model aluminum foam structure under impact loading.
Experimental results showed that the increase of the weight fraction of alumina powder as
reinforcement raises the acceleration-time curves. The decrease of alumina particle size leads
to an increase in the acceleration-time response of aluminum foam. Theoretical results of the
models are in good agreement with the experimental acceleration-time, velocity-time and
displacement-time curves of 7020 aluminum alloy foam.

Keywords: Impact loads, Aluminum foam, Alumina particles, aluminum foam models,
Calcium carbonate.

I. INTRODUCTION
Metal foams are new, as yet imperfectly-characterized, class of materials with low densities
and novel physical, mechanical, thermal, electrical and acoustic properties[1]. They offer
potential for light-weight structures, for energy absorption such as crash boxes in
automobiles, for thermal management such as heat insulation or heat exchangers according to
cells type, and for acoustic absorption such as sound insulation, and some of them, at least,
are cheap. Metal foam is a cellular solid, just like wood, coral, bone and bread, but with the
cells made out of metal. Usually the metal is an aluminum alloy, but it can also be made of

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

other metals, for example steel, nickel, titanium or gold [2]. In other words, metal foamsare
solids with high fraction of porosity.
Metallic foams are generally divided into two types, open and closed cell microstructures. In
the open-cell foam the cells are interconnected and the foam has the same appearance as a
scouring pad. The connections in open-cell foam are called struts, which meet in nodes. For
closed-cell foams the cells are closed by so-called faces, which meet in so-called cell edges,
which in turn meet in nodes. Generally, closed cell microstructures have higher mechanical
strength than open cell microstructures. The closed cell type of microstructure is particularly
attractive for applications in the field of light weight construction and energy absorption.

II. EXPERIMENTAL WORK

All foams made in this work were prepared by using 7020 aluminum alloy with the chemical
composition shown in table (1). A calcium carbonate CaCO3 powder, as a blowing agent,
with particle size of less than 10 µm and weight fractions (2%) was used to generate pores
inside the aluminum alloy.

Many significant factors affect the use of CaCO3 powder instead of TiH2 powder as blowing
agent. The main factors are

1- Calcium carbonate is cheap as compared with TiH2 as blowing agent[3].
2- The density of CaCO3 is (2.71 to 2.83 gr/cm3), almost identical to the density of
molten aluminum. Moreover, its decomposition temperature is above the melting
point of aluminum, usually in the temperature interval between 660 °C and 930 °C.
Therefore, CaCO3 is particularly suitable for the melt-route settling-free production
of foamed aluminum based materials.
3- The use of CaCO3 was found to be potentially suitable as a foaming agent for direct
(melt-route) foam manufacturing. Moreover, the decomposition products of CaCO3
have a significant effect on foam stabilization [4].

In this work, 7020 aluminum alloy foams were produced with different weight fraction of
alumina particles (0%, 2% and 4%) as reinforcement. The alumina particles were prepared by
sieving them to multi sizes of 90-106 µm, 106-125µmand 125-150 µm. An electrical furnace
was setto a temperature of 800ºC to melt the7020 aluminum alloy by using a graphite
crucible.

Alumina particles with specific particle size and weight fraction were added to the melt of
7020 aluminum alloy at a temperature of 800ºC. An electrical stirrer was used to mix the
alumina particles inside the melt of aluminum for about one minute. This melt was turned
back to the furnace to rise up its temperature, and this process was repeated three times until a
good distribution of alumina particles inside the melt of aluminum was achieved. Calcium
carbonate was added to the melt with 2% weight fraction, and again the stirrer was used to
get a good distribution of the blowing agent particles inside the melt of aluminum. This
mixture was turned back to the furnace but this time at a temperature of 740ºC for about 15
minutes to get a 7020 aluminum alloy foam reinforced with alumina powder. Aluminum
foam samples have a cylindrical shape with a diameter of 50.24mm, and a height of 44mm,
as shown in fig. 1.

