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INSPECTION OF COMPRESSOR DISCS BY ULTRASONIC LEAKY WAVES USING AN AUTOMATED C-SCAN SYSTEM INTRODUCTION A Fahr, N.C. Bellinger•, P. Stoute•• and A.K. Koul Structures and Materials Laboratory National Aeronautical Establishment National Research Council Ottawa. Canada, KlA OR6 "Department of Mechanical and Aeronautical Engineering Carleton University, Ottawa Presently with Orenda Division of Hawker Siddeley Canada Inc. Toronto. Ontario "*Department of Mechanical and Aeronautical Engineering Carleton University, Ottawa Presently with Vac Aero Intemational, Oakville, Ontario Damage tolerance concepts are currently being investigated for life extension of critical components of military aircraft engines. The successful implementation of the damage tolerance approach is dependent upon the availability and cost effectiveness of nondestructive inspection (NDI) techniques capable of detecting and sizing small cracks with a high degree of reliability. The reliability of NDI techniques can be determined by using a demonstration program in which a statistically valid number of flawed and flaw free parts are inspected by NDI procedures that duplicate proposed maintenance inspections. As part of a research program on life extension of aircraft engine discs using damage tolerance concepts. an NDI demonstration was carried out. The objective was to determine the sensitivity and reliability of several NDI procedures in the detection and sizing of low cycle fatigue cracks in the bolt holes of compressor discs. In addition to the standard eddy current and liquid penetrant techniques commonly used in aircraft engine maintenance depots to inspect engine components. a new procedure based on ultrasonic leaky waves using an automated C-scan was also employed. Earlier investigations(l,2) on ceramic test coupons containing artificial defects (e.g. Knoop indentation) had shown that ultrasonic leaky waves have considerable potential for detection of small surface breaking flaws. However, no data was available on the performance of leaky waves on service-induced cracks in real engine parts. Therefore, a statistical evaluation of this new method compared to the more established NDI techniques was considered to be a logical step in the development of surface ware techniques. This report describes the principles of the ultrasonic leaky wave technique and the procedures used for inspection of compressor discs. The inspection results for the leaky wave method have been compared with those of the conventional liquid penetrant and eddy current techniques using POD curves and 95% confidence bounds. ULTRASONIC LEAKY WAVE (ULW) TECHNIQUE When compressional waves are incident from a liquid onto the surface of a solid at or ncar the Rayleigh angle, 8R. as shown in Figure 1, in addition to reflected and Review of Progress in Quantitative Nondestructive Evaluation, Vol. 9 Edited by D.O. Thompson and D.E. Chimenti Plenum Press, New York, 1990 941
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Page 1: Inspection of Compressor Discs by Ultrasonic Leaky Waves ...

INSPECTION OF COMPRESSOR DISCS BY ULTRASONIC LEAKY WAVES USING AN

AUTOMATED C-SCAN SYSTEM

INTRODUCTION

A Fahr, N.C. Bellinger•, P. Stoute•• and A.K. Koul

Structures and Materials Laboratory National Aeronautical Establishment National Research Council Ottawa. Canada, KlA OR6

"Department of Mechanical and Aeronautical Engineering Carleton University, Ottawa Presently with Orenda Division of Hawker Siddeley Canada Inc. Toronto. Ontario "*Department of Mechanical and Aeronautical Engineering Carleton University, Ottawa Presently with Vac Aero Intemational, Oakville, Ontario

Damage tolerance concepts are currently being investigated for life extension of critical components of military aircraft engines. The successful implementation of the damage tolerance approach is dependent upon the availability and cost effectiveness of nondestructive inspection (NDI) techniques capable of detecting and sizing small cracks with a high degree of reliability. The reliability of NDI techniques can be determined by using a demonstration program in which a statistically valid number of flawed and flaw free parts are inspected by NDI procedures that duplicate proposed maintenance inspections.

As part of a research program on life extension of aircraft engine discs using damage tolerance concepts. an NDI demonstration was carried out. The objective was to determine the sensitivity and reliability of several NDI procedures in the detection and sizing of low cycle fatigue cracks in the bolt holes of compressor discs.

