SIMULTANEOUS MEASUREMENT OF GRAIN SIZE AND SHAPE
FROM ULTRASONIC BACKSCATTERING MEASUREMENTS
MADE FROM A SINGLE SURFACE
Y. Guo, R. B. Thompson, and F. J. Margetan
Center for Nondestructive Evaluation
Iowa State University
Ames, Iowa 50011, USA
ABSTRACT. Ultrasonic techniques for the characterization of grain size have been investigated for
over two decades, including important practical applications. Generally, however, these make the
assumptions that the grains are equi-axed. In this paper, we consider the more general case in which
the grains are elongated. Inversion procedures are presented to infer the geometrical parameters of
the grains from various combinations of attenuation and backscattering data. To provide a theoretical
foundation, an expression is presented relating the ultrasonic backscattering coefficient to the
geometrical parameters of the grains for shear incidence waves and its experimental verification is
reported. This complements previously reported theories for backscattering and attenuation of
longitudinal waves. Measurement results are presented which demonstrate the effectiveness of these
new sizing approaches on a set of aluminum samples that were rolled as either rods or plates. One of
the techniques has the major practical advantage that all data (backscattering) can be taken from the
single side of a sample with no requirements for a parallel back surface.
INTRODUCTION
The characterization of the microstructure of materials is an important NDE
application, with a primary motivation being the control of mechanical properties.
Ultrasonic measurements have a long history of application in this area based on the
dependence of both attenuation and backscattering on grain size [1-3]. Early approaches
were based on a direct measurement of attenuation, an application restricted to parts with
parallel surfaces [1,2]. The desire for a technique for single sided measurements on parts
of complex geometry led to a backscattering approach [3]. However, the objective
remained to infer grain size from attenuation, with the latter being inferred from the rate
of decay of the backscattered noise. Most recently, Good has used the time dependence of
the backscattered noise to gain information about microstructural changes, for example
those associated with hardening processes [4].
All of these techniques have produced valuable results in appropriate application
areas. However, to the knowledge of the authors, the primary applications have been to
microstructures in which the grains are equi-axed. It can be speculated that this is a direct
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
1347
consequence of the fact that only a single parameter is inferred from the measurements,
e.g. the attenuation. Obviously, one parameter can only provide information about a
single attribute of the microstructure, e.g. grain size. In this work, we seek new
techniques that can provide information on both grain size and shape.
The motivation for our approach was a series of measurements reported in a
previous volume of this series [5]. Measurements of attenuation and backscattering were
reported on a set of aluminum samples with elongated grains produced by rod and plate
rolling. It was observed that, whereas the backscattering was highly anisotropic as
expected, the attenuation varied only slightly with direction. In the concluding remarks, it
was suggested that a better understanding of these effects could lead to improved
techniques for microstructural characterization. Further discussion of the initial
observations has been provided by Thompson [6].
In this paper, we will describe three methods that were examined with the
objective of the simultaneous determination of" grain size and shape. The initial
motivation was to take advantage of this fundamental difference in the dependence of
attenuation and backscattering on grain parameters. After a brief review of the sample
characteristics, the three methods will be described. The first two were motivated by
gaining an increased understanding of the underlying measurement principles and impose
restrictions on the sample geometry. The final technique utilized only data that could be
obtained from one surface without the availability of a second, parallel surface.
SAMPLES
The aluminum alloy samples, including micrographs, have been previously
described [5,6]. Table 1 lists the average grain dimensions, as inferred from an analysis of
micrographs. Two samples had "cigar-shaped" grains, with an elongation of more that
10:1. The other two had "pancake-shaped" grains, also with an aspect ratio of more that
10:1. In both cases, the defects were ellipsoidal rather than spheroidal, i.e. there was no
axis of rotational symmetry.
THEORY
A theoretical description of the effects of grain elongation on attenuation and
backscattering is a key element of our approaches. Description of those theories is beyond
the scope of this paper. The starting points are theories initially reported by Stanke and
Kino for attenuation [7] and Rose for backscattering [8] for equi-axed grains . Extensions
to elongated grains and other complex microstructures include contributions by Ahmed,
Han and Panetta, and references to those works may be found in [6]. The predictions of
those theories have been found to be in semi-quantitative agreement with the previously
reported measurements on the aluminum samples that are the subject of this study [5].
TABLE 1. Average grain dimensions (semi-axes) in microns.
