experimental investigation of energy-absorption ... components of sandwich structures s....

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doi:10.1016/j.iji

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International Journal of Impact Engineering 34 (2007) 1119–1146

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Experimental investigation of energy-absorption characteristicsof components of sandwich structures

S. Nemat-Nasser�, W.J. Kang, J.D. McGee, W.-G. Guo, J.B. Isaacs

Center of Excellence for Advanced Materials, Department of Mechanical and Aerospace Engineering, University of California,

San Diego, La Jolla, CA 92093-0416, USA

Received 7 July 2004; received in revised form 5 May 2006; accepted 17 May 2006

Available online 28 September 2006

Abstract

Two series of experiments are performed to investigate the dynamic response of various essential components of a class

of sandwich structures, under high-rate inertial loads. One consists of dynamic inertia tests and the other involves dynamic

impact tests. A split Hopkinson bar apparatus is modified and used for these experiments.

First, the energy-absorbing characteristics of the plate material in a sandwich structure are investigated using novel

dynamic inertia tests, paralleled by detailed finite-element simulations. The loading conditions in this case are similar to

those in high-rate pressure loading situations, and hence more closely simulate potential blast effects on structures. Plates

made of DH-36 naval structural steel are used in the dynamic inertia tests. The plates subjected to inertia loading show

membrane deformation behavior, but as the deflection or thickness increases, the bending deformation near the clamped

joint becomes significant.

Second, the dynamic behavior of the core material in a sandwich structure is studied through dynamic impact

(compression) tests, using high-speed photography. In addition, both the quasi-static and dynamic response of the material

is quantified using hydraulic testing machines and the Hopkinson-bar techniques. Aluminum foam as a core material is

used in these experiments. Aluminum foam is a lightweight material with excellent plastic energy absorbing characteristics.

The experimental results show a localized deformation in the metal foam specimens, at suitably high impact velocities. The

simulation results correlate well with the test results in the overall behavior of the metal foam specimens.

With these two experimental methods, the dynamic behavior of sandwich structures under high-rate inertial loading

conditions can be examined minimizing the need for direct pressure-induced impulse experiments. Each series of

experiments is relatively simple and can be performed separately to study the complex behavior of sandwich panels in

simple and well-controlled tests. The validity of separate performance test is shown by a finite element analysis with

aluminum foam core sandwich specimen subjected to blast loading.

r 2006 Published by Elsevier Ltd.

Keywords: Energy absorption; Sandwich structures; Experiments; Blast loading; Modeling

ee front matter r 2006 Published by Elsevier Ltd.

mpeng.2006.05.007

ing author. Tel.: +1858 534 4914; fax: +1 858 534 2727.

ess: [email protected] (S. Nemat-Nasser).

www.elsevier.com/locate/ijimpeng

dx.doi.org/10.1016/j.ijimpeng.2006.05.007

mailto:[email protected]

ARTICLE IN PRESSS. Nemat-Nasser et al. / International Journal of Impact Engineering 34 (2007) 1119–11461120

1. Introduction

Sandwich structures consisting of two plates separated by metal foam, have been considered as potentialcandidates to mitigate impulsive (short duration) loads. Their optimal design, subject to ease of manufacturingand field implementation, cost, and weight constraints, has been a subject of current interest [1]. Some recentinvestigations suggest excellent energy-absorbing characteristics under high-velocity impact loadingconditions [2]. The inner and outer plates, as well as the core material and their dimensions and morphology,may be adjusted to suit specific applications.

Impulsive loads are usually characterized by a pressure field that decays with time. The impulse duration isoften very short compared with the time-characteristics of the deformation response of most structures.Therefore, when a pressure-impulse load is imposed on a sandwich structure, the load may be represented byassigning an appropriate initial velocity field to the outer hull plate. The kinetic energy of the outer plate isabsorbed during the deformation of the sandwich structure. To enhance energy absorption, it is important toselect optimal materials under a given set of design constraints.

The behavior of clamped circular plates subjected to uniformly distributed blast loads has been intensivelystudied and three failure modes are theoretically analyzed [3]. Experimental techniques have also beendeveloped to examine three failure modes as the impulse increases—large inelastic mode, tearing mode andtransverse shear failure mode [4,5].

In this paper, we report the results of our experimental investigation of the dynamic response of a sandwichstructure to impulsive loads. The structure has a metal foam core and metal outer and inner hull plates that aremade of the naval structural steel, DH-36. This steel shows good ductility and plasticity at low temperaturesand high strain rates, without displaying any noticeable damage and micro-cracking. At relatively hightemperatures and low strain rates, its strength is not very sensitive to the temperature. The material has goodweldability, and its micro-structural evolution does not seem to be very sensitive to the changes in the strainrate and temperature; see [6].

For the core material, we consider aluminum foam which is lightweight and potentially attractive for itsenergy-absorbing characteristics. It has been used in various energy-absorbing structural designs, as well as fornoise and heat protection. Various techniques have been developed to manufacture metal foams [7]. Liquidmetal can be foamed directly by injecting gas or gas-releasing blowing agents, or by producing supersaturatedmetal gas solutions. Indirect methods include investment casting or melting of powder compacts whichcontain a blowing agent. If inert gas is entrapped in powder compacts, a subsequent heat treatment canproduce cellular metals even in the solid state. The same holds for various sintering methods, metal powderslurry foaming, or extrusion and sintering of polymer/powder mixtures. The idea of using aluminum foam tomitigate blast loading is briefly mentioned in the design handbook for metal foams [8] and two reports [9,10]on full-scale explosion tests used to investigate the behavior of aluminum foam panels under blast conditions.They show that surface effects due to the panel deformation and fracture, control the energy and impulsetransfer.

