Acta Materialia 55 (2007) 2829–2840
www.actamat-journals.com
Inertial stabilization of buckling at high rates of loading and low
test temperatures: Implications for dynamic crush resistance
of aluminum-alloy-based sandwich plates with lattice core
Xin Tang a, Vikas Prakash
a
a,*
,
John J. Lewandowski b, Gregory W. Kooistra c,
Haydn N.G. Wadley c
Department of Mechanical and Aerospace Engineering, Case School of Engineering, Case Western Reserve University, Cleveland, OH 44106-7222, USA
b
Department of Materials Science and Engineering, Case School of Engineering, Case Western Reserve University, Cleveland, OH 44106-7222, USA
c
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904, USA
Received 26 September 2006; received in revised form 4 November 2006; accepted 11 December 2006
Available online 6 March 2007
Abstract
In the present study, the dynamic compressive behavior of aluminum-alloy-based tetrahedral-core truss structures is investigated as a
function of impact velocity using a split Hopkinson pressure bar. The results are used to understand the phenomenon of buckling in truss
structures as a function of loading rates and test temperatures, and its implication on the dynamic crush resistance of tetrahedral-trussbased sandwich structures. In order to understand the effects of the flow strength of the core on the dynamic crush resistance, truss structures of both T6 and OA heat-treatments of AA6061 were investigated. A high-speed digital camera was used to record the sequence of
the deformation and failure events that occur during the dynamic compression and failure of the truss sub-elements. A buckling instability was observed to occur consistently for both the T6 and OA microstructures at all test temperatures employed in the present study.
Moreover, the T6 heat-treatment and the lower-than-room test temperatures significantly increase the specific energy absorption capabilities of the truss structures.
2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Aluminum-alloy 6061; Tetrahedral core truss structure; Inertial stabilization of buckling; Dynamic crush resistance; Low test temperatures
1. Introduction
The response of monolithic beams and plates to impact
loading has been extensively investigated in the past. For
example, Seiler and Symonds [15] and Wang and Hopkins
[23] have analyzed the impulsive response of beams and
clamped circular plates, respectively. More recently,
advances in material fabrication and processing have led
to the emergence of a new class of ultra-lightweight,
high-energy-absorption cellular material systems. Examples of such systems include metal foams and truss core lattice structures. In particular, Wadley et al. introduced a
*
Corresponding author. Tel.: +1 216 368 6440; fax: +1 216 368 3007.
E-mail address: [email protected] (V. Prakash).
new fabrication methodology to fabricate metal-based
open-cell tetrahedral truss core structures from aluminum
alloy sheets [16,22,9]. These cores are made by folding
stretched hexagonally perforated Al-6061 sheets. Simple
air-brazing is then used to construct sandwich panels with
cellular cores with relative densities between 0.02 and 0.08.
Research on periodic cellular materials has been widely
reported in the context of minimum weight design,
advances in manufacturing, mechanical characterization,
structural integrity and large-scale simulations. Amongst
these efforts, experimental studies providing a fundamental
understanding of the mechanical behavior of these materials have been of particular importance. Quasi-static tests
have been accurately reconciled with models of metalbased foams that account for ligament bending. Those
1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2006.12.037
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X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
for periodic truss-element cellular cores have addressed
plastic yielding and inelastic truss buckling. However, it
is now understood that the dynamic response of these
materials is significantly different from that measured
under quasi-static conditions. Besides material strain rate
sensitivity [14,6,2,3,27,17,28], two other dynamic effects
[21,26] are understood to significantly affect the core behavior: (i) inertial resistance of the core to the motion of the
front face-sheet and the consequent plastic-wave propagation in the core; and (ii) inertial stabilization of the core ligaments that can delay the onset of buckling, thereby
maintaining the effective strength of the core to much larger crushing strains than under quasi-static crushing. Core
ligament stabilization is also understood to lead to significant increase in the energy-absorption capacity of the lattice core sandwich plates.
In some of the earlier studies on cellular materials, BartSmith et al. [1] reported both the measured and simulated
bending performance of sandwich panels with thin cellular
metal cores (an Alporas core and two Al alloy face sheets).
Using collapse load criteria for face yielding, core shear
and indentation, they developed a mechanism map that
characterized the observed predominant failure phenomena. Xue and Hutchinson [25] compared the performance
of metal sandwich plates and solid plates made from the
same material and mass under impulsive blast loads. In
their study, three core geometries were evaluated: pyramidal truss, square honeycomb and the folded plate. They
reported that sandwich plates made from these three core
geometries can sustain a much larger blast loading when
compared to a solid plate of equal mass; the square honeycomb and folded plate cores were consistently observed to
outperform the truss cores. They also proposed the possibility of using structural optimization schemes that could
possibly lead to even greater improvements in the performance of the sandwich plates. Wicks and Hutchinson [24]
examined the mechanical performance of sandwich plates
with truss cores. They found the truss core construction
to be as efficient as the honeycomb cores at carrying the
prescribed combinations of moment and transverse forces
when a realistic minimum crushing strength was imposed.