413


All aluminum foam samples are impacted by a drop weight, as shown in fig. 2. An aluminum
foam specimen was put on the solid base. A block which weighs 0.71 kg was let free to fall
onto the foam sample from a height of 1 m. This represents 6.965 J of kinetic energy at
impact. In the center of the block, a one axis accelerometer, type B&K 4370, was installed.
Electrical signals were generated by the accelerometer at the moment of impact. These
signals were sent to the charge conditioning amplifier, type B&K 2626 for amplification, and
were displayed by data storage oscilloscope, type ADS 1022C, 25MHz. This test involves a
dynamic load being applied to a cylindrical shape specimen. The impact load has a velocity
of 4.429 m/sec at impact moment. After impact, specimen’s deformation was measured, and
by using equation (10), the maximum force and the acceleration exerted by the impactor can
be calculated.

TABLE I
Chemical composition of 7020
Si % Fe % Cu % Mn Mg Cr % Ni % Zn % Ti % P% Pb % Sn % V% Zr % Al %
% %
0.127 0.168 0.084 0.084 0.95 0.24 0.001 4.03 0.041 0.001 0.001 0.001 0.008 0.129 Bal

-A- -B- -C-
Fig. 1: A- 7020 aluminum alloy foam samples, B-side view, C- Top view.

Fig. 2: Drop weight tester machine

414


III. THEORETICAL ANALYSIS
A drop weight test of aluminum foam samples can be modeled, as shown in fig.3. A weight
W is released from rest at a height of h above an aluminum foam sample with cross sectional
area A, and a length L. The aluminum foam sample is modeled as a spring with stiffness k
and a mass Wb.

Fig. 3: Vertical beam (aluminum foam sample) under impact [5]

This model can be solved by the application of the law of conservation of energy to the
system.
The kinetic and potential energy are illustrated in equations at the start, when the block is at
rest above the spring at height h, and at the end, when the block is at its lowest point.
At the start,
Kinetic energy=0
Potential energy= W (h).
where W=mg, and h= height.
At the bottom,
ଵௐ ଶ
Kinetic energy= ଶ ௚ ‫ݒ‬௛
By equating the total energy at the start (at height h), and at the end (when contacting the
spring):
ଵௐ ଶ
W (h) = ଶ ௚ ‫ݒ‬௛ → ‫ݒ‬௛ ൌ ඥ2݄݃ … (1)
Wherevh=velocity of weight W at contacting point.
First, it should be noted that the spring mass will contribute to the kinetic energy during
deflection of the spring, since each differential element of mass along the length will move
downward with some kinetic energy during the deflection. This will decrease the potential
energy of the system. The uppermost element of mass will move the same amount as the
block, since it is immediately below it.
Second, the block, upon falling through a height, and gaining speed, now impacts another
mass (the mass of the spring), and the change in speed upon impacting the spring needs to be
ascertained using the principle of conservation of momentum.
The next element will move slightly less, etc. The lowest element will not move at all,
since it is contiguous with the base of the spring.

415


This equivalent mass is 1/3 of the spring mass [5], and it is then assumed that the spring has
no mass and an “effective” mass is mounted on top of the spring as a lumped mass. That is,
the original spring is replaced by a weightless spring, and on top of this spring is attached a
block having 1/3 the original weight of the spring.
By applying, the conservation of momentums to the system of block, and lumped mass at the
time of contact. The spring weight will be defined as WS. It will be assumed that the impact is
totally inelastic (e = 0). The two masses then move as one at a common velocity of vS.
ௐ ௐ ௐ
‫ݒ‬௛ ൌ ቀ + ଷ௚ ቁ ‫ݒ‬௦
ೞ
௚ ௚
ௐ
‫ݒ‬௦ ൌ ‫ݒ‬
ௐାௐ௦ൗଷ ௛
… (2)
The kinetic energy of the combined masses will now be:
ௐାௐ௦ൗଷ ଶ ௐାௐ௦ൗଷ ௐమ
‫ݒ‬௦ ൌ
ௐ
K.E. = మ 2݃ℎ = ௐାௐ௦ൗ (ܹℎ) … (3)
ଶ௚ ଶ௚ ൫ௐାௐ௦ൗଷ൯ ଷ

