Full text of DOI:10.1557/JMR.2000.0015

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Nondestructive evaluation of cavitation in an Al–Mg material
deformed under creep conditions
Eric M. Taleff
Texas Materials Institute, University of Texas at Austin, Austin, Texas 78712
Teodoro Leon-Salamanca
Reinhart and Associates, Inc., Suite 173, P.O. Box 9802, Austin, Texas 78766
Richard A. Ketcham
Department of Geological Sciences, University of Texas at Austin, Austin, Texas 78712
Reuben Reyes
Aerospace Engineering Learning Resource Center, University of Texas at Austin, Austin, Texas 78712
William D. Carlson
Texas Materials Institute and Department of Geological Sciences, University of Texas at Austin,
Austin, Texas 78712
(Received 30 April 1999; accepted 20 October 1999)
Cavitation was examined in an Al–Mg solid-solution alloy deformed in tension at
400 °C under conditions providing solute-drag creep, which can produce tensile
ductilities from 100% to over 300%. Two nondestructive evaluation techniques were
employed to measure the extent of cavitation: ultra-high-resolution x-ray computed
tomography and pulse-echo ultrasonic evaluation. Subsequent to nondestructive
evaluation, the sample was sectioned for examination by standard metallographic
techniques. Metallographic examination confirmed that both nondestructive techniques
accurately indicated the extent of cavitation. Ultrasonic testing provided a practical
means of distinguishing material with cavities from that without cavities. Ultra-
high-resolution x-ray computed tomography provided an accurate three-dimensional
image of internal cavitation.
I. INTRODUCTION
were (i) use nondestructive evaluation (NDE) techniques
Recent investigations have revealed enhanced tensile
ductility in Al–Mg solid-solution alloys deformed at
warm and hot-working temperatures.1–3 Enhanced duc-
tility occurred during solute-drag creep associated with
Mg solute additions in Al.1–3 Under conditions promot-
ing solute-drag creep, tensile ductilities of up to 325%
have been observed in binary Al–Mg materials; this
maximum value was achieved in an Al–2.8Mg (wt%)
alloy at a temperature of 400 °C and a strain rate of
10−4 s−1.2 The large tensile ductilities observed in Al–Mg
materials approach those of superplastic materials, yet do
not require the fine grain sizes necessary to achieve su-
perplasticity.3 Thus, enhanced ductility in Al–Mg mate-
rials may be attractive where superplastic forming is not
currently economical because of material costs. One of
the important factors limiting tensile ductility during
solute-drag creep of Al–Mg materials with ternary alloy-
ing additions, such as is typical of commercial 5xxx-
series alloys, is cavitation.2 It is this importance of
cavitation in limiting enhanced ductility that prompted
the present investigation. The goals of this investigation
to measure the amount of cavitation in an aluminum
alloy deformed under conditions promoting solute-
drag creep, and (ii) correlate measurements of cavitation
by NDE techniques with data from metallographic
examination.
Cavitation was studied in a sample of ternary Al–Mg–
Mn alloy deformed in tension at 400 °C under repeated
step changes in strain rate until failure by cavity coales-
cence and ductile fracture. In addition to metallographic
examination of the sectioned sample, two NDE tech-
niques were utilized: ultra-high-resolution (UHR) x-ray
computed tomography (CT) and pulse-echo ultrasonic
evaluation. UHR x-ray CT scans provided two-
dimensional images of the deformed sample’s cross-
section and a composite, three-dimensional image of its
interior. This is the first report of UHR x-ray CT being
used for such an application in a metal object.4–6 Pulse-
echo ultrasonic measurements were taken at three points
along the gage region of the deformed sample. These
data, when compared with data from undeformed mate-
rial, indicated the extent of cavitation in the sample.
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
II. EXPERIMENTAL PROCEDURE
quency of 15 MHz and a physical diameter of 5.4 mm.
The width of the contact surface between the search unit
and the sample was 2.3 mm. The sender provided a
pulsed ultrasonic signal, and a fast digitizing computer
board operating at 100 MHz acquired data from echoes
of the original signal. Data for signal amplitude were
obtained in both the time and frequency domains. Ultra-
sonic evaluation was conducted in an undeformed
sample and at three positions on the longest piece of the
failed sample: 13, 6, and 3 mm from the failure surface.