Truss cores were found to possess an inherent crushing
advantage at the low core densities typical of most sandwich plate designs. For the case of woven textile cores,
Lee et al. [10] presented the compressive behavior of 304
stainless steel woven textile core materials obtained over
a wide regime of deformation rates. A well-defined failure
mode transition was observed when the deformation rate
was increased from 500 s1 to 1 · 104 s1, and the peak
stress was found to be deformation rate sensitive. At low
strain-rates, the collapse zone was observed to be in the
central region, with shear bands at ±45 in orientation,
while at the high strain-rates the collapse occurred adjacent
to the impact surface and propagated through the specimen
in the direction of impact. The overall dynamic response of
the textile cores was classified to be in between the opencell foams and the pyramidal truss core cellular materials.
Following these early ideas, Qiu et al. [11,12] conducted
extensive research involving structural optimization and
developed analytic approximations for the behavior of
sandwich panels subjected to blast loading. Valdevit et al.
[20] evaluated the optimal dimensions and the minimum
weight of sandwich panels with prismatic cores. They
reported that the corrugated core sandwich panels performed best when loaded longitudinally, and attributed
this to their greater buckling resistance; the diamond prismatic core panels (with corrugation order = 4) were found
to be slightly more weight efficient when compared to the
truss, when optimized for a specific loading direction.
Rathbun et al. [13], using a shock simulation technique
involving high-speed impact of Al-foam projectile, studied
and compared the performance of stainless steel square
honeycomb core sandwich and solid monolithic beams subjected to high-pressure, short-duration impulses. These
studies confirmed that sandwich beams with square honeycomb cores demonstrated considerably smaller displacements when compared to the solid steel beams of equal
mass when subjected to impulse/shock loading. In particular, for low-amplitude impulses, i.e. when the core has sufficient dynamic strength to prevent appreciable crushing,
the benefits of the sandwich structure were particularly
large. Hutchinson and Xue [7] analyzed square honeycomb
core plates for the best achievable performance and for
optimal mass distribution between the face plates and the
cores. The model was also used to discuss a number of
issues related to the design of effective metal sandwich
plates, including differing requirements for air and water
environments, face-sheet shear-off resistance, the role of
core strength and the relation between small-scale tests
and full-scale behavior.
From these studies it is now understood that all-metal
sandwich plates have distinct advantages over monolithic
plates of equal mass for structures designed to withstand
intense short-duration pressure pulses, especially in water
environments. To be effective under intense impulsive
loads, a sandwich plate must be able to dissipate, via core
crushing, a significant fraction of the kinetic energy initially
acquired. Consequently, if a plate is to retain its integrity
with only limited crushing, its core must have ample crushing strength and high energy-absorbing capacity. The
higher core strength is expected to limit core crushing,
enable high specific energy absorption, and maintain bending strength of the plate; sandwich plates with weaker cores
require a much higher fraction of their mass in their core.
The objective of the present paper is to better understand inertial stabilization of buckling as a function of
loading rates and the material yield strength and its role
in controlling the crush resistance of aluminum-alloy-based
sandwich structures (Fig. 1). Both T6 and over-aged (OA)
of AA6061, which are known to have very different yield
and flow strengths under dynamic compression [18], were
utilized. Moreover, the test temperatures were varied from
room to lower-than-room temperature (down to 170 C).
The focus of our study was the tetrahedral truss core
X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
2831
Virginia. Age-hardenable Al–Mg–Si aluminum alloy (6061)
tetrahedral lattice truss sandwich panels were made using a
recently developed sheet folding process [16]. The lattices
were brazed to solid face sheets of similar alloy composition and tested in both the annealed and peak age-hardened conditions. Details of the fabrication of the
tetrahedral lattice sandwich panels are provided next.
