TOFD (time of flight diffraction)
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1.6.05
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Related topics
Non-destructive testing, TOFD method (time of flight diffraction), ultrasonic diffraction, sound velocity,
shear waves (transverse waves), corner echo, B-scan, and preferential corrosion measurement
Principle
The depth of the cracks of an aluminium test block with seven cracks of different depths (saw cuts) is determined with two methods. During the experiment, the cracks in the material are examined with the aid
of the ultrasound angle beam probe and the depth of the cracks is determined with the aid of the signal
amplitude and the TOFD method (time of flight diffraction). Both methods are compared based on their
measurement results and in view of their performance and detection limits. The test block is scanned in
accordance with the TOFD method as well as with a special probe combination so that the corresponding scan image of the crack distribution can be generated.
Equipment
1 Basic Set “Ultrasonic echoscope”
consisting of:
1x Ultrasonic echoscope
1x Ultrasonic probe 1 MHz
1x Ultrasonic probe 2 MHz
1x Ultrasonic test block
1x Ultrasonic cylinder set
1x Ultrasonic test plates
1x Ultrasonic gel
1 Extension set: Non-destructive testing
1 Ultrasonic probe 2 MHz
1 Vernier calliper
1 Ruler, plastic, 200 mm
Additional equipment
1 PC with a USB port, Windows XP or higher
Fig. 1:
13921-99
13921-01
13921-05
03010-00
09937-01
Equipment for the TOFD measuring method, experimental set-up
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TOFD (time of flight diffraction)
Caution!
Pay close attention to the special operation and safety instructions in the manual of the ultrasonic echoscope.
Tasks
1. Determine the sound velocity of the shear wave in a test block for the crack depth determination with
the angle beam probe based on the corner echoes at half and full skip distance.
2. Prepare a characteristic groove curve for the cracks of the aluminium test block for determining the
crack depth based on the echo amplitude.
3. Determine the crack depths of the test block with the TOFD method and compare the results to the
results of the echo amplitude method.
4. Scan the test object with a TOFD scanning head and analyse the cracks in the TOFD scan.
Set-up and procedure
Prepare the echoscope (read the echoscope manual).
Connect the echoscope to the PC.
Set the selector switch to “Reflection”.
Connect the 2 MHz probe to the “Probe (Reflection)” port.
Start with a medium setting of the "GAIN" and "OUTPUT" controllers.
Couple the 38° delay line to the 2 MHz ultrasonic probe with the aid of some coupling gel. Apply a
pea-sized quantity of gel to the centre of the probe surface and attach the delay line. Move the delay
line back and forth in order to distribute the gel evenly on the probe surface. Ensure that no air is
entrapped in the coupling layer.
Couple the resulting angle beam probe to the test object with the aid of some gel or water. The use
of water makes it easier to move the probe on the test object without affecting the quality of the
coupling. This is particularly important when measuring the signal amplitude, since poor coupling
may lead to incorrect measurement results. The estimation of the correct amount of water comes
with practice. Too little water results in poor coupling, whereas too much water may flow down the
test block and cause an acoustic coupling between the test block and the tabletop, which in turn
would also change the signal amplitude.
Move and rotate the angle beam probe on the test object until the echo shows a maximum. This ensures that the sound cone fulfils the geometrical requirements that are necessary for the calculations.
Fig. 2: Corner echo at half and full skip distance
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Adjust the emitting power (“OUTPUT”) and the gain (“GAIN”) at the ultrasonic echoscope so that the
echo amplitude reaches approximately 0.5 to 0.8 V. TGC is usually not required.
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TOFD (time of flight diffraction)
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Sound velocity determination:
Determine the transverse sound velocity of the test block (see the experiment P5160400) based on the
measured times of flight of the corner echo at half and full skip distance. Find the corner echo that is
nearest to the edge of the test block. Measure the distance between the probe and the edge of the test
cursor position
Fig. 3: Measurement of the time of flight of the corner echo at half skip distance
block with a vernier calliper or a ruler. Determine the time of flight with the measurement cursor in the ultrasound software. Position the cursor at the base of the echo (not in the middle of the peak). Then, move
the probe to the maximum of the corner echo at full skip distance. Ensure that the delay line remains
coupled to the test block. If necessary, apply some fresh ultrasound gel.
Crack depth determination in accordance with the echo amplitude method
Fig. 4: Corner echo at the edge of the test block
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TOFD (time of flight diffraction)
Determine the crack depth in accordance with the echo amplitude method. Use the 38° delay line as
described above. Set up the test object so that the cracks face downward. We recommend using water
as the coupling agent between the test block and the delay line. In order to measure the echo maximum,
adjust the “GAIN” and “OUTPUT” switches so that all of the cracks can be measured with the same setting without overamplifying the signals ("GAIN" = 15 dB, "OUTPUT" = 30 dB).
