ATTENUATION AND GRAIN NOISE PARAMETERS IN Ni-BASE ALLOYS
B.R. Tittmann and L. Ahlberg
Rockwell International Science Center
Thousand Oaks, CA 91360
F. Cohen-Tenoudji and G. Quentin
G.P.S., University of Paris VII
Paris, France
SUMMARY
The frequency dependent ultrasonic attenuation and grain noise
were determined for samples of three alloys often used in jet
aircraft engine turbine discs: Waspa11oy, IN-lOa, and Ti-6246.
In addition to propagation of longitudinal waves, also shear waves
were considered. The frequency dependence was extracted from
broadband echos received through a low attenuation buffer. A key
feature of the results for IN-IOO is the presence of a low concentration of micropores which appear to influence the scattering
of ultrasound and therefore the attenuation and material noise
values. Of the three alloys, Waspa110y was found to have the
highest attenuation value and Ti-6246 the lowest.
INTRODUCTION
The work reported here is part of a program on flaw detection
in turbine rotor component bore geometries whose objective is to
determine the feasibility of detecting non-surface breaking
fatigue cracks near the bore hole surface of an aircraft engine
disk using ultrasonic techniques. As part of this program the
attenuation and grain noise parameters of IN-lOa, Waspa110y and
Ti-6246 were determined as needed to develop measurement models
for the overall program.
129
B. R. TITTMANN ET AL.
130
Recent reports of quantitative attenuation analysis have been
devoted to the scattering caused by grains. l ,2 The most detailed
treatment of this mode of attenuation has been developed by
Papadakis,l based on scattering calculations by Liftshitz and
However, there are several problems with the
Parkhomovskii. 3
analysis in the present form. The approach identifies two regimes
of behavior; the Rayleigh regime where w < 1.O<D> (w is the
wavelength and D is the grain diameter) and a "stochastic" regime
which prevails atw > lO<D>. Analytic expression for the
attenuation ° have been developed in these frequency regimes for a
variety of crystal structures; viz., for cubic materials,2
3
Z Z
8rr (C ll - C1Z - ZC 44 ) p
°1
375E 4
[2
+
3
(::f]
Tf4
(w < O.l<D»
°1
=
Z
Z
16'JT (C ll - C1Z - ZC 44 ) p
5Z5E 3
<D>f Z
(w > lO<D»
and
(1)
where E is Young's modulus of the polycrystal, p is the density of
the material, the C's are the single-crystal elastic constants, v
is the wave speed, the subscripts ~ and t refer respectively to
the longitudinal and transverse modes, and T is given by
(2)
The T term in the Rayleigh regime recognizes that real materials
contain a contribution of grain diameters;2 the term is then
derived on the premise that each grain is a single scatterer
(cross section, « D6) and that the attenuation is a summation of
the scattering over all grains (<< D-3). Interaction effects are
thus neglected, and this constitutes a conceptual difficulty with
the analysis. In the stochastic regime, the grain radius distribution does not appear to have been afforded the same recognition,
and the direct use of the mean grain diameter has generally been
advocated. 2
This inconsistency is disconcerting, but the effect
of grain size variability may not be as important as in the Rayleigh regime. The major limitation of the existing analysis, however, is that it does not provide explicit relations for the attenuation at frequencies between the Rayleigh and "stochastic"
regimes (O.l<D> < w < lO<D». Yet, most frequencies of practical
interest lie within this intermediate regime. Papadakis 2 has suggested an interpolation procedure that affords a good
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
131
approximation, but a more exact treatment of the attenuation would
clearly be preferred.
A different approach has recently been deve,loped4 that circumvents the above problems and, of particular importance for ceramics, has a flexibility that allows the effects of more than one
microstructural constituent to be analyzed. The approach is based
on numerical computations of the cross section and extreme-value
size distributions of the predominant scatterers. Attenuation
data, obtained on a range of ceramic material, are used to correlate with analysis. 4
SAMPLE PREPARATION
Representative samples of IN-lOO, Waspalloy, and Ti-6246 were
obtained from Pratt and Whitney Co and were subsequently machined
and polished to have flat and parallel faces in at least two directions. Micrographs were obtained for each of the samples and
for the IN-lOa samples, specifically, an additional effort was
made to obtain approximate micropore size and density distributiuons.