Sample
Tl
T2
T3
T4
2-axis (b)
45
17
60
65
1-axis (a)
52
35
170
183
1348
3-axis (c)
539
420
17
12
METHOD A: SIMULTANEOUS MEASUREMENT OF ATTENUATION AND
BACKSCATTERING
METHOD A: SIMULTANEOUS MEASUREMENT OF ATTENUATION AND
BACKSCATTERING
The basic idea in Method A is to measure both the attenuation and the absolute
level ofThe
thebasic
backscattering,
as Aquantified
by aboth
material
propertyand
known
as the
idea in Method
is to measure
the attenuation
the absolute
backscattering
for waves
propagating
single direction,
normal
level of the coefficient,
backscattering,
as quantified
by in
a amaterial
property i.e.,
known
as to
thea
part
surface. Grain
size parameters
attenuation
backscattering
models
are to
then
backscattering
coefficient,
for waves in
propagating
in and
a single
direction, i.e.,
normal
a
adjusted
to optimize
experiment
theory. In models
our employment
part surface.
Grain the
sizeagreement
parametersbetween
in attenuation
and and
backscattering
are then
ofadjusted
the technique,
we have
assumed that
a sample
is available
with two
parallel
surfaces.
to optimize
the agreement
between
experiment
and theory.
In our
employment
However,
we
note
that
the
same
information
could
be
obtained
with
single-sided
access if
of the technique, we have assumed that a sample is available with two parallel surfaces.
the
attenuation
werethat
inferred
frominformation
the rate of decay
of the
backscattered
noise [3].access if
However,
we note
the same
could be
obtained
with single-sided
Figure 1were
illustrates
basic
this plot,
grains werenoise
assumed
the attenuation
inferredthefrom
theidea.
rate ofIndecay
of thethe
backscattered
[3]. to have
two of the
three1 major
axesthe
(a,b,c)
Thethis
wave
to propagate
in have
the b
Figure
illustrates
basicequal.
idea. In
plot,was
the assumed
grains were
assumed to
direction
andthree
it was
assumed
that a =equal.
b for The
samples
andassumed
T2, andtob propagate
= c for samples
two of the
major
axes (a,b,c)
waveT1was
in the T3
b
and
T4. The
ratio (b/c
fora =
T1b and
T2, b/a Tl
forand
T3 T2,
andand
T4)b would
small T3
for
direction
and itaspect
was assumed
that
for samples
= c for be
samples
samples
andaspect
T2 and
forTlsamples
PartT4)
(a)would
showsbea small
plot offora
and T4. T1The
ratiolarger
(b/c for
and T2,T3b/aand
forT4.
T3 and
theoretical
of attenuation,
at a frequency
as shows
a function
of of
grain
samples Tlprediction
and T2 and
larger for samples
T3 and of
T4.7 MHz,
Part (a)
a plot
a
volume
andprediction
aspect ratio.
It is interesting
to note of
that,
for theas range
of parameters
theoretical
of attenuation,
at a frequency
7 MHz,
a function
of grain
volume and
ratio.is much
It is interesting
to note
that, volume
for thethan
range
of shape.
parameters
examined,
the aspect
attenuation
more sensitive
to grain
grain
Part
examined,
the attenuation
much
grain volume than
grain shape.
Part
(b)
shows the
comparableisplot
formore
the sensitive
predictedtobackscattering
coefficient,
a material
(b) shows
comparable
plot for of
thethe
predicted
backscattering
coefficient,
a material
property
thatthe
quantifies
the capacity
microstructure
to generate
noise. Techniques
quantifies thecoefficient
capacity of
microstructure
to generate
noise. Techniques
toproperty
infer thethat
backscattering
or the
its square
root (FOM)
from experimental
data are
to infer the
backscattering
or its
root
from experimental
data are
discussed
elsewhere
[9]. Itcoefficient
is interesting
to square
note that
the(FOM)
dependence
of the backscattering
discussed
[9]. It isparameters
interesting to
the dependence
thethe
backscattering
on
the twoelsewhere
microstructural
is note
quitethat
different
than thatofof
attenuation,
on the twowith
microstructural
parameters
different data.
than that
of suggests
the attenuation,
consistent
the previously
reportedis quite
experimental
This
that a
consistent with
the previously
reported experimental
data.
suggests
a
measurement
of attenuation
and backscattering
on the same
sampleThis
would
providethat
a way
of determine
attenuationgrain
and backscattering
on the
samePart
sample
would provide
tomeasurement
independently
volume and aspect
ratio.
