QUANTITATIVE APPROACHES TO FLAW SIZING BASED-ONULTRASONIC 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 KoreaCurrently, Center for NDE, Iowa State University, Ames, IA 50011, USA

ABSTRACT. Flaw sizing is one of the fundamental issues in ultrasonic nondestructive evaluation ofvarious materials, components and structures. Especially, for cracks, accurate sizing is very crucialfor quantitative structural integrity evaluation. Therefore, robust and reliable flaw sizing methods arestrongly desired. To address such a need, using ultrasonic testing models, we propose quantitativemodel-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 areference curve named as the SAC (Size Amplitude Curve) for sizing of vertical cracks. Theaccuracy 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 integrityrequires the flaw size information. To address such a need, various ultrasonic flaw sizingmethods have been proposed up to now. These approaches can be divided into twocategories; 1) the amplitude-based approaches such as the DAC (Distance AmplitudeCorrection) 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 SPOTtechnique are the most widely used in practical field inspection. But, these approaches havesome limitations as follows: 1) the DGS diagram usually requires a large number ofspecimens, 2) the DAC curve is primarily not for flaw sizing but for the decision making ofacceptance/rejection, and 3) the SPOT technique has difficulty in acquiring tip diffractionsignals. In addition, all of these methods are largely dependent of operators, and do notquite often perform well in practice. Thus, for the reliable flaw sizing, of course,quantitative ultrasonic flaw sizing methods are strongly desired. The theoretical ultrasonictesting models can be a very promising tool for this purpose.

Until now, extensive research has been carried out to develop theoretical models topredict the ultrasonic testing (UT) signals. As a result of this endeavor, several models havebeen proposed, for example, Thompson and Gray's ultrasonic measurement model [2] andSchmerr'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

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showed the outstanding capability of predicting the UT signals in a computationallyefficient manner [4, 5].

In this study, we propose the quantitative ultrasonic flaw sizing approaches based onthe normal beam UT models and the angle beam UT models that are constructed based onthe multi-Gaussian beams. In the case of normal beam UT, we propose the efficient way forthe construction of DOS diagrams, and the optimal distance for intensity drop methods. Inthe case of angle beam UT, we propose a SAC (Size Amplitude Curve) as a new approachto the vertical crack sizing. The performance of these approaches is demonstrated with theinitial 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 modelfor a flat-bottomed hole (FBH), of which the test set-up is shown in Fig. 1. The voltagereceived 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 thespecimen respectively, Z1?Z2 are the distance from the transducer to the front surface ofthe specimen, and the distance from the front surface of the specimen to the FBH,respectively, TP

2-P is the transmission coefficient, a is radius of the transducer, p}9p2 arethe densities of the fluid and the specimen, respectively, cl9c* are the P-wave speeds in thefluid and the specimen, respectively, and A(CD) is the far-field scattering amplitude from theFBH which can be given by Eq. (2).

if)2cP;PA(6)) = ———— J, (2k} b sin Si) (2)

4sin#z

where 9t is the incidence angle, b is the radius of the FBH, CP;P is defined in thereference [5]. The diffraction correction, C(co), is given by Eq. (3).

JdetG?(o)rCXp (3)

where An,Bn are the height and width factors of the individual Gaussian beams [7], zr isthe 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 referencereflector 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 (4)

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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 reflectioncoefficient.

Fig. 2 shows comparison between experimentally measured signal and predictedtime domain waveform of the FBH with the diameter of 1.98 mm, in the case of using atransducer of 5 MHz center frequency, and 0.375 inch diameter. As shown in Fig. 2, theagreement between the theoretical prediction and the experiments is very good, withdemonstrating 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 variationin 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 50mm 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) thevariation in the water path, and (b) the variation in the metal distance.

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(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 inchdiameter (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 exactamount of overestimation is quite often not kwon. To get rid of this opaqueness, weperformed the model-based synthetic sizing of the FBH with the diameter of 1.98 mmadopting the 6 dB drop method, by use of the FBH model given in Eq. (1). Fig. 4 shows thepeak 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 theflaw size is estimated. As shown in Fig. 4, the flaw size determined by the 6 dB dropmethod varied by the choice of the water path. To investigate this variation moresystematically, we performed the flaw sizing with the variation in water path from 20 mmto 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 basedon 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 cracksizing, 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. Toovercome such a difficulty, we propose a new approach to vertical crack sizing using theangle beam UT models.

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(a) (b)FIGURE 6. Schematic representation of angle beam UT for (a) the vertical crack comer, (b) (b) the specimencomer.