Fig. 1. Schematic of the manufacturing process of the tetrahedral lattice
truss cores involving perforation and folding.
because it has been shown to have a relatively high specific
crushing strength and energy absorption capacity that is
essential if the sandwich plate is to outperform the solid
plate construction. In order to conduct the dynamic experiments, the AA6061 alloy truss sub-elements, in the two
heat-treatments, were dynamically deformed in compression using the split Hopkinson pressure bar (SHPB) facility
in the Department of Mechanical and Aerospace Engineering at Case Western Reserve University. Moreover, a modified SHPB facility, which incorporates a low-temperature
chamber, was used to conduct the lower-than-room test
temperature experiments. The results of these experiments
were used to examine the effects of the changes in yield
strength and flow behavior of the lattice core material on
inertial stabilization of the truss ligaments, and hence the
specific energy absorption and crush resistance of the tetrahedral core sub-elements.
2. Experimental procedure
2.1. Materials
In the present study, the AA6061 alloy sandwich panels
were acquired as 4 in. square plates from the University of
2.1.1. Tetrahedral lattice truss and sandwich panel
fabrication
A folding process was used to bend elongated hexagonal
perforated
AA6061
(Al–0.6Si–1.0Mg–0.28Cu–
0.20Cr wt.%) sheet to create a single layer 50% occupancy
tetrahedral truss lattice [9]. Fig. 1 schematically shows the
process. The folding was accomplished node row by node
row using a paired punch and die tool with the sheets
folded so as to form regular tetrahedrons (i.e. the angle
h = 54.7).
An example of an elongated hexagonal perforated sheet
(with open area fraction of 0.82) that would create a tetra ¼ 0:067 is
hedral lattice with predicted relative density, q
shown in Fig. 2a. Fig. 2b shows a folded tetrahedral lattice
truss with a (measured) pre braze relative density,
¼ 0:048. The relative density of the truss cores was varied
q
by using different perforated sheet thicknesses and appropriately spacing the perforating punches to maintain a
square truss cross section. This required only one punch/
die set to produce the five relative density lattices
investigated.
Sandwich panels were constructed from the folded truss
structures by placing a tetrahedral lattice core between
AA6951 alloy sheets clad with AA4343 braze alloy. Alloy
compositions, melting and brazing temperatures are shown
in Table 1. The assembly was then coated with a proprietary metal-halide flux slurry (Handy Flo-X5518, Lucas
Milhaupt Inc., Cudahy, WI), dried and placed in a muffle
furnace for brazing. Each assembly was heated to between
595 ± 5 C for approximately 5–10 ± 1 min (depending on
sandwich mass) to minimize the joint weakening associated
with silicon interdiffusion from the brazing alloy. After
Fig. 2. (a) Photographs of the perforated sheet used to form a 4.8% relative density core and (b) the corresponding tetrahedral lattice truss after the
folding operation.
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X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
Table 1
Aluminum alloy compositions and temperatures for melting and brazing
AA designation
Composition (wt.%)
Temperatures (C)
Si
Cu
Mg
Zn
Mn
Fe
Cr
Ti
Melting
Brazing
6061
6951
4343
0.4–0.8
0.2–0.5
6.8–8.2
0.15–0.40
0.15–0.40
0.25
0.80–1.2
0.40–0.8
–
0.25
0.20
0.20
0.15
0.10
0.10
0.7
0.8
0.8
<0.35
–
–
0.15
–
–
616–652
616–654
577–602
593–616
air-cooling to ambient temperature, one set of sandwich
panels was solutionized at 530 C for 60 min and subsequently furnace cooled to place the alloy in the annealed
(O) condition. A second set of panels was water quenched
from the solutionizing temperature and then aged at 165 C
for 19 h. This achieved the peak strength (T6 temper) for
the AA 6061 alloy. No visible distortion was observed after
water quenching. Tensile test coupons of AA6061 accompanied the cores through each thermal process step and
were later used to approximate the mechanical properties
of the parent material used in the tetrahedral lattice trusses.
Fig. 3 shows the schematic laboratory brazing/heat-treatment process flow. Two orthogonal views of a sandwich
panel with a post braze 3.0% relative density core are
shown in Fig. 4. The brazing step resulted in an increase
in the relative density of up to 0.8% and depended on the
AA4343 clad thickness.
For the purposes of the present study, two different heat
treatments, i.e. T6 and over-aged (OA), were selected for
the AA6061 truss structures. The as-received AA6061alloy-based truss structure was in the T6 heat-treatment
condition. It was subsequently exposed to 260 C for
10 h, followed by air cooling (24 C) at room temperature
to obtain the OA condition. High strain-rate tension and
compression studies on monolithic AA6061 alloy, in both
the T6 and OA heat treatments and as a function of test
temperatures, have been previously conducted by the
authors [18,19]. The results of the study are summarized
in Table 2. It provides the uniaxial compression flow stress
of both AA6061-T6 and AA6061-OA alloys at a true strain
of 0.1, as a function of both the strain-rate and test
temperatures.
