shear waves on tofd

7/28/2019 shear waves on tofd

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Technical Report

The Application of Shear Waves

to the Time-Of-Flight Diffraction Method

Che Chien Ng, Xiaodong Wang, and Ming J Zuo

Department of Mechanical Engineering

University of Alberta

Edmonton, Alberta, T6G 2G8

June 28, 2006

1. IntroductionIn the early establishment of ultrasonic nondestructive evaluation, typical crack sizingmethods utilized the reflected amplitude of echoes returning from a crack. An ultrasonic

NDE that uses separate transmitting and receiving transducers is referred to as the tandem

or pitch-catch method. Such a configuration is commonly used in through-transmission

testing, in which transducers are placed geometrically aligned and facing one anotherwith a test object resting in between. Defect detection is carried out based on the

amplitude level of the signal collected by the receiving transducer. In the absence of

defect, the ultrasound signal arriving at the receiving transducer is expected to showconstant amplitude. If, on the other hand, the transducer pair encounters a defect, the

amplitude of the signal observed at the receiving end will decrease or vanish according to

the crack size. This approach is usually referred to as the decibel-drop approach. It is

important to note that the through-transmission technique requires good and consistentcoupling apart from the obvious: good and consistent alignment of the transducer pair.

This technique is used mostly in coarse testing where accuracy was not critical; the

advantage to it is that, compared to the commonly used pulse-echo testing, it is a morereliable technique when one inspects a material that has a high scatter or attenuation level

such as plywood and reinforced plastics (Szilard 1982)

In the late 1970s, a new ultrasonic NDE method was developed by Silk and Ladington

(1975). It utilized the pitch-catch configuration of an angle beam transducer pair, with

time delay being the only analyzed parameter. This method was later called Time-of-flight Diffraction (TOFD) because crack sizing was carried out based on these two

aspects: the time-of-flight and the diffraction phenomenon. In this case, time-of-flight isdefined as the time required by the ultrasound to propagate through the material; it ismeasured as the difference between ultrasound excitation time at the transmitter and

arrival time at the receiving transducer.

The explanation of the diffraction phenomena originated from Huygens principle

(Baskaran et al 2004). According to this principle, the crack tip acts as a secondary point

source of waves upon wave incidence. The tip thus reradiates ultrasonic energy over a


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wider angular range than in the case of reflection and transmission in conventional

ultrasonic inspection. These diffracted waves are the main object of attention in theTOFD technique.

2. Principles of TOFDThe typical configuration of the TOFD technique and its corresponding A-scan areillustrated in Figure 1. Essentially, there are 4 types of waves that need to be observed in

an inspection based on the TOFD technique. The first type is the lateral or near-surface

wave that travels directly from the transmitter to the receiver just under the specimenssurface with a wave speed equal to that of the bulk longitudinal wave. This wave has a

relatively short pulse and a low amplitude standing signal that occurs at a fixed position

determined by the probe separation distance. It is used as the first reference for defect

depth measurement. In the case of a defective test object, diffracted signals coming fromthe top and bottom tips of the crack will appear following the lateral wave. The primary

backwall reflection signal that is caused by the reflection of the ultrasonic wave at thebackwall will close the time envelope in which crack-tip-diffracted signals appear. Thisbackwall reflection is used as the second reference for determining crack location.

Fig 1 - Typical TOFD setup and the resulting A-scan (Apragaz 2004)

In general, there are three cases that can be considered when using TOFD method. The

first case involves embedded or internal crack. In this case, there will be 2 crack-tip-diffracted waves observed between the lateral wave and the backwall reflection in the

TOFD scanning results. The other two cases involves surface breaking cracks in whichthere is only one crack tip and, hence, only one crack-tip-diffracted wave appears in thescanning results (Silk 1979). See Figure 2 for an illustration of these phenomena. Note

that, in the case of surface breaking cracks, the amplitude of the backwall reflection and

the lateral wave are significantly reduced when the crack is located either on the opposite

side or on the same side of the probe.