In addition to the standard eddy current and liquid penetrant techniques commonly used in aircraft engine maintenance depots to inspect engine components. a new procedure based on ultrasonic leaky waves using an automated C-scan was also employed. Earlier investigations(l,2) on ceramic test coupons containing artificial defects (e.g. Knoop indentation) had shown that ultrasonic leaky waves have considerable potential for detection of small surface breaking flaws. However, no data was available on the performance of leaky waves on service-induced cracks in real engine parts. Therefore, a statistical evaluation of this new method compared to the more established NDI techniques was considered to be a logical step in the development of surface ware techniques.

This report describes the principles of the ultrasonic leaky wave technique and the procedures used for inspection of compressor discs. The inspection results for the leaky wave method have been compared with those of the conventional liquid penetrant and eddy current techniques using POD curves and 95% confidence bounds.

ULTRASONIC LEAKY WAVE (ULW) TECHNIQUE

When compressional waves are incident from a liquid onto the surface of a solid at or ncar the Rayleigh angle, 8R. as shown in Figure 1, in addition to reflected and

Review of Progress in Quantitative Nondestructive Evaluation, Vol. 9 Edited by D.O. Thompson and D.E. Chimenti Plenum Press, New York, 1990

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transmitted waves. wave fronts of the incident waves propagate along the liquid-solid interface in the form of surface waves. The ~ is given by:

(1)

where V1 and V2 are the sound velocities in the medium 1 (liquid) and the medium 2 (test material). respectively. Since,in this case enetgy is "leaked" into the fluid. the excitation has been termed ''Leaky Waves". If a defect is present in the propagation path of the surface waves, then a reflected surface wave will propagate and leak energy into the water at angle ~. This returning leaky wave energy can be picked up by the transducer. The leaky surface waves attenuate rapidly so that only those flaws which are located very close to the point of incidence of the beam onto the specimen can be detected. This is in fact an advantage since reflections from the neighbouring flaws or sharp edges do not significantly affect the signal from the flaw of interest. Cracks or sharp edges tend to result in relatively strong signals which can be differentiated from low amplitude signals associated with surface features such as machining marks .

Early attempts to use the Immersion technique to generate surface waves were made by Derkacsi3J who found that the mode converted waves were very sensitive to surface condition. Later Khuri-Yakub et ai.I4l applied the technique to evaluate machining damage on silicon nitride rods. Fahr et al.ll.2l employed leaky surface waves to detect crack simulating Knoop indentations on ceramic samples. Indentations as small as 25~ deep and 50~ long were detected on polished silicon nitride using a 100 MHz focused probe. It was also found that the acoustic reflection coefficient of cracks was dependent on the crack size and the ultrasonic wavelength. In another Investigation, Bond et al.ISJ reported that the frequency spectra and spatial distribution of leaky waves contained information about the size of defects. All the above investigations used artificial defects on laboratory test specimens. The present work made use of the ultrasonic leaky wave method in conjunction with other techniques in a study of a large population of service induced cracks in real engine components.

Figure 1.

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~ ......... ~

' '

WATER

SOUD

\en 1

v; \ ' LEAKY \' /WAVES

SURFACE BREAKING CRACK

ft,..- PRESENCE OF A I• CRACK ,,

ABSENCE OF A 1\ I : CRACK ~11 11 n

_'\ 'lJ\ - - --- 1 rti-!'(- --

\1 \ : :: 11 ,, \J

Ultrasonic leaky wave test configuration and a typical CRr presentation at the absence and the presence of a crack.

Page 3: Inspection of Compressor Discs by Ultrasonic Leaky Waves ...

TEST COMPONENTS AND NDI PROCEDURES

Compressor Discs

The disc material was AM-355, a precipitation hardened martensitic stainless steel. Ten seiVice exposed discs that were known to have developed low cycle fatigue cracks in the tie bolt holes were selected. It was known that cracks grow radially with the majority in the direction towards the base of the discs. Each disc contained forty bolt holes so that the sample population was 400.

