time of flight diffraction and phased array techniques for

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JULY 2011 • MATERIALS EVALUATION 891 ABSTRACT The paper deals with the detection and sizing of small transversal cracks in hydrocracking units. The minimum sensitivity code requirements for the tests were based on 4 4 0.3 mm planar discon- tinuities. This level of sensitivity was significantly higher than the normal requirements for side- drilled holes from ASME Code Case 2235-9: Use of Ultrasonic Examination in Lieu of Radiography, Section V, Article 4; the difference was at least 12 to 18 dB (ASME, 2005). Special test blocks were prepared with electric discharge machining slits embedded in the weld thickness at different depths. Time of flight diffraction and phased array testing procedures were validated on these blocks. Height sizing was important in the testing as required by ASME Code Case 2235-9 (ASME, 2005). Both techniques optimized on the test blocks were able to detect and size small trans- versal cracks. Diffracted echoes were essential for sizing the height of cracks using the phased array technique. KEYWORDS: diffracted echo, discontinuity height, pulse-echo, time of flight diffraction, phased array. Introduction This paper used heavy vessels with thicknesses ranging from 170 to 380 mm in hydrocracking units. The purpose of hydro- cracking is to increase the percentage of light hydrocarbons during crude oil processing. Previously, 75% of products from each barrel of crude oil were light hydrocarbons, while 25% consisted of heavy products like bitumen or asphalt. With the new process technology of hydrocracking, at least 12% of this 25% can be processed to obtain light hydrocarbons such as gasoline and diesel. The main parameters of this process are: high temperature of 400–800 °C (673.15–1073.1 K); high pressure of 70–140 bar; and a high content of hydrogen. To reduce the thickness of these hydrocracking units, a small percentage of vanadium was added to the standard, 2.25Cr-1Mo steel, with a benefit of 20% thickness reduction. Contrarily, the presence of vanadium in steel makes the welding process extremely difficult. Small variations in preheating, post-heat treating and stress relieving may cause dramatic cracks in the weld and in the adjacent material. Figure 1 shows small transversal cracks, detected in a 300 mm thickness circumferential weld. ASME Code Requirements for Sizing Indications The manufacturing of large pressure vessels used in the oil and gas industry requires heavy forged components for shells and heads more than 350 mm thick. These components are assem- bled by welding using narrow gap techniques. The testing of these welds is done according to ASME Code Case 2235:9, Section V, Article 4, which allows computerized ultrasonic systems, like time of flight diffraction (TOFD), phased array and computerized pulse-echo techniques, when ultrasonics is used in lieu of radiography. This code also requires all relevant indica- tions with the length and the height of discontinuities to be noted, as indicated in Table 1 (ASME, 2005). In accordance with ASME Code Case 2235:9, Section V, Article 4, research was carried out to establish a technique to size the height of the indications with good accuracy in the range of 10 to 15% for discontinuity heights between 3 and 4 mm (ASME, 2005). The findings of this research, shown in Time of Flight Diffraction and Phased Array Techniques for the Detection of Small Transversal Cracks in Hydrocracking Unit Welds in CrMoV Steel by G. Nardoni * , M. Certo * , P. Nardoni * , M. Feroldi * , D. Nardoni * , L. Possenti , A. Filosi and S. Quetti * I&T Nardoni Institute, Via D.C. Pontevica, 21 25124 Folzano, Brescia, Italy. ATB Riva Calzoni, 13, Via Industriale, Roncadelle, 25030, Brescia, Italy. ME TECHNICAL PAPER w x

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Page 1: Time of Flight Diffraction and Phased Array Techniques for

J U L Y 2 0 1 1 • M A T E R I A L S E V A L U A T I O N 891

A B S T R A C T

The paper deals with the detection and sizing ofsmall transversal cracks in hydrocracking units. The minimum sensitivity code requirements for thetests were based on 4 4 0.3 mm planar discon-tinuities. This level of sensitivity was significantlyhigher than the normal requirements for side-drilled holes from ASME Code Case 2235-9: Use ofUltrasonic Examination in Lieu of Radiography,Section V, Article 4; the difference was at least 12 to 18 dB (ASME, 2005). Special test blockswere prepared with electric discharge machiningslits embedded in the weld thickness at differentdepths. Time of flight diffraction and phased arraytesting procedures were validated on these blocks.Height sizing was important in the testing asrequired by ASME Code Case 2235-9 (ASME,2005). Both techniques optimized on the testblocks were able to detect and size small trans-versal cracks. Diffracted echoes were essential forsizing the height of cracks using the phased arraytechnique. KEYWORDS: diffracted echo, discontinuity height,pulse-echo, time of flight diffraction, phased array.

