CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
THE MECHANISM OF STRAIN RATE STRENGTHENING DURING
DYNAMIC COMPRESSION OF CLOSED-CELL ALUMINUM FOAM
Kathryn A. Dannemann, James Lankford, Jr. and Arthur E. Nicholls
Southwest Research Institute, Mechanical and Materials Engineering Division
P.O. Drawer 28510, San Antonio, TK, 78228
Abstract. A series of compression experiments were conducted on closed-cell aluminum foams at
strain rates ranging from 10~5 s"1 to 2600 s"1. Compression tests were conducted at ambient temperature
and pressure, and in vacuum (25 torr). A split Hopkinson pressure bar system was used for experiments
at high strain rates; low strain rate tests were performed with a servo-controlled hydraulic machine.
Closed-cell Alporas foam demonstrated a strain-rate effect over the range of strain rates investigated.
Tests on samples with holes machined through the cell walls to permit intercellular gas flow confirmed
that the strain rate sensitivity of the Alporas foam is related to sequential rupture of the cell walls, which
allows the gas to exit the structure. Comparison of results for tests conducted in air and in vacuum
showed the strength increase at high strain rates is attributed to the stabilizing influence of the gas (i.e.,
air) pressure within the closed-cell structure. Evaluation of sectioned microstructures following interrupted high strain rate testing at a series of increasing strains, and high speed imaging of selected samples during dynamic testing, provided further insight on the deformation mechanism.
Several investigators have reported a strain rate
effect for Alporas aluminum foam. [3-6] Other aluminum foams appear relatively strain rate insensitive. [7,8] These differences have been attributed to
differences in processing and cell structure. Yet, the
nature of the strain rate strengthening has not been
adequately addressed. Strain rate strengthening of
aluminum foams is of particular interest since the
strain rate insensitivity of aluminum metals is well
documented. The experiments reported herein were
undertaken in an effort to explain the mechanism of
strain rate strengthening in Alporas aluminum foam.
INTRODUCTION
Recent advances in the processing of metal
foams, combined with low density and attractive
mechanical properties, have generated increased
interest in these cellular materials. Structural and
energy absorption applications are of particular interest. The quasistatic mechanical performance of
metal foams, specifically aluminum foams, is fairly
well understood. [1,2] However, until recently, mechanical property investigations of metal foams did
not address strain rate effects. Initial high strain rate
studies involved limited tests on available aluminum
foams. More extensive high rate studies of aluminum and other metallic foams (e.g., steel and Mg),
including ballistic testing, have evolved due to
promising test results that highlight the potential
energy absorption capabilities of foam materials.
EXPERIMENTAL PROCEDURE
Alporas closed-cell, aluminum foam was obtained
from Shinko Wire Ltd. The compression experiments were conducted on Alporas foam with a density of 0.41 g/cm3 (p/ps = 0.15) and an approximate
729
cell size of 2 to 4 mm. Cylindrical compression test
samples were electrodischarge machined (EDM'd)
from the material supplied, and measured approximately 23.6 mm in diameter by 25.4 mm long. The
specimen size was chosen to maximize the number
of cells across the sample diameter based on the split
Hopkinson bar system (SHPB) available. A representative cross-sectional microstructure is shown in
Fig. 1.
to system differences. The SHPB vacuum chamber
setup is illustrated in Fig. 2.
Similar tests, in air and in vacuum, were also
conducted on Alporas samples with holes intentionally machined through the cell walls to allow intercellular gas flow. These experiments were performed to determine the nature of the strain rate sensitivity and the effect of air flow. Very small (300
|Lim) diameter holes were EDM'd through the entire
sample diameter in a repetitive pattern at specific
sample heights. The hole size was chosen to minimize the extent of cell wall damage prior to testing.
The spacing between holes was 4 mm in all directions throughout the sample.
For selected high strain rate tests, deformation
was recorded during testing using an Imacon, ultra
high-speed imaging camera. Several interrupted
high strain-rate tests were also conducted to allow
microstructural evaluation of the deformed samples
at a series of increasing strains. Further details on
interrupted test and evaluation procedures, and the
high-speed camera setup are included in Ref. 6.