Leaky Wave Inspection

For inspection of compressor discs by ultrasonic leaky waves, the disc was placed on a tumtable immersed in a water tank. A 10 MHz, 2.5 em focal length probe was positioned at an angle of about 20-.J to the normal to the disc in order to send and receive ultrasonic waves. Based on an optimization process carried out before the inSpections. a lOMHz frequency and a 20..Jincident angle were found to result in an optimal signal-to­noise ratio for the compressor disc sinvestigated. The optimal incident angle of 20..Jis larger than the critical angle for longitudinal waves in steel (15..f)but less than the critical angle for shear waves (28--J). Since the bolt hole cracks occurred radially, the transducer positioned in such a way that the resulting surface waves were perpendicular to the crack face where the retum signal was found to be optimal. The transducer-disc distance was adjusted such that the beam was focused on the surface of the disc. The disc was then automatically rotated while the probe was indexed 0.25 mm radially towards the bore after each revolution until the required area of the disc was scanned. Inspections were carried out in an automated C-scan system (California Data Model 644) equipped with the Metrotek Model203 pulser, 101 receiver and two 601 alarm gates.

The most time consuming part of the inspection process was the initial optimization of transducer position and angle and gate threshold. Once this was accomplished for one disc, the other discs were inspected by simply replacing the inSpected disc with a new one and repeating the inSpection process which usually took less than fifteen minutes for each disc.

When the ultrasonic beam struck a crack, signals such as that illustrated schematically in Figure 2-a appeared on the oscilloscope screen. Figures 2-b and 2-c show corresponding signals for the beam striking both crack and the fastener hole and striking only the fastener hole. The next step was to position the alarm gates and to set the threshold levels so that a C-scan image can be obtained. The width of Gate 1 was set to cover the full range over which the peak crack signal occurred (see Figure 2). The threshold on Gate 1 was set just above the noise level. The Gate No. 2 was set to cover the full range over which signals from fastener holes occurred. The threshold on Gate 2 was set at a higherlevel than Gate 1 so that low amplitude crack signals would only trigger the alarm on Gate 1.

Liquid Penetrant and Eddy Current Inspections

For purposes of comparison, all the discs were also inspected by the liquid penetrant and eddy current techniques. The liquid penetrant inspections (LPI) were done by Level II certified technicians using military standard MIL-STD-6866 as a guideline. Three different processes were employed but only results for the best of the three are given in this report. Details of the procedures are described in another report(6).

The eddy current inspections (ECI) were carried out by two certified technicians (Level 1) using a Nortec Reichii I inStrument equipped with a rotating probe scanner designed specifically for fastener hole inspection. The unit operates at 500kHz frequency, with a maximum penetration depth of about 6 mm in the disc material. Two different gains were used, but only the results for the best of the two are reported in this work. Further information on the procedure and the results is provided elsewhere[6).

Crack Verification Procedure

To verify the NDI results. all bolt holes from the ten discs were examined by optical as well as scanning electron microscopy. A detailed description of the procedures used is given in another report(6. 7J. Briefly, coupons were cut out from the area surrounding

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INCIDENT BEAll ==I -I -I -I

I I I

INCIDENT BEAll

Jl=~--JJ\_ 1--------l GA1E1

(a)

GA1E1

GA1E2 (b)

GATE2

(c)

Figure 2. Schematic diagrams showing different position of incident beam with respect to the bolt hole and the oscilloscope view of echoes produced.

each bolt hole, which were then polished on both sides and examined under an optical microscope. Eventually all the coupons were pried open along the crack faces and crack length was measured by SEM.

RESULTS AND DISCUSSION

Ultrasonic Leakf Wave IIlSl!ection

Figure 3 illustrates a C-scan image of the disc obtained by using the leaky wave technique. The geometrical discontinuities on the disc produced traces on the C-scan image. For a crack free bolt hole, there were two indications which were produced as the result of the scattering of ultrasonic waves by portions of the top edge of bolt holes which were nearly perpendicular to the incident beam (see Figure 2-c ). For a cracked bolt hole, a third indication occurred adjacent to the bolt hole indications. Figure 3 also represents the position of a bolt hole with a crack relative to C-scan image. From C-scan indications estimates of the location and size of cracks can be made. Figure 4 illustrates the crack length estimated from the C-Scan images compared to the actual crack length along the surface of the disc as determined by scanning electron microscopy. The slope of the mean line and the correlation coefficient in this case were 0.93 and 0.73, respectively. When the estimated crack lengths are compared to the maximum crack length (also determined by scanning electron microscopy), the slope and correlation coefficient were 0.99 and 0.92 as also shown in Figure 4. This indicates that the crack lengths determined using the C-scan indications are closer to the maximum crack length rather than the crack length along the surface of the disc. This effect may be due to the fact that ultrasonic surface waves penetrate about 1.5 times the wavelength (ratio of sound velocity to the frequency which is as approximately 0.3 rom for steel at 10 MHz) into the material, interacting with the surface area of cracks. On a number of occastons during this investigation, the ULW method picked up cracks beneath the disc surfaces.