The composition of the aluminum sample studied is
provided in Table I. The sample was tested at 400 °C in
tension under repeated steps of constant true-strain rate,
calculated based on the assumptions of constant volume
and no neck formation.1,2 An initial prestrain of approxi-
mately 20% elongation was introduced to stabilize the
microstructure prior to stepping in strain rate. The range
of strain rates varied from a low value of 10−4 s−1 at the
first step to a high value of 2 × 10−2 s−1 at the last step of
each series, with seven intermediate steps making a total
of nine steps per series. Failure occurred during the sev-
enth step of the third series repetition, at a true strain of
0.90 (145% elongation). Data from this test have been
previously reported in the literature, and clearly indicate
deformation controlled by solute-drag creep.1,2 The pri-
mary factor limiting tensile ductility in this material un-
der the prescribed conditions was cavitation.1–3,7–10
C. X-ray CT
UHR x-ray CT involved scanning planar sections of
the failed sample’s longest piece, perpendicular to its
tensile axis. X-rays were produced using a microfocal
source with a spot size of approximately 20 ␮m, operated
at 150 kV and 0.153 mA. The detector system consisted
of a 229-mm image intensifier and a charge-coupled de-
vice video camera system. Each scan field had a diameter
of 4.7 mm and contained 3600 views with five samples
per view. Each sample used 1/30 s of data acquisition.
Each scan had a thickness of 30 ␮m and an offset be-
tween contiguous slices of 25 ␮m, providing 5 ␮m of
overlap for each pair of contiguous slices. Data were
taken by scanning three alternating slices simultaneously,
requiring two passes of interleaved scans to acquire data
in a continuous region. A region containing 36 contigu-
ous slices was scanned using this method. This region
extended from 1.2 to 2.1 mm below the failure surface.
An additional 30-␮m-thick scan slice was taken at
3.3 mm below the failure surface. Each data scan was
digitized and saved in both 12- and 8-bit formats. The
12-bit data files were used for all analysis.
A. Metallography
A segment from the longest piece of the failed sample
was subjected to UHR x-ray CT and pulse-echo ultra-
sonic evaluation prior to sectioning for metallography;
the procedures for these NDE techniques will be pre-
sented subsequently. Width and thickness were measured
with Vernier calipers at 2.5-mm increments along the
length of both pieces of the failed sample for calculation
of cross-sectional area reduction. After obtaining data
from nondestructive evaluation, the entire sample was
sectioned along its length. The longest piece of the failed
sample was then cut into three separate segments for
mounting in 32-mm-diameter molds for metallographic
preparation. The mounted samples were ground and pol-
ished using standard metallographic preparation tech-
niques. Measurements of cavity vol% were made at
several positions using the point-count technique after
polishing and prior to etching.11 Measurements were
made at a magnification of 32× using a grid-point spac-
ing of 2.5 mm. After measuring cavity vol%, metallo-
graphic etching was performed using Barker’s reagent
and an electrolytic technique. Microstructures were then
observed using an optical microscope with polarizing
filters.
III. RESULTS
A. Metallography
The longest piece of the failed sample is shown at the
top of Fig. 1 in a digital radiograph. Measurements of the
cross-sectional area at several positions along the sample
length were used to calculate true strain from area reduc-
tion, and these data are plotted against position in Fig. 1.
The data indicate a significant rise in strain near the
failure surface, as expected from necking. A composite
micrograph of the sample interior near the failure surface
is shown in Fig. 2 after being sectioned and polished.
Measurements of cavity vol% were made from a similar
composite micrograph at a magnification of 32×, taken
before electrolytic etching. These data for cavity vol%
are shown in the lower portion of Fig. 1, with the hori-
zontal axis corresponding to distance along the digital
radiograph.
B. Ultrasonic evaluation
Ultrasonic evaluation was conducted prior to section-
ing using a pulse-echo technique with a shear-wave
transducer. The ultrasonic search unit had a central fre-
TABLE I. Alloy composition in wt%.
Metallographic measurements of cavity vol% were
compiled from both pieces of the failed sample and are
plotted in Fig. 3 against true strain, measured from cross-
Al
Mg
Mn
Si
Fe
Cu
Zn
Ti
Balance
4.05
0.46
0.039
0.023
0.002
0.024
0.001
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
sectional area reduction. True strain was computed with
the constant-volume assumption, which neglects the ef-
fects of cavitation. True strain was not compensated for
the effects of cavitation in order that direct comparisons
to data in the literature can be made. These data indicate
the expected exponential increase of cavity vol% with
true strain. The data from Fig. 3 were evaluated on the
basis of the following equation:12
growth rate. In fitting Eq. (1) to the data of Fig. 3, the
reference strain was fixed at ⑀0 ס 0.25. A least-squares
fit resulted in the following relation:
CV ס 0.36 exp (2.81(⑀ − 0.25))
.
