QUANTITATIVE APPROACHES TO FLAW SIZING BASED-ON
ULTRASONIC TESTING MODELS
Hak-Joon Kirn1'2, Sung-Jin Song1 and Young H. Kim1
School of Mechanical Engineering, Sungkyunkwan University, 300, Chonchon-dong,
Jangan-gu, Suwon, Kyounggi-do, 440-746 Korea
Currently, Center for NDE, Iowa State University, Ames, IA 50011, USA
ABSTRACT. Flaw sizing is one of the fundamental issues in ultrasonic nondestructive evaluation of
various materials, components and structures. Especially, for cracks, accurate sizing is very crucial
for quantitative structural integrity evaluation. Therefore, robust and reliable flaw sizing methods are
strongly desired. To address such a need, using ultrasonic testing models, we propose quantitative
model-based flaw sizing approaches such as 1) construction of DOS (Distance-Gain Size) diagrams,
2) suggestion of a criterion for the proper use of the 6 dB drop method, and 3) proposal of a
reference curve named as the SAC (Size Amplitude Curve) for sizing of vertical cracks. The
accuracy of the proposed approaches is verified by the initial experiments.
INTRODUCTION
Flaw sizing is one of the fundamental issues in ultrasonic nondestructive evaluation
(NDE) of various materials and structures, since the estimation of structural integrity
requires the flaw size information. To address such a need, various ultrasonic flaw sizing
methods have been proposed up to now. These approaches can be divided into two
categories; 1) the amplitude-based approaches such as the DAC (Distance Amplitude
Correction) curve, the DGS (Distance-Gain Size) diagram, the intensity (dB) drop method,
and 2) the time-of-flight approaches such as the TE (Tip Echo) measurement, the SPOT
(Satellite Pulse Observation Time) technique, the TOFD (Time-Of-Flight Diffraction)
method [1]. Among these approaches, the DGS diagram, the DAC curve, and the SPOT
technique are the most widely used in practical field inspection. But, these approaches have
some limitations as follows: 1) the DGS diagram usually requires a large number of
specimens, 2) the DAC curve is primarily not for flaw sizing but for the decision making of
acceptance/rejection, and 3) the SPOT technique has difficulty in acquiring tip diffraction
signals. In addition, all of these methods are largely dependent of operators, and do not
quite often perform well in practice. Thus, for the reliable flaw sizing, of course,
quantitative ultrasonic flaw sizing methods are strongly desired. The theoretical ultrasonic
testing models can be a very promising tool for this purpose.
Until now, extensive research has been carried out to develop theoretical models to
predict the ultrasonic testing (UT) signals. As a result of this endeavor, several models have
been proposed, for example, Thompson and Gray's ultrasonic measurement model [2] and
Schmerr's near-field measurement model [3]. Among them, the multi-Gaussian beams
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
703
showed the outstanding capability of predicting the UT signals in a computationally
efficient manner [4, 5].
In this study, we propose the quantitative ultrasonic flaw sizing approaches based on
the normal beam UT models and the angle beam UT models that are constructed based on
the multi-Gaussian beams. In the case of normal beam UT, we propose the efficient way for
the construction of DOS diagrams, and the optimal distance for intensity drop methods. In
the case of angle beam UT, we propose a SAC (Size Amplitude Curve) as a new approach
to the vertical crack sizing. The performance of these approaches is demonstrated with the
initial experiments.
MODEL-BASED, QUANTITATIVE FLAW SIZING: NORMAL BEAM UT
FBH Model
To construct a DOS diagram theoretically, we need to have a normal beam UT model
for a flat-bottomed hole (FBH), of which the test set-up is shown in Fig. 1. The voltage
received by the transducer from the FBH can be written as Eq. (1) [6].
V(CD) = j3((Jt})Qxp(2klZl )exp(2&f Z2 jT^CMf A(0)\
-iTtfa2 p\c\
where p(ai) is the system efficiency factor, kl9k2 is the wave number in the fluid and the
specimen respectively, Z1?Z2 are the distance from the transducer to the front surface of
the specimen, and the distance from the front surface of the specimen to the FBH,
respectively, TP2-P is the transmission coefficient, a is radius of the transducer, p}9p2 are
the densities of the fluid and the specimen, respectively, cl9c* are the P-wave speeds in the
fluid and the specimen, respectively, and A(CD) is the far-field scattering amplitude from the
FBH which can be given by Eq. (2).
if)2cP;P
A(6)) = ———— J, (2k} b sin Si)
4sin#z
where 9t is the incidence angle, b is the radius of the FBH,
reference [5]. The diffraction correction, C(co), is given by Eq. (3).
(2)
CP;P is defined in the
JdetG?(o)
rCXp
(3)
where An,Bn are the height and width factors of the individual Gaussian beams [7], zr is
the Rayliegh distance, and definition of other terms can be found in references [4] or [5].
For the calculation of the system efficiency factor, /?(#>), we need to have the reference
reflector model. In this study, we chose the Rogers & Van Buren's model [8] given by Eq.
(4).