In Figure 4 also, the crack lengths determined by the ltquid penetrant method are plotted against the actual crack length obtained by SEM. The slope and correlation coefficient for this technique was 0. 78 and 0.88, respectively, indicating that the ULW method is more accurate than the conventional LPI for crack stzmg.No estimate of the crack size could be extracted from the eddy current data obtained in the present investigation.

Comparison of the Tecbnigues

A comparison of the ultrasonic leaky wave technique with the conventional liquid penetrant and manual eddy current techniques is provided in Table 1 where the total and percentage of the number of cracks detected, missed or false calls are shown for each method. Of the 400 bolt holes which were examined by optical microscopy and later by SEM, 333 of them contained cracks from a few microns up to 8.5 rom in length. The LPI technique resulted in 125 cracks detected (37.5%), 208 missed (62.5%) and 2 false calls (0.6%). The largest crack missed by the LPI method was 3.69 rom in length. The results for the eddy current inspection were much better. The nmnber of cracks detected by ECI was 253 (76%), the number of cracks missed was 80 (24%) and the

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Table 1. Summary ofNDI Results

NDI NO. OF CRACKS NO. OF CRACKS NO. OF FALSE SMALLEST LARGEST

DETECTED MISSED CALLS CRACK CRACK TECHNIQUE DETECTED MISSED

TOTAL % TOTAL % TOTAL Oh, (mm) (mm)

Ultrasonic leaky wave C.scan 167 50.2 166 49.8 2 0.6 0.17 1.48 (automated)

Eddy current (manual)

253 76 80 24 8 2.4 0.09 2.7

Liquid penetrant 125 37.5 208 62.5 2 0.6 0 .55 3.7 (manual)

number of false calls was 8 (2.4%) . The largest crack missed by ECI was 2. 7 rnrn. Although the number of cracks detected by the ULW technique at 167 (50.2%) was not as high as for ECI, this technique did detect all cracks larger than 1.5 rnrn. Also. the number of false calls was only 2 (0.6%) .

Figure 3 . A C-scan image of a compressor disc showing bolt holes with and without cracks. The position of a bolt hole with a crack relative to its C-scan image is also illustrated.

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1.0

: .. •o ~ <il . 1.0 s ~e ~! 4,0

..,~

~"' : ~ J.O .. .s :~;::

r. c 10 . .... ... .. 10 l!

<.>

00 00

X •

lO r-----------------------------,

10

60

... . . . . .. \' X

00 ~--~--~--~--~----L---~--~ 0 0 '0 1.0 , 0 .. 0 50 f 0 10

LPI Ettlm•t•d Cnd Length (mm}

LIQUID PENETRANT TECHNIQUE

lO r-----------------------------,

10

'0

"" 00~~~--~--~--~----~--~--~

ro 10 .30 •o 5o 10 10 00 10 10 30 4 0 50 IO 70

UL W Esllmated Crack Length (mm} UL w Estimated Crack Length (mm}

ULTRASONIC LEAKY WAVE TECHNIQUE

Figure 4.A comparison of crack lengths estimated from the NDI techniques with those measured using scanning electron microscopy.

To evaluate the performance of different NDI methods as the function of crack size, cracks were grouped Into 0.5 mm Intervals and histograms Indicating the number of detections, misses and total cracks per crack length Interval were generated. Figure 5 shows histograms for the three NDI techniques. Although the ULW method picked up all cracks larger than 1.5 mm In length, the detection sensitivity for smaller cracks was not very good. This is attributed to factors such as low transducer frequency ( 10 MHz) and large scattering by the edges of bolt holes due to a large beam focal spot size. Further improvement In the sensitivity of the ULW method may be possible by utillzing a higher frequency focused probe with a smaller beam diameter at the focal point. Of the techniques investigated, the eddy current method was found to be the most sensitive for the detection of small cracks.

Probabilitv of Detection

To reflect the statistical nature of NDI results, the reliabillty of detection as a function of crack size is expressed In terms of the probabillty of detection (POD). Since only one Inspection per crack was performed for each technique and there were not a sufficient number of cracks of the same length, the crack lengths were grouped Into

946

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Figure 5.