(2)
This fit to the data has a root-mean-square deviation of
rmsd ס 1.66. The cavity growth rate of ␩ ס 2.81 is
higher than that typically found in superplastic materials,
such as superplastic microduplex stainless steels, which
have a cavity growth rate of approximately two.10,13
CV ס CV exp (␩(⑀ − ⑀0))
,
(1)
0
in which CV is cavity vol%, CV is the concentration of
cavities at a reference strain of0 ⑀0, and ␩ is the cavity
B. Ultrasonic evaluation
The results of pulse-echo ultrasonic evaluation are pre-
sented in Fig. 4 as plots of relative (unitless) amplitude
against time and against frequency. Amplitude as a func-
tion of time is shown as dark traces plotted against the
top axis, and amplitude as a function of frequency is
shown as light traces plotted against the bottom axis.
Frequency data are from analysis of the first “back wall”
(BW) echo produced at each position using a fast Fourier
transform (FFT) method; i.e., the BW signal was gated
for analysis. Each graph of amplitude versus frequency
was scaled such that the maximum amplitude of the BW
echo reached full scale. Because of this scaling, the am-
plitudes of the frequency responses cannot be compared
between the four different graphs of Fig. 4. Data were
taken from an undeformed sample, graph I at the top of
Fig. 4, and three positions within the gage region of the
deformed sample. These three positions were located by
the distance, d, from the failure surface of the longest
piece of the failed sample. The positions were d ס 13 mm,
d ס 6 mm, and d ס 3 mm, which are given as positions
II, III, and IV, respectively, at the top of Fig. 1.
Consider data from the undeformed sample, given in
graph I at the top of Fig. 4. The initial pulse, which may
be considered as the response shown at label A in graph
I, initiated two echoes. The echo shown at label B was
the first BW echo from the back surface of the sample,
and the echo shown at C was a second BW echo pro-
duced from the portion of echo B reflected by the front
surface of the sample. The natural attenuation of the alu-
minum, without cavities, caused a decrease in amplitude
FIG. 1. A digital radiograph image is presented above plots of true
strain and cavity content versus position. Ultrasonic measurements
were made at positions labeled II, III, and IV on the radiograph image.
UHR x-ray CT data were taken at position a and from positions b to
c, as labeled on the radiograph image.
FIG. 2. This composite image from optical microscopy shows the interior of the long piece of the failed sample near the failure surface.
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
between echoes B and C. Natural attenuation signifi-
cantly suppressed echoes beyond C. Data from the un-
deformed material indicated the time of travel across the
sample thickness and back again, approximately 9.2 mm,
was 2.8 ␮s. The shear wave velocity was calculated from
these data to be 3300 m/s, approximately 6% higher than
the value of 3100 m/s typically reported in the litera-
ture.14 Measurements of signal velocity were not at-
tempted in the deformed sections. The central frequency
of the BW echo in the undeformed material was
11.2 MHz, which was a 25% decrease from the initial
pulse. The logarithmic decrement in the signal was meas-
ured to be ␦I ס 0.67. The thickness of the undeformed
sample was measured with calipers as tI ס 4.6 mm, giv-
ing an attenuation of ␣I ס 0.073 mm−1 [␣ ס ␦/(2t),
FIG. 3. Data from metallographic examination are plotted as cavity
vol% against true strain measured from area reduction.
where 2t is the distance traveled by the signal]. These
data from the undeformed sample, as well as data from
three positions on the longest piece of the failed sample,
are reported in Table II. The general trend of increasing
attenuation with increasing cavity concentration is ob-
served, except at location IV (Fig. 1). One explanation
for this is the dependence of attenuation on cavity sizes
and frequency, which will be addressed in Sec. IV.
C. X-ray CT
Images from UHR x-ray CT scans of planar cross-
sections in the deformed sample at the positions labeled
a, b, and c in Fig. 1 are given in Fig. 5. These positions
were 1.2, 2.1, and 3.3 mm below the failure surface, re-
spectively. The images clearly indicate an increase in
cavity concentration and typical cavity size near the fail-
ure surface. These images also indicate a reduction in
cross-sectional area near the failure surface, as was meas-
ured by mechanical means (see Fig. 1).
