IDENTIFICATION OF SINTERED IRONS WITH ULTRASONIC
NONLINEARITY
Y. Ohara1, K. Kawashima1, M. Murase1, and N. Hirose2
Department of Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho,
Nagoya, 466-8555, Japan
Department of Mechanical Engineering, Tokyo Metropolitan College of Aeronautical
Engineering, Tokyo, 116-0003, Japan
ABSTRACT. Two kinds of sinters made of reduced and atomized iron powders were identified by
nonlinear ultrasonic measurement to detect higher harmonics generated at micro gaps comparable to
the incident wave amplitude using PZT contact transducers of 5 MHz and 10 MHz. Furthermore, the
advantage of the nonlinear ultrasonic measurement was demonstrated by the attenuation coefficient
measurement for same samples.
INTRODUCTION
Ultrasonic flaw detection has been widely applied to cracks or voids of some finite
volumes. However, the detection of semi-closed cracks such as initial fatigue cracks or
initial creep voids appeared grain boundaries is extremely difficult. Through these nearly
closed cracks or voids, compressive stress wave is partially transmitted. Therefore we can
not detect clear reflection signals, which are visible for open cracks or large voids.
One possibility detecting such closed cracks or voids is to use higher harmonics
generated by clapping of crack surfaces. For nonlinear continuum, the generation of
higher harmonics has been known well and theoretical [1] and experimental [2]
investigations have been reported. For structural materials including minute cracks, the
relation between fatigue damage and the second harmonic was measured [3] and a simple
theoretical model of generation of higher harmonics has been derived [4] for elastic half
spaces of an infinite crack plane. Russian schools developed a measurement method of
higher harmonics of large cracks clapped by an externally excited source [5, 6]. A new
concept of " Contact Acoustic Nonlinearlity", CAN, has been proposed by Solodov [7] to
distinguish it from acoustic nonlinearity of continuum. The most significant feature of
CAN is extremely high ultrasonic nonlinearity, namely 100 or 1000 times higher than
continuum. This opens new possibility to measure cracks of far small openings by the
conventional ultrasonic measurement apparatus.
The present authors have been detected a group of minute cracks [8], which were
generated under high speed plate impact tests, by measuring the second harmonic with
PZT transducers and a pulser exciting large amplitude of some 10 nm. Also, they have
confirmed the main feature of the dependence of the second harmonic on the incident
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/S20.00
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wave amplitude and crack openings by FEM wave
Tension
propagation analyses with contact elements [9]. Compression
Furthermore, they have extended the higher harmonic
measurement to an artificial crack [10] and a laminated
structure model [11] with imperfect bonding.
In the present paper, the nonlinear ultrasonic
measurement is applied to characterization of sintered
iron powder with longitudinal wave. Furthermore, the
attenuation measurement for the same samples is
performed to show the advantage of the nonlinear
FIGURE 1. Nonlinear stress-strain
ultrasonic measurement.
curve of continuum.
THEORY
Higher Harmonics Generation in Nonlinear Elastic Solid
Assume that a nonlinear stress strain relation shown in Fig.l is given by Eq. (1).
a=K2£-K3e2/2
(i)
The corresponding solution of wave equation is expressed [l]by
u = U expi(kx - cot) + ((3K2 +K3)/8K2)U2k2x expi2(bc - cot)
(2)
where U is the fundamental wave amplitude, K2 and KS are elastic stiffness of the second
and third order, j8 — (3+K3/K2) is the nonlinear parameter of the second harmonic.
Eq.(2) tells us that the second harmonic amplitude is proportional to the square of the
fundamental wave amplitude and wave number as well as the propagation distance and
j8. When we use a burst wave of a fixed frequency, the second harmonic amplitude
divided by U, the second harmonic ratio, is proportional to U, j8 and x.
Stress-Strain Relationship at Micro Gap
For an elastic solid including planar cracks of the opening comparable to the
incident wave amplitude, a plane longitudinal wave will close the crack surfaces when
the crack opening is smaller than the incident wave amplitude, as show in Fig.2.