Note that the kinetic energy is less than that just prior to collision (Wh). This is a necessary
result whenever there is an inelastic collision, where a portion of the energy is lost to heat and
deformation.
The maximum deflection of the spring, δ, can now be determined by equating the total energy
at the top of the spring, and at the point where the masses come to a stop at a distance δ down
from the top:
At the top,
ௐ
Kinetic energy= ௐାௐ௦ൗ (ܹ݄)
ଷ
Potential energy=0
At the bottom, kinetic energy=0 (Block reaches zero speed).
ௐೞ ଵ
Potential energy=− ቀܹ + ଷ
ቁ ߜ + ଶ ݇δଶ
Equating the energies:
ௐ ௐೞ ଵ
(ܹ݄) + 0 ൌ 0 − ቀܹ + ቁ ߜ + ଶ ݇δଶ … (4)
ௐାௐ௦ൗଷ ଷ
The average force F, due to the impact occurs at the maximum deflection, δ.
ଵ
Since, ‫ ܨ‬ൌ ଶ ݇δ, …(5)
andsubstituting equation 5 into equation 4 gives,
ௐ ௐೞ
(ܹ݄) + ቀܹ + ቁ ߜ ൌ ‫ܨ‬δ … (6)
ௐାௐ௦ൗଷ ଷ
Dividing equation (6) by δ
ௐమ ௛ ௐೞ
‫ ܨ‬ൌ ௐାௐ௦ൗ + ቀܹ + ቁ … (7)
ଷஔ ଷ
But W=mg
(௠௚)మ ௛ ௠ೞ
‫ ܨ‬ൌ ൫௠ା௠௦ + ቀ݉ + ቁ݃ …(8)
ൗଷ൯௚ ஔ ଷ
௠మ ௛ ௠ೞ
‫ܨ‬ൌ ݃൤ + ቀ݉ + ቁ൨ … (9)
൫௠ା௠௦ൗଷ൯ ஔ ଷ

416


௠ೞ ௠మ ௛
Term ቀ݉ + ଷ
ቁ is small as compared with ൬൫௠ା௠௦ ൰ , so equation (9) can be written as,
ൗଷ൯ ஔ
௠మ ௛
‫ ܨ‬ൌ ݃ ൤൫௠ା௠௦ ൨ … (10)
ൗଷ൯ ஔ
Equation (10) is used to determine the magnitude of maximum acceleration exerted by the
impact load by dividing the force F by a mass of impactor.

VI. THEORETICAL WORK

The Finite Element Method (FEM) offers a way to solve complex continuum problems by
subdividing it into a series of simple interrelated problems. FEM is most commonly used in
numerical analysis for obtaining approximate solutions to wide variety of engineering
problems [6]. In the present study, a commercial general purpose finite element program
ANSYS® 12.0 is used for numerical simulation of aluminum foam structure. ANSYS®
program has many finite element analysis capabilities, ranging from simple, linear, static
analysis to a complex nonlinear, transient dynamic analysis [7]. The mechanical behavior of
aluminum foam under impact loading was investigated by finite element simulations. In this
study, many suggested structural models are investigated in impact mode.

V. ALUMINUM FOAM MODELS

Three types of 7020 aluminum alloy foams are modeled; the first is aluminum foam without
reinforcement, and its bulk density is 0.753 g/cm3.
The second type is aluminum foam reinforced with 2% weight fraction of alumina whose
particle size is 90-160µm, and its bulk density is 0.565 g/cm3.
The third type is aluminum foam reinforced with 4% weight fraction of alumina whose
particle size is 90-160µm, and its bulk density is 0.464 g/cm3.
The samples of aluminum foam are modeled in three dimensions using closed honeycomb
cells models with two types of arrangements, as shown in figures 4-Aand 4-B, and a cubic
model, as shown in figure 5. The behaviors of these models under impact loading are
compared with experimental results.