We report here the results of two series of experiments that are performed to investigate the dynamicresponse of sandwich structures under high-rate inertial loads. One consists of dynamic inertia experimentsand the other involves dynamic impact experiments. A split Hopkinson bar apparatus is modified and used forthese experiments. Our results show that the dynamic response of each component of a sandwich structure canbe studied and characterized independently.

First, we study the energy-absorbing characteristics of the plate material in a sandwich structure, using thedynamic inertia tests, paralleled by detailed finite-element simulations. The loading conditions in this case aresimilar to those in high-rate pressure impulse situations. Plates made of DH-36 naval structural steel are used inthe dynamic inertia tests. The specimen under inertia loading shows a membrane deformation behavior at lowdeflections. From experiments and finite-element simulations, it is also found that, as the deflection increases, thebending effects become important and cannot be ignored in the design of such structural systems.

Second, the dynamic behavior of the core material in a sandwich structure is studied through dynamicimpact (compression) tests and finite-element simulations. Aluminum foam is used as a core material in theseexperiments. Aluminum foam is a lightweight material that is considered to have excellent plastic energyabsorbing characteristics. The experimental results show a localized deformation in the metal foam specimens

ARTICLE IN PRESSS. Nemat-Nasser et al. / International Journal of Impact Engineering 34 (2007) 1119–1146 1121

at suitably high impact velocities. The simulation results correlate well with the test results in the overallbehavior of the metal foam specimens.

Third, the dynamic behavior of sandwich panels composed of DH-36 plate and aluminum foam is analyzedby finite-element simulations. A blast loading condition is imposed to the model. Explosion energy is almostabsorbed by front plate and core. If we effectively design the sandwich panel, back plate could be safe duringblast loading. The simulation results show the deformed shape of the plate is similar to that obtained fromdynamic inertia test.

With these two experimental methods, the dynamic behavior of sandwich structures under high-rate inertialloading conditions can be examined, minimizing the need for direct pressure-induced impulse experiments whichare costly and require highly specialized facilities and expertise. In our approach, each series of experiments isrelatively simple and can be performed separately to study the complex behavior of sandwich panels by simpleand well-controlled tests. Based on this kind of test, it is possible to optimize the material and configuration ofthe sandwich structures in order to maximize their energy-absorption capacity under impulsive loads.

2. Dynamic inertia experiments of plates and finite-element simulations

2.1. Dynamic inertia experiments

Fig. 1 shows the experimental setup. A circular (DH-36 steel) plate of uniform (denoted as type-I) orvariable (denoted as type-II) thickness, having a circular rim, is bolted to a 3-in cylindrical (7075 aluminum)tube of 3-in outer and 2.5-in inner diameter. It is propelled by a gas gun at a controlled velocity towards animpedance-matched, 12-in long incident tube of the same material and cross section, resting against a 3-inHopkinson bar. Upon impact, an elastic compressive wave is produced in both tubes, and within a short timeinterval (about several hundreds microseconds), the tube with the attached plate comes to rest, allowing theunsupported part of the plate to deform under its own inertia force. The deformation mode is similar to

(a)

(b)

TYPE IITYPE I

Striker tube( 7075 Al )

Incident tube(7075 Al )

Circular platespecimen(DH-36 steel )

Incident Barφo=3inch

φi=2.5inch

L1=3inch L2=12inch

Initial Velocity(30 ~ 60 m/sec)

Fig. 1. Schematic diagram of the experimental setup for inertia test plates in a sandwich structure: (a) test setup; (b) plate geometry

specimens.

Table 1

Dynamic inertia test conditions and test results

Test no. Thickness

(mm)

Mass (g) Impact velocity

(m/s)

Permanent

deflection (mm)

Initial kinetic

energy (J)

TYPE 1 DH1 1.35 85.5 40.2 2.56 306.2

DH2 0.89 73.9 32.1 2.08 189.0

DH3 1.45 87.7 36.1 2.10 248.2

DH4 1.30 84.0 57.4 4.32 621.6

DH5 0.83 72.3 60.2 4.85 662.8

DH6 2.07 102.9 36.0 1.56 256.9

TYPE 2 DH7 1.38 94.3 35.7 2.15 247.7

DH8 1.32 91.3 60.6 4.82 706.0

S. Nemat-Nasser et al. / International Journal of Impact Engineering 34 (2007) 1119–11461122

the one that results from a short-duration pressure impulse which would impart an initial velocity to the plate.The actual impact velocity is measured, using velocity sensors.

A number of tests were performed at various velocities, using plates of different thicknesses. Theexperimental conditions and the corresponding results are summarized in Table 1. In tests 7 and 8 a type-IIspecimen are used. The impact velocity is varied from about 32 to 60m/s, and the thickness of the plates variesfrom about 0.8 to 2mm. Fig. 2a shows a deformed plate, and Fig. 2b summarizes the observed permanentdeflection (measured at the center of the plates) per unit plate thickness, as a function of the impact velocity.At the same impact velocity, both the kinetic energy and the strength of the specimen increase as the thicknessincreases. The membrane stiffness varies linearly with the plate thickness while the bending stiffness relateslinearly to the square of the thickness. At low velocities, the deflection is small and hence the membranedeformation is dominant, while the bending effect becomes significant at high impact velocities which producelarge bending deformations. The plastic work in the membrane deformation is much larger than that of thebending deformation, when the deflection is small. Therefore, the energy absorbed by the specimen’s plasticdeformation has a linear relation with the thickness at low velocities. This means that for the same impactvelocity, as the thickness of the specimen increases, the kinetic energy that is converted into the deformationenergy increases linearly with the thickness. However, as the deflection increases, the bending mode begins todominate the deformation. In this regime, the energy-absorbing ability and the permanent deflection of theplate is a complex function of its thickness, as is shown in what follows. In Fig. 2, the experimental results forthe type-II plates are given.