FIGURE 1. Representative microstructure of an Alporas foam
test sample. The photo height and width correspond to the sample
length and diameter.
RESULTS
Compression experiments were conducted at
strain rates ranging from 10~5 s"1 to 2600 s"1. A
SHPB system was used for experiments at strain
rates ranging from 400 s"1 to 2600 s"1. A servocontrolled hydraulic test machine was used for tests
in the range from 10"5 s"1 to 1 s"1. Most compression
tests were conducted at ambient temperature and
pressure in laboratory air. However, several tests
were performed in vacuum (~25 torr). This was
accomplished using a small vacuum chamber around
the test assembly, and attached to a mechanical
roughing pump. Different vacuum chambers were
used for the SHPB and the hydraulic machine owing
The strain rate sensitivity of Alporas, closed-cell
aluminum foam (p/ps = 0.15) was confirmed. At
high strain rates, a significant increase in the plateau
stress was observed relative to the quasi-static response. The effect is most apparent for tests conducted in air at the strain rate extremes (i.e., 10"5 s"1
and 2500 s"1), as shown in Fig. 3. Each curve represents a single compression test and is illustrative of
other tests performed at similar strain rates.
10
5
10
15
20
25
30
Strain (°/$
FIG. 3. Stress-strain response of closed-cell Alporas foam in air
and in vacuum.
FIGURE 2. Vacuum chamber setup on the SHPB system.
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For samples with interconnected cells (i.e. EDM'd
holes), a strain rate effect was not detected. Representative data is shown in Fig. 4 for the strain rate
extremes investigated in air. As reported previously
[6], the compression test data for Alporas foams
with interconnected cells generally fell within a 1
MPa scatterband for the plateau stress range. This is
significantly less than the 5 MPa differential in plateau stress for closed cell foam, as shown in Fig 3.
03
Q.
Interconnected Cells
1.E05
1.E03
1.E01
1.&01
1.Ef03
o>
oo c
Strain Rate (s1)
o ro .&>
Stress (MPa)
• QosecMjell/Ar
OQosecMjellA/acuum
4 Interoomected^Jr
4 IrterconractecJVacuum
FIGURE 5. Maximum stress (in plateau region) versus strain
rate for Alporas foam with closed cells (CC) and interconnected
cells (1C) for tests conducted in air and in vacuum.
1.8x10 3 s 1 ,Air
<r~~~
1 .6 x 10 3s"1, Vacuum
4.2X10 •V , Air
1
)
5
10
15
DISCUSSION
20
25
3
These results confirm the strain rate strengthening effect previously reported by the authors, Mukai,
Paul and others.[3-6] Several mechanisms have
been proposed to explain the strain rate effect, including microinertial cell wall effects on the kinetics
of gas flow through broken cell walls. The test results reported here in combination with earlier work
by the authors [5,6], including micro structural findings from interrupted tests and high speed images,
provide sufficient evidence to better define the nature of the strain rate strengthening mechanism in
Alporas foams.
Imacon images of the high rate deformation
process showed that damage concentrates initially at
the sample surface and progresses through the sample with time, causing sequential destabilization of
the cell walls.[6] For the quasistatic case, damage
does not necessarily initiate at the sample surface.
On a macroscale, damage development in the Alporas foams under dynamic conditions was found to
mimic the quasistatic development: damage progressed by the formation of discrete damage bands.
It was inferred from micro structural evaluations
of Alporas test samples that initial damage
(throughout the samples) occurred by axial flexing
and kinking of the cell walls. The extent of damage
increased with increasing local strain; buckling and
tearing of the deformed cell walls were observed.
Illustrations of kinking and extensive buckling are
shown in Fig. 6 for closed-cell samples following
interrupted testing to 10% strain. Cell wall rupture
Strain (%)
FIGURE 4. Stress-strain response of Alporas foam with interconnected cells (i.e. EDM'd holes) in air and in vacuum.
The results of high strain rate tests performed in
vacuum on closed-cell foams show a decline in the
plateau stress relative to tests conducted in air. The
stress-strain response in air versus vacuum is compared in Figs. 3 and 4, respectively, for closed-cell
and interconnected Alporas foams. There is little
difference in vacuum or air response for the foams
with interconnected cells. The decline in stress is
significant for the closed-cell foams. The extent of
strain rate strengthening is reduced for the closedcell foams relative to the high strain tests in air.