VI. CALCULATION OF CELLS WALL THICKNESS

Wall thickness of suggested models is calculated based on real values of aluminum foam and
aluminum solid densities. Aluminum foam density isρf and aluminum density as solid isρs.
Calculations of cell wall thickness are derived based on the rule of densities and volumes,

417

ఘ೑ ௏
ఘೞ
ൌ ௏ೞ … (11)
೑

A Three-dimensional honeycomb cell is shown in fig.6-A, and a cubic cell is shown in fig.6-
B, and the equations of wall thicknesses are:
1- A three-dimensional honeycomb structure,
ఘ೑ ଷ௟ ௧ ௧೎ ାଷ௟ ௧ ோ ୡ୭ୱ ଷ଴
ఘೞ
ൌ ଷ௟ ௧೎ ோ ୡ୭ୱ ଷ଴
… (12)

where: -
ߩ௙ ൌAluminum foam density,
ߩ௦ ൌAluminum solid density,
݈ ൌ Side length of cell,
(݈ ൌ 2ܴ sin 30).
‫= ݐ‬Wall thickness of cell,
‫ݐ‬௖ =Cell length,
ܴ =Radius of honeycomb cell (R=0.5 d).

2- A three-dimensional cubic cell,
ఘ೑ ଷ௧
ఘೞ
= ௟
… (13)

In equations 11, 12, and 13, ߩ௦ is 2.7 g/m3 for 7020 aluminum alloy, ߩ௙ is foam density which
is calculated from measuring the weight and volume of aluminum foam.
VII. DIMENSIONS OF ALUMINUM FOAM MODELS

The honeycomb structure model-1 has a width of 34.641 mm, but honeycomb model-2 has a
width of 35 mm, and these differences are due to cell arrangement.
Honeycomb models 1, and 2 have height of h=44mm, cell length of tC=2mm (cell length
equal to sample thickness), and wall thickness of 0.1685mm which is calculated using
equation (12).
Cubic cell model has a width of 20 mm (equal to seven cells or more in each side) [8],
height of h=44mm which is equal to a real sample height, cell length of tC=2mm (cell length
equal to the sample thickness), and wall thickness of 0.186mm which is calculated using
equation (13).

-A- -B-
Fig.4: A three-dimensional closed honeycomb cells model for 7020 aluminum alloy foam
under impact (A- model-1, B- model-2).

418


Fig.5:A three-dimensional closed cubic cells model for 7020 aluminum alloy foam under
impact (model-3).

Fig.6: A- A honeycomb cell, B-A cubic cell.

VIII. ELEMENTS USED IN IMPACT LOADS.
A nonlinear transient (large displacement) solution is used for the analytical behavior of
aluminum foam under impact loads by using ANSYS Multi-physics. Elements used in
transient solution are of two types, the first is for aluminum foam structure which is SHELL
181,as shown in fig.7-A. The second is for drop weight which is SOLID 45, as shown in
fig.7-B.
Elements of SHELL 181 are suitable for analyzing thin to moderately-thick shell structures.
It is a 4-node element with six degrees of freedom at each node: translations in the x, y and z
directions, and rotations about the x, y and z-axes. SHELL 181 is well-suited for linear, large
rotation, and/or large strain nonlinear applications. Change in shell thickness is accounted for
in nonlinear analyses. In the element domain, both full and reduced integration schemes are
supported [7].

419


SOLID 45 is used for the 3-D modeling of solid structures. The element is defined by eight
nodes having three degrees of freedom at each node: translations in the nodal x, y and z
directions. The element has plasticity, creep, swelling, stress stiffening, large deflection, and
large strain capabilities. A reduced integration option with hourglass control is available [7].

-A- -B-
Fig.7:A-SHELL 181 geometry, B- A solid 45 geometry[7].