(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, asshown in Fig. 6 (a), since the crack corner trap signal can be acquired very easily during theinspection of surface breaking vertical cracks. As a reference for the sizing of surfacebreaking vertical cracks, we considered the reflection signal from the specimen corner asshown Fig. 6 (b). In these cases, the footprints of the incident ultrasonic beam around thevertical crack corner (Fig. 7 (a)), and the specimen corner (Fig. 7 (b)), are to be obtained asshown in Fig. 7. Fig. 7 shows that the vertical crack corner reflects only a portion of theincident beam, while the specimen corner does the entire beam.

Since the specimen corner reflects the entire beam, the reflection signal from specimencorner can be calculated by Eq. (5).

S-Ea «=

(5)

(z2) ^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 themajority of beam energy is confined) ultrasonic beam, R$f is the reflection coefficient atthe 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 tothe 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

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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 effectiveradius ( E a ) of the footprint of the beam over the specimen corner was introduced tosimplify 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 thespecimen bottom lastly, and Vbtm(co) is the reflected velocity through the specimen bottomfirstly 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) ydetG3(z3) <JdQtGs4(z4) ydetGf (z.

(ik8? \P™(ilrS7 ]rS;P(RS;sV-TP;S\iK2 z3 ;exp\iK2z4)il2 \K23 } i2l

(8)

lE*dS»,

where Zl is the distance from transducer to the interface, z2 is the distance from theinterface to the vertical crack surface, z3 is the distance from the vertical crack surface tothe 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 begiven by Eq. (9).

P-P(KW(/))i ( j (9)

p-p(rwW)where Aa is the Aa factor, P-?(vvc(t)) is the peak-to-peak amplitude of the vertical crackcorner trap signal in the time-domain, which can be obtained by taking the inverse Fouriertransform to Eq. (6), P-?(vcor(t)) is the peak-to-peak amplitude from the specimen cornerreflection 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 verticalcrack sizing can be performed quantitatively. The SAC is a plot of the Aa versus the vertical

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crack size. Fig. 8 shows two examples of the S ACs constructed for the specimens with theheights of 10 mm and 15 mm. As shown in Fig. 8, the SACs are very similar in spite of thedifference in the specimen heights.

Performance of Vertical Crack Sizing

To demonstrate the sizing performance using the theoretically constructed SAC, weperformed 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, ofwhich the peak-to-peak voltage is measured to be 1.55 mV. For the flaw sizing using theSAC, 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-peakvoltage is calculated to be 6.5 mV. Then, we can calculate the 4, factor, which in thisparticular example, is turned out to be 23.85%. Then, finally, we can estimate the unknownvertical crack size from the SAC, as shown in Fig. 9 (c), to be 1.85 mm. Considering thefact that actual size of the crack is 2.0 mm, one can recognize that the accuracy of the SACsizing is very good.

CONCLUSIONS

In this study, we have proposed new, quantitative approaches to flaw sizing based onthe ultrasonic testing models. Specifically, we have construction of DGS diagrams with theFBH model in a computationally efficient manner. In addition, we have suggested that thenear-field length of the transducer is the optimal distance for the intensity drop method. Forthe sizing of surface-break vertical cracks, we have proposed the vertical crack reflectionmodel using the multi-Gaussian beams and defined the Aa factor, from which the newlyproposed the SACs are constructed theoretically. Then, finally, we have demonstrated theperformance 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 10 11 12 13 14Crack Size (mm)

Crack Size (mm)FIGURE 8. Estimated the SACs for two specimens with different heights: transducer: 5 MHz centerfrequency, 0.375 inch diameter, and 45 degrees diffraction angle.

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0 1 2 3 4 5Crack Size (mm)—^

(c)FIGURE 9. (a) The experimentally measured corner trap signal from the 2 mm vertical crack, (b) predictedcorner reflection signal from the 15 mm height specimen, and (c) the estimation of the vertical crack sizeusing 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 ResearchProgram of the Korea Science & Engineering Foundation.

REFERENCES

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Approach, Plenum, New York, 1998.4. Schmerr, L. W., Materials Evaluation, 58, 882-888 (2000).5. Schmerr, L. W., Lecture Note on Ultrasonic NDE Systems - Models and Measurements,

Sungkyunkwan University, Suwon, Korea, 2000.6. S. J. Song, H. J. Kim and C. H Kim, Prediction of Flaw Signals of the Ultrasonic

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Gaussain Beams, in Review Progress in QNDE, eds. D. O. Thompson and D. E. Chimenti,AIP, 21, New York, 2002, 839-846.

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