(c) illustrates
this inaaway
plot
to independently
grain volume
ratio. value
Part (c)
this in a plot
of
grain volume determine
versus aspect
ratio. and
Foraspect
a given
of illustrates
either attenuation
or
of
grain
volume
versus
aspect
ratio.
For
a
given
value
of
either
attenuation
or
backscattering alone, there is a family of {volume, aspect ratio} pairs, lying on a curved
backscattering
alone,
there is aforfamily
of {volume,
aspect ratio}
pairs, lying on
a curvedif
line,
that could be
responsible
that value
of attenuation
or backscattering.
However,
line,
that
could
be
responsible
for
that
value
of
attenuation
or
backscattering.
However,
if
attenuation and backscattering have both been measured, the grain volume and aspect
attenuation
and
backscattering
have
both
been
measured,
the
grain
volume
and
aspect
ratio are uniquely defined by the intersection of these lines. It is interesting to note, that
ratiothearecase
uniquely
definedthebytwo
the intersection
theseorthogonal,
lines. It is indicating
interesting that
to note,
for
illustrated,
curves are of
nearly
the that
two
for the case illustrated,
the two on
curves
are nearlyoforthogonal,
measurements
have good leverage
the quantities
interest. indicating that the two
measurements have good leverage on the quantities of interest.
K10 6
Volume (Micron**3)
FIGURE
FIGURE1.1.(continued)
(continued)
Volume (Micron**3)
(a)
(a)
(b)
(b)
1349
6
x 10
5
6
x 10
5
4.5
fixed backscattering
fixedbackscattering
attenuation
fixed
fixed attenuation
4.5
4
r
4
3.5
) 3.5
3
3
)**
n
3*o
3
*r
nci 2.5
orM
ci ( 2.5
e
M
(m
2
eul
2
mo
ulV 1.5
o
V 1.5
1
1
0.5
0.5
0
0 0
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
1
1.2
0.8 Aspect
1 ratio
1.2
Aspect ratio
1.4
1.4
1.6
1.6
1.8
1.8
2
2
(c)
(c)
FIGURE 1. Determination of grain size and shape from attenuation and backscattering data. (a)
FIGURE 1.
1. Determination
Determination of
of grain
grain size
size and
and shape
shape from attenuation
attenuation and
andbackscattering
backscatteringdata.
data, (a)
(a)
Attenuation versus
grain volume
and aspect
ratio atfrom
7 MHz. (b) Backscattering
versus grain volume
and
Attenuation versus grain
grain volume
volume and
and aspect ratio
ratio atat 77 MHz.
MHz. (b)
(b) Backscatteringversus
versusgrain
grainvolume
volumeand
and
aspect ratio at 7 MHz. (c)
Illustrationaspect
of determination
of grain Backscattering
volume and aspect ratio
from knowledge
of
aspect ratio at 7 MHz.
MHz. (c)
(c) Illustration
Illustration of
ofdetermination
determinationof
ofgrain
grainvolume
volumeand
andaspect
aspect-1ratio
ratiofrom
fromknowledge
knowledge
ofof
3
attenuation and backcscattering. (Units: Attenuation, Np/cm, backscattering, cm-11 , volume, µm3 3.)
attenuation and backcscattering.
backcscattering. ((Units:
Attenuation, Np/cm,
Np/cm, backscattering,
backscattering,cm
cm' ,,volume,
volume,µm
Jim.).)
Units: Attenuation,
300
300
600
600
Micrograph
Micrograph
500
Ultrasound
§500
500
Ultrasound
400
|
400 400
300
0^300
300 H
N
200
^200
200 100
T2
'£ 100
100
T2
0
0
0o
1-axis
2-axis
3-axis
400
2-axis
3-axis
400 n 1-axis
_400
Micrograph
Direction
T4
C/5
Micrograph
Micrograph
Direction
T4
Ultrasound
300
Ultrasound
Ultrasound
300
§300
Grain
GrainSize
Size(microns)
(microns)
600
600
500
500
400
400
300
300
200
200
100
100
0
0
400
400
Micrograph
Micrograph
Ultrasound
Ultrasound
T1
T1
1-axis
1-axis
2-axis
2-axis
Micrograph
Direction
Micrograph
Direction
Ultrasound
Ultrasound
3-axis
3-axis
T3
T3
Grain
GrainSize
Size(microns)
(microns)
Grain
GrainSize
Size(microns)
(microns)
Grain
GrainSize
Size(microns)
(microns)
Figure 2 presents results of an experimental test of this idea. The previously
Figure
2 presents
presents results
results of
of an
an experimental
experimental test
test of
of this
this idea.