TECHNIQUE FOR ATTENUATION MEASUREMENTS
The measurement technique was already described in detail
previously in reference (4) and is only briefly summarized here.
The data were obtained in the 10 MHz to 100 MHz band of frequencies analyzing the echos within smaller sub-bands. A lowattenuation buffer (AI or fused silica) was typically used to
obtain the transducer response and the reflection coefficient of
the sample interface. The technique and calculations are illustrated in Fig. 1. For the case of shear waves, an additional
technique was employed for rapid data acquisition and is illustrated in Fig. 2. Here the buffer is water and the angle of
incidence is such that the longitudinal waves in the water produce
shear waves in the sample. Because of the possible generation of
leaky waves generated at the interfaces and the non-circular beam
spreading associated with non-normal incidence, the meaurements
were augmented with calibration measurements, carried out with
narrow band quartz shear wave transducers.
In reference to Fig. 2, Tal' TlO are the water-sample, samplewater transmission coefficients; as is the sample shear wave
attenuation in nepers/cm, a W is the water longitudinal attenuation
in nepers/cm, t S1 ' tS2 are the shear wave paths in the sample
under test, t Wl ' tW2 are the wave path length in water.
132
B. R. TITTMANN ET AL.
TRANSDUCER
BUFFER - AIR SIGNAL
!~
/" U . . .,
_~_
~
A
BUFFER
BUFFER - SAMPLE SIGNAL ~ (R)A
SIGNAL TRANSMITTED INTO SAMPLE IS:
T - A6
1/2
(1- I R I 2 )
1/2
SAMPLE - AIR SIGNAL IS:
- 1/2
C~ T6
(k=
Fig. 1.
2 112 2 1
(1 - I R I )
e- (k
1/21. [1n(1 - 1 R 21) + In(A/ C)
Sample measurement configuration.
A1 = T 01 T 10 exp - (as 's1 + CXw I w1 '
A2
I
= T 01
T 10 exp - (as Is2 + a w I w2 '
-.!.
a =
(In A 1) + a
s
~Is
A2
w
Ax
Tx
Fig. 2.
Shear attenuation method.
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
133
RESULTS
Waspalloy
The Waspalloy sample was found to have a relatively coarse
grained structure with grain diameters in the range from about
50 ~m to 500 ~m. A representative micrograph is shown in Fig. 3
and the graph of the frequency dependence of the attenuation is
shown in Fig. 4. At 10 }lliz the longitudinal wave attenuation a L
is about 10 dB/cm and the shear wave attenuation as about
11 dB/cm. The corresponding velocities are vL = 6.04 mm/~s and
Vs = 3.23 mm/~s. The frequency dependence has an exponent between
2 and 3 as expected for the transition between the Rayleigh and
stochastic regimes.
WASPALLOY
•
Fig. 3.
Micrograph for Waspalloy sample.
Ti-6246
In contrast to the Waspalloy, the Ti-6246 sample was fine
grained with an average grain diameter of 2-4 ~m. The micrograph
shown in Fig. 5 displays the basket weave structure with a mosiac
of a- and 8-grains. As demonstrated in Fig. 6 the attenuation is
low with values of about a L = 10 dB/cm at 100 MHz and exponent of
about 3.5 for the frequency dependence.
IN-lOa
In contrast to the Waspalloy and Ti-6246, the IN-lOa sample
displayed a fine grain structure with a low concentration of
micropores. The microporosity was observed on three separate
samples.
B. R. TITTMANN ET AL.
134
100
80
U L TRASON IC ATTENUATION, WASPALLOY
60
50
40
30
~
20
--"
~
E
.0
V
0
10
8
~
lJ.
6
5
4
••
lJ.