For dynamic compression testing, identically sized truss
sub-elements were electro-discharge machined with squareedge length of 16 mm (0.63 in.) and height 15 mm
, of
(0.59 in.), as shown in Fig. 5. The relative density, q
the present tetrahedral truss core, which is defined as the
ratio of the core density to the parent material density, is
given by Kooistra et al. [9]
t 2
2
1
¼ pffiffiffi
q
:
2
3 cos h sin h l
Fig. 3. Furnace brazing and heat treatment process used to create AA6061 tetrahedral lattice truss sandwich panels.
ð1Þ
X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
2833
Fig. 4. Views of the 3.0% relative density brazed tetrahedral lattice.
In Eq. (1) h is the angle between each tetrahedral strut and
the corresponding base tetrahedron, and t and l are the tetrahedral strut thickness and length, respectively. Considering the topology
properties of a regular tetrahedron,
pffiffiffi
h ¼ arctanð 2Þ ¼ 54:7 . For the sample used in present
study, t and l are 1.5 mm (0.059 in.) and 13.4 mm
, for
(0.53 in.), respectively. Thus, the relative density, q
the truss core used in the present investigation is 0.0524.
Table 2
The uniaxial compression flow stress of AA6061-T6 and AA6061-OA
alloys at a true strain of 0.1 and at different strain-rates and test
temperatures [18,19]
Materials
AA6061-T6
Test temp. (C)
24
170
AA6061-OA
24
170
Strain-rate
(_e, s1)
Flow stress
(at etrue = 0.1, MPa)
1 · 102
1.536 · 103
3.267 · 103
4.660 · 103
4.889 · 103
5.814 · 103
7.966 · 103
5.293 · 103
325
425
445
485
460
440
435
535
1 · 102
1.555 · 103
2.122 · 103
3.254 · 103
4.142 · 103
5.298 · 103
9.136 · 103
6.817 · 103
195
275
270
265
275
280
295
380
2.2. Dynamic compression testing: the split Hopkinson
pressure bar (SHPB)
The high-strain-rate dynamic compression experiments
on the aluminum-alloy-based tetrahedral sub-elements
(shown in Fig. 5) were conducted using the SHPB facility
in the Department of Mechanical and Aerospace Engineering at Case Western Reserve University. The schematic of
the SHPB facility is shown in Fig. 6. The SHPB comprises
a striker bar, an incident bar and a transmitter bar, all
made from high-strength maraging steel with nominal yield
strength of 2.2 GPa. The striker bar used in the experiments was approximately 0.6 m long, while the incident
and transmitter bars were 1.524 m in length. The diameter
of all the pressure bars was 19.05 mm (0.75 in.). A pair of
semiconductor strain gages (BLH SPB3-18-100-U1) were
strategically attached on the incident and transmitter bars;
Fig. 5. Photographs of the aluminum alloy-based open-cell tetrahedral
core truss structure sub-element used in the present study.
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X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
Fig. 6. Schematic of the split Hopkinson pressure bar (SHPB) at CWRU.
these gages were used in the combination with a Wheatstone bridge circuit, connected to a differential amplifier
(Tektronix 5A22N) and a digital oscilloscope (Tektronix
TDS 420) to record the strain-gage profiles in the incident
and the transmitter bars during the test.
In order to conduct the experiments, the truss sub-element specimen was placed between the incident and transmitter bars, as shown schematically in Fig. 7. In all
experiments, the contacting surfaces of the sub-element
were polished with ultra-fine sandpaper (up to 2400 grit).
Moreover, molybdenum-disulfide grease was used between
the sub-element surfaces and the incident and transmitter
bars to minimize friction.
An IMACON 200 high-speed digital camera, with a
maximum framing rate of 200 million frames per second,
was used to monitor the dynamic deformation process.
The camera allows a maximum of 16 frames of a typical
short-duration event to be recorded. The framing rate is
adjustable so as to allow for the best coverage of the entire
event. For simple visual imagery, the high-speed camera
uses a Photogenic Power Light 2500 DR flash, which
illuminates the test sample (sub-element) with 1 kJ of
light energy within a span of about 200 ls. The camera is
configured with appropriate Nikon lenses for the best
magnification and visibility, and is placed at an optimum
distance from the test sample for the required
magnification.