2.2. Comparison between simulation and experimental results

The inertia experiments are simulated using the LS-DYNA [11] finite-element code. The finite-elementmodel is shown in Fig. 3. The plate and both tubes are discretized using solid elements, and a 1/4 symmetricmodel is analyzed. In the simulation, it is assumed that the plate is perfectly fixed to the striker tube along itsboundary, and no residual stresses are considered. A complete surface-to-surface contact over the interfacebetween the striker tube and the incident tube is assumed. Since the plate and the striker tube are joined bybolts, there is some flexible interaction between the plate and the striker tube. This interaction is notconsidered in the simulation. The striker and incident tubes are considered to be elastic. For the plates, thephysically based constitutive model proposed by Nemat-Nasser and Guo [6] is used. This model is based onthe concept of dislocation kinetics, and extensive experimental data over a broad range of strain rates andtemperatures. Eq. (1) gives the effective stress as a function of the effective strain, effective strain rate, andtemperature for DH-36 structural steel. In Fig. 4, the corresponding stress–strain curves are plotted forvarious indicated strain rates at room temperature.

t ¼ 750g1=4 þ 1500 1� �6:6� 10�5T lng�

2� 1010

" #1=28<:

9=;

3=2

. (1)

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Fig. 3. 1/4 symmetric finite element model and boundary conditions for the dynamic inertia experiment.

0

1

2

3

4

5

6

7

30 35 40 45 50 55 60 65

Impact Velocity (m/sec)

δ/H

0.89 mm

1.30 mm

2.07 mm

1.45 mm

1.35 mm

0.83 mm

1.38 mm

1.32 mmSpecimen Type - II

(b)

(a)

Fig. 2. Dynamic inertia experimental results: (a) deformed shape of a plate; (b) normalized permanent deflection measured at the plate’s

center, as a function of impact velocity, for indicated plate thickness.

S. Nemat-Nasser et al. / International Journal of Impact Engineering 34 (2007) 1119–1146 1123

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0

100

200

300

400

500

600

700

800

900

1000

0 0.1 0.2 0.3 0.4 0.5 0.6

Strain

Str

ess[

MP

a]100/s

3000/s

quasi-static

1/s10/s

1000/s

Fig. 4. Stress–strain curves of DH-36 structural steel for indicated strain rates.


The measured permanent deflection profiles are compared with the corresponding simulation results in Fig. 5.As mentioned above, in the simulation, a perfect joint condition between the plates and the striker tube isassumed, whereas, in reality, the plates are bolted to the tube, providing some flexibility at the boundary. As aresult, the predicted permanent deflection falls somewhat short of the experimental observations.

In addition, we have conducted a series of parametric studies to explore the effect of the plate thickness andimpact velocity on the permanent deformation and energy absorption. For an impact velocity of 45m/s, thetime variation of the stress in a typical element of the incident tube is given in Fig. 6a, with the portion markedA being magnified in Fig. 6b. As is seen, the thickness of the plate has a minor effect on the transmitted stresspulse, as should be expected; the pulse duration increases slightly with the increase in the plate thickness, dueto the increase in the total length of the striker.

For a 45m/s impact velocity, the time variation of the plate’s center deflection is plotted in Fig. 7, forindicated thicknesses. The results show a minor effect of the plate’s thickness on the permanent deflection, atthis impact velocity. Because of the oscillatory nature of the solution, which is inherent to an explicitcalculation, the permanent deflection is estimated by suitably averaging the calculated values over 100 ms. Fig.8 shows the time variation of the energy absorption with the plate’s thickness for the same impact velocity.The deflection reaches a maximum value at about 100 ms and then rebounds and oscillates around itspermanent value.

The effect of the impact velocity is examined in Fig. 9, which shows the initial peak value of the deflection asa function of the impact velocity, for indicated thicknesses, ranging from 0.76 to 3.05mm. As is expected, ahigher impact velocity produces a greater peak stress. At the same impact velocity, the peak value of thedeflection decreases with the increasing plate thickness.

Wang and Hopkins [12] have analyzed a rigid perfectly-plastic thin circular plate under an impact load, andconcluded that, for infinitesimal displacements, the permanent deflection at the center of the plate under animpulse load, is given by

dmax ffi0:28rV 2

0R2

sYH, (2)

where V0 is the impulse velocity, r is the density, R is the radius, H is the thickness, and sY is the yield stress ofthe plate. This expression is limited to very thin plates undergoing infinitesimal deflections (less than half of theplate’s thickness).

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Specimen : DH 1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40 45 50

Distance from CTR (mm)

Def

lect

ion

(m

m)

SimulationExperiment Simulation

Experiment

SimulationExperiment

SimulationExperiment

SimulationExperiment Simulation

Experiment

Specimen : DH2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40 45 50


Def

lect

ion

(m

m)

Specimen : DH 3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40 45 50


Def

lect

ion

(m

m)

Specimen : DH4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40 45 50


Def

lect

ion

(m

m)

Specimen: DH 5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40 45 50


Def

lect

ion

(m

m)

Specimen: DH 6

0

0.5

1

1.52

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40 45 50


Def

lect

ion

(m

m)

Fig. 5. Comparison between simulation and experimental deflection profiles.