~~
3
2
~
•
•
•
•
•
•
• L-WAVE
~
~o
1
1
2
3
4 56
8 10
20
S- WAVE
304050 70 100
FREQUENCY, MHz
Fig. 4.
Attenuation values for Waspalloy.
Fig. 5.
Micrograph for Ti-6246.
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
135
1000,
ULTRASONIC ATTENUATION, Ti 6246
100
10
1L-__________- L_ _ _ _ _ _ _ _ _ _ _ _~_ _ _ _ _ _ _ _ _ _~
1
10
100
1000
FREQUENCY, MHz
Fig. 6.
Longitudinal wave attenuation in Ti-6246.
One of the samples is a section from a used F-100 second turbine
disk on which spin pit testing was carried out. All three samples
contained micropores, but showed differing pore sizes and spacings. Some microporosity known as TIP (thermally induced porosity) is normal and is a result of the final heat treatment. 5
Typical micrographs showing the grain and pore structure are shown
in Figs. 7 and 8, respectively. These distributions were analyzed
with the aid of a Cambridge Instruments Quantiment 900, one of
whose outputs is shown in Table I.
Figs. 9, 10, and 11 present graphs of grain size and micropore
size distributions for the two samples. Typical grain sizes are
about 2-4 ~m and micropore sizes average about 15 ~m with nonnegligible contributions from 50 ~m diameter pores. On the other
hand the density of microEores was considerably greater for sample
B with about 200 pores/mm than for sample A with about 4
pore/mm2, indicating some difference in the treatments.
136
B. R. TITTMANN ET AL.
Fig. 7.
Photomicrograph of IN-lOO grains.
Fig. 8.
Pores in IN-lOO.
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
Table I.
137
Pore Size Distribution
CAMBRIDGE INSTRUMENTS QUANTIMET 900
DATE : 23-MAR-82
ROUTINE : PORE
QUIPS/SM
RUN
X66.01
USER
16
SPECIMEN
DISTRIBUTION OF FEATURE COUNT vs LENGTH
TOTAL FEATURE COUNT = 4365.
UNDERSIZE COUNT = O.
LIMITS
5.008.0011.0014.00 17.00 20.00 23.00 26.00 29.00 32.00 35.00 38.00 41.0044.00 47.00 -
MEAN = 13.1
STDDEV = 7.23
OVERSIZE COUNT = 64.
COUNT
** * * ** * * ** * * * * * * ** * .. * * ** * * **
* * * * * * ** * * ** * * * * * * * * * * * * * * * * * * * * ** * * * *
960.
8.00
11.00
14.00
17.00
20.00
23.00
26.00
29.00
32.00
35.00
38.00
41.00
44.00
47.00
50.00
1269.
855.
351.
330.
188.
140.
78.
53.
41.
27.
26.
21.
12.
14.
CAMBRIDGE INSTRUMENTS QUANTIMENT 900
ROUTINE : PORE
DATE: 23-MAR-82
CALIBRATE MICROSCOPE
QUIPS/8M: X66.01
USER:
RUN
16
SPECIMEN:
(CALIBRATION VALUE = 0.8104 MICRONS
PER PIXEL)
(OPTICS TURRET = INCIDENT)
(OBJECTIVE LENS ID. =x 4.0, PROJECTION LENS ID. =x 8.0)
LOAD SHADING CORRECTOR (PATTERN - 4X)
STAGE SCAN
(
X
Y
SAMPLE
B
40
CI)
z
«c:::
30
-
(!)
u..
0
'it
r--
Z
u
c:::
w
c...
-
20
IW
SAMPLE
A
-
10 r
r-0.5 1
Fig. 9.
2
4
Mm
n
8 16
0.5 1
2
4
n
8 16
~m
Grain size distribution in IN-IOO.
B. R. TITTMANN ET AL.
138
1.0
N
3.9 PORES/mm 2
17.5 (.J. AVERAGE SIZE
0.8
E
E
.....
en
w
a: 0.6
0
c..
II..
0
:tI:
0.4
0.2
10
1 COUNT AT 82 (.J.m
Fig. 10.