In order to conduct the experiments on the truss sub-elements, the striker bar is accelerated by means of a compressed-air gas-gun to impact the incident bar; the impact
Fig. 7. Expanded view of incident bar/sub-element/transmitter bar region.
results in an elastic compression wave, with a strain profile
ei(t), traveling along the incident bar towards the sub-element sample. Because of the impedance mismatch between
the sub-element and the pressure bars, part of the wave,
er(t), is reflected back into the incident bar, and the rest,
et(t), is transmitted through the sub-element specimen into
the transmitter bar. Based on the one-dimensional elastic
wave-propagation and SHPB theory [4,5] the engineering
stress r(t), engineering strain-rate e_ ðtÞ, and the engineering
strain e(t) in the sub-element can be calculated:
A0
et ðtÞ;
As
c0
e_ ðtÞ ¼ 2 er ðtÞ;
Ls
Z t
eðtÞ ¼
e_ ðtÞ dt:
rðtÞ ¼ E
ð2Þ
ð3Þ
ð4Þ
0
In Eqs. (2)–(4), E, A0 and c0 are the Young’s modulus,
cross-sectional area and longitudinal wave speed of the
pressure bars, and As and Ls are the initial contact crosssectional area and height of the sub-element tested.
Due to the anisotropic topology of the truss structure,
the true-stress vs. true-strain profile in the sub-element is
difficult to estimate, since in the analysis of the traditional
SHPB tests on isotropic and homogeneous specimens, isochoric and uniform deformation conditions are assumed to
prevail within the specimen [4,5]. Instead, a force vs. displacement curve for the truss sub-element sample is estimated by multiplying the nominal engineering stress with
the original sub-element contact area, while the displacement of the sub-element during dynamic compression
was calculated by multiplying the nominal engineering
strain by the original specimen height.
To conduct the low-temperature SHPB tests, a simple
lightweight plastic foam cooling tank, shown in Fig. 8,
was designed to keep the specimen immersed in liquid
nitrogen (at 196 C) prior to the dynamic compression
testing. To accommodate the incident and the transmitter
bars within the cooling tank, two holes, with diameters
close to those of the incident and transmitter pressure bars,
X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
2835
Fig. 8. Schematic of the split Hopkinson pressure bar (SHPB) coupled with the cooling foam tank at CWRU.
were drilled on the opposite curved surfaces of the tank.
Prior to impact, the sub-element sample was clamped at
the ends of the incident and transmitter bars within the
foam cooling tank. Liquid nitrogen was then poured into
the cooling tank to fully immerse the specimen as well as
the ends of the pressure bars. The temperature of the
sub-element was monitored by a 0.015 in. chromel–alumel
thermal couple wire attached to the sub-element.
3. Experimental results and discussion
Table 3 provides a summary of all the experiments conducted in the present study. It provides the test number, the
heat-treatment of the aluminum alloy used for the truss
sub-element, the projectile bar velocity and the test temperature. In order to compare the dynamic deformation characteristics of the truss sub-elements at the room and
170 C test temperatures, the impact velocity of the striker bar was controlled to be approximately 20 m s1. This
corresponds to an input stress level of 400 MPa. For all
experiments the length of the striker bar was fixed at
0.6 m (24 in.). This corresponds to a input pulse duration
of 250 ls. For Test 4 an impact velocity of 11.3 m s1 was
used. The motivation using the lower impact velocity was
to deform the truss sub-element to an intermediate stage,
such that it is pushed into the post-buckled regime but
not completely crushed. Post-test examination of the truss
core was then used to elucidate the modes and sequence of
events that lead of failure, e.g. initiation of plastic buckling
instability, role of micro-inertia, etc., in the truss elements
prior to complete collapse.
The force vs. displacement profiles obtained during
dynamic crushing of the AA6061-T6 and AA6061-OA
sub-elements at both room and lower-than-room test temperatures are shown in Fig. 9. The oscillations in the force–
displacement curves are understood to be a consequence of
stress wave dispersion in the truss sub-element and also due
to the complex load transfer path changes during collapse
of the truss core structure during dynamic compression.
The average strain-rate, estimated from the transmitter
bar gage signals, was 1000 s1. However, for Test 4, the
nominal strain rate was 500 s1. This is because a lower
impact velocity was used in this experiment. In both the
room temperature and lower-than-room test temperature
tests, the AA6061-T6 sub-elements exhibited higher compressive strength and consistently absorbed higher impact
energy when compared to the AA6061-OA alloy structures.
This behavior is consistent with the dynamic yield strength
and flow-stress reported for the two alloys on monolithic
cylindrical compression specimens [18,19], as discussed in
Table 3.
In addition to obtaining the force–displacement curves,
in some of the room temperature tests the IMACON 200
high-speed camera was utilized to observe the deformation
and failure process of the truss sub-elements. Analysis carried out by Xue and Hutchinson [26] and Vaughn et al. [21]
Table 3
List of all experiments performed to study the crush resistance of AA6061-T6/AA6061-OA truss structures at room and lower-than-room temperatures
Test no.