Introduction

This paper used heavy vessels with thicknesses ranging from170 to 380 mm in hydrocracking units. The purpose of hydro-cracking is to increase the percentage of light hydrocarbonsduring crude oil processing. Previously, 75% of products fromeach barrel of crude oil were light hydrocarbons, while 25%consisted of heavy products like bitumen or asphalt. With thenew process technology of hydrocracking, at least 12% of this25% can be processed to obtain light hydrocarbons such asgasoline and diesel. The main parameters of this process are:high temperature of 400–800 °C (673.15–1073.1 K); highpressure of 70–140 bar; and a high content of hydrogen.

To reduce the thickness of these hydrocracking units, asmall percentage of vanadium was added to the standard,2.25Cr-1Mo steel, with a benefit of 20% thickness reduction.Contrarily, the presence of vanadium in steel makes thewelding process extremely difficult. Small variations inpreheating, post-heat treating and stress relieving may causedramatic cracks in the weld and in the adjacent material.Figure 1 shows small transversal cracks, detected in a 300 mmthickness circumferential weld.

ASME Code Requirements for Sizing IndicationsThe manufacturing of large pressure vessels used in the oil andgas industry requires heavy forged components for shells andheads more than 350 mm thick. These components are assem-bled by welding using narrow gap techniques. The testing ofthese welds is done according to ASME Code Case 2235:9,Section V, Article 4, which allows computerized ultrasonicsystems, like time of flight diffraction (TOFD), phased array andcomputerized pulse-echo techniques, when ultrasonics is used inlieu of radiography. This code also requires all relevant indica-tions with the length and the height of discontinuities to benoted, as indicated in Table 1 (ASME, 2005).

In accordance with ASME Code Case 2235:9, Section V,Article 4, research was carried out to establish a technique tosize the height of the indications with good accuracy in therange of 10 to 15% for discontinuity heights between 3 and 4 mm (ASME, 2005). The findings of this research, shown in

Time of Flight Diffraction and Phased ArrayTechniques for the Detection of Small TransversalCracks in Hydrocracking Unit Welds in CrMoV Steelby G. Nardoni*, M. Certo*, P. Nardoni*, M. Feroldi*, D. Nardoni*, L. Possenti†, A. Filosi† and S. Quetti†

* I&T Nardoni Institute, Via D.C. Pontevica, 21 25124 Folzano, Brescia,Italy.

† ATB Riva Calzoni, 13, Via Industriale, Roncadelle, 25030, Brescia, Italy.

METECHNICAL PAPER wx

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892 M A T E R I A L S E V A L U A T I O N • J U L Y 2 0 1 1

Table 1, have demonstrated that the sizing technique, based onthe diffracted echo, is very accurate for planar and volumetricdiscontinuities, and fully complies with ASME codes (ASME,2005). The sizing technique is applicable to three ultrasonictesting (UT) techniques: pulse-echo, phased array and TOFD.

In this paper, the results of such research are reported fordetection and sizing transversal microcracks in pressure vesselwelds.

Modeling and Computer Simulation of Diffraction fromPlanar Slits and Side-drilled HolesTip diffraction occurs when a discontinuity partially obstructsthe wave propagation (Sharp, 1980; Uberall, 1998). When thediscontinuity is planar and its tip is rectilinear or curved, witha curvature radius much larger than the wavelength, then thediffracted wave is cylindrical. The width of the diffractedbeam increases as the wavelength increases, while the inten-sity of the diffracted wave is significantly less than that of thereflected wave.

When the angle between the incident direction and thediscontinuity surface is greater than 90°, the diffracted wave is inphase with the incident wave. When the angle between theincident direction and the discontinuity surface is less than 90°,the diffracted wave is in opposite phase to the incident wave.

Figures 2a–d show a series of computer simulations thatillustrate the diffraction behavior of an incident wave by a slit.