Pore size distribution for IN-IOO sample A
60
50
rN
206.7 PORES/mm 2
13.1 ~ AVERAGE SIZE
I-
40
E
~w
'-
a: 30
...
0
LL
0
"
20
I10
0
0
10
15
rhn
20
25
30
SIZE
Fig. 11.
(~ml
~f:l8l:;;:8
"':"':cicici
40
50
60
3 - 0.5/mm2
OVERSIZE
Pore size distribution for IN-IOO sample B
139
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
The consequence of the presence of micropores may be perceived
with the aid of some analysis. The normalized single scattering
cross section for a sphere is: 6
(2m + 1)[ A 2 + m(m + 1)(k/K) B 2]
m
m
(1)
where ~, Bm are expansion coefficients which are evaluated by
matching boundary conditions between the sphere and the matrix.
Here
k = w[p/(>"
+ 211)]1/2
where w is the radial frequency, e the density, and>" and 11 Lame's
constant. In the Rayleigh regime where w < 0.2a the cross section
for longitudinal waves is
r2
47T
"'"9
g
k4 6
a
(2)
Equation (2) shows that the scattering cross section depends on
the sixth power of the sphere radius. In the IN-100, each pore
acts to scatter energy out of the ultrasonic beam according to
Eq. (2) and contributes to the attenuation. It is reasonable to
expect that the attenuation values depend strongly on pore density
and pore size distribution. In the case of sparse distributions,
the large pores would be expected to dominate the attenuation and
could influence the values differently depending on the specific
sample or even the site for a given sample where the measurements
are obtained.
The measurements are summarized in Fig. 12 and 13 which display attenuation values as a function of frequency for two different samples and for three different locations for the same
sample.
Table II summarizes the information collected by given representative values for attenuation and velocity for Waspalloy, IN100 and Ti-6246.
B. R. TITTMANN ET AL.
140
100
SAMPLE A
~~
SAMPLE B
10
",0
•
E
u
:a
'tJ
•
•
o '"
0
9
0
•
•
00
•
A
0
0.1
0
~AOo
10
S -WAVE A}
6mmTx
L- WAVE B
L- WAVE A}
1 mmTx
L- WAVE B
100
1000
FREQUENCY. MHz
Fig. 12.
Attenuation in IN-lOO.
THREE DIFFERENT LOCATIONS
OF 1 mm DIAM ETER TRANSDUCER
1 L-__~__~~~~~____~~~~~~
10
100
1000
FREQUENCY. MHz
Fig. 13.
Attenuation in IN-lOO at three different
locations for one sample.
141
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
Table
n.
Attenuation and Velocity
vL
Vs
Grain
Size
(].lm)
Waspalloy
6.04
3.23
100
4
11
IN-100
6.52
3.29
2
4 ± 1
20
Ti-6246
6.11
3.16
2-4
10
Velocity
Sample
(mmhlID)
Atten
(dB/cm)
aL
as
Freq
(MHz)
Freq Dep
aL
as
10
f2.2
f2.5
50
f2
f2.2
100
f3.5
TECHNIQUE FOR GRAIN NOISE MEASUREMENTS
Grain noise measurements were carried out as shown schematically in Fig. 14 with a broadband transducer in a water bath.
For purposes of deconvolution a reference waveform was obtained,
as shown in Fig. 14b, by using the sample corner as a corner reflector. Fig. 15 shows the power frequency spectra for (a) the
sample corner as a reference; (b) the backscattering from the
sample; (c) the ratio between (b) and (a). The backscattering (b)
power frequency spectra was obtained by averaging 10 scattering
waveforms from different regions of the sample. Each waveform was
averaged 512 times to eliminate electronic noise.
SCATTERING MEASUREMENTS
to.634 em
(a) SCATTERING MEASUREMENT
(b) CALIBRATION MEASUREMENT
Fig. 14.
Grain noise measurement technique.