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Figure 2 Three general cases of TOFD test objects: (a) internal crack, (b) surfacebreaking crack on opposite side of probe and (c) surface breaking crack on

same side of probe (Silk 1979)

When the probe spacing and the thickness of the material are known, defect depth and

size can be calculated based on the arrival times of the lateral, primary backwall and

diffracted waves. Additionally, one will find a secondary backwall reflection due to modeconversion from longitudinal to shear waves. This signal will arrive at the receiving

transducer after the primary backwall echo. Although it is often not included in the

analysis, this secondary echo may provide better resolution of the flaws (than dolongitudinal waves alone) due to its lower velocity (Al-Nuamiy and Zahran 2005 andBirring and Nidathavolu 2005).

Unlike conventional ultrasonic inspection which relies on reflected echo amplitude fordefect size measurement, TOFD is not amplitude dependent because it observes low

amplitude signals diffracted from the extremities of a crack. This forms an absolute basis

for crack detection and sizing, regardless of the amplitude of the signal captured by thereceiving transducer. Another benefit over conventional pulse-echo ultrasonic inspection

is that due to the wide beam probes used and TOFDs focus on extremities of cracks,

TOFD is not as dependent on defect orientation as much as pulse-echo is.

Nevertheless, TOFD is not without its limitations. Due to the inevitable appearance of

lateral waves traveling near the surface (typically 3-5 mm), defects existing in this region

are often left undetected. This region is referred to as the dead zone. Since thediffracted signals resulting from the defect are superimposed above the lateral wave

signals, detection is still possible, although defect sizing will be less reliable. One

solution is the use of a short pulse transducer with small beam divergence; this will limitthe effect of lateral waves to 2-3 mm below the surface of steel specimens. It is also


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possible to electronically process the lateral waves in the same way noise is removed; this

is because the signals are consistent, appearing at recurrent position (Browne 1997). It iscommon to obtain busy A-scan signals only because of the weak amplitude of the

diffracted signals combined with the existence of noise originating from small pores or

non-uniformity within the specimen (Lawson 1996).

TOFD is mostly applicable to, although not limited to, the inspection of welded joints.

Experiments on TOFD have been carried out during inspection of pipelines, pressure

vessels and railroad tracks. Based on a cracks location, both embedded and surfacebreaking cracks have been included in the experiments. Baby et al (2003) concluded that

TOFD is an excellent method for measuring vertical and inclined slits (100

and 150

from

vertical) used as simulated surface-breaking cracks on steel blocks. Mean crack heightserrors in vertical and inclined slits are reported to be 0.13 mm and 0.06 mm, respectively.

Comparisons were carried out between the actual and the estimated sizes of the cracks.

Zippel et al (2000) used saw-cut notches and real fatigue cracks on steel plates for theirexperiments on the TOFD method. The reported accuracy ratio between the specified and

the calculated depths of the cuts were within 5%. Both of these studies agreed that theaccuracy of crack depth estimation was reduced when crack tips were located near the

surface. In the case of artificial or simulated cracks, Zippel et al (2000) reported aminimum accuracy of 20% for saw-cut notches with depths greater than or equal to 6

mm, while Baby et al (2003) reported difficulty in sizing cracks (slits) having depths of

less than 2 mm.

3. Locating and Sizing CracksProvided a crack exists in a specimen, and assuming the crack is oriented in a plane

perpendicular to the inspection surface, both cracks size and location can be calculatedbased on the arrival time of various waves as illustrated in Figure 3. It is expected that

lateral waves will have the shortest arrival time, followed by diffracted waves coming

from the top and bottom of a cracks extremities. The backwall reflection closes the timeenvelope inspected in TOFD.

Figure 3 Crack measurement in TOFD (Silk 1987)


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Complementing variables shown in Figure 3, let:

tl = time travel of the lateral wavetdt = time travel of the diffracted wave from the top extremity of the crack

tdb = time travel of the diffracted wave from the bottom extremity of the crack

tbw = time travel of the backwall reflected wave

clw = longitudinal wave speed in the material2a = crack length

Using Pythagoras Theorem (Baby et al 2003) and assuming that the crack is equidistantfrom the transmitter and receiver, the formulations are:

a)lw

lwc

St

2=

b)lw

dtc

Sdt

222 +=

c)lw

dt c

Sad

t

22)2(2 ++

=

d)lw

dtc

SHt

222 +

=

The crack is positioned midway between the transmitter and receiver in order to obtain

the shortest time-of-flight for the crack tip diffracted waves. By differentiating the

general formula (Figure 4) with respect to the lateral distance between the crack tip and

the centerline, the line which marks half the distance separating the transducers, it wasfound that when this centerline coincides with the crack tip position (X=0), the time-of-

flight of the crack-tip-diffracted waves are at their minimum and thus, the location of the

crack tip can be determined.