All odd scan slices from positions a to b in Fig. 1 and
the scan at position c were analyzed for cavity vol%. The
12-bit data were converted to 16-bit files and normalized
by the CT values of air and aluminum. A cutoff CT value
at 325/512 of full scale was used to distinguish pixels of
data representing cavities, below the cutoff, from pixels
of data representing aluminum, above the cutoff. The
limitations of these procedures will be addressed in Sec.
TABLE II. Data from ultrasonic evaluation of an undeformed sample,
location I, and three locations in the longest piece of the failed sample
(II–IV) are provided as distance from the failure surface (d), sample
thickness from measurement with calipers (t), logarithmic decrement
(␦), attenuation (␣), and cavity vol% from metallography (c).
FIG. 4. Data from pulse-echo ultrasonic evaluation are presented as
unitless amplitude against both time (dark traces measured against the
top scale) and frequency (light traces measured against the bottom
scale). Frequency data were taken by gating the signal from the first
back wall echo, labeled as B in each graph. The four graphs represent
I, an undeformed sample; II, a position 13 mm from the failure surface;
III, a position 6 mm from the failure surface; and IV, a position 3 mm
from the failure surface.
Location
d (mm)
t (mm)
␦
␣ (mm−1
)
c (%)
I
II
III
IV
иии
13
6
4.6
2.7
2.4
2.3
0.67
1.2
5.4
0.073
0.22
1.1
0.0
3.2
3.4
7.7
3
2.7
0.59
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
FIG. 5. (a–c) Three images from UHR x-ray CT data slices are pre-
sented. The images correspond to slices at positions a, b, and c, re-
spectively, of Fig. 1.
IV. Identically sized boxes of data were taken within
each slice for the computation of cavity vol%. The results
from calculations of cavity vol% are presented in Fig. 1.
Whereas the absolute value of cavity vol% depended
strongly on the cutoff CT value chosen, the gradient in
cavity vol% with position did not depend strongly on the
cutoff CT value. The cutoff CT value was chosen to
make the cavity vol% calculated from UHR x-ray CT
data match that measured by metallography and re-
mained the same at each position. The matching slopes of
data in Fig. 1 from UHR x-ray CT and metallography
FIG. 6. Images of UHR x-ray CT data are shown indicating the alu-
minum material (top) and the cavities (bottom) between positions b
and c indicated in Fig. 1.
confirm the choice of cutoff CT value and support the
accuracy of UHR x-ray CT data in measuring cavity vol%.
Data from the 36 contiguous scan slices taken in sec-
tion b–c, as labeled in Fig. 1, are presented in Fig. 6 as a
connected cavities along the direction of rolling passes,
three-dimensional reconstruction. The top image shows
as suggested by the very long cavity indicated by the
the aluminum material while the bottom image shows
bottom arrow in Fig. 7(b).
only the cavities. The bottom image is valuable in its
representation of cavity geometry. Long cavities, which
form by the interlinkage of several small cavities, are
clearly evident along the tensile axis.
B. Ultrasonic evaluation
Theoretical predictions of the expected ultrasonic re-
sponse due to cavities in the aluminum sample can aid
interpretation of data from ultrasonic evaluation. Attenu-
ation by spherical cavities in an elastic medium is a func-
tion of cavity radius, number density, and the frequency
of the ultrasonic signal.15,16 Analytical results for the
scattering cross section, ␥, of longitudinal elastic waves
by a single spherical cavity in an infinite medium are
available from Ying and Truell.15 Once ␥ has been cal-
culated for a single cavity, the attenuation of multiple,
noninteracting cavities is given by,16,19
IV. DISCUSSION
A. Metallography
The micrographs in Fig. 7 clearly show cavity forma-
tion at grain boundaries and triple points, as indicated by
arrows. The tensile axis is horizontal in Fig. 7, and is the
direction in which cavities are elongated. The aluminum
material in this investigation was previously found to
contain fine particulates, most likely Al6Mn proeutectic
products.1,2 Ternary aluminum alloys that contain par-
ticulates have been found to cavitate more readily than
binary Al–Mg alloys without such particulates.2 The par-
ticulates may act in conjunction with grain boundaries,
with which they are often associated, as locations of cav-
ity nucleation. Particulates can be present in stringers
along the direction of rolling passes; the direction of
rolling passes was the same as the tensile axis for the
sample under investigation. Stringers can result in inter-
1
␣ ס ⁄
2
n␥
,
(3)
where n is the number density of cavities. This attenua-
tion can be rewritten in terms of the nondimensional
function, ⌫, following the work of Adler et al.,16 which
depends on the nondimensional quantity ka, where k is
the magnitude of the wave vector and a is the cavity
radius. This formulation is convenient for computational
reasons, and yields the following relation:
␣ ס ␲a2n⌫
.