Experimental Testing with Phased Array and Pulse-echoTechniques

Diffraction from Planar Slits

Research has shown that both volumetric and planar disconti-nuities can generate diffracted echoes to be used for sizing theheights of indications (Klyuev, 2005; Wilcox, 2007). Forplanar indications, the diffracted echoes take place from bothtips of the slit. The amplitude of the echoes is similar. Figure 3shows diffracted echoes generated by a 5 mm high slit usingthe phased array technique.

METECHNICAL PAPER wx detection of small transversal cracks

Figure 1. Micrographs showing detected cracks in CrMoV steel welds:(a) optical micrograph of cracking; (b) detail of the microcracks.

(a)

(b)

TABLE 1Relationship between height, thickness and length of indication

Discontinuity 25 mm t 64 mm 25 mm t 64 mm 100 mm t 300 mm 100 mm t 300 mmaspect ratio surface discontinuity subsurface discontinuity surface discontinuity subsurface discontinuity

(discontinuity/length) (discontinuity/thickness) (discontinuity/thickness) (discontinuity/thickness) (discontinuity/thickness)0.00 0.031 0.034 0.019 0.0200.05 0.033 0.038 0.020 0.0220.10 0.036 0.043 0.022 0.0250.15 0.041 0.049 0.025 0.0290.20 0.047 0.057 0.028 0.0330.25 0.055 0.066 0.033 0.0380.30 0.064 0.078 0.038 0.0440.35 0.074 0.090 0.044 0.0510.40 0.083 0.105 0.050 0.0580.45 0.085 0.123 0.051 0.0670.50 0.087 0.143 0.052 0.076

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Diffraction from Side-drilled holes: Volumetric Discontinuities

In practice, generation of a secondary echo from a cylindricalreflector involves a creeping wave, which appears like adiffracted echo (Krautkrämer and Krautkrämer, 1985; Sharp,1980). The incident beam generates a creeping wave on thereflector surface that flows around the discontinuity andreflects back a wave of the same nature as the incident one.The path difference between the direct echo and thediffracted echo allows for the calculation of the size of thehole diameter. It is possible to determine hole diameter, D,by measuring the path difference, L.

Figure 4 shows an example of diffraction generated by 3 mm diameter side-drilled holes in a calibration block. Thediffracted echoes are clearly visible on the image; the pathdifference between the reflected echo and the diffracted echois 4.3 mm. From the hole sizing formula, a 3.2 mm side-drilledhole diameter was obtained, which overestimated the realvalue by only 0.2 mm.

Figure 2. Computer simulations of diffraction behavior of planardiscontinuities and mode transformation at the longitudinal/shearboundary: (a) ultrasonic longitudinal/transverse wave traveling insteel; (b) upper tip diffraction from planar discontinuity; (c) lower tipdiffraction from planar discontinuity; (d) mode transformation at theboundary.

(a)

(b)

(c)Figure 3. Test block: (a) with slit used for tip diffraction with thephased array technique; (b) screenshot.

(a)

(b)

121 mm

25 mm

Electric discharge machining planar slit4 × 4 × 0.2 mm

A

B

Block no. 1

(d)

Figure 4. Screenshot of diffractions in a test block with a side-drilled hole.

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Procedure Validation for 300 mm Thickness Weld Testing

To validate the application of the diffraction technique forsizing discontinuities, a 300 mm thick test block was preparedto simulate small transversal cracks (Komura et al., 2001). Tomake this type of test block, eleven 4 4 0.3 mm slits weremade at different depths, as shown in Figure 5 and Table 2.The system for manufacturing the test block was made inorder to avoid welding over the slits during the embeddingprocess to maintain their original height with a tolerance of0.1 mm. In addition, a second block was prepared with 3 mmdiameter side-drilled holes, distributed across the thickness on

the centerline axis of the weld. On this second block, thebeam focusing, according to the scan plan for the phased arraytechnique, was verified.

The first objective of the validation process was toevaluate the results of the phased array technique, based ondiffraction, compared to those of TOFD. The second objec-tive was to verify the detection capabilities using probability of detection (POD), for both techniques, of small planar verticaldiscontinuities (4 4 mm) at depth values up to 300 mm.