Symonds and Wierzbicki [13] have examined the finite pure membrane displacement response of impulsivelyloaded clamped circular plates. The maximum deflection is then given by

dmax

Rffi 0:83V 0

ffiffiffiffiffiffirsY

r. (3)

Xue and Hutchinson [14] also solved the same circular plate problem using dimensionless parameters andfinite-element simulations based on Eq. (3). The maximum deflection is now given by

dmax

Rffi V 0


rþ 0:84

ffiffiffiffirE

r� 0:03

� �1� 8:3

H

Rþ 25

H

R

� �2" #

. (4)

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-400

-300

-200

-100

0

100

200

0 50 100 150 200 250 300 350 400

Time(μsec)

Str

ess(

MP

a)

H=0.762mm (0.03 in)H=1.143mm (0.045 in)H=1.524mm (0.06 in)H=1.905mm (0.075 in)

A

(a)

-400

-350

-300

-250

-200

-150

-100

-50

0

50

50 55 60 65 70 75 80 85 90 95 100

Time(μsec)

Str

ess(

MP

a)

H=0.762 mm (0.030 in)H=1.143 mm (0.045 in)H=1.524 mm (0.060 in)H=1.905 mm (0.075 in)

(b)

Fig. 6. (a) Time variation of stress in a typical element of the incident tube; (b) magnified region A.


In the present work, we have noted that the numerical simulation results exceed the results based on Eq. (3) by10–15% depending on the thickness to radius ratio, leading to the following empirical modification of Eq. (3):

dmax

Rffi 0:827


rV0

H

R

� ��0:03. (5)

While the maximum deflection is assumed to depend linearly on the impact velocity, as in Eq. (3), it is nownon-linearly dependent on the normalized thickness of the plate. In Fig. 10, simulation results are comparedwith the results from Eq. (5).

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0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400

Time(μsec)

Def

lect

ion

(m

m)

H=0.762 mm (0.030 in)

H=1.143 mm (0.045 in)

H=1.524 mm (0.060 in)

H=1.905 mm (0.075 in)

Fig. 7. Time variation of plate’s center deflection for indicated thicknesses.

00

10

20

30

40

50

60

70

80

50 100 150 200 250 300 350 400

Time(μsec)

En

erg

y A

bso

rpti

on

(J)

H=0.762 mm (0.030 in)

H=1.143 mm (0.045 in)

H=1.524 mm (0.060 in)

H=1.905 mm (0.075 in)

Fig. 8. Time variation of energy absorption for indicated thicknesses.


Fig. 11 shows the relation between the maximum plate deflection and its thickness, as the impact velocity ischanged. For the same impact velocity, the deflection decreases as the thickness increases. For the same impactvelocity, the kinetic energy of the plate is linearly related to its thickness. However, the dissipated energyrelates non-linearly to the plate thickness. This effect becomes more pronounced as the thickness of the plateincreases and the bending effect becomes more important; for a perfectly-plastic model, the bending momentof the plate is proportional to the square of its thickness. Zaera et al. [15] explain this for a thin plate and small

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0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80


Max

imu

m D

efle

ctio

n (

mm

)

H=0.762 mm (0.030 in)

H=1.143 mm (0.045 in)

H=1.524 mm (0.060 in)

H=1.905 mm (0.075 in)

H=3.048 mm (0.120 in)

Fig. 9. Maximum deflection of plate’s center as a function of impact velocity, for indicated thicknesses.

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50 60 70 80


Max

. Def

lect

ion

/ T

hic

knes

s

H=0.762 mm (0.030 in)H=1.143 mm (0.045 in)H=1.524 mm (0.060 in)H=1.905 mm (0.075 in)H=3.048 mm (0.120 in)eq (5)

Fig. 10. Comparisons of simulation results with the results from Eq. (5).


deformations, to be due to the dominance of the membrane effect; the membrane energy is proportional to theplate thickness. Experimental and simulation results also show that the deflection has a linear relation withthe plate thickness at low velocities, but when the impact velocity is increased and the deformation is large, thebending effect cannot be ignored. This can be seen from the results presented in Fig. 12, which gives thepermanent deflection per unit thickness as a function of the impact velocity, for various indicated plate

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0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3 3.5

Thickness (mm)

Max

. Def

lect

ion

/ T

hic

knes

s

10 m/sec30 m/sec45 m/sec60 m/sec

Fig. 11. Maximum deflection of plate’s center per unit thickness as a function of thickness, for indicated impact velocities.

0

1

2

3

4

5

6

7

8

9

10

25 35 45 55 65 75 85


Per

man

ent

Def

lect

ion

/ T

hic

knes

s

H=0.762 mm (0.030 in)

H=1.143 mm (0.045 in)

H=1.524 mm (0.060 in)

H=1.905 mm (0.075 in)

Fig. 12. Permanent deflection of plate’s center per unit thickness as a function of impact velocity, for indicated thicknesses.


thicknesses. As the impact velocity increases, the permanent deflection increases, depending non-linearly onthe thickness.

Fig. 13 represents the relation between the deformation energy and the thickness of the plate for indicatedimpact velocities. The membrane energy is more important when the deflection at the plate’s center is largerthan the thickness of the plate. Since the ratio of the radius over the thickness is greater than 20, in theseexperiments the primary energy absorption is by the membrane mode [15]. The energy absorption of the platehas a linear relation to its thickness for a 30m/s impact velocity. For a 60m/s impact velocity, although the

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0

2

4

6

8

10

12

14

16

18

0.5 1.5

Thickness (mm)

En

erg

y ab

sorp

tio

n (

J)

30 m/sec45 m/sec60 m/sec

1 2

Fig. 13. Energy absorption as a function of thickness, for indicated impact velocities.


membrane mode dominates the deformation, bending of the specimen near the clamped area cannot beignored, which is producing a non-linear dependency on the plate thickness as seen in Figs. 12 and 13.