idea. The
The previously
previously
measured values of the attenuation and backscattering served as inputs and the data was
measured values of
of the
the attenuation
attenuation and
and backscattering
backscattering served
served as
as inputs
inputs and
and the
the data
datawas
was
interpreted using the procedures illustrated in Figure 1. In this comparison, it had to be
interpreted using the
the procedures
procedures illustrated
illustrated in
in Figure
Figure 1.1. In
In this
this comparison,
comparison, itithad
hadtotobe
be
assumed that a = b for the grains. There is good overall agreement between the predicted
for the grains.
grains. There
There is
is good
good overall
overall agreement
agreement between
between the
the predicted
predicted
assumed that aa == bb for
and observed values of the grain size parameters.
of the
the grain
grain size
size parameters.
parameters.
and observed values of
200
200
N
C/)
100
100
0
0
200
200
100
.£ 100
100
05
5
1-axis
1-axis
1-axis
2-axis
3-axis
2-axis
3-axis
2-axis
3-axis
Direction
Direction
Direction
0
0o
1-axis
1-axis
1 -axis
2-axis
3-axis
2-axis
2-axis 3-axis
3-axis
Direction
Direction
Direction
FIGURE 2. Comparison of ultrasonically predicted and actual grain sizes for all samples based on Method
FIGURE
2.
FIGURE
2. Comparison
Comparisonof
ofultrasonically
ultrasonicallypredicted
predictedand
andactual
actualgrain
grainsizes
sizesfor
forall
allsamples
samplesbased
basedon
onMethod
Method
A.
A.
A.
1350
L-wave
.rwave
L-wave
L-wave T-wave
T-wave
T wave
'
1-axis
1-axis
1-axis
'* !-axis
3-axis
L-wave
L-wave
2-axis
3-axis
2-axis
L-wave
L-wave
FIGURE 3. Schematic illustration of Methods B (left) and C (right) based on backscattering measurements
FIGURE
3. Schematic illustration of Methods B (left) and C (right) based on backscattering measurements
alone.
alone.
METHOD B: MEASUREMENT OF BACKSCATTERING FOR WAVES
METHOD
B: MEASUREMENT
OF BACKSCATTERING
FOR WAVES
PROPAGATING
IN THREE ORTHOGONAL
DIRECTIONS
PROPAGATING IN THREE ORTHOGONAL DIRECTIONS
Since the backscattering is more sensitive to the grain aspect ratio than is the
Since the backscattering is more sensitive to the grain aspect ratio than is the
attenuation,
and since backscattering measurements do not require parallel surfaces, the
attenuation, and since backscattering measurements do not require parallel surfaces, the
possibility
of
recovering grain
grain size
size and
andshape
shapefrom
frombackscattering
backscatteringmeasurements
measurementsalone
alone
possibility of recovering
was
examined.
Figure
3
illustrates
both
Method
B
and
Method
C.
In
the
former,
was examined. Figure 3 illustrates both Method B and Method C. In the former, thethe
longitudinal wave
wave backscattering
backscattering isis measured
measured for
for waves
wavespropagating
propagatingalong
alongthree
three
longitudinal
orthogonal
directions.
Although
this
is
generally
not
possible
in
the
laboratory,
it
provides
orthogonal directions. Although this is generally not possible in the laboratory, it provides
means of
of examining
examining the
the leverage
leveragethat
thatbackscattering
backscatteringhas
hasononthethegrain
grainsize
sizeand
andshape.
shape.
aa means
For future
future reference,
reference, the
the configuration
configuration used
used inin Method
Method CCis isalso
alsoshown.
shown. The
The
For
backscattering is
is measured
measured for
forlongitudinal
longitudinalwaves
wavesatatnormal
normalincidence
incidenceand
and
transverse
backscattering
forfor
transverse
waves at
at oblique
oblique incidence
incidencein
intwo
twoorthogonal
orthogonalplanes.
planes.
waves
To
test
Method
B,
an
algorithm
was
written
whichdata
datapropagating
propagating
three
To test Method B, an algorithm was written ininwhich
in in
thethe
three
orthogonal
directions
was
compared
to
the
theoretical
predictions
of
the
backscattering
orthogonal directions was compared to the theoretical predictions of the backscattering
models [6,8].