AA6061 Heat
treatment
Impact velocity of striker bar
(m s1)
Amplitude of input pulse
(MPa)
Duration of input pulse
(ls)
Test temperature
(C)
1
2
3
4
5
6
7
Al-6061-T6
Al-6061-T6
Al-6061-T6
Al-6061-T6
Al-6061-T6
Al-6061-OA
Al-6061-OA
22.7
22.6
22.8
11.3
23.3
19.5
23.6
444
440
445
220
455
380
460
258
260
260
238
218
221
219
24
24
24
170
170
24
170
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X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
5
SHPB Tests on Al-6061-T6 and Al-6061-OA
Lattice Core Structures
4.5
Al-6061-T6:Test 1 (RoomTemp)
Al-6061-T6:Test 3 (RoomTemp)
o
Al-6061-T6:Test 4 (-170 C)
o
Al-6061-T6:Test 5 (-170 C)
o
Al-6061-OA: Test 6 (24 C)
o
Al-6061-OA:Test 7 (-170 C)
4
Force (kN)
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
Displacement (mm)
Fig. 9. SHPB results on the AA6061-T6 and AA6061-OA truss subelements at both room and lower-than-room test temperatures.
have shown that strong dynamic effects come into play
when sandwich plates are subject to high-intensity stress
pulses. They introduced an important dimensionless
parameter governing the inertial effects, Vo/(coeY), where
Vo ispffiffiffiffiffiffiffiffi
theffi relative velocity of the sandwich faces,
co ¼ E=q is the elastic wave speed in the truss core material, and E, q and eY are the Young’s modulus, density and
the initial yield strain of the metal ligaments, respectively.
To gain an appreciation of the timescales involved in the
experiments discussed here, consider the AA6061-T6 truss
sub-element with a core thickness of h = 15 mm, whose
front face is abruptly accelerated to a velocity of
Vo = 20 m s1. For this case, Vo/(coeY) 4 (assuming
eY = 0.001)
and
the
overall
strain
rate
is
e_ ¼ V o =H ¼ 1333=s. In this range the material strain-rate
dependence is understood to be important. The other
dynamic effects that are also expected to play an important
role include the inertial resistance of the core to the motion
of the front face-sheet and the consequent plastic wave
propagation in the truss core, and the inertial stabilization
of the truss core that delays the onset of the truss buckling,
thereby maintaining the effective strength of the core to
much larger crushing strains than observed under quasistatic crushing.
Fig. 10 shows a sequence of selected frames taken from a
typical dynamic compression test for an AA6061-T6 truss
sub-element. The exposure time for each frame is 30 ns,
while the inter-frame time is 5 ls. The images in Fig. 10
represent every two frames taken from the photography
sequence; thus the time interval between photos is 10 ls.
For typical elastic and plastic wave speeds, co = 5000 m/s
and cp = 500 m/s, and the elastic and plastic wave fronts
are expected to reach the back face at times t = 3 ls and
30 ls, respectively. Fig. 11a shows the voltage vs. time signal showing the incident pulse, the reflected pulse and the
transmitted pulse signals obtained in Test 1. Fig. 11b shows
the corresponding force vs. time and the strain vs. time signals obtained from the measured incident and the transmitter bar strain profiles using Eqs. (2)–(4). Superimposed on
the figure are selected frames from the high-speed video of
the dynamic crush event. The amplitude of the force in the
input stress pulse is 126 kN with a rise time of approximately 50 ls. The maximum crush force in the truss subelement is 2.2 kN, and is reached at 70 ls after the stress
pulse loading.Thereafter the force carried by the truss sub-
Fig. 10. The initiation of plastic instability in Al-6061-T6 truss sub-element during a typical dynamic compression test conducted using the SHPB at room
temperature (frames are selected from the high-speed camera photography). Bold arrows indicate loading direction while thin arrows locate initiation of
the plastic instability.
X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
0.1
2
Test 1: Al-6061-T6 Truss sub-element
RoomTemperature
Incident Bar Signal (Volt)
1.5
1
0.05
0.5
Reflected Signal
0
0
-0.5
Incident Signal
-1
-0.05
Transmitter Bar Signal (Volt)
a
2837
Transmitted Signal
-1.5
-2
-400
-300
-200
-100
0
100
200
-0.1
300
Time (μs)
0.3
5
SHPB test of Al-6061-T6 Truss Core Sub-element
Test 1(RoomTemperature)
Average Strainrate1072 s-1
4.5
4
0.25
Force (kN)
3.5
0.2
3
Frame 1
91 μs
2.5
0.15
Frame 16
171 μs
2
Engineering Strain
b
0.1
1.5
1
Frame 8
131 μs
0.5
0
0
50
100
0.05
Frame 12
151 μs
150
200
250
300
0
350
Time (μs)
Fig. 11. (a) Strain gage voltage vs. time profile showing the incident bar signal, the reflected bar signal and the transmitter bar signal on the truss subelement at room temperature in Test 1. Note: the incident and reflected bar signals and the transmitter bar signal do not have the same scale. (b) The
corresponding force–time curve measured during the dynamic compressive test on the Al-6061-T6 alloy at room test temperature (average nominal strainrate 1072 s1).