V (ct)) = R ex (ik Z }\l ex fefc a2 !2Z 1 J \ kl°" I U I *l°~ I I I
704
(4)
Ultrasonic Transducer
Water
Steel
FIGURE 1. The ultrasonic immersion testing setup for the normal beam ultrasonic testing.
Time(|i sec)
FIGURE 2. Comparison of predicted the FBH signal to the experimental signal.
where VR(co) is the received voltage in the frequency domain, and Rn is the reflection
coefficient.
Fig. 2 shows comparison between experimentally measured signal and predicted
time domain waveform of the FBH with the diameter of 1.98 mm, in the case of using a
transducer of 5 MHz center frequency, and 0.375 inch diameter. As shown in Fig. 2, the
agreement between the theoretical prediction and the experiments is very good, with
demonstrating the validity of the model.
Model-Based DCS Diagram
Fig. 3 (a) shows the DOS diagram constructed by the FBH models given by Eq. (1).
The diameters of the FBHs are 1.98 mm, 3.0 mm, and 4.0 mm diameter with the variation
in the water path from 10 mm to 200 mm, while fixing the metal distance of 9.65mm. Fig. 3
(b) shows the DGS diagrams predicted by changing the metal distance from 5 mm to 50
mm while fixing the water path to 10 mm.
(a)
(b)
FIGURE 3. Constructed DGS diagrams for FBHs in the steel specimen immersed in water with (a) the
variation in the water path, and (b) the variation in the metal distance.
705
(a)
(b)
(c)
FIGURE 4. The peak amplitude variations of the FBH (5/64 inch diameter) response with the water path of
(a) Zl/N = 0.23, (b) Zl/N=Q. 29, and (c) Z^N= 0.73: Transducer: 5 MHz center frequency and 0.5 inch
diameter (N is the near filed length).
FIGURE 5. The variation of the estimated FBH size according to the water path.
Model-Based Intensity Drop Method
In many practical situations, the intensity drop methods overestimate the size of flaws,
especially when the flaw size is very small than the transducer diameter. However, the exact
amount of overestimation is quite often not kwon. To get rid of this opaqueness, we
performed the model-based synthetic sizing of the FBH with the diameter of 1.98 mm
adopting the 6 dB drop method, by use of the FBH model given in Eq. (1). Fig. 4 shows the
peak amplitude variation of the FBH response with three different water paths. In Fig.4,
horizontal lines denote the 6 dB drop positions from the peak amplitude from which the
flaw size is estimated. As shown in Fig. 4, the flaw size determined by the 6 dB drop
method varied by the choice of the water path. To investigate this variation more
systematically, we performed the flaw sizing with the variation in water path from 20 mm
to 200 mm as shown in Fig. 5. From this figure, one can notes that the near-field length
(denoted by an arrow) would be the optimal distance for the evaluation of flaw size based
on the intensity drop method.
MODEL-BASED, QUANTITATIVE FLAW SIZING: ANGLE BEAM UT
Cracks are usually considered more dangerous than non-crack-like flaws. Thus,
quantitative crack sizing methods have always been paid a great attention. For the crack
sizing, the SPOT technique is widely used in practice. As mentioned before, however,
acquisition of the crack tip signal is very difficult in the many practical situations. To
overcome such a difficulty, we propose a new approach to vertical crack sizing using the
angle beam UT models.
706
(a)
(b)
FIGURE 6. Schematic representation of angle beam UT for (a) the vertical crack comer, (b) (b) the specimen
comer.
(a)
(b)
FIGURE 7. Ultrasonic beam distributions around (a) the vertical crack corner, and (b) the specimen corner:
Transducer: 5 MHz center frequency, 0.375 inch diameter, and 45 degrees diffraction angle.
Vertical Crack Reflection Model
In this study, we considered the reflection signal from the vertical crack corner, as
shown in Fig. 6 (a), since the crack corner trap signal can be acquired very easily during the
inspection of surface breaking vertical cracks. As a reference for the sizing of surface
breaking vertical cracks, we considered the reflection signal from the specimen corner as
shown Fig. 6 (b). In these cases, the footprints of the incident ultrasonic beam around the
vertical crack corner (Fig. 7 (a)), and the specimen corner (Fig. 7 (b)), are to be obtained as
shown in Fig. 7. Fig. 7 shows that the vertical crack corner reflects only a portion of the
incident beam, while the specimen corner does the entire beam.
Since the specimen corner reflects the entire beam, the reflection signal from specimen
corner can be calculated by Eq. (5).
S-Ea
«=
(5)
(z 2 ) ^detfif (
where Vcor(a>) is the reflected velocity from the specimen corner in the frequency domain,
Sw is the specimen width, Ea is the effective radius of spreading (within which the
majority of beam energy is confined) ultrasonic beam, R$f is the reflection coefficient at
the specimen corner, 7^ is the transmission coefficient from the specimen to the wedge,
zl is the distance from transducer to the interface, z2 is the distance from the interface to
the specimen corner, z3 is the distance from the specimen corner to the interface, and z4
is the distance from interface to the transducer. Definition of the other terms including
707
G2?(o)and Gf (z3) matrices can be found in the references [4] or [5]. Here, it is worthwhile
to note that Fig. (5) is, in fact, identical to Eq. (5) in reference [9], however, the effective
radius ( E a ) of the footprint of the beam over the specimen corner was introduced to
simplify the calculation of the response.