IX. EXPERIMENTAL RESULTS

Impact tests have been performed on 7020 aluminum alloy foam samples reinforced
with 2%, and 4% alumina with different weight fraction of particle size (d=90-106, d= 106-
125, and d=125-150 µm). The impactor acceleration with respect to time from the moment of
impact is shown in figures (8to 11). These curves represent experimental results recorded by
data storage oscilloscope. The increase of weight fraction of alumina as reinforcement in
figures (9to 11) increases the acceleration of impactor. Figures (12and 13) show the influence
of particle size with 2%, and 4% weight fraction of alumina on the behavior of acceleration-
time curves. The decrease of alumina particle size increases the acceleration. The impactor
acceleration with respect to time is fitted to quadratic equations using a curve expert software
version 1.4. The integration of these curves gives the velocity and the double integration
gives the displacement of impactor with the boundary conditions: initial velocity of -4.429
m/sec and initial displacement of zero. The acceleration, velocity, and displacement curves
with respect to time are shown in figures (14 to 17). Figures (15 A, 16 A and 17 A) show an
increase in the impactor acceleration as the weight fraction of alumina particles increases and
the time needed to reach the maximum value of acceleration decreases. The increase of
acceleration means an increase in the impact force according to Newton’s law (Force = mass
x acceleration) where mass=mass of impactor.
Increasing the weight fraction of alumina as reinforcement in aluminum foam increases the
strength of aluminum foam samples. The increase in strength of Al 7020 foam is due to the
distribution of alumina particles around boundaries of pores. This distribution decreases the

420


pore size, and the number of pores is increased as illustrated by MarchoHaeche [9]. This
increase in the number of pores means an increase in the number of walls that carry the
compression load.

.
Fig.8:Impactor acceleration- Time curve for 7020 aluminum alloy foam.

Fig.9:Impactor acceleration-Time curve for 7020 aluminum alloy foam reinforced by (90-
106 µm) alumina particles

125 µm) alumina particles.

421


150 µm) alumina particles.

Fig.12:The influence of alumina particle size on impactor acceleration- Time curve for 7020
aluminum alloy foam reinforced by 2% weight fraction of alumina particles

Fig.13: The influence of alumina particle size on impactor acceleration-Time curve for 7020
aluminum alloy foam reinforced by 4% weight fraction of alumina particles.
The impactor velocity in figures (15B, 16B and 17B) at impact is -4.429 m/sec, and the time
needed to reach a zero velocity value decreases as the weight fraction of alumina particles is
increased in aluminum foam samples. The decrease of the time to reach zero value of velocity
is due to the increase of the reaction force generated by impact with the high strength
∆୚
aluminum foam samples according to (F = m ୲ ) where ∆V = Vϐ୧୬ୟ୪ െ V୧୬୧୲୧ୟ୪ .
The negative values of velocity represent the downward movement of the impactor which
compresses the aluminum foam sample while the positive values represent the velocity of the
impactor after rebound. Impactor displacements in figures (15C, 16C and 17C) represent the
deflection of aluminum foam samples when displacements lie between zero, and maximum
negative values. Maximum deflection occurs when the velocity is zero. Displacements
between maximum negative values and to the end of the displacement curve represent the
rebound displacement of the impactor. The ability for deformation of aluminum foam

422


samples is decreased when weight fraction of alumina particles is increased due to increased
strength.

-A- -B-

-C-
Fig.14:A- Acceleration–Time (sec) -B- Velocity–Time -C- Displacement–Time for 7020
aluminum alloy foam without reinforcement.

-A- -B-

-C-
Fig.15: A- Acceleration–Time -B- Velocity–Time -C- Displacement– Time for 7020
aluminum alloy foam reinforced with alumina particles of (d=90-106 µm).

423


-A- -B-

-C-
Fig.16:A- Acceleration–Time -B- Velocity–Time -C- Displacement– Time for 7020

-A- -B-

-C-
Fig.17: A- Acceleration–Time -B- Velocity–Time -C- Displacement–Time for 7020