element is observed to decrease. This decrease in force is
understood to be due to the initiation of elastic/plastic
buckling in the ligaments as the stress builds up in the truss
sub-element. As mentioned before, the time taken for the
plastic wave to propagate to the back surface of the truss
sub-element is 30 ls after the arrival of the incident stress
pulse. However, the first evidence of the initiation of plastic
instability occurs in frame 4 (at 111 ls); the progression of
damage/buckling can be observed after frame 6 (141 ls).
This provides direct evidence of the beneficial effects of
micro-inertia in delaying the initiation of plastic instability
within the ligaments of the truss sub-elements. As the
dynamic compression proceeds, the instability spreads to
the other ligaments and eventually the entire core as the
sub-element is fully crushed.
Fig. 12 shows the post-test pictures of the Al-6061 alloy
truss sub-elements. In all the high-velocity impact experiments (impact velocity 20 m s1), the truss sub-element
structures are observed to completely crush during the
dynamic deformation process. However, for the case of
the 10 m s1 impact velocity, the truss sub-element is
observed to undergo only plastic buckling, and is recovered
prior to complete crushing of the truss core. At the room
temperature, the peak compressive forces in AA6061-T6
sub-elements ranged from approximately 2.2 kN to
2.5 kN, while those in AA6061-OA sub-elements were
2838
X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
Fig. 12. Post-test examination of the AA6061-T6 and AA6061-OA truss
sub-elements at room and lower-than-room temperatures. (a) The original
AA6061-T6 truss sub-element sample. (b) The buckled AA6061-T6 truss
sub-element from Test 4. (c) The completely crushed AA6061-T6 truss
sub-element.
approximately 1.4 kN. At the lower-than-room test temperatures (170 C), the peak compressive forces in the
AA6061-T6 sub-elements were in the range of 3.0–
3.3 kN, while for the AA6061-OA sub-elements the peak
forces were 2.1 kN. Also, for the room temperature tests,
the specific energy absorption ranged from 16 to 21 J kg1
for the AA6061-T6 sub-elements, while for the AA6061-
OA sub-elements the absorption was 11 J kg1. At the
lower-than-room test temperatures (170 C), the specific
energy absorption in the AA6061-T6 sub-elements was
approximately 28 J kg1, and that of AA6061-OA sub-elements was approximately 21 J kg1. Thus, the levels of
crush resistance and impact energy absorption are much
higher for the case of the T6 alloys (higher strength truss
core materials), and at lower-than-room test temperatures.
Table 4 summarizes the main results of the tests: it provides
the average nominal strain-rate achieved in the tests, the
maximum compressive force sustained by the truss core
(maximum crush force), and the specific energy absorption
obtained from all the dynamic compression tests conducted
in the present study at both the room and lower-than-room
test temperatures.
The dynamic force vs. displacement curves, for both the
T6 and the OA heat-treatments (presented in Fig. 9), are
higher by a factor of 2 when compared to those obtained
under quasi-static deformation conditions (6.7 ·
102 s1). The beneficial effects on energy absorption are
understood to be due to the elevated strain rates and the
low test temperatures that result in an elevation of the force
vs. displacement curve during testing. This must occur due
to changes in the deformation and flow behavior of these
aluminum alloys when tested at low temperature and high
strain rates, as summarized in Tang [19], and discussed
below. Perhaps more importantly, this elevation of the
force vs. displacement curve is a result of the micro-inertia
in the truss ligaments that results in a delay in the buckling
instability, as shown in Fig. 10, thereby increasing the
crush resistance.
The beneficial effects of testing various aluminum alloys
at low test temperatures and/or high strain rates have occasionally been reported for Charpy impact testing as well as
fracture toughness testing of a variety of commercial aluminum alloys [8]. Tabular summaries of various aluminum
alloys have also indicated measurable increases in the
quasi-static yield strength, UTS and notch tensile strength
on reducing the test temperature from room temperature to
320 F, with further increases on going down to 452 F.
Recent results [18,19] clearly show that increasing the
strain-rate as well as decreasing the test temperature
increased the yield and UTS, without significantly degrading the reduction in area for 6061 in both the T6 and OA
Table 4
Average nominal strain-rate, maximum crush force, and the specific energy absorption capability obtained in the dynamic tests on AA6061 truss core
structures at both room and lower-than-room test temperatures
Test
no.