Thereafter compressive stress wave passes partially through the crack surface, however,
tensile stress wave is reflected at the crack surface. In gap free area, the stress-strain
relationship will be linear as shown in Fig.2 (a). In gap area which opening is smaller
than ultrasonic wave amplitude, tensile stress will not be transmitted, while compression
stress will be transmitted after closing the crack by ultrasonic wave in compression phase
as shown in Fig.2 (b, c). In gap area which opening is larger than ultrasonic amplitude,
ultrasonic wave will not be transmitted as shown in Fig.2 (d). Thus, the stress-strain
response passing through the micro gap is expressed by superposition of stress-strain
relations shown in Fig. 2 (e). The resultant stress-strain curve shows the similar shape
shown in Fig. 1. Longitudinal wave velocity is given by
V-
E(l-v)
p(l + v)(l-2v)
1258
(3)
a
Plane wave
Compression
/\
Tension
No gap
-x-
(a) No gap
(b) Si<A
FIGURE 2.
(c) 6i<A
(d) #3>A
(e)
Nonlinear stress-strain response around internal gap.
Displacement
A
- - - • Incident wave
Compression
—— Transmitted wave
3
'On
Time
Tension
f
2f
Frequency
FIGURE 3.
Wave distortion by nonlinear effect.
FIGURE 4.
Higher harmonics generation.
where E is Young's Modulus, p is density and v is Poisson's ratio. The elastic
modulus is higher in compression than in tension. Therefore elastic wave propagates at
higher velocity in compressive phase as shown in Fig.3 and higher harmonics appear as
shown in Fig.4. This crack surface clapping brings in marked nonlinearity in the
transmitted wave as that of acoustic nonlinearity of nonlinear continuum.
It should be noted that the stress-strain relation shown in Fig.2 is extremely
simplified. Namely, the real cracks in structural metals have rough surface of the grain
size order, therefore, the crack surfaces will contact at some points at first. Under
compressive stress, the contact points extend to microscopic contact areas with local
plastic deformation. Also, the plastic deformation accompanies hysteresis loop under
crack clapping. The stress-strain relations shown in Fig.2, however, assume that the crack
surfaces are perfectly flat and parallel, perfectly bonded after crack closure under
compressive stress wave and reopen under tensile stress wave.
EXPERIMENTAL SETUP AND METHOD
Samples
Two kinds of sinters made of reduced and atomized iron powders with porosity
shown in Table. 1 were used in experiment. The shape of samples is of 9 mm in thickness
and 30 mm in diameter. Two kinds of iron powders were pressed under 98 to 886 MPa,
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(b) Sintered iron of atomized powder
(a) Sintered iron of reduced powder
FIGURE 5.
Microstructure of sintered iron.
TABLE 1. Sample.
Sintered iron of reduced powder
Sintered iron of atomized powder
0.11
0.10
Porosity
0.21
0.26
0.25
0.20
0.30
0.31
then sintered in condition to 1473 K in temperature and 25 MPa in pressure in the air of
hydrogen[12]. Fig.5 shows the surface micrograph of sinters. For two kinds of sinters of
the same porosity, the sinter of reduced iron powders contains more micro gaps suitable
for harmonic generation than the sinter of atomized one.
Nonlinear Ultrasonic Measurement
Fig.6 shows a schematic diagram of an experimental setup constructed to measure
precisely the magnitude of fundamental and 2nd harmonic amplitudes in received
ultrasonic wave signals. Ultrasonic signal generator (RAM 5000 SNAP RITEC USA)
controlled by a personal computer outputs high voltage, from 98 V to 540 V, to
transmitted transducer. A 7.5 MHz PZT transducer (Panametrics V 121, 6.55 mm in
diameter) was used as a transmitter. The transmitting signal was a 5 MHz burst
longitudinal wave of 20 cycles. The transmitted wave was sensed by a 10 MHz PZT
transducer (Ultran KC 25-10, 6.55 mm in diameter). The received signal was processed
by super heterodyne frequency analysis system in RITEC SNAP-5000 and the
fundamental and second harmonic amplitude were measured.
FIGURE 6.
Experimental setup.
1260
Couplant
x /\
Transducer
Buffer
Uc
Sample
FIGURE 7.
Attenuation measurement setup.
Attenuation Measurement
An attenuation measurement method [13, 14] with inserted buffer rod between
transducer and sample was used. As shown in Fig.7, the absolute amplitude of reflected
wave is expressed by
A = UR, B= UTBSTSB exp(-2ofc), C = UTBSRTSB exp(-4a/*)
(4)
where a is attenuation coefficient of sample, U is common factor for three sample, eg,
incident wave amplitude and attenuation in buffer rod, R is the reflected coefficient at
interface between buffer rod and sample, TBS(TSB) is the transmitted coefficient to
sample(buffer rod) from buffer rod(sample). By using relationship between eq.(4) and
R2+TBsTsB=l, attenuation coefficient a is expressed by
a
i
-In
2h
J-
1
I
•"•
I
r»
R
I
^J-Vx
x-x^
5 MHz and 10 MHz PZT transducers were used to measure the attenuation coefficient at
these frequencies. Pulse waves were transmitted to the samples through buffer rod by the
transducers connected to pulser-receiver (Panametrics, Model 5900PR). Reflected wave
signals (UA, UB, UG) are processed by FFT analysis and each absolute amplitude (A, B, C)
at 5 MHz and 10 MHz signal were measured.