IIO r------------------------------------------------------, roo 9181

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•o

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E 40 ·

~ 30

20

10

LIQUID PENETRANT TECHNIQUE

~ No ot Cr~ch O•l•c:fllld c:::J No ol Ctu:·h Mllud

No ot Cttei:.J Pttunt

o~~~~~~~~~~~~~~~~~LW~

~ u

"' cJ .... 0

0; .Q

E ~

0 0 1.0 2.0 3 .0 4.0 5.0 0.0 7.0 1.0 1.0 10.0

Creek Length lmm}

110 -.-------------------------------------------------------,

80

70

•o

50

40

30

20

10

EDDY CURRENT TECHNIQUE

cz:J Ho ol Ct•cll Oarac:r•d 0 No ol C,ecl.f M ltud

No ol Ct~ch P1UIIIM

4 o • o e.o Creek Length lmm}

110 -,-------------------------------------------------------,

100

tO

eo

70

eo

50

40

3 0

20

10

00 10

UlTRASONIC LEAKY WAVE TECHNIQUE

(Z] No ol c,ec-h Otttclad Cl No ol Ct•ch MIUIIId

No ol Cr•ch Pt111unr

20 30 • o • o e.o Creek Length lmm}

1.0 1.0 1 .0

Histograms showing the number of cracks detected, missed and present as a function of crack length interval for different NDI techniques.

intervals of 0.5 mm. This crack length interval was found to be the best compromise between the number of crack length intervals and the rruudmum number of cracks contained in each intervali6J. The POD data points were then calculated by dMding the number of cracks detected in a given crack length interval by the total number of cracks present in that interval. For reasons explained elsewhere[6), a log-logistic distribution was used to obtain the best fit curve through the experimental POD data. The log-logistic distribution is given by the equation:

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Page 8: Inspection of Compressor Discs by Ultrasonic Leaky Waves ...

948

~ c: .2 0 ., Qj Cl ..... 0

c :B "' .Q 0 ct

~ c: .2 0 ., Qj Cl .....

100

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80

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•o

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0 0.0

100

90

80

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40 -

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· j . I I

1.0

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LIQUID PENETRANT TECHNIQUE

--------Observed Data

---Filled Log Loglsllcs Curve

-.- 95% Confidence (Norms/ Distribution)

2.0 3 .0 4.0 6.0 4. 0 7.0 80 9.0

Crack Length (mm)

• ·=· __;:.;.----

_v-= --.-- ----- .----.-

Observed Dsts

---Filled Log Logistics Curve

100

0

c :B

•o I - · - 95% Confidence (Norms/ Dlstrlbu!/on) 30 I "' .Q

0 20

I ct 10

0 .0

100

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~ 80 c: .2 70 0 .,

60 Qj Cl

60 ..... 0

c •o -:.:: :.0 30

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0 00

Figure 6.

EDDY CURRENT TECHNIQUE

1.0 2.0 3.0 4.0 6.0 6.0 7.0 8.0 9.0

Creek Length (mm)

--------------~--

/ I

. I Observf!d Dsla

I I

.I I

1.0

ULTRASONIC LEAKY WAVE TECHNIQUE

---Filled Log Logistics Curve

- · - 95% Confidence (Norms/ Dls!rlbu!lon)

2.0 3 .0 •.o r;.o eo 70 8.0 9.0

Creek Length (mm)

10 0

10 0

Probability of detection of cracks in compressor discs for three NDI techniques.

Page 9: Inspection of Compressor Discs by Ultrasonic Leaky Waves ...

pi = exp(J3o+l3t In ai)

1 +exp(J3o+J3t In ai) (2)

where P1 is the POD value for the ith crack length interval with a mean crack length of a1

and ~0 and ~~are respectively the intercept and slope parameters. In Equation 2, i varies between 1 and n, where n is the total number of crack length intervals used to plot the POD curve. The log-logistic curve represents the mean POD as a function of crack length. It is known that the probability of detection of a given NDI technique is subject to statistical variations from one test to another due to a. number of uncontrollable factors such as the ability and attitude of inspectors, component material and geometry and the flaw type and size. Standard statistical regression methods can be used to find confidence bounds for the POD curve. Mter evaluation and comparison of several methods which are described elsewhere(6) the normal distribution was chosen for presenting confidence bounds. The 95% confidence bound in the case of the normal distribution was determined by:

POD =IDD ± 1.96 Sy/x 95% confidence mean

where 1. 96 is the normal standard variate for a confidence interval of 0. 95 and Sy /x is the conditional standard variance(6) :A crack size detectable at 90% POD with 95% confidence level has been suggested in U.S. Air Force MIL-SID-1783 for use as the initial crack length in damage tolerance applications. Hence, It was decided to use the crack size at 90% POD and the 95% confidence bound to compare the different NDI techniques.