3. Dynamic compression test of aluminum foam

Metal foams may be used as energy-absorbing lightweight materials, e.g., in crash zones of lightweightstructures [16,17], as well as for noise and heat protection. Due to their cellular microstructure, metal foamsdeform at a nearly constant plateau stress, absorbing impact and shock energy by plastic-work dissipation incompression. For engineering design, the mechanical behavior of this material must be experimentallyestablished. The compressive flow stress and energy-absorption ability depend on the material’s density thatcan be modified to tailor the resulting properties [18]. In the present study, the dynamic compressive behaviorof an aluminum foam as a core material for sandwich structures is studied experimentally and by numericalsimulation.

3.1. Experimental setup and results

The experiments are performed using a 3-in Hopkinson bar setup shown in Figs. 14–16. With this facility,the dynamic behavior of the core material of a sandwich structure or a micro-truss structure can beinvestigated. Large strains at high deformation rates can be imposed on the specimen to study its dynamicresponse. In this experiment, a short projectile impacts an aluminum foam specimen and the deforming sampleis photographed using an Imacon 200 high-speed camera. Just before the impact, the velocity of the projectileis measured by velocity sensors attached near the end of the gas gun. The force transmitted through the sampleis measured by a strain gauge attached to the 3-in output bar. The projectile is a 3-in diameter, 4.5-in long 7075aluminum bar, weighing 1460 g. The round-trip travel time for the elastic wave in the projectile is about 50 ms.The samples are made from Duocels Aluminum Foam Alloy 6101 and have 8–10% nominal density (40PPI).The impact velocity can be varied from 30 to about 55m/s.

The time-history of the projectile velocity may be estimated by assuming that the sample is in equilibriumand using the stress data to determine the time-variation of the force retarding the projectile. This calculatedprojectile velocity is compared with the measured one in Fig. 17. The impact duration depends on the impact

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Fig. 14. Schematic diagram of the dynamic compression test of the core material for a sandwich structure.

Fig. 15. Photo of an aluminum foam specimen attached to the output Hopkinson bar.


velocity, and in these tests it ranges from 1000 to 4000 ms. Equally spaced marks are placed on the specimenand used to estimate the engineering strain distribution at several stages in the course of the specimendeformation. Below, we report our experimental results for two tests, denoted as test-I and test-II,corresponding to impact velocities of 32.3 and 52.6m/s, respectively.

Figs. 18–20 represent the test-I results. Fig. 18 shows the deformed shape of the specimen, captured by anImacon-200 high-speed camera at 125 ms time intervals. The total nominal strain of the specimen is 58%. Fig.19 shows the corresponding nominal stress history. Within the first 900 ms after impact, the specimen is mostlyunder a plateau stress of about 3MPa. The stress increases gradually as the specimen is compacted. Fig. 20shows the specimen’s local engineering strain history, directly calculated from the markings on the specimen.The impact initiates deformation at the impacted face. As time elapses, the far end region of the specimenbegins to deform at a greater rate relative to the region close to the impacted end. The maximum engineeringstrain near the impact surface is about 40%, and, near the far end, it is about 70%. This non-uniform distribution of strain is caused by the compressive stress pulse that reflects as compression off the

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Fig. 16. Experimental setup for dynamic compression tests of metal foams.

-10

0

10

20

30

40

50

600 0.0005 0.001 0.0015 0.002 0.0025

Time (sec.)

Vel

ocity

(m

/sec

)

Velocity from stress Calc

Measured Velocity

Fig. 17. Measured and calculated projectile velocity.


output bar, back into the specimen, increasing the total stress in the region near the far end. Onck [19] studiedthe effect of specimen size relative to the cell size of aluminum foams. The Young’s modulus and plasticcollapse strength of foams increase to a plateau level as the ratio of the specimen size to the cell size increases.

Figs. 21–23 represent the test-II results. In this case, the impact velocity was 52.6m/s. Fig. 21 shows thedeformed shape of the specimen. The time interval between the photos again is 125 ms. The total nominalstrain of the specimen is 85%. Fig. 22 shows the nominal stress history. At about 1250 ms after impact, there isa sudden jump in the stress. Prior to this, the specimen is under a plateau stress regime. Fig. 23 shows theestimated engineering strain history at various indicated regions within the specimen. Initially, the region nearthe impact face is rapidly deformed to 60% in about a 300 ms time interval, while the strain in the far-end

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Fig. 18. Result of Test-I: Deformed shapes of the foam specimen at the impact velocity of projectile of 32.3m/s.

Stress vs time Sample ALF 2

0

1

2

3

4

5

6

7

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016

Time (seconds)

No

min

al S

tres

s (p

si)

Fig. 19. Result of Test-I: Nominal stress history of the foam specimen at the impact velocity of projectile of 32.3m/s.


region is less than 10%. In time, first the central and then the far-end regions of the specimen begin to undergolarge deformations, also reaching about 60%. Thereafter, the specimen deforms more or less uniformly to amaximum engineering strain of about 85%. This deformation history differs considerably from that of thetest-I. For an impact velocity of about 32.3m/s, large deformations are initiated first at the far end of thespecimen (Fig. 20), whereas for the 52.6m/s impact velocity, large deformations first occur near the impactzone (Fig. 23). Furthermore, the engineering strain distribution is initially non-uniform in both cases, but,

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Fig. 21. Result of Test-II: Deformed shapes of the foam specimen at the impact velocity of projectile of 52.6m/s.