Phased Array Technique

Instrumentation Set-upTwo ultrasonic channels (which operated simultaneously)were set up on the electronic instrumentation. Channel 1 wasconfigured for testing at depths ranging from 50 to 300 mm.Channel 2 was configured for testing at depths ranging fromthe subsurface to 60 mm. The configuration parameters forthe two channels are shown in Table 3.

Scanning DirectionThe scan direction was perpendicular to the 4 4 mm slits.The origin was 17 mm from the side where the deepestdiscontinuity was embedded and the scan length was set to700 mm. A scan line path was chosen so that the ultrasonicbeam axis lay in the vertical plane passing through the centerof each slit.

Testing ResultsFor each detected slit, the best probe position was selected todisplay the slit itself on an S-scan image in order to show slitlocation and size. An example of such images is shown inFigure 6. Table 4 summarizes location data and height of eachof the 11 slits.

The phased array testing on the test block with steppedslits produced the following results:� The 11 slits were fully detectable.� A pair of diffracted echoes was present in all of the slits. � For each slit, the sizing was always possible with an averageerror of ±5% in height estimation for a 4 mm electricdischarge machining (EDM) notch height.

894 M A T E R I A L S E V A L U A T I O N • J U L Y 2 0 1 1

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TABLE 2Depth values of the 4 × 4 mm planar vertical discontinuities

Slit number Depth (mm)1 42 303 604 905 1206 1507 1808 2109 24010 27011 294

300 mm

270 mm450 mm270 mm

12

34

56

78

910

11

4 × 4 mmembedded slits

30 mm

1.5 mm side-drilledhole

3 mm side-drilledhole

75 mm

75 mm

75 mm

Figure 5. Test block used for procedure validation.

TABLE 3Configuration parameters for the two channels of instrumentation set-up

Parameter Channel 1 Channel 2Probe frequency 2.25 MHz 2.25 MHzNo. of probe elements Total: 32; active: 32; starting from no. 1 Total: 32; active: 16; starting from no. 1Distance between elements 1.4 mm 1.4 mmSectorial scan angles Between 35 and 70° Between 50 and 80°Receiver dynamics focus range Between 25 and 600 mm Between 8 to and 150 mmTransmitter focus range 400 mm 100 mmAcquisition gate Between 26 and 600 mm Between 6 and 150 mmProbe delay 61.76 mm 35.03 mm

* Sensitivity calibration: use of time corrected gain to maintain echo amplitude from the test block’s 3 mm side-drilled holes at 80% of screen height.

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To obtain the best resolution between the twodiffracted echoes, the appropriate scan angle on the slitshould be selected.

Time of Flight Diffraction Technique

Instrumentation Set-upFour ultrasonic channels were used to cover the 300 mmlength of the test block. Table 5 and Figures 7a–d show thefour channels and depth zones with the relevant probe parameters selected.

Testing ResultsThe TOFD maps related to the different depth zones are indi-cated in Figure 8, and the average error in the testing of the 11slits is shown in Table 6.

Figure 6. Cluster of slits from 75 to 180 mm depth.

TABLE 4Summary of estimated data relevant to position, depth and size from phased array testingDiscontinuity Real data Ultrasonic testing

number Center depth Position Channel Upper tip Lower tip Center depth Position Height(mm) (mm) no. depth (mm) depth (mm) (mm) (mm) (mm)

Est. Error Est. Error Est. Error1 4 725 – – – – – – – – –2 30 680 1 31.8 36.5 34.15 +4.15 681.1 +1.1 3.7 –0.32 30 680 2 21.7 26.4 24.05 –5.95 674.5 –6.5 4.7 +0.73 60 635 1 62.6 66.6 64.60 +4.60 640.5 –5.5 4.0 0.03 60 635 2 60.1 63.6 61.85 +1.85 628.3 –5.7 3.5 –0.54 90 590 1 93.8 97.5 95.65 +5.65 592.9 –2.9 3.7 –0.74 90 590 2 91.4 95.5 93.45 +3.45 581.9 –9.1 4.0 0.05 120 545 1 131.0 134.8 132.90 +12.90 543.1 –1.9 3.9 –0.16 150 500 1 149.1 152.9 151.00 +1.00 502.8 –2.8 3.9 –0.17 180 455 1 187.9 191.9 189.90 +9.90 450.4 –4.6 4.0 0.08 210 410 1 212.3 216.3 214.30 +4.30 408.7 –2.3 4.0 0.09 240 365 1 242.4 246.6 244.50 +4.50 362.8 –3.2 4.2 +0.210 270 320 1 270.3 273.7 272.00 +2.00 319.1 –0.9 3.4 –0.611 294 284 1 295.7 298.6 297.15 +3.15 282.3 –1.7 3.1 –0.9

* Est. = estimated.