Figure 4 - Generalized formulation of TOFD (Silk 1987)

T R

S X

2S

M L

d

Crack

centreline

clw.tdt = M + L

=22 )( XSd ++ + 22 )( XSd +


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4. Experimental Results and DiscussionsTOFD is commonly done using an angle beam longitudinal wave transducer pair thatintroduces refracted longitudinal waves into the specimen. Refraction phenomena can be

predicted using Snells Law, which relates the angle of incidence to the angles ofrefraction and reflection based on the ratio of material sound velocity:

rl

rl

rs

rs

i

i

v

Sin

v

Sin

v

Sin ==

where i, rs and rl correspond to the angles of incident, the refracted shear wave and therefracted longitudinal wave, respectively, and vi, vrs and vrl are the material soundvelocity of the incident, the refracted shear wave, and the refracted longitudinal waves,

respectively. An illustration of Snells Law can be seen in Figure 5. Regardless of wave

type, ultrasound velocity is different for each material and, generally, shear wave velocity

is approximately half of longitudinal wave velocity. For mild steel, longitudinal wave

velocity is approximately 5.9 mm/s and shear wave velocity is 3.2 mm/s.

Figure 5 - Representation of Snells Law.

No literature has reported the use of shear waves in the TOFD method due to their higher

attenuation compared to longitudinal waves. Still, there are several advantages to using

shear waves. Due to their slower sound velocity, the time-of-flight of a shear waveultrasound is increased and, as a result, detection and measurement of smaller defects is

improved (Golan 1981). It is harder to distinguish between upper and lower crack tips

with longitudinal waves because their higher velocity leads to a shorter time-of-flight

and, in the case of small cracks, the two diffracted waves superimpose upon each other.Moreover, shear wave amplitude possesses higher sensitivity to changes in transducer

displacement and this leads to better positioning to obtain maximum signal amplitude.

Note that, in the case of fatigue cracks, Golan reported higher amplitude sensitivity fromangle beam transducer pairs that introduce shear waves rather than longitudinal waves

into the test object (Golan 1980).

Experiments on the use of shear waves for the TOFD method were conducted in the joint

laboratory of the Reliability Research Group and the Advance Structures and Materials

Research Group at the University of Alberta. The experimental setup consisted of an

i

rs

rl

Transducer

Test object


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AFG320 arbitrary function generator, a TDS3000 digital oscilloscope and a pair of 2.25MHz, and 0.5 diameter angle beam transducers with 450, 600 and 700 wedges. The

specimens being tested were 22.8 mm-thick 4340 steel blocks. One of the steel blocks

had an EDM-cut slit with a depth of 12.8 mm. The width of the slit was 0.4 mm. The

function generator was set to excite a narrowband pulse, and the subsequent signal

response was displayed on an oscilloscope.

The first step of the experiment was calibration. Based on the separation distance, thetransducer pair was tested on specimen with no slit to confirm the marked beam index on

the transducers wedges. Note that, the separation distance, 2S in Figure 4, was measured

as the distance between the marked index on the transmitters and receivers wedges.Using the Pythagoras formulation described earlier, it was expected that backwall

reflection with maximum amplitude will be obtained when the transmitter and receiver

were separated by approximately 45.6 and 78.9 mm on 450

and 600

wedges, respectively.

Because the center of the beam exiting the transmitter did not reach the receiver, areduction of these separation distances led to decreasing amplitude as can be observed in

Figure 6. A similar effect was observed as separation distance was increased, becausemaximum amplitude could be obtained only when the center of the beam from thetransmitter reached the receiver.

Figure 6 - Backwall reflections of a non-defective steel block at separation distances of39 mm, 58.5 mm, and 78 mm using a wedge angle of 60

0

Since the steel block used for calibration in our experiment was defect-free, it was

expected that in each scanning, two signals would be found: lateral wave and backwall

reflection. From Figure 6, however, it can be seen that the lateral waves were non-existent. Later, it was learnt that lateral waves are actually longitudinal waves traveling

close to the specimens surface. They can be generated only if the transducer has

sufficient beam spread so that the outer edge of the beam spread reaches the specimensupper surface. The formulation for beam spread half angle is as follows.