-1.00

-0.90

-0.80

-0.70

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Time (msec)

En

g. S

trai

n

P1P2P3P4P5P6

IMPACT

P4P6 P1P2P5 P3

Fig. 20. Engineering strain history of the specimen impacted at a 32.3m/s velocity.


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-5

0

5

10

15

20

25

0 0.0005 0.001 0.0015 0.002 0.0025

Time (sec.)

Nom

inal

Str

ess

(MP

a)

ALF-3 Nominal Stress

Fig. 22. Result of Test-II: Nominal stress history of the foam specimen at the impact velocity of projectile of 52.6m/s.

-1.00

-0.90

-0.80

-0.70

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0 200 400 600 800 1000 1200 1400 1600 1800

Time(μsec)

En

g.S

trai

n

P1P2P3P4P5P6

IMPACT

P4P6 P1P2P5 P3

Fig. 23. Engineering strain history of the specimen impacted at a 52.6m/s velocity.


after compaction, it becomes more uniform in the test-II than in the test-I regime. In the test-II regime, themaximum engineering strain in the region near the impact face is about 80%, but at the far end, it is about90%.

Shock-wave propagation in metal foams has been examined by Lopatnikov et al. [20,21], Deshpande andFleck [22,23], and Paul and Ramamurty [24]. The effective sound velocity, c, in a metal-foam bar may beestimated using

c ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

rð�; r0Þ

sqsð�; r0Þ

q�

� �, (6)

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0

50

100

150

200

250

300

350

400

450

500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Eng. Strain

Eff

ecti

ve s

ou

nd

vel

oci

ty (

m/s

ec)

AL FOAM (DUOCEL, 40PPI)

Fig. 24. Effective sound velocity in aluminum foam.


where sð�; r0Þ is the instantaneous uniaxial stress, and sð�; r0Þ is the current density that may be estimatedfrom

rð�; r0Þ ¼r0

1� �, (7)

where r0 is the initial density. While not exact, these estimates are appropriate since most metallic foams showminimal lateral expansion in uniaxial compaction; i.e., they have very small Poisson’s ratios even at ratherlarge deformations. Fig. 24 shows the effective sound velocity in a Duocel aluminum foam bar, calculatedusing Eq. (6). In the elastic range, this velocity is about 450m/s, but it decreases to about 50m/s in the plateaurange of the stress–strain curve. As the compaction proceeds, the sound velocity increases. When fullcompaction is approached, the sound velocity approaches that of the constituent material. Since the effectivesound velocity in the plateau range varies from 50 to 200m/s, a shock front forms for an impact velocitygreater than 50m/s, as in the test-II regime. Initially, an elastic pulse propagates to the far end of the specimenat a 450m/s velocity. This elastic precursor moves along the sample faster than the shock front, which thenforms near the impact face, once the stress in the bar reaches the plateau level.

3.2. Quasi-static and dynamic properties of aluminum foam

To aid the simulations, compressive stress–strain curves are obtained for the foam material, using Instronand split-Hopkinson bar testing facilities. Fig. 25 shows the quasi-static engineering stress–engineering straincurve of the aluminum foam. The dotted straight line is the volumetric strain. The Poisson’s ratio of thematerial is measured and plotted in Fig. 26. As is seen, the Poisson’s ratio is very small in the plateau region,i.e., less than 1% for strains up to 35%, then increases to about 3% for a 60% axial strain, and does notexceed 8% even for a 70% axial strain.

The strain-rate effect in aluminum foams has been studied by a number of investigators. It has been shownthat Duocel aluminum foams deform more or less uniformly and their plateau stress is insensitive to the strainrate in the 10�3–10+3 s�1 strain-rate range [20–24]. Deshpande and Fleck [22,23] investigated the strain-rateeffect in Alulight and Duocel aluminum foams, using a split Hopkinson bar apparatus. They found that, overthe range of 10�3–5000 s�1 strain rates, there is essentially no change in the dynamic flow stress. We have alsoperformed similar experiments, and some of the results are given in Fig. 27, showing that the strain-rate effectcan be neglected in the considered aluminum foam.

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Fig. 26. Poisson’s ratio–engineering strain curve of aluminum foam.

0

2

4

6

8

10

12

14

16

18

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Eng. Strain

Eng

. Str

ess

(MP

a)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

Vol

ume

Str

ain

Aluminum Foam, 296K, 0.001/s

Fig. 25. Engineering stress and volumetric strain versus engineering strain for aluminum foam.


3.3. Numerical simulations

The dynamic compression tests of aluminum foams are simulated with the aid of the explicit finite-elementcode, LS-DYNA 960 [11]. Fig. 28 shows a finite-element model of the projectile, aluminum foam, and theoutput bar, using a 1/4 symmetric model with 8-node brick elements. The contact between the aluminum-foamspecimen and the projectile, as well as that with the output bar is modeled using the code’s surface-to-surfacecontact option with no friction. Since the bulk modulus of steel is considerably greater than that of thealuminum foam, solution stability is attained using contact stiffness based on the nodal mass and the globaltime-step size provided by the SOFT option in the code; see [11] user’s manual. Since the length of the outputbar in the finite-element model is much less than the actual one in the experiment, a non-reflecting boundary

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Fig. 28. Finite-element model of the dynamic compression test.

0

5

10

15

20

25

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Eng. Strain

Eng

. Str

ess

(MP

a)

Al Foam, 40 PPI8.4%, density, 296K

2200/s

10-3/s

10-1/s

Fig. 27. Engineering stress–engineering strain curves of aluminum foam at indicated strain rates.


condition is imposed at the far end of the bar in the model calculations to prevent back reflections of the elasticwaves.