Figure 6 illustrates the observed data, a mean log-logistic POD curve fitted to the data and a 95% lower confidence bound obtained by using the normal distribution for each NDI technique. The confidence bound is a measure of the reliability, that is, the closer the confidence line to the mean POD line, the more reliable is the NDI technique. Following similar logic, the smaller the initial crack length at 900;6 POD with 95% confidence (90/95% point) the more sensitive and reliable is the NDI technique. The 90/95% crack lengths for the three techniques are shown in Figure 6. The values for the LPI, ECI and ULW techniques are respectively, 6.0 mm, 4.1 mm and 2.9 mm. Based on these data, although the ECI technique was the most sensitive for detecting small cracks (less than 1 mm), the ULWmethod appears to be the most reliable of the techniques investigated since It detected all cracks larger than 1.5 mm. If the 2. 7 mm crack missed by the ECI technique could be attributed to operator error and considered detected, then the resulting POD curve would give a 90/95% limit of 1.75 mm. This in tum would change the outcome of the study showing that the manual ECI method was the most sensitive and reliable of the techniques examined followed by the ULW method. It should be noted that the eddy current and liquid penetrant inspections were carried out manually whereas the ultrasonic leaky wave inspections were done using an automated C-scan. The higher reliability of the ULW method is attributed to the use of an automated inspection system.

CONCLUSIONS

Ultmsonic leaky waves using a C-scan system can be employed as an altemative to the liquid penetrant and eddy current techniques to detect service-induced cracks in relatively flat components. The C-scan image of cmcks can provide an estimate of crack size. Based on the results of a demonstmtion program on bolt hole cmcks in compressor discs, the technique appeared to be more sensitive than the conventional liquid penetrant but less sensitive than the eddy current method. However, in terms of reliability and speed of inspection, the use of leaky waves with an automated C-scan system provided the most impressive results. The detectable cmck sizes at 900;6 probability of detection with 95% confidence for the liquid penetrant, eddy current and leaky waves were respectively 6.0 mm, 4.1 mm and 2.9 mm. Further improvement in the sensitivity and reliability of NDI methods is required if damage tolerance based life extension procedures are to be used effectively.

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REFERENCES

1. A Fahr, S. Johar, M.K. Murthy and W.R Sturrock, Surface Acoustic Wave Studies of Surface Cracks in Ceramics, Review of Progress in Quantitative NDE, Volume 3, 1984, pp. 23.

2. A Fahr, NDE of Structural Ceramics by High Frequency Ultrasonics. Proc. Fifth Canadian Conf. on NDT, published by Atomic Energy of Canada, AECL-8707. 1985. pp. 307.

3. T. Derkacs, Ultrasonic Detection of Surface Flaws in Gas Turbine Ceramics, AD I A-076-023, TRW Incorporated, Cleveland, Ohio, Aug. 1979.

4. B.T. Khurt-Yakub, et al, Nondestructive Evaluation of Ceramics, Review of Progress in QuantitatiVe NDE, Vol. 1, 1982, pp. 601.

5. L.J. Bond and N. Saffart, Crack Characterization in Turbine Disks, Review of Progress in QuantitatiVe NDE, Vol. 3, 1984, pp. 251.

6. N.C. Bellinger, A Fahr, AK. Koul, R Gould and P. Stoute, The Reliability and Sensitivity of NDI Techniques in Detecting LCF Cracks in Fastner Bolt Holes of Compressor Discs, NAE LTR-s"f-1651, Feb. 1988.

7. AK. Koul, A Fahr, R Gould and N. Bellinger, Importance of Sensitivity and Reliability of NDI Techniques on Damage Tolerance Based Life Prediction of Turbine Discs, AGARD/SMP Review of Damage Tolerance for Engine Structures, AGARD-R-768, 1988, pp. 4.

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