[6,8]. The
The degree
degree of
of agreement
agreementininaaleast
leastsquares
squaressense
sensewas
wascomputed
computedand
and
models
thethe
values of
of the
the grain
grain size
size and
and shape,
shape, (a,b,c),
(a,b,c),were
werevaried
variedtotoobtain
obtainbest
bestfit.fit.Figure
Figure4 4shows
shows
values
the results.
results. Although
Although there
there appear
appear totobebesome
somesystematic
systematicdisagreements
disagreementsforforthethelarger
larger
the
dimensions, there
there isis generally
generallygood
goodagreement.
agreement.
dimensions,
METHOD C:
C: SINGLE-SIDED
SINGLE-SIDEDMEASUREMENT
MEASUREMENTOF
OFBACKSCATTERING
BACKSCATTERING
FOR
METHOD
FOR
NORMAL LONGITUDINAL
LONGITUDINALAND
ANDOBLIQUE
OBLIQUESHEAR
SHEARWAVES
WAVES
The
ofof
Figure
3. 3.ToTo
The basic
basic strategy
strategyof
ofMethod
MethodCCisissketched
sketchedininthe
theright
righthand
handside
side
Figure
test this, a theory
was
developed,
theory for
for the
thebackscattering
backscatteringcoefficient
coefficientfor
fortransverse
transversewaves
waves
was
developed,
with the result
result (for
(for cubic
cubic crystallites
crystalliteswith
withrandomly
randomlyoriented
orientedprincipal
principalaxes)
axes)
η (ω ) =
3k 4 ( C11 − C12 − 2C 44 )
(
175 4πρ v
2
t
)
2
1351
2
v
ò P (s) e
v
2 ikˆe⋅ s
v
d 3s
(1)
400
300
200
T1
100
0
1-axis
Grain Size (microns)
Grain Size (microns)
500
Micrograph
Ultrasound
400
300
2-axis
Direction
Micrograph
Ultrasound
3-axis
Grain Size (microns)
Grain Size (microns)
600
600 i
T3
200
100
0
11-axis
-axis
2-axis 3-axis
3-axis
2-axis
Direction
Direction
600
500
Micrograph
Ultrasound
400
300
200
T2
100
0
1-axis
2-axis
3-axis
1 -axis
2-axis
3-axis
Direction
400
Micrograph
T4
Ultrasound
300
200
100
0
1-axis
1 -axis
2-axis 3-axis
3-axis
2-axis
Direction
Direction
FIGURE 4.
4. Comparison
Comparisonofofultrasonically
ultrasonicallypredicted
predictedand
andactual
actual
grain
sizes
samples
based
Method
grain
sizes
forfor
samples
based
on on
Method
B. B.
FIGURE
where pρ is
is the
the density,
density,vvisisthe
thetransverse
transversewavespeed,
wavespeed,C/yCare
crystallite
elastic
constants,
where
crystallite
elastic
constants,
k k
IJ are
v
theprobability
probabilitythat
thattwo
tworandomly
randomly
selected
points,
separated
is the
the wavevector,
wavevector, and
andP(s)
P( s )isisthe
is
selected
points,
separated
v
by
a
vector
s
,
lie
in
the
same
grain.
It
is
interesting
to
note
that,
for
a
given
material
andand
by vector s , lie in the same grain. It is interesting to note that, for a given material
frequency,
larger
than
thatthat
forfor
frequency, the
the predicted
predictedtransverse
transversewave
wavebackscattering
backscatteringis issignificantly
significantly
larger
than
longitudinal
is is
shorter
forfor
transverse
longitudinal waves.
waves. This
Thisisisaaresult
resultofoftwo
twoeffects,
effects,thethewavelength
wavelength
shorter
transverse
waves
which
is the
physical
waves and
and hence
hence closer
closer totothe
thegrain
grainsize,
size,and
andthe
theelastic
elasticanisotropy,
anisotropy,
which
is the
physical
cause for
forfor
longitudinal
waves.
for the
the backscattering,
backscattering,isisgreater
greaterfor
forshear
shearwaves
wavesthan
than
longitudinal
waves.