78 mm58.5 mm

39 mm


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fD

cSin

=

22.1

where denotes the divergence or half beam spread angle, c the material sound velocity,f the transducer central frequency, and D the transducer element diameter. From this

formula, it can be seen that using transducers with similar central frequency and element

diameter, longitudinal wave transducers, with their higher material sound velocity willproduce wider beam spreads than will shear wave transducers and, hence, they allow the

generation of lateral waves. Using the specified transducers, the calculated divergence

angle is approximately 80. The amount of beam spread in TOFD is commonly sufficient

for covering the thickness of a test object at a single scan. It is expected that deficiency in

beam spread could be offset by using the transducer pair at various separation distances.

In order to observe the effect of beam spread on crack-tip-detection, a 600

transducer pairwas positioned so that the slit was located exactly in the middle and the separation

distance was varied to direct the center of the beam at different points along the breadth

of the specimen. As the separation distance increases, the center of the beam points

further down toward the specimens bottom surface. From Figure 7, one can see that theamplitude of the crack-tip-diffracted wave is reduced because the center of the beam

moves away from the tip of the slit as the transducers are moved further apart. From thistrend, it can be deduced that ultrasonic waves, which are emitted by the transmitter, are

not unidirectional. Instead, there is a certain amount of beam spread and, amplitude of the

ultrasound weakens away from the beam center.

On experiments with the 450

angle beam wedges, calibration steps similar to those

previously discussed were repeated. The resulting separation distance was 46 mm and

differed by 0.4 mm of the calculated value. From literature reviews, we learnt that thecenter of the beam exiting the transducer needs to be directed to approximately half of the

specimens thickness midway between the transmitter and receiver. Also, from previousexperimental results, we learnt that the maximum diffracted signal amplitude wasobtained if the center of the beam impinged on the crack tip (Silk and Lidington 1975).

In order to locate the crack tip, two approaches were tested. In the first approach, the

separation distance was fixed at 46 mm, and the transducer pair was moved together

laterally from the left side to the right side of the slit while keeping a consistentseparation distance. Total lateral displacement of the transducer pair was 16 mm, with a

2-mm increment. Zero displacement was set when the centerline between the transmitter

and the receiver aligned with the slit. The second approach is to start from a separationdistance that is as close as possible to twice the slit depth (25.6 mm) instead of twice the

specimen thickness (46mm). This leads to a shorter wave propagation path and betterpossibility that crack-tip-diffraction echo will be observed. Similarly, a 2-mm increment

is used, up to a separation distance of 35.6 mm. In the following, we discuss these twoapproaches in details.


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Figure 7 - Signal response of 600

transducer pair obtained under different separation

distance on steel block with slit.

In Figure 8, scanning results based on the first approach are shown from the crack

position midway between the transducer pair with signals recorded at lateraldisplacements of 0, 2, 4, 6 and 8 mm to the right. Since no crack-tip-diffracted echo was

found using the first approach, and in order to improve time-series observation, only the

backwall reflections are displayed. The slight differences among the times-of-flight of the

signals are due to the small variation of separation distances. With further observation,one can see that the amplitude of the backwall reflection decreases as the transmitting

transducer approaches the slit. The lowest amplitude of the backwall reflection signalshown in Figure 8 was obtained at an 8-mm lateral displacement of the transducer pair. In

this case, the distance between the transmitter and the slit location was at its minimum.

As the transmitter moved closer to the slit, the portion of the beam reaching the backwall

was reduced and as a result, the amplitude of the backwall reflection decreased. At thesame time, increasingly the portion of the beam impinged on the tip of the slit;

2S = 55.5 mm 2S = 58.5 mm

2S = 61.5 mm 2S = 72 mm

Crack Tip Crack Tip

Crack Tip

Backwall

Reflection

Backwall

Reflection

BackwallReflection

BackwallReflection


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theoretically, diffraction is supposed to occur. It is suspected that as an incident waveimpinges on a crack tip, the low amplitude diffracted wave is unable to overcome the

attenuation due to the wave propagation path.