(4)
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
The central frequency of the input was assumed to
be 11.2 MHz, and its standard deviation was taken as
2.5 MHz, as is plotted in Fig. 8. The amplitude of the BW
frequency spectrum was then predicted for cavitated ma-
terial using the following equation:
O( f ) ס I( f ) exp (−␣x)
,
(5)
where x is the distance traveled by the signal, assumed
from the original sample thickness to be a constant value
of 9.2 mm, an assumption that neglects sample thinning.
The attenuation, ␣, was found from a sum of individually
calculated attenuations when more than one cavity radius
was assumed. For several different cavity sizes, each
with attenuation ␣i, total attenuation is given by
␣ =
␣
.
(6)
Α
i
i
The results of these calculations are presented in Fig. 9,
which contains three plots of relative (unitless) amplitude
versus frequency. The amplitude peak in each plot of
Fig. 9 was scaled to unity, as were the data of Fig. 4.
The frequency response plotted in Fig. 9(a) assumed a
cavity concentration of 6 vol% and a single cavity radius
of 140 ␮m. A bimodal response was produced which
closely resembles that of graph II (Fig. 4) in both shape
and frequencies of the peaks in amplitude. This bimodal
distribution was a direct result of a plateau in attenuation
at high values of ka, as is demonstrated in Fig. 10 for four
different cavity radii: 25, 50, 100, and 150 ␮m. A cavity
concentration of 5 vol% was assumed for the values cal-
culated in Fig. 10. The cavity size and density assumed to
predict the bimodal response shown in Fig. 9(a) did not
reproduce the volume fraction and diameters of cavities
evident at location II in Fig. 1 because of previously
discussed limitations in the analytical models used.
These predictions do, however, explain the origin of the
bimodal frequency response in Fig. 3, graph II.
FIG. 7. (a,b) Optical micrographs are shown from the failed sample.
The arrows indicate selected cavities.
Attenuation was calculated for cavitated aluminum in
this manner as a function of frequency, cavity concen-
tration, and cavity radius. These calculations predicted
the relative attenuation at various frequencies for as-
sumed cavity radii and number densities. These theoreti-
cal predictions were used to qualitatively predict the
shapes of BW frequency responses, but not the logarith-
mic decrement in amplitude of the signal. These analyti-
cal models assume longitudinal elastic waves scattered
by spherical, noninteracting cavities and do not allow the
exact prediction of ultrasonic data obtained in this study,
which used shear waves. These models, however, are
extremely valuable when used to predict the general be-
haviors observed and determine the causes of these
behaviors.
The amplitude of an input frequency spectrum is mod-
eled by a function I( f ), where f is frequency. A normal
distribution of frequency was assumed for the input spec-
trum, and its peak amplitude was scaled to a value of one.
FIG. 8. The input signal used for theoretical predictions of frequency
response is plotted as amplitude against frequency.
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
The plateau in attenuation versus frequency (Fig. 10)
has another important ramification. The total attenuation
predicted below 20 MHz in Fig. 10 for 5 vol% of cavities
with a radius of 100 ␮m is greater than that for 5 vol% of
cavities with a radius of 150 ␮m. This apparent contra-
diction of larger cavities providing less attenuation is a
result of two effects: (i) a change in both the height and
edge location of the plateau in attenuation with changing
cavity radius, and (ii) a decrease in cavity number density
with an increase in cavity radius at a constant cavity
vol%. Herein lies an explanation for the ultrasonic data
indicating ␣IV < ␣III, Fig. 4 and Table II, despite a higher
cavity concentration at position IV than at III. A larger
average cavity radius at position IV than at III could
mimic the predictions in Fig. 10, leading to less attenu-
ation at position IV. This result is most likely when an
increase in average cavity radius shifts the attenuation
plateau edge to a frequency equal to or less than that of
the test signal, considered to be approximately 11.2 MHz
in the present study.