AA6061 heat
treatment
Impact velocity of striker bar
(m s AA6061)
Test
temperature
(C)
Average strainrate (s1)
Max crush force
(kN)
Specific energy absorption
(N m kg1)
1
2
3
4
5
6
7
Al-6061-T6
Al-6061-T6
Al-6061-T6
Al-6061-T6
Al-6061-T6
Al-6061-OA
Al-6061-OA
22.7
22.6
22.8
11.3
23.3
19.5
23.6
24
24
24
170
170
24
170
1072
1060
1071
520
1039
904
1125
2.2
2.4
2.3
3.0
3.3
1.4
2.1
20.8
15.6
18.3
16.1
27.9
11.2
20.9
X. Tang et al. / Acta Materialia 55 (2007) 2829–2840
conditions. Furthermore, in situ high-speed video that was
integrated with the high-rate uniaxial test results have
enabled a comparison of calculated necking instability
strains to those revealed via the high-speed video under
these different test conditions. The results clearly showed
an elevation of the tensile necking strains with an increase
in strain-rate and decrease in test temperature. This effect
was maximized at the highest strain rates and lowest test
temperatures. The source of the increased necking strain
was shown to be due to the increased work-hardening rate
exhibited by the samples tested under these conditions. The
increased work-hardening rate counteracts the geometric
softening experienced during tensile deformation, thereby
prolonging the uniform strain regime. The increased yield
stress, UTS and work-hardening rates obtained under these
conditions indicate that the energy-absorbing ability of the
material under tensile or compressive conditions should
increase with respect to that obtained at room temperature.
This has been documented in other published summaries
[19], although the source(s) of these improvements were
not discussed.
The present tests on the AA6061-T6 and AA6061-OA
truss sub-elements, where the buckling instability is inhibited at low temperatures and high strain-rates thereby
increasing the crush resistance, are broadly consistent with
these other recent observations made on the effects of high
strain-rate and low temperature on the energy absorbed
during tensile or compression testing of monolithic
AA6061-T6 and AA6061-OA. The increased yield strength,
UTS and work-hardening rate exhibited by the monolithic
AA6061-T6 and AA6061-OA obtained at high strain-rates
and low test temperatures are consistent with the elevated
load vs. displacement curves obtained during high-rate/
low-temperature testing of the truss sub-elements (Fig. 9).
The delay of the buckling instability in the truss sub-element ligaments that accompanies these rate and temperature induced changes in properties thereby increases the
crush resistance and energy-absorbing characteristics of
such structures constructed of these monolithic aluminum
alloys. Additional work is needed on structures constructed
from other aluminum alloys and heat treatments in order
to determine if the presently reported results are broadly
representative of the behavior of other aluminum alloy
structures.
4. Conclusions
In the present study, the dynamic compressive behavior
of AA6061-based open-cell tetrahedral core truss structures under two different heat treatment conditions, T6
and OA, has been investigated under uniaxial dynamic
compression loading over a range of test temperatures
from room temperature down to 170 C. At all loading
rates, truss structures constructed of AA6061-T6 exhibit
a higher crush resistance and greater energy-absorbing
capability than those constructed of AA6061-OA, which
is in good consistency with the previous studies on the
2839
dynamic compressive properties of monolithic AA6061T6 and AA6061-OA materials. In addition, lower test temperatures were found to produce significant effects on the
force–displacement curves of the truss structures. Reduced
test temperatures increase the crush resistance and mechanical energy absorption capability of the truss structures
tested in the present study. These results have important
implications in the design and performance of blast-resistant lightweight truss structures, and indicate that at lower
than room temperatures and at elevated strain-rates, the
truss structure made from these alloys have a potential to
sustain higher deformations and absorb more impact
energy prior to complete failure. The dynamic compressive
deformation process of the truss structure was also captured by a high-speed camera.
Acknowledgments
The authors acknowledge the Case Western Reserve
University (Case Prime Fellowship) and the Office of Naval
Research (ONR-N00014-03-1-0351) for financial support.
The authors also acknowledge the Major Research Instrumentation award, CMS 0079458, by the National Science
Foundation for the acquisition of the ultra-high-speed digital camera used in the present experiments. Critical reading and comments by Prof. J.W. Hutchinson, Harvard
University, are particularly appreciated.
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