TABLE 5Scan plan for thickness of 300 mm

TOFD pair number Thickness of block Angle beam Depth zone Beam centerline, probe center(depth zone and (mm) (°) (mm) spacing, probe shear wave channel no.) angle and megahertz

Beam centerline = 15 mm1 300 70 0 – 35 Probe center spacing = 80 mm

Probe : 70°, 5 MHzBeam centerline = 55 mm

2 300 52 25 – 70 Probe center spacing = 160 mmProbe: 52°, 3.5 MHzBeam centerline = 150 mm

3 300 45 50 – 200 Probe center spacing = 300 mmProbe: 45°, 2.2 MHzBeam centerline = 260 mm

4 300 35 180 – 300 Probe center spacing = 370 mmProbe: 35°, 2.2 MHz

* TOFD = time of flight diffraction.

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896 M A T E R I A L S E V A L U A T I O N • J U L Y 2 0 1 1

Figure 7. Graphical representations of: (a) Depth zone 1 with 70°, 5 Mhz, Ø6 mm and probe center spacing (PCS) of 80 mm; (b) Depth zone 2with 52°, 3.5 Mhz and Ø18 mm and PCS of 160 mm; (c) Depth zone 3 with 45°, 2.2 Mhz and Ø24 mm and PCS of 300 mm; (d) Depth zone 4with 35°, 2.2 Mhz and Ø24 mm and PCS of 360 mm.

(a)

(d)(b)

(c)

Figure 8. Time of flight diffraction images of: (a) 1° and 2° slit with Channel 1, 70°, 5 Mhz and Ø6 mm; (b) 2° and 3° slit with Channel 2, 52°,3.5 Mhz and Ø18 mm; (c) 3°, 4°, 5°, 6° and 7° slits with Channel 3, 45°, 2.2 Mhz and Ø24 mm (EDM = electric discharge machining); (d) 3°, 4°, 5°, 6° and 7° slits with Channel 4, 35°, 2.2 Mhz and Ø24 mm (EDM = electric discharge machining).

(a)

(b)

(c)

(d)

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Image Evaluation

The contrast of gray level, which referred to the positive andnegative value of the TOFD images, is fundamental for sizing,as well as for validating the correct set-up of the probes atdifferent depths. Figure 9 shows a set-up of the TOFDscanner for parallel scanning to detect transversal cracksduring calibration. To be more objective in the evaluation ofthe results, two classification parameters were established: thetip resolution and the contrast between the positive andnegative phase of the indications. These criteria are shown inTable 6, along with the results of the measured height of the 4 mm EDM slits at different depths. In Figure 10, twoscanners are shown during the testing of pressure vessel weldsfor transversal crack detection.

ConclusionIn regards to the testing of CrMoV steel welds, in order todetect very small transversal cracks of an average height of 2 to 4 mm, the phased array technique and TOFD are bothcapable with additional requirements, such as an increase ofthe amplitude in the phased array technique and the calibra-tion of measuring slit heights in TOFD.

The diffracted echo used in the phased array technique isa very important parameter for sizing cracks or volumetricindications when the height is less than the crystal size (Dube,2004; Lafontaine and Cancre, 2000). The accuracy in theheight estimation of 4 mm high slits was ±5%. The 6 dBamplitude drop for this type of indication overestimated thereal value by approximately 200 to 300%. The POD forphased array on planar indications, as with the cracks in theweld, was confirmed to be acceptable for the ASME coderequirements (ASME, 2005).

As for the described crack, the detection of small planarindications takes place not by the reflection from the surface,but by diffraction from the two tips. To obtain this result, itwas necessary to increase the gain level calibration from

J U L Y 2 0 1 1 • M A T E R I A L S E V A L U A T I O N 897

Figure 9. Scanner used during parallel scanning on 300 mm welds forreheat cracks detection on hydrocracking unit welds.