In the second approach, the separation distance is reduced to approximately half that was

used in the first approach. Scanning was conducted while keeping the slit locationmidway between the transmitter and receiver as the separation distance varied from 27.6

mm to 35.6 mm in 2 mm increments. In order to reduce transducer placement error, theseparation distance was measured from the front side of the transducers wedges instead

of from the beam indexes marked on the side of the wedges. This alteration in

measurement from 2S to 2Sfw is illustrated in Figure 9.

Figure 8 - Back wall reflections of a defective steel block using a 46 mm separation

distance and 0 mm (red plot) to 8 mm (green plot) lateral displacement of the

transducer pair

Figure 9 - Wedge distance measurement (2S = separation distance, 2Sfw = distance

between transmitters wedge and receivers wedge front walls)

8 mm displacement

0 mm displacement


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The distance between the marked beam index and the front wall of the transducer wedge

is 12.8 mm as measured with a digital caliper. Hence, the wedge distance, 2Sfw, varied

from 2 mm to 10 mm in 2 mm increments. In order to avoid the transmitters coming into

contact with the receiver, 2 mm of wedge distance or a 27.6 mm of separation distance is

the closest possible transducer pair configuration. Under this condition, the center of thebeam will be pointed at a depth of 13.8 mm from the scanning surface, or 1 mm below

the tip of the slit; and the corresponding signal response will be marked as the maximumcrack-tip-diffracted-wave amplitude. Scanning results from the second approach are

presented in Figures 10 and 11.

Figure 10 - Time series for a defective steel block with transducer separation distances of

31.6 mm (green plot), 33.6 mm (red plot) and 35.6 mm (blue plot)

Figure 11 - Time series for a defective steel block with transducer separation distances of

27.6 mm (cyan plot), 29.6 mm (purple plot) and 31.6 mm (green plot)

Crack Tip

Signals

Back wallreflections

Crack Tip

Signals

Back wall

reflections


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From Figures 10 and 11, it can be seen that both crack-tip-diffraction waves and backwall

reflections can be observed when separation distances of the transducer pair are

sufficiently small. Note that, amplitude of backwall reflection was reduced because it was

measured using the side lobe of the beam. Certain trends regarding the times-of-flight and

signal amplitudes of the crack-tip-diffracted waves and backwall reflections are plotted inFigures 12 14.

Time-of-flight vs . Separation Distance

0

5

10

15

20

25

25 30 35 40

Separation Distance [mm ]

Tim

e-of-Flight[s

]

Diffracted

Wave

Backwall

Reflection

Figure 12 Time-of-Flight vs. Separation Distances ranging from 27.6 to 35.6 mm

Amplitude of Diffracted Waves vs.

Separation Distance

0

0.001

0.002

0.003

0.004

0.005

25 27 29 31 33 35 37

Separation Distance [mm]

Amplitude

Figure 13 Amplitude of Diffracted Waves vs. Separation Distances ranging from 27.6

to 35.6 mm


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Amplitude of Backwall Reflections v s.

Separation Distance

0

0.01

0.02

0.03

0.04

0.05

25 27 29 31 33 35 37

Separation Distance [mm]

Amplitude

Figure 14 Amplitude of Backwall Reflections vs. Separation Distances ranging from

27.6 to 35.6 mm

From Figure 12, it can be observed that time-of-flight of backwall reflections and

diffracted waves increases as separation distance, which proportionally affects wavepropagation distance, increases. From Figures 13 and 14, opposite trends are found

regarding the amplitude of diffracted waves and backwall reflections. As separation

distance increases, the center of the beam moves further away from the tip of the slit, and

this leads to weaker diffracted waves from the crack tip. At the same time, amplitude ofbackwall reflection increases as the stronger portion of the beam is reflected against the

backwall and is collected at the receiver.

The same separation distances of 27.6 cm to 31.6 mm were used to scan a defect-free

steel block. The resulting times-of-flight show that the group of signals on the right in

Figures 10 and 11 do, indeed, arrive from the backwall. The average difference in times-of-flight of the backwall reflection from defective and defect-free specimens was

approximately less than 1 s. By comparing signal responses from defect-free anddefective steel blocks, it can be deduced that flaw tip diffracted signals can be observed

experimentally using a shear-wave-angle-beam transducer pair. One drawback is its low

signal amplitude; it is desirable to incorporate the use of a low-noise amplifier for signal

amplification.