Calibration of Displacement of Amplitude of Free Surface
The output of the PZT transducer was calibrated by a laser interferometer, then the
received signal was transformed displacement. Free surface amplitude was measured by
laser interferometer. A schematic diagram of an experimental setup is illustrated in Fig.8.
Input voltage is proportional to displacement amplitude as shown in Fig.9. We use an
experimental formula;
Displacement [nm] = 0.037 [nm/V] X Input voltage [V] -Q.369 [nm]
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20F
H
110
f
Transducer
Specimen
cd
£
Digital
Oscilloscope
100 200 300 400 500
Exciting voltage [V]
FIGURE 8. Amplitude measurement on
FIGURE 9.
free surface.
and wave amplitude.
Relation between exciting voltage
RESULTS
Dependence of the 2nd Harmonics on Porosity and Kinds of Iron Powder
The second harmonic ratio, the second harmonic amplitude divided by the
fundamental one, is plotted against the incident wave amplitude in Fig. 10. For every
value of porosity, the ratio is nearly proportional to the fundamental wave amplitude. The
slopes are higher for low porosity.
At nearly same porosity, the reduced iron powder gives higher second harmonic than
the atomized one as shown in Fig. 10. The former includes small voids as shown in Fig.5,
while the latter does include only large voids. To excite the second harmonic, the gap
distance or crack opening should be comparable to the incident wave amplitude. Large
voids or gaps remain open under compressive wave, therefore no clapping occurs. It
should be noted that the sensitivity of the second harmonic ratio is about 0.01%.
0.4
Porosity
-^-0.11-^-0.10
-•- 0.21 -o- 0.20
0.3 -»- 0.26 -a- 0.25
-^ 0.30-v-0.31
2
Reduced Atomized
powder powdi
0.1
0
FIGURE 10.
20
5
10
15
Incident wave amplitude [nm]
Second harmonic ratios.
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s
u
o
^
-*—>
Reduced
a 5-
'1.5
-_____— ——-—•——t
\
3U
~g3
CD
O
O
<?*
—•— Reduced
—°— Atomized
1
0
0.2
Porosity
0.1
FIGURE 11.
n
0.3
Attenuation coefficients at 5 MHz
and 10 MHz.
1
0.1
,
1
0.2
Porosity
,
1
0.3
FIGURE 12. Attenuation coefficients
^ 10MHz/ & 5MHz-
Comparison Between 2nd Harmonic Ratio and Attenuation
Measured attenuation coefficients at 5 MHz and 10 MHz are shown in Fig. 11. The
attenuation coefficients do not show clear dependence on iron powder and porosity. Thus,
it is difficult to identify the porosity on the same powder as well as the kind of iron
powder at nearly same porosity.
The attenuation coefficient ratio, in which the attenuation coefficient at 10 MHz a
10MHz is divided by the 5 MHz one a5MHz, is plotted against the porosity in Fig.12. The
attenuation coefficient ratio of sintered iron of reduced powder is larger than the atomized
one. Therefore, this result shows that the difference of 2nd harmonic ratio shown in
Fig. 10 is not caused by the attenuation. Thus, the nonlinear ultrasonic method is more
suitable for the identification of sintered iron than attenuation coefficient measurement.
CONCLUSIONS
The effectiveness of the nonlinear ultrasonic measurement, the second harmonic
amplitude, for nearly closed cracks was demonstrated for sintered iron of internal gaps, as
compared to attenuation coefficient measurement. In these measurements, the
conventional PZT contact transducer was combined with commercial ultrasonic pulser
and receiver. The resolution of the second harmonic ratio, A2/Ai, is about 0.1%. This
method can detect the set of nearly closed cracks or gaps of the opening comparable to
incident wave amplitude, however, there is a detectable range of the crack opening, which
depends on the incident wave amplitude.
ACKNOWLEDGEMENT
This work has been supported by Grant-in-Aids for Scientific Research (B
10450047, B 12555024) from the Ministry of Education, Science, Sports and Culture,
Japan.
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