Figure
Figure 55 shows
shows aa test
test ofof this
this theory
theory against
againstnew
newmeasurements
measurementsof ofthethe
backscattering
for
transverse
waves
propagating
at
45
degrees
with
respect
to to
thethe
sample
backscattering for transverse waves propagating at 45 degrees with respect
sample
normal.
The
4-axis
and
5-axis
correspond,
respectively,
to
propagation
in
the
1-2
plane
normal. The 4-axis and 5-axis correspond, respectively, to propagation in the 1-2
plane
and the
were
input
to to
and
the 2-3
2-3 plane
plane respectively
respectively(see
(seeFig.
Fig.3).
3). Measured
Measuredgrain
grainsize
sizeparameters
parameters
were
input
the
model,
and
reasonably
good
agreement
with
experiment
is
observed
with
no
adjustable
the model, and reasonably good agreement with experiment is observed with no adjustable
model parameters.
model
parameters.
As
thethe
backscattering
As was
was done
done for
for Method
MethodB,B,ananalgorithm
algorithmwas
waswritten
writtenininwhich
which
backscattering
data
for
longitudinal
and
transverse
waves
propagating
in
the
various
directions
data for longitudinal and transverse waves propagating in the various directionswaswas
compared to the theoretical predictions of the backscattering models. The degree of
compared to the theoretical predictions of the backscattering models. The degree of
agreement in a least squares sense was computed and the values of the grain size and
agreement in a least squares sense was computed and the values of the grain size and
shape, (a,b,c), were varied to obtain a best fit. Figure 6 shows the results, which are very
shape, (a,b,c), were varied to obtain a best fit. Figure 6 shows the results, which are very
similar to those obtained with Method B. Although there appear to be some systematic
similar
to thoseforobtained
with
Method B.
Although
theregood
appear
to be some
disagreements
the larger
dimensions,
there
is generally
agreement.
Thissystematic
is very
disagreements
for
the
larger
dimensions,
there
is
generally
good
agreement.
very
encouraging since this data was obtained in a single-sided measurement and This
doesisnot
encouraging
since
this
data
was
obtained
in
a
single-sided
measurement
and
does
require a second, parallel surface. We note that for all three techniques we assumed thenot
require
a second, of
parallel
surface. We
that forthat
all crystalline
three techniques
we assumed
elastic constants
pure aluminum,
andnote
assumed
axes were
randomlythe
elastic
constants
of
pure
aluminum,
and
assumed
that
crystalline
axes
were
randomly
oriented.
oriented.
1352
0.25
0.20
0.15
Exp (4-axis)
The (4-axis)
Exp (5-axis)
The (5-axis)
0.10
0.05
0.00
0
0.30
,0.30
Figure of Merit (cm**-0.5)
Figure of Merit (cm**-0.5)
T1
5
10
15
10
15
Frequency
Frequency (MHz)
(MHz)
Exp (5-axis)
The (5-axis)
Exp 4-axis)
The (4-axis)
0.25
0.20
T3
0.15
0.10
0.05
0.00
0.00
00
55
10
15
10
15
Frequency
Frequency (MHz)
(MHz)
0.30T
0.30
0.25
0.20
0.10
T2
0.05
0.00
0
20
20
Exp (4-axis)
The (4-axis)
Exp (5-axis)
The (5-axis)
0.15
20
20
Figure of Merit (cm**-0.5)
Figure of Merit (cm**-0.5)
0.30
,0.30
0.30
0.30
5
10
15
5
10
15
Frequency (
(MHz)
Frequency
MHz)
Exp (5-axis)
The (5-axis)
Exp (4-axis)
The (4-axis)
0.25
0.20
20
20
T4
0.15
0.10
0.05
0.00
00
55
10
15
10
15
Frequency (MHz)
(MHz)
Frequency
20
20
FIGURE
to experiment.
experiment.
FIGURE 5.
5. Comparison
Comparison of
of the
the theory
theory for
for transverse
transverse wave
wave backscattering
backscattering to
CONCLUSIONS
CONCLUSIONS
Three
determining grain
grain size
size and
and shape
shape were
were
Three methods
methods for
for simultaneously
simultaneously determining
evaluated
based on
on rolled
rolled rod
rod and
and plate
plate of
of an
an aluminum
aluminum alloy.
alloy. Each
Each
evaluated based
on measurements
measurements on
measurement
to produce
produce good
good results.
results. Method
Method A
A requires
requires both
both
measurement scheme
scheme was
was shown
shown to
attenuation
waves propagating
propagating in
in the
the same
same direction.
direction.
attenuation and
and backscattering
backscattering information
information for
for waves
Although
with parallel
parallel surfaces,
surfaces, this
this could
could be
be
Although our
our measurements
measurements were
were made
made in
in samples
samples with
implemented
were inferred
inferred from
from the
the rate
rate of
of decay
implemented from
from aa single
single surface
surface if
if the
the attenuation
attenuation were
decay
of
of the
the backscattering.
backscattering.