5. Future WorkIn order to completely assess the use of shear waves for the TOFD method, additional

experiments with different specimen conditions need to be conducted. Since theexperiments carried out in the development of this report compare only ultrasonic

responses of defect-free steel block to another block with a single defect size, asensitivity assessment of shear wave with regards to small defects has not yet been


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investigated. Hence, this would be a natural next step. Meanwhile, one long term goal isthe completion of experiments on steel blocks that consider different crack orientations; it

is hoped these will provide a foundation for testing cylindrical structures such as

pipelines and tubing.

References

Al-Nuamiy, W., Zahran, O., Time-of-flight-diffraction From semi-automatic inspection

to semi-automatic interpretation,Insight, Vol. 47, No. 10, October 2005, pp: 639-644.

Apragaz, TOFD (Time-of-flight Diffraction) / Pulse Echo Ultrasonic Inspection Proposal,

http://www.apragaz.com/common/tofd.htm, 2004.

Baby, S., et al, Time-of-flight diffraction (TOFD) technique for accurate sizing of

surface-breaking cracks, Insight, Vol. 45, No. 6, June 2003, pp: 426-430.

Baskaran, G., et al., Ultrasonic TOFD Flaw Sizing and Imaging in Thin Plates using

Embedded Signal Identification Technique (ESIT), Insight, Vol. 46, No. 9, September

2004, pp: 537-542.

Birring, A.S., Nidathavolu. B.K., Ultrasonic Testing of Welds by Time-of-flight

Diffraction: Codes, Guidelines and Standards, Materials Evaluation, September 2005,

pp: 910-914.

Browne, B., Time-of-flight Diffraction Technique Its Limitations: Actual and

Perceived,NDT.net Ultrasonic Testing On-line Journal, Vol. 2, No. 9, September 1997.

Golan, S., Optimization of the Crack Tip Ultrasonic Diffraction Technique for Sizing of

Cracks,Materials Evaluation, Vol. 39, No. 2, February 1981, pp:166-169.

Golan, S., et al, Ultrasonic Diffraction Technique for Characterization of Fatigue Cracks,

Journal of Nondestructive Evaluation, Vol. 1, No. 1, March 1980, pp: 11-19.

Lawson, S., Ultrasonic Testing and Image Processing for In-progress Weld Inspection,

NDT.netUltrasonic Testing On-line Journal, Vol. 1, No. 4, April 1996.

Silk, M.G., Changes in ultrasonic defect location and sizing, NDT International, Vol. 20,

No. 1, February 1987, pp: 9-14.

Silk, M.G., The Transfer of Ultrasonic Energy in the Diffraction Technique for Crack

Sizing, Ultrasonics, May 1979, pp: 113-121.

Silk, M.G., Lidington, B.H., Defect Sizing using an Ultrasonic Time Delay Approach,

British Journal of Nondestructive Testing, Vol. 17, No. 2, March 1975, pp: 33-36.


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Szilard, J., Ultrasonic Testing: Non-conventional testing techniques, John Wiley & Sons,Ltd., New York, 1982.

Zippel, W.J., Pincheira, J.A. and Washer, G.A., Crack Measurement in Steel Plates Using

TOFD Method, Journal of Performance of Constructed Facilities, Vol. 14, No. 2, May

2000, pp: 75-82.


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Appendix: Sample Calculation

It is important to note that the resulting time-series in TOFD scanning consists of time

measured from ultrasonic pulse excitation to pulse reception. Hence, this includes traveltime of the ultrasound within the transmitter and receiver wedges. In order to measure

crack depth and length, it is necessary to include this variable in calculations. It has beenmentioned previously how calibration of the transducer is done using the combination ofarbitrary function generator and oscilloscope. This calibration only confirms, however,

the directivity of the transducers. In order to measure travel time within wedges or wedge

delays, a pulser-receiver unit was used to scan the corner of a non-defective steel block of

known thickness. The wedge delay has been measured as 5.93 s.

Table 1 shows the measured time-of-flight and amplitude of diffracted waves andbackwall reflections at 5 different separation distances. These results were obtained using

a 450

angle beam transducer pair.