The linearly elastic projectile and the output bar are modeled using the MAT-ELASTIC option of the code,suitable for linear elasticity. MAT-CRUSHABLE-FOAMmaterial model in the code is based on a continuumelastic–plastic relation that allows for large volumetric strains; in the present case, essentially uniaxial strain.The MAT-CRUSHABLE-FOAM material model in [11] can be used to simulate low-density foams with zeroPoisson effect. This foam model is isotropic and assumes that the Young’s modulus is constant; see [11] theorymanual. It thus may be used to simulate the compaction of the aluminum foam specimen.

The basic mechanical properties are summarized in Table 2. The compaction strain is calculated using Eq.(7). The engineering stress–true volumetric strain curve of the aluminum foam is shown in Fig. 29, togetherwith those of two copper foams of different densities, as comparison. Based on the data in Fig. 27, the strain-rate effects are negligible for the aluminum foam. On the other hand, the behavior of metal foams highlydepends on the loading paths. Various constitutive models have been suggested to account for this; see, e.g.,[19,22,23,25,26]. These constitutive models allow for different yielding behaviors under tension and

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Table 2

Basic mechanical properties used in the simulation of the dynamic compression of an aluminum foam specimen

Density (kg/m3) Young’s Modulus

(GPa)

Poisson ratio

Projectile (7075 Al.) 2,770 70 0.345

Output bar (Steel) 7,830 210 0.290

Specimen (Al. foam) Initial Full compact Initial Full compact Initial Full compact

258 2770 0.054 70 0 0.345

Fig. 29. Engineering stress–volumetric strain curves of several metal foams.


compression, as well as for differential hardening along different loading paths. Hanssen et al. [9,10] havediscussed and compared several formulations of the yield surface, and hardening and plastic flow rules for analuminum foam material model. The LS-DYNA [11] material model has also been calibrated and evaluatedusing the established validation program. Even for a relatively simple loading path, these constitutive modelsyield different predictions, with none being able to accurately represent the experimental results.

3.4. Comparison between experimental and simulation results

Figs. 30a–c show the simulation results for indicated impact velocities. In all cases, the engineering strain atthe impact surface is greater than that at any other point. However, in time the response changes, dependingon the impact velocity. At a low velocity of 10m/s, sufficient compaction does not occur, leading to a highlynon-uniform strain distribution. On the other hand, for much greater impact velocities that can lead to 60% orgreater compactions, the strain distribution eventually becomes more or less uniform.

In order to compare the energy-absorbing ability of the metal foams in terms of their strength and density,the responses of aluminum and copper foams are compared. While the plateau stress for the aluminum foam islarger than that of the copper foam, the density of the aluminum foam is much less than that of the copperfoam. The quasi-static volumetric strain-engineering stress curves of these materials are shown in Fig. 29.Fig. 31 gives the simulated collapse length of these foam specimens, for a common initial length of 76.2mm,

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Impact velocity : 10m/sec

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0 200 400 600 800 1000 1200 1400 1600

Time(μsec)

Axi

al s

trai

n

Impact velocity : 30m/sec

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 500 1000 1500 2000 2500

Time(μsec)

Axi

al S

trai

nP1 (Impacted end)P2P3P4P5 (Fixed end)

P1 (Impacted end)P2P3P4P5 (Fixed end)

Impact Velocity : 50m/sec

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 200 400 600 800 1000 1200 1400 1600

Time(μsec)

Axi

al s

trai

n

P1 (Impacted end)P2P3P4P5 (Fixed end)

(a) (b)

(c)

Fig. 30. Simulation results-Engineering strain distribution in aluminum foam: (a) 10m/s; (b) 30m/s; and (c) 50m/s.


and Fig. 32 compares the corresponding energy-absorbing ability. The average force is calculated by dividingthe total dissipated energy by the total length reduction. The average force is a measure of the energy-absorption ability per unit collapse length. Hence, from the results in Fig. 31 it may be inferred that thealuminum foam is more effective than the corresponding copper foams as a light-weight energy absorbingmaterial.

Figs. 33 and 34 compare the simulated engineering–strain histories with the corresponding experimentalresults. As mentioned in Section 3.3, the engineering–strain distribution in a tested specimen is non-uniform.Although simulation results show this to some degree, they predict more uniform deformation histories thanthose observed experimentally. The real aluminum foam has a cellular structure with numerous defects thatare not considered in the finite-element model. In an actual dynamic deformation, strain localization generallyoccurs; see photos in Fig. 25. To consider this, in materials with cellular structures, refined unit cells must bemodeled. Using a multiple-cell model, the localization of deformation caused by, e.g., density variation andmaterial defects may be simulated; see, e.g., [27,28]. The finite-element model used in the present study is basedon a continuum approximation of the metal foams, thus, predicting more uniform strain distributions. Theoverall behavior however is predicted reasonably well.

4. Deformation of sandwich panels subjected to blast loads

In order to investigate mechanical performance of sandwich panels under blast loading condition, steel plateand aluminum foam core were tested separately. Primary deformation modes obtained from each test are largeinelastic membrane deformation for steel plate and compression for aluminum foam core. Since the plate and

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0

5

10

15

20

25

30

35

0 10 20 30 40 50 60

Impact velocity (m/sec)

Ave

rag

e fo

rce

(N)

AL FOAM (40PPI)CU FOAM (100PPI)CU FOAM (50PPI)

Fig. 32. Simulated average force for several metal foams.