Method
practical application,
application, but
but as
as aa test
test of
of the
the leverage
leverage
Method B
B was
was not
not intended
intended for
for practical
of
the needed
needed size
size and
and shape
shape
of backscattering
backscattering data
data at
at multiple
multiple angles
angles in
in gathering
gathering the
information.
information. The
The positive
positive results
results led
led to
to the
the evaluation
evaluation of
of Method
Method C,
C, which
which has
has the
the desired
desired
attributes
for aa second,
second, parallel
parallel
attributes of
of aa single
single sided
sided measurement
measurement without
without the
the requirement
requirement for
surface.
surface.
These
be imagined,
These measurements,
measurements, and
and variants
variants that
that could
could be
imagined, show
show great
great promise
promise of
of
extracting
than is
is commonly
extracting more
more information
information about
about grain
grain size
size and
and shape
shape than
commonly done.
done. A
A key
key
ingredient
ingredient is
is aa theoretical
theoretical basis
basis to
to interpret
interpret multiple
multiple measurements,
measurements, in
in one
one sense
sense aa form
form of
of
data
data fusion.
fusion.
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
This
Cooperative Research
This work
work was
was supported
supported by
by the
the NSF
NSF Industrial/University
Industrial/University Cooperative
Research
Program
Program in
in Nondestructive
Nondestructive Evaluation.
Evaluation.
1353
600
500
§500 -
400 -| 400
300
300 0 300
200
200
<^ 200
100
100 £ 100
0
0
N
0
1-axis
Grain Size (microns)
T1
400
2-axis
Direction
Micrograph
Ultrasound
300
3-axis
400
400
T3
Micrograph
-^-Micrograph
Ultrasound
~*~~ Ultrasound
300\
300
|
T2
T2
/
/ s~
*^^//^
11-axis
-axis
Grain Size (microns)
Grain Size (microns)
Micrograph
Ultrasound
Grain Size (microns)
600
'c/T 500
§500
400
_600
i
I
2-axis 3-axis
3-axis
2-axis
Direction
Micrograph
Ultrasound
T4
T4
E,
200
0)200
200
.N
CO
100
100.E 100
0
11-axis
-axis
2-axis
3-axis
2-axis
3-axis
Direction
Direction
0
11-axis
-axis
2-axis 3-axis
3-axis
2-axis
Direction
Direction
FIGURE6.6. Comparison
Comparisonofofultrasonically
ultrasonicallypredicted
predictedand
andactual
actualgrain
grainsizes
sizesfor
forsamples
samplesbased
basedononMethod
MethodC.C.
FIGURE
REFERENCES
REFERENCES
1.1.
2.2.
3.
3.
4.4.
5.5.
6.
6.
7.7.
8.
8.
9.
9.
E.P.P.Papadakis,
Papadakis,"Ultrasonic
“UltrasonicAttenuation
AttenuationCaused
CausedbybyGrain
GrainScattering
ScatteringininPolycrystalline
Polycrystalline
E.
Metals”,/.J.Acoust.
Acoust.Soc.
Soc.Am.,
Am.,37,
37,p.p.711
711(1965).
(1965).
Metals",
E.R.
R.Generazio,
Generazio,"Scaling
“ScalingAttenuation
AttenuationData
DataCharacterizes
CharacterizesChanges
ChangesininMaterial
Material
E.
Microstructure”,Mater.
Mater.Eval.
Eval.49,
49,p.p.198
198(1986).
(1986).
Microstructure",
K.Goebbels,
Goebbels,"Structure
“StructureAnalysis
Analysisby
byScattered
ScatteredUltrasonic
UltrasonicRadiation",
Radiation”,ininResearch
Research
K.
TechniquesininNondestructive
NondestructiveTesting,
Testing,Vol.
Vol.IV,
IV,R.R.S.S.Sharpe,
Sharpe,Ed.