The differences in vacuum response, relative to
air, are summarized in Fig. 5 for Alporas foams with
closed cells and interconnected cells. The maximum
stress in the plateau region is plotted versus strain
rate. The trend line in the figure represents the behavior of the foam with interconnected cells (1C) in
air. The shallow slope indicates the absence of a
significant strain rate effect for the 1C foam. However, strain rate strengthening occurs for the closedcell Alporas foam in air, as shown by the increased
stress at high strain rates. In vacuum, the plateau
stress decreases for the closed-cell foam, approaching that of the interconnected cell foams. There is
little difference in plateau stress for the 1C foams in
air or vacuum.
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CONCLUSIONS
appeared to occur by a blowout process, resulting
from cell wall instability. [6] This view is supported
by the absence of strain rate strengthening (other
than the intrinsic structural contribution) for the interconnected versus closed cell samples. Compare
Figs. 3, 4 and 5.
The experimental evidence presented shows that
a strain rate effect is operative in closed-cell Alporas
foam. The results of tests conducted in vacuum, as
well as tests on Alporas foams with micron-sized
holes for cell connectivity, confirmed earlier hypotheses on the nature of the strain-rate strengthening. The effect is attributed to sequential cell destabilization and rupture. Failure starts at the sample
surface and ultimately moves to the interior. Sequential cell wall rupture is the rate-controlling step.
ACKNOWLDEGMENTS
The authors appreciate the support of the Office
of Naval Research (Contract NOOO14-98-C-0126),
and the advice of Dr. Steven Fishman, ONR technical monitor. We extend gratitude to Mr. Tetsuji
Miyoshi of Shinko Wire Co., Osaka, Japan for the
Alporas foam materials supplied. The technical contributions of Mr. Andrew Nagy of SwRI are also
gratefully acknowledged.
REFERENCES
1.Y. Sugimara, J. Meyer, M.Y. He, H. Bart-Smith, J.
Grenestedt, and A. G. Evans, Acta Mater., Vol. 45, pp.
5245-59, 1997.
2. H. Bart-Smith, A. F. Bastawros, D. R. Mumm, A. G.
Evans, D. J. Sypeck, H. N. G. Wadley, Acta Mater.,
Vol. 46, pp. 3583-92, 1998.
3. T. Mukai, H. Kanahashi, T. Miyoshi, M. Mabuchi, T.
G. Nieh and K. Higashi, Scripta Met., Vol. 40, p. 921,
1999.
4. A. Paul and U. Ramamurty, J. of Mat. Sci. & Engr. A,
Vol.A281,pp. 1-7,2000..
5. K.A. Dannemann and J. Lankford, Jr., /. of Mat. Sci. &
Engr. A, Vol. A293, pp. 157-164, 2000.
6. K.A. Dannemann, J. Lankford, A.E. Nicholls, in Fundamental Issues & Applications of Shock Wave and
High-Strain-Rate Phenomena, Elsevier Science Ltd.,
2001, pp. 219-225.
7. V. S. Deshpande and N. A. Fleck, Intl. J. of Impact
Engrg., Vol. 24, pp. 277-298, 2000.
8. C.J. Yu, T.D. Claar, H.H. Eifert, I.W. Hall, F.E. Franz,
K.T. Leighton, D.F. Hasson, in Met Foam '99 Proceedings, p. 347-352.
FIGURE 6. Micrographs of cell wall damage in a closed cell
Alporas foam following interrupted testing to 10% strain, (a)
Kinking at 10~3 s"1. (b) Extensive buckling at 103 s"1.
The vacuum tests were conducted to further test
this hypothesis. The vacuum test results do not
show a significant difference for the Alporas samples with interconnected cells. This is not surprising
since the cell walls are already perforated (with
EDM holes), thus limiting any pressure differential
across the cell walls. However, a reduction in
strength was observed for the closed cell foam tested
in vacuum. This suggests that the vacuum serves to
destabilize the outer walls of the sample, thereby
confirming the effect of the internal gas pressure as
the major contributor to the strain rate effect.
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