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60


Co

llap

se le

ng

th (

mm

)

AL FOAM (40PPI)CU FOAM (100PPI)CU FOAM (50PPI)

Fig. 31. Simulated collapse lengths for indicated metal foams.


the core of sandwich panels have interactions each other, it is necessary to investigate the deformationsubjected to blast loads. Radford et al. [29] reported a higher shock resistance of aluminum foam coresandwich panels than plate structures when a metal foam projectile impacts a sandwich panel.

In this study, to investigate blast loading effects, a finite element model of aluminum foam core sandwichpanel is modeled as like in Fig. 35. Small explosion takes place at one side of the specimen and a portion of theother side is fixed. The diameter of the specimen is same as in the inertia test. DH-36 is used as a 1mm plateand 5mm aluminum foam core is used. LS-DYNA [11] is also used in simulation and the constitutive relationsfor each material are the same as explained in the previous sections. To model the explosion, the ConWep

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-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 200 400 600 800 1000 1200 1400 1600

Time(μsec)

En

g. s

trai

n

P1 (Simulation)P2 (Simulation)P3 (Simulation)P1 (Experiment)P2 (Experiment)P3 (Experiment)

P1P2P3

IMPACT

Fig. 34. Simulated engineering-strain history at indicated points of for a 52.6m/s impact velocity.

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Time(μsec)

En

g. S

trai

n

P1 (Simulation)P2 (Simulation)P3 (Simulation)P1 (Experiment)P2 (Experiment)P3 (Experiment)

P1P2P3

IMPACT

Fig. 33. Simulated engineering-strain history at indicated points of for a 32.3m/s impact velocity.


function is used, which is known as adequate for blast loading on simple structural surfaces; see [11] user’smanual. The schematic diagram of the pressure field induced from the function is shown in Fig. 36. Since thespecimen is very small and in order not to induce tearing, small amount of TNT is used, which is 2 g.

Deformed shapes of the sandwich panel are represented in Fig. 37. Energy is almost absorbed by front plateand core. The deformation of core is compression at the center of the explosion. Maximum compression of the

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Time

Pre

ssur

e

Distance from the center ofthe explosion

Fig. 36. A schematic diagram of the pressure field produced by CONWEP function.

Fig. 35. A blast loading condition and a 1/4-symmetric finite-element model of a sandwich panel.


foam core is reached at around 80 ms. Since the maximum velocity of the center of the front plate is above100m/s, a shock front formed in the core as explained in Section 3.1. Due to this shock front, the deformationof the front plate is much faster than that of back panel. The profiles of the front and back panels arerepresented in Fig. 38 with respect to time. The maximum displacement of the front plate is about 4.5mm at80 ms, and the amount of the compression is about 3.3mm.

The transient deformation profile between sandwich panel and dynamic inertia test can be compared withFig. 38(a) and 39. In Fig. 39, deformation profile is obtained from a dynamic inertia simulation with 1mmspecimen. To get around 4.5mm maximum deflection as like in the blast simulation, the impact velocity 45m/sfrom Fig. 11 was used. The two deformation profiles are similar but not exactly same. Before the maximumdeflection reached, the transient shape is different because, in case of the dynamic inertia test, the impulse istransmitted from the incident tube. However, since the final shape of the plate is quite similar in both cases, theenergy absorption ability can be examined by the inertia test.

5. Conclusion

Two series of experiments are performed to investigate the dynamic response of sandwich structures underhigh-rate inertial loads: (1) dynamic inertia tests to characterize the plate response, and (2) dynamic impact

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0.0

1.0

2.0

3.0

4.0

5.0

0 5 10 15 20 25 30 35 40


80μsec

20μsec

40μsec

200μsec

Def

lect

ion

(mm

)

0.0

1.0

2.0

3.0

4.0

5.0

0 5 10 15 20 25 30 35 40Distance from CTR (mm)

Def

lect

ion

(mm

)

40μsec

80μsec

200μsec

(b)(a)

Fig. 38. Comparison of the deformed shape of front and back panels: (a) deformed shape of front plate, (b) deformed shape of back plate.

Fig. 37. Deformation shape of the sandwich panel at indicated instances.


tests to characterize the core material response. Hence, the dynamic response of each component of asandwich structure is studied and characterized independently.

The loading conditions are similar to that of a blast loading. The plates under inertia loading showmembrane deformation behavior, but as the deflection or thickness increases, the bending deformation nearthe clamped joint becomes significant. The dynamic behavior of the core material is studied using dynamiccompression tests. Aluminum foam is used in the experiments. Aluminum foam is a lightweight material withgood plastic energy absorbing characteristics. The experimental results show a localized deformation beforethe specimen is compacted to 60%. The simulation does not predict this kind of non-uniform deformation, butit does produce the overall observed behavior of the metal foam. The experiment and simulation results showthat the localized deformation changes as the impact velocity is varied. If the impact velocity is greater than50m/s, the deformation begins near the impacted face.

Blast loading onto a sandwich panel is simulated and compared to the separated test methods. The foamcore compressed very fast from the front face and shows effective shock resistance behavior. The front platedeformation is quite similar to the dynamic inertia test except some early transient time. From these results,

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0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40


Def

lect

ion

(mm

)80μsec

200μsec

300μsec

40μsec

Fig. 39. Deformed shapes of the inertia-test specimen.


the separate test methods can be successfully used to verify the energy absorption ability of each material insandwich panels.

Acknowledgements

This work has been supported by ONR (MURI) Grant N000140210666 to the University of California, SanDiego, with Dr. Roshdy G. Barsoum as Program manager.

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