424


X. THEORETICAL RESULTS
Tensile tests were performed on 7020 aluminum alloy samples with, and without
reinforcement to determine the parameters of Young’s modulus, yield stress, and slope of
stress- strain diagram at the plastic region.
Mechanical properties of the as cast 7020 aluminum alloy is:
Modulus of elasticity is 4.2 GN/m2.
Yield stress is 120MPa.
Slope of plastic stress- strain region is 2GN/m2.
Mechanical properties of the as cast 7020 aluminum alloy reinforced with 2% of weight
fraction of alumina powder with particle size of 90-106 µm is:
Yield stress is 112 MPa.
Slope of plastic stress- strain region is 1.5GN/m2.
Finally the mechanical properties of the as cast 7020 aluminum alloy reinforced with 4% of
weight fraction of alumina powder with particle size of 90-106 µm is:
Yield stress is 116 MPa.
Slope of plastic stress strain region is 2 GN/m2.
The above parameters are used in ANSYS12 to make, and solve the models.
The comparison of acceleration- time, velocity-time, and displacement- time curves for the
suggested models under impact, and experimental curves for 7020 aluminum alloy foam
without and with reinforcement are shown in figures (18to 20).
A comparison of experimental, and theoretical results (transient solution) for many
types and densities of aluminum foam shows good agreement in displacement-time, and
velocity – time response, especially in the region between zero, and maximum displacement
or velocity (i.e. impacting region). However, there is a slight difference in acceleration-time
response in the same region. The differences between experimental and theoretical results
increased in the region of rebound of impactor which is less important than the impact region.
The best suggested model is a three-dimensional cubic model which shows a good
response in acceleration, velocity and displacement with time.
Fig. 21 shows acceleration-time, velocity-time and displacement-time for solid 7020
aluminum alloy subjected to impact.
It can be observed that the maximum acceleration for aluminum foam is less than one half
that for the solid aluminum alloy. For this reason, aluminum foam is widely used today to
absorb impact energy for many applications.

425


-A- -B-

-C-
Fig.18:A- Acceleration–Time -B- Velocity– Time-C- Displacement – Time for 7020
aluminum alloy foam (without reinforcement).

-A- -B-

-C-
Fig.19:A- Acceleration–Time -B- Velocity–Time (sec) -C- Displacement–Time for 7020
aluminum alloy foam reinforced with 2% alumina particles of (d=90-106 µm).

426


-A- -B-

-C-
Fig.20:A- Acceleration–Time -B- Velocity–Time-C- Displacement– Time for 7020
aluminum alloy foam reinforced with 4% alumina particles of (d=90-106 µm).

-A- -B-

-C-
Fig.21:A- Acceleration–Time -B- Velocity–Time -C- Displacement– Time for solid 7020
aluminum alloy.

427


XI. CONCLUSION

Aluminum alloy foams reinforced with Al2O3 particles have been successfully produced.
Impact tests results exhibit a decrease in the amount of deformation of aluminum foam
samples and the Impact tests results exhibit a decrease in the amount of deformation of
aluminum foam samples and an increase in the impactor acceleration with decreasing particle
size and increasing weight fraction of alumina powder. Maximum deformation of aluminum
foam samples at zero velocity of impactor and the time needed to reach zero velocity
decrease with decreasing particle size and increasing weight fraction of alumina powder.
Impacting force increases as the particle size decreases and the weight fraction of alumina
powder increases.
The suggested models are in general in good agreement with experimental acceleration,
velocity, deformation, and force response with time curves of 7020 aluminum alloy foam but
the best model is the three-dimensional cubic model.

ACKNOWLEDGEMENTS
The authors would like to acknowledge the mechanical engineering department of Al-
Nahrain University, for the provision of laboratory facilities.

REFERENCES
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[3] VaružanKevorkijan, Lowcostaluminum foams made by CaCO3 particulates,
Association of Metallurgical Engineers of Serbia, MJoM,16 (3), 205-219, (2010).
[4] J. D. Bryant, M. D. Clowley, M. D. Wilhelmy, J. A. Kallivayalil, W. Wang, In
Metfoam 2007, DEStech Publications Inc., Lancaster, PA, pp. 27, 2008.
[5] Matthew Huang,Vehicle crash mechanics, CRC Press LLC, 2002.
[6] Huebner, H.H., Dewhirst, D.L., Smith, D. E., and Byrom, T. G. The Finite Element
Method for Engineers. 4th ed., New York: J. Wiley. 2001.
[7] ANSYS® Release 12.0 Documentation, ANSYS Inc, 2009.
[8] M.F. Ashby, A.G. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson and H.N. G.
Wadley, Metal foam: A design guide,Butterworth-Heinemann, 2000.
[9] MarchoHaeche, Jorg Weise, Francisco Garcia-Moreno and John Banhart, Influence of
particle additions on the foaming behavior of AlSi11/TiH2 composites made by semi-
solid processing, Materials Science and Engineering, A480 (1, 2), 283-288, 2008.

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