142
B. R. TITTMANN ET AL.
:~I Z
4
8
:::>
0.0006
~
0.0004
aJ
1
,1
12
16
20
FREO (MHz)
U)
I-
Z
:s: 1
(b)
ex: 0.0002
w
O~~~~__- L_ _~_ _L-~~~_ _~~~
~
4
~
O~2!
0.0001
o
4
: :::z
8
12
16
IOI
20
FREO (MHz)
Fig. 15.
Frequency spectra for (a) the sample corner;
(b) backscattering from sample; (c) the ratio
of (b) to (a).
It is interesting to calculate the theoretical back-scattering
amplitude for a spherical scatterer in the regime of ka < 1. 3 The
result is shown in Fig. 16 which displays the characteristic (ka)4
rise associated with the Rayleigh regime. An examination of the
backscattering data obtained in the experiments shows a similar
trend at low frequencies (see Fig. 17) which opens the possibility
for deducing an average a (grain radius) for the material.
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
0.50
0.40
t
0.30
I A I fa
0.20
0.10
ka--
Fig. 16.
Theoretical scattering amplitude as a function ka.
IN 100 PORE SCATTERING x 1000
-40
-42
N
]1]
-44
>0::
~
C!l
o...J
-46
-48
-50
18
19
20
21
22
23
24
25
20 LOG (F [MHz] )
Fig. 17.
Log-log plot of grain/pore backscattering vs
frequency for IN-I00 compared to theoretical
frequency dependence.
143
B. R. TITTMANN ET AL.
144
CONCLUSION
This study determined the frequency dependence of the attenuation for three alloys: Waspalloy, IN-100, and Ti-6246. Except
possibly for the Waspalloy, the attenuation values are quite low
and therefore negligible for typical ultrasonic NDE applications
in the 2-10 MHz range of frequencies. The results obtained for
IN-100 are complicated by the presence of microporosity, which was
found to be variable from sample-to-sample and from site-to-site
within each sample. Preliminary measurements were also carried
out to determine the grain and pore scattering for IN-100.
Preliminary comparisons at about 10 MHz shows the w4 dependence
for the backscattering amplitude expected for the Rayleigh regime
where ka < 1. Additional experiments are planned on an actual
engine disk component to confirm that these results are
representative of results expected in real components.
ACKNOWLEDGMENT
This work was sponsored by the Center for Advanced Nondestructive Evaluation, operated by the Ames Laboratory, USDOE, for
the Air Force Wright-Aeronautical Laboratories/Materials
Laboratories and the Defense Advanced Research Projects Agency
under Contract No. W-7405-ENG-82 with Iowa State University.
REFERENCES
1.
2.
3.
4.
5.
6.
E.M. Papadakis, J. Acoust. Soc. Am. 37, 711 (1965).
W.P. Mason and H.J. McSkimin, J. App~Phys. 19, 940 (1948).
I.M. Lifshitz and G.D. Parkhomovskii, J. Expt:--Theoret. Phys.
(USSR) 20 175 (1950).
A.G. Evans, B.R. Tittmann, L. Ahlberg, B.T. Khun-Yakub, G.S.
Kino, "Ultrasonic Attenuation in Ceramics," J. Appl. Phys. ~,
2669 (1978).
"Effects of Defects in Powder Metalurgy SuperaUoys," Air
Force Report AFWAL TR 81-4191, 1981.
R.L. Roderick and Rohn Truell, J. Appl. Phys. 2~, 267 (1952).
ATTENUATION AND GRAIN NOISE PARAMETERS IN NI-BASE ALLOYS
145
DISCUSSION
R.B. Thompson (Ames Laboratory): You identified the porosity scattering as being in the Rayleigh regime, but you said that the attenuation had a frequency dependence somewhere between the Rayleigh and
stochastic regimes. If it's the same scattering mechanism in the
two processes, why do they appear to be in different regimes?
B.R. Tittmann (Rockwell International Science Center): As Ken Fertig
will tell you, there are other effects that play a role in the
noise scattering which will, in fact, shed light on that. Part of
it is the beam spreading that he will discuss, so I'll defer that
question to him.