Table 1 Scanning results on a defective steel block at various separation distances

Diffracted Wave Backwall ReflectionSeparation

Distance[mm]

Time-of-flight

[s]

Amplitude

[V]

Time-of-flight

[s]

Amplitude

[V]

27.6 17.60 0.003985 22.14 0.0088

29.6 18.05 0.003172 22.53 0.0128

31.6 18.48 0.002507 22.95 0.0202

33.6 18.91 0.001627 23.33 0.0278

35.6 19.34 0.001373 23.78 0.0416

As an example, a separation distance of 31.6 mm is selected. With reference to Figure 4,

wave propagation path and time within the specimen can be calculated using simplePythagoras theorem and a prescribed formula.

Wave propagation path = M + L = 22 )( XSd ++ + 22 )( XSd +

d = 12.8 mmS = 0.5 x 31.6 mm = 15.8 mm

X = 0 mm

Hence, M + L 40.67 mm

With a material sound velocity of shear wave equal to 3.25 mm/s, wave propagation

time is expected to be 12.51 s. Hence, adding the wedge time delay of 5.93 s yields a

total wave propagation time of 18.44 s for the transducer separation distance of 31.6mm. Table 2 compares theoretically calculated and experimentally measured times-of-

flight of diffracted waves and backwall reflections for other separation distances.


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Table 2 Comparison between theoretical calculations and experimental times-of-flightof diffracted waves and backwall reflections

Time-of-Flight

Diffracted Wave Backwall Reflection

SeparationDistance

[mm]Theoretical

[s]

Experimental

[s]

Theoretical

[s]

Experimental

[s]

27.6 17.51 17.60 22.33 22.14

29.6 17.97 18.05 22.65 22.53

31.6 18.44 18.48 23.00 22.95

33.6 18.92 18.91 23.36 23.33

35.6 19.42 19.34 23.73 23.78

From Table 2, it can be seen that the effect of separation distance on measurement

accuracy can not be observed clearly. By comparing measurement error for diffractedwaves times-of-flight from one separation distance to another, one can find the change

from over-sizing to under-sizing. On the other hand, backwall reflections time-of-flight

measurement shows the opposite trend. This means accuracy assessment by comparing

time-of-flight on the basis of wave propagation path may be unreliable.

Still, crack depth and thickness can also be measured using experimental time-of-flight

data. From the general formula, the total wave propagation path of a particular signal, M+ L, is equal to the multiplication of material sound velocity by the time-of-flight of the

corresponding signal. Since we used shear waves in our experiment and the only crack tipobserved was the bottom crack tip located midway between the transmitter and receiver,the formula becomes:

M + L = csw.tdb= 222

Sd +

Note that tdb is the time of travel inside the test object and it can be obtained bysubtracting the wedge delay from the measured time-of-flight. By varying the transducer

separation distance, the position of the tip can be estimated. In Table 3, the resulting

crack tip depth and specimen thickness measurements by ultrasonic TOFD are compared

with the physical measurements using a digital caliper. One will find that opposing trendsin the measurement accuracy of crack tip and specimen thickness can be observed

clearly. As the separation distance lengthens, the measurement error of crack tip depthincreases. At the same time, it can be seen that values of ultrasonically measured

specimen thickness approach the value of physically measured specimen thickness.


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Table 3 Comparison between ultrasonic and digital caliper measurements of crack tipdepth and specimen thickness

Crack Tip

Depth Measurement

Specimen

Thickness MeasurementSeparationDistance[mm]

Ultrasonic

[mm]

Digital Caliper

[mm]

Ultrasonic

[mm]

Digital Caliper

[mm]

27.6 12.480 12.8 22.016 22.8

29.6 12.446 12.8 22.202 22.8

31.6 12.427 12.8 22.34 22.8

33.6 12.153 12.8 22.459 22.8

35.6 12.114 12.8 22.614 22.8

These trends can be explained if one takes beam spread into consideration. Note that the

marked angle on a particular wedge represents the angle at which the centerline ofultrasonic waves is refracted. Due to beam spread, part of the ultrasonic wave away from

the centerline will come into contact with the backwall and/or crack at a slightly differentangle. Thus, it will lead to a different length of wave propagation path and time-of-flight.

More accurate measurements can be obtained using a configuration that yields highest

signal amplitude that identifies the contact of the center of the beam with the backwalland/or the crack tip.

shear waves on tofd

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