TABLE 6Summary of size estimation results and image evaluationSlit no. Probe 70°, PCS 80 Probe 52,° PCS 160 Probe 45°, PCS 300 Probe 35°, PCS 370

5 MHz, Ø6 mm 3.5 MHz, Ø18 mm 2.2 MHz, Ø24 mm 2.2 MHz, Ø24 mmHeight Depth Image Height Depth Image Height Depth Image Height Depth Image

1 4.5 6 1-B – – 3-C – – NVI – – NVI2 3.9 30 2-A 4.7 30 2-B – – 3-C – – NVI3 – – NVI 4.2 60 1-A 4.6 60 2-C – – NVI4 – – NVI – – NVI 4.8 90 1-A – – NVI5 – – NVI – – NVI 3.8 120 1-A – – NVI6 – – NVI – – NVI 4.1 150 1-A 3-C7 – – NVI – – NVI 4.3 180 2-B 4.8 180 2-B8 – – NVI – – NVI – – 3-C 4.5 210 2-B9 – – NVI – – NVI – – NVI 4.2 240 1-A10 – – NVI – – NVI – – NVI 4.0 270 1-A11 – – NVI – – NVI – – NVI 3.2 294 1-B

* NVI = no visible indication; PCS = probe center spacing.

Figure 10. Two scanners positioned on two circumferential welds fortime of flight diffraction parallel scanning to detect transversal crackson a 300 mm pressure vessel.

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12 to 18 dB (ASME, 2005). In this condition, the deepest slitat 285 mm was clearly detected and sized. To obtain the bestresolution between the two diffracted echoes, the proper scanangle on the slit should be selected.

The TOFD technique was confirmed to be the best tech-nique for POD and sizing of planar/volumetric indications inregards to the sizing accuracy, as shown in Table 6. Toachieve these results, it was necessary to implement and use aproper procedure for discontinuity image classification, asindicated in Table 7. This criterion is fundamental in the defi-nition of the scan plan and to make different testing resultscomparable.

REFERENCES

ASME, Code Case 2235-9: Use of Ultrasonic Examination in Lieu of Radiog-raphy; Section V, Division 4, American Society of Mechanical Engineers,New York, New York, 2005.ASME, Rules for Inservice Inspection of Nuclear Power Plant Components;Section XI, Mandatory Appendix VIII, Supplement 2, American Society ofMechanical Engineers,New York, New York, 2010, p. 295.Dube, N. (ed.), “Introduction to Phased Array Ultrasonic TechnologyApplications: R/D Tech Guideline (Advanced Practical NDT Series),”Quebec, QC, Canada, R/D Tech, Inc., 2004. Klyuev, V. V. (ed.), Handbook of Nondestructive Testing, Russian Society forNondestructive Testing and Technical Diagnostics, Moscow, Russia, 2005. Komura, I., T. Hirasawa, S. Nagai, J. Takabayashi and K. Naruse, “CrackDetection and Sizing Technique by Ultrasonic and ElectromagneticMethods,” Nuclear Engineering and Design, Vol. 206, Nos. 2–3, 2001, pp. 351–362. Krautkrämer, H. and J. Krautkrämer, Ultrasonic Testing of Materials, 3rd ed.,Springer-Verlag, Berlin, Germany, 1985. Lafontaine, G. and F. Cancre, “Potential of Ultrasonic Phased Arrays forFaster, Better and Cheaper Inspection,” NDT.net, Vol. 5, No. 10, 2000,www.ndt.net/article/v05n10/lafont2/lafont2.htm. Sharp, R. S., “Research Techniques in Non-destructive Testing,” Vol. IV,Academic Press, New York, New York, 1980. Uberall, H., “Interference and Steady-state Scattering of Sound Waves,”Handbook of Acoustics (ed. M. J. Crocker), John Wiley and Sons, Inc.,Hoboken, New Jersey, 1998, pp. 47–59. Wilcox, P. D., C. Holmes and B. W. Drinkwater, “Advanced ReflectorCharacterization with Ultrasonic Phased Arrays in NDE Applications,”IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol.54, No. 8, 2007, pp. 1541–1550.

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TABLE 7Time of flight diffraction images characterization parameters:phase contrast (gray level) and tip resolution

Phase contrast Tip resolution1: Very good A: Well resolved2: Good B: Slightly resolved3: Poor C: Not resolved

* Best image: image 1-A; worst image: 3-C (sensitivity not acceptable).