Ed.(Academic
(AcademicPress,
Press,New
New
Techniques
York, 1980),
1980),p.p.87.
87.
York,
M.Good,
Good,S.
S.Good,
Good,and
andJ.J.L.
L.Rose,
Rose,"Measurement
“MeasurementofofThin
ThinCase
CaseDepth
DepthininHardened
HardenedSteel
Steel
M.
byUltrasonic
UltrasonicPulse-Echo
Pulse-EchoAngulation
AngulationTechniques",
Techniques”,ininNondestructive
NondestructiveMethods
Methodsfor
for
by
Material
MaterialProperty
PropertyDetermination,
Determination,C.
C.O.
O.Ruud
Ruudand
andR.R.E.E.Green,
Green,Jr.,
Jr.,Eds.
Eds.(Plenum
(PlenumPress,
Press,
New
NewYork,
York, 1984),
1984),p.p.189-203.
189-203.
Y.
Y.Guo,
Guo,R.
R.B.
B.Thompson,
Thompson,D.
D.K.
K.Rehbein,
Rehbein,F.F.J JMargetan,
Margetan,and
andM.
M.Warchol,
Warchol,"The
“TheEffects
Effectsofof
Microstucture
Microstuctureon
onthe
theResponse
ResponseofofAluminum
AluminumE-127
E-127Calibration
CalibrationStandards',
Standards’,Review
Reviewofof
Progress
Progressin
inQuantitative
QuantitativeNondestructive
NondestructiveEvaluation,
Evaluation,18B,
18B,D.D.O.O.Thompson
Thompsonand
andD.D.E.E.
Chimenti,
Chimenti,Eds.
Eds.(Kluwer/Plenum,
(Kluwer/Plenum,New
NewYork,
York,1999),
1999),pp.
pp.2337-2334.
2337-2334.
R.
R.B.
B.Thompson,
Thompson,"Elastic
“ElasticWave
WavePropagation
PropagationininRandom
RandomPolycrystalsiFundamentals
Polycrystals:Fundamentalsand
and
Application
ApplicationtotoNondestructive
NondestructiveEvaluation,"
Evaluation,”ininImaging
ImagingininComplex
ComplexMedia
Mediawith
withAcoustic
Acoustic
and
andSeismic
SeismicWaves,
Waves,M.
M.Fink,
Fink,W.
W.A.
A.Kuperman,
Kuperman,J.-P.
J.-P.Montagner,
Montagner,and
andA.A.Tourin,
Tourin,Eds.
Eds.
(Springer,
(Springer,Berlin,
Berlin,2002),
2002),pp.
pp.233-253.
233-253.
F.
F.E.
E. Stanke
Stankeand
andG.
G.S.
S.Kino,
Kino,"A
“AUnified
UnifiedTheory
Theoryfor
forElastic
ElasticWave
WavePropagation
Propagationinin
Polycrystalline
PolycrystallineMaterials",
Materials”,J.J.Acoust.
Acoust.Soc.
Soc.Am.,
Am.,75,
75,p.p.665
665(1984).
(1984).
J.J. H.
H.Rose,
Rose, "Ultrasonic
“UltrasonicBackscatter
Backscatterfrom
fromMicrostructure",
Microstructure”,Review
ReviewofofProgress
Progressinin
Quantitative
QuantitativeNondestructive
NondestructiveEvaluation,
Evaluation,11B,
11B,D.
D.O.O.Thompson
Thompsonand
andD.D.E.E.Chimenti,
Chimenti,Eds.
Eds.
(Kluwer/Plenum,
(Kluwer/Plenum,New
NewYork,
York,1992),
1992),p.p.1677.
1677.
F.
F. J.J.Margetan,
Margetan,R.
R.B.
B.Thompson,
Thompson,and
andI.I.Yalda-Mooshabad,
Yalda-Mooshabad,"Modeling
“ModelingUltrasonic
Ultrasonic
Microstructural
MicrostructuralNoise
NoiseininTitanium
TitaniumAlloys",
Alloys”,Review
ReviewofofProgress
ProgressininQuantitative
Quantitative
Nondestructive
NondestructiveEvaluation,
Evaluation,12B,
12B,D.
D.O.
O.Thompson
Thompsonand
andD.D.E.E.Chimenti,
Chimenti,Eds.
Eds.
(Kluwer/Plenum,
(Kluwer/Plenum,New
NewYork,
York,1993),
1993),p.p.1735.
1735.
1354