The BW response shown in Fig. 9(b) was produced by
considering three different cavity sizes acting simulta-
neously. The cavity radii and concentrations assumed
were 25 ␮m at 2 vol%, 50 ␮m at 2 vol%, and 125 ␮m at
4 vol%. The predicted response gave a plateau stretching
over several MHz in frequency, which is quite similar to
data in graph III of Fig. 4. The final BW response pre-
dicted is shown in Fig. 9(c), which assumed cavity radii
and concentrations of 50 ␮m at 8 vol%, 125 ␮m at
2 vol%, and 150 ␮m at 2 vol%. Fig. 9(c) is similar to
graph IV of Fig. 4.
These predictions based on analytical results were able
to reproduce the shapes of BW frequency responses and
provide explanations for these shapes. Experiments that
measure cavity size and concentration have been con-
ducted by Adler et al., who used a wide spectrum of
frequencies in order to measure the edge of the plateau in
attenuation versus frequency.16 Such measurements, al-
though beyond the scope of the present investigation,
provide very useful information on cavity size.16 Practi-
cal application of ultrasonic evaluation to the determina-
tion of part quality degradation from cavitation may not
require such advanced techniques. Graphs II through IV
in Fig. 4 clearly indicate the presence of cavitation in the
deformed material. In addition, differences in attenuation
were clearly evident between undeformed material
(Fig. 4, graph I), slightly cavitated material (Fig. 4,
graph II), and extensively cavitated material (Fig. 4,
graphs III and IV). Qualification of an industrial inspec-
tion process may require only the use of a few standard
samples with and without cavitation to regularly calibrate
the technique used in this investigation.
FIG. 9. (a–c) Three predicted frequency responses are plotted as unit-
less amplitude against frequency.
C. X-ray CT
A histogram of the UHR x-ray CT values at position c
of Fig. 1 is presented in Fig. 11. The left peak represents
data for air outside the sample volume. The right peak
represents pixels of data corresponding to aluminum ma-
terial with internal cavitation. It is noted that there is no
peak in Fig. 11 that corresponds to the cavities within the
sample volume. The primary reason for this is that the
pixels that included cavities tended to also include some
aluminum, and thus had CT values that reflected an av-
FIG. 10. Predictions of attenuation are plotted against frequency for
four different cavity radii.
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E.M. Taleff et al.: Nondestructive evaluation of cavitation in an Al–Mg material deformed under creep conditions
(2) Analytical predictions of frequency response from
the scattering of noninteracting, spherical cavities in alu-
minum produced frequency response curves similar to
those obtained by ultrasonic evaluation and explains the
origins of their shapes.
(3) UHR x-ray CT data were used to image cavity
morphology during the later stages of cavity growth and
interlinkage, where structures were significantly larger
than 25 ␮m.
(4) After calibration using accurate metallographic
data for cavity vol%, UHR x-ray CT data were used to
quantitatively measure cavity vol%.
FIG. 11. A histogram of UHR x-ray CT data from a scan slice at
position a of Fig. 1 is shown.
ACKNOWLEDGMENTS
This work was supported by the National Science
erage between the end-members of aluminum and air.
Foundation under Grant No. DMR-9702156. Additional
This partial-volume effect was accentuated by slight
support for this work was provided by Reinhart and As-
blurring, attributed to the finite resolution of the data and
sociates, Inc., Austin, Texas. UHR x-ray CT data and
the image reconstruction process, causing pixel values to
images were produced at the High-Resolution X-Ray
be slightly contaminated by material from surrounding
Computed Tomography Facility of the University of
pixels. Because of these factors, data for cavities spanned
Texas at Austin, supported by National Science Founda-
the continuum from the left slope of the right peak in the
tion Grant No. EAR-9816020. The authors thank Dr.
histogram to the right slope of the left peak.
Donald R. Lesuer of Lawrence Livermore National
The approach to cavity vol% calculations employed
Laboratory for providing the aluminum sample. The lead
here required calibration of a cutoff CT value, for which
author thanks Professor Mark Hamilton for useful dis-
cussions on the subject of scattering phenomena.
data from metallographic evaluation were used. A more
independent and rigorous porosity calculation can also be
used that explicitly takes partial-volume effects into ac-
count, but requires careful calibration of the CT values of
the end-member materials, in this case nonporous alumi-
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UHR x-ray CT provided measurements of cavity vol% in
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