The corner trap signal of the vertical crack, however, can be calculated by Eq. (6).
V (/"t\=V
(/"t\±V
(/"i\
(f^\
where Vvc(co) is the reflected velocity from the crack corner in the frequency domain,
Vside(co) is the reflected velocity through the vertical crack side firstly and from the
specimen bottom lastly, and Vbtm(co) is the reflected velocity through the specimen bottom
firstly and from vertical crack side lastly. F^e(#)and Vbtm(co) are given by Eqs. (7) and (8),
respectively.
-I-/1-
^
)exp(/^z3 )exp^25z4 )r£p (ft*5 J2 T™
(7)
expl * 2
J(z 2 ) ydetG 3 (z 3 ) <JdQtGs4(z4) ydetGf (z.
8
S
(ik ?z \P™(ilr
7 ]rS;P( S;sV- P;S
\iK
2 3 ;exp\iK 2 z 4 )i l2 \K23 } i2l
R
T
(8)
lE*dS»,
where Zl is the distance from transducer to the interface, z2 is the distance from the
interface to the vertical crack surface, z3 is the distance from the vertical crack surface to
the specimen bottom, z4 is the distance from the specimen bottom to the interface and z5
is the distance from interface to the transducer.
If we define the amplitude ratio (in the time-domain) of the crack corner trap signal to
that of the specimen corner signal, which is named as amplitude-area (Aa) factor, it can be
given by Eq. (9).
P-P(K W (/))i
(
j
(9)
p-p(r w W)
where Aa is the Aa factor, P-?(vvc(t)) is the peak-to-peak amplitude of the vertical crack
corner trap signal in the time-domain, which can be obtained by taking the inverse Fourier
transform to Eq. (6), P-?(vcor(t)) is the peak-to-peak amplitude from the specimen corner
reflection signal in the time-domain, which can be obtained from Eq. (5) similarly.
Size Amplitude Curve (SAC)
In this study, we proposed a size amplitude curve (SAC), from which the vertical
crack sizing can be performed quantitatively. The SAC is a plot of the Aa versus the vertical
708
crack size. Fig. 8 shows two examples of the S ACs constructed for the specimens with the
heights of 10 mm and 15 mm. As shown in Fig. 8, the SACs are very similar in spite of the
difference in the specimen heights.
Performance of Vertical Crack Sizing
To demonstrate the sizing performance using the theoretically constructed SAC, we
performed sizing for an unknown vertical crack the specimen with the height of 15 mm. Fig.
9 (a) shows the corner trap signal captured from the unknown vertical crack corner, of
which the peak-to-peak voltage is measured to be 1.55 mV. For the flaw sizing using the
SAC, we need to estimate the peak-to-peak voltage of the specimen corner. Fig. 9 (b)
presents the result of the theoretical prediction (using Eq. (5)) of which the peak-to-peak
voltage is calculated to be 6.5 mV. Then, we can calculate the 4, factor, which in this
particular example, is turned out to be 23.85%. Then, finally, we can estimate the unknown
vertical crack size from the SAC, as shown in Fig. 9 (c), to be 1.85 mm. Considering the
fact that actual size of the crack is 2.0 mm, one can recognize that the accuracy of the SAC
sizing is very good.
CONCLUSIONS
In this study, we have proposed new, quantitative approaches to flaw sizing based on
the ultrasonic testing models. Specifically, we have construction of DGS diagrams with the
FBH model in a computationally efficient manner. In addition, we have suggested that the
near-field length of the transducer is the optimal distance for the intensity drop method. For
the sizing of surface-break vertical cracks, we have proposed the vertical crack reflection
model using the multi-Gaussian beams and defined the Aa factor, from which the newly
proposed the SACs are constructed theoretically. Then, finally, we have demonstrated the
performance of the vertical crack sizing using the proposed SAC in the initial experiments.
In the present study, however, fatigue crack and inclined crack were not considered at all,
remaining for the future work.
8
9
Crack Size (mm)
10
11
12
13
14
C r a c k Size ( m m )
FIGURE 8. Estimated the SACs for two specimens with different heights: transducer: 5 MHz center
frequency, 0.375 inch diameter, and 45 degrees diffraction angle.
709
0
1
2
3
4
5
Crack Size (mm)—^
(c)
FIGURE 9. (a) The experimentally measured corner trap signal from the 2 mm vertical crack, (b) predicted
corner reflection signal from the 15 mm height specimen, and (c) the estimation of the vertical crack size
using the SAC: Transducer 5 MHz center frequency, 0.375 inch diameter, and 45 degrees diffraction angle.
ACKNOWLEDGEMENTS
This work was supported by grant No. (RO1-2000-000-00312-0) from Basic Research
Program of the Korea Science & Engineering Foundation.
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