Move the probes and measure the maximum corner echo for each of the cracks. Determine the maximum signal amplitude with the aid of the cursor. For this purpose, stop the display of the measurement program (STOP button) and move the cursor of the mouse over the maximum of the signal
Fig. 5: Measurement of the signal amplitude at the corner echo of the second crack (crack depth ~2 mm)
amplitude. Read the signal amplitude that is displayed in the lower right-hand corner of the screen
and transfer the values into a table.
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TOFD (time of flight diffraction)
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Then, determine the depths of the cracks with the aid of a vernier calliper.
Crack depth determination in accordance with the TOFD method
In a second measurement, localise the maxima of the diffraction echoes at the crack tip, which can
be identified based on the smaller peaks prior to the actual corner echo and measure the time of
flight. Since for this measurement the amplitude does not need to be determined, the receiver gain
("GAIN") can be varied. It should be between 25 and 30 dB since the TOFD signals are diffraction
echoes with a small signal amplitude. In order to identify the maximum, it may be recommendable to
switch the display to "HF+AMP", since the maximum amplitude is easier to identify in the case of a
HF signal. For the corner echoes, the receiver gain ("GAIN") must be considerably reduced, since
otherwise the signal would be overamplified, in turn making it impossible to determine the maximum
of the signal amplitude.
Fig. 6: Diffraction echo (TOFD signal) at the 8 mm crack
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TOFD (time of flight diffraction)
Measure the shortened projection distance s1 (distance between the test block edge and the angle
beam probe with the calliper vernier or the ruler. Then, move the angle beam probe to the maximum
of the corner echo and measure the time of flight as well as the distance s2 between the angle beam
probe and the edge of the test block.
In the case of small cracks, the two echoes overlap. As a result, the diffraction echo cannot be determined for the two smallest cracks.
TOFD B-scan
Fig. 7: Corner echo at the 8 mm crack
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Couple the TOFD angle combination with some ultrasound gel to the two 2 MHz angle beam
probes.
Switch the selection knob to “Transmission”.
Connect one 2 MHz probe to the “Probe (Reflection)” port and the other one to the “Probe (Transmission)” port.
Set the "GAIN" and "OUTPUT" switches to their respective
maximum values.
Couple the angle beam probe with some water to the test
block. The program should now display the bottom echo.
Adjust the TGC so that the area of the test block is further
amplified. It must be taken into consideration that due to the
delay lines there will be no echoes in the range up to approximately 17µs and that the echoes that occur after the
bottom echo are of no interest for the evaluation.
Switch to the B-mode. Activate the HF signals in the top
right-hand corner of the B-mode screen.
Click the START button and move the angle beam probe
Fig. 8: TOFD angle combination
slowly and steadily over the test block. The test block must
be covered with a sufficient water film in order to ensure
consistent coupling.
After the scan has been completed, click the STOP button. The area on the screen can be limited to
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TOFD (time of flight diffraction)
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Fig. 9: Equipment settings for the TOFD scan
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the area of interest with the aid of the zoom values.
Perform several experiments with varying settings in order to obtain a TOFD image with a good contrast and high resolution. In addition, the grey scale representation can be further optimised via the
brightness and contrast settings.
Calibrate the unit by adapting the sound velocity (c = cT*cos   2400 m/s).  is the angle of incidence ( = 44.5°).
Repeat the TOFD scan with depth scaling. In order to measure the values, activate the measurement mode (click both mouse buttons simultaneously). The left mouse button represents the starting
point and the right mouse button the end point.
Fig. 10: TOFD B-mode
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TOFD (time of flight diffraction)
Software
The “measure Ultra Echo” software records, displays, and evaluates the data that are transferred from
the echoscope. After the start of the program, the measuring mode is active and the main screen “AScan mode” is displayed. All of the available actions and evaluations can be selected and started in this
window.
The upper part of the main screen shows the A-scan signal, the frequency of the connected transducer,
and the operating mode (reflection/transmission). The current positions of the cursors (red and green
line) are displayed at the bottom of the window. The cursors can be positioned by a mouse click. The time of flight is displayed under the cursor buttons.
Note
The ultrasonic cylinders and the probes should be cleaned immediately after use with water or a standard detergent. Dried residues of ultrasonic gel are difficult to remove. If necessary, use a soft brush.
Never use alcohol or liquids with solvents to clean the cylinders or probes. Deep surface scratches affect
the coupling and can induce measurement errors.
Theory and evaluation
Sound velocity determination:
The sound velocity is calculated based on the difference between the measured times of flight for the
half and full skip distance.
With the double path lengths for the echo and the measured times of flight t 0 and t1, the sound velocity in
the test block material is:
Sound velocity c = 2xa/(t2-t1). With the skip distance xa² = d² + (s2-s1)², the following results for the sound
velocity in the test block: cT 
2 d 2  s 2  s1 
2
t 2  t1 
Table 1: Measurement with the 38° delay line at the test block at half and full skip distance
Projection distance [mm]
Time of flight [µs]
Half skip distance
16.5 [s1]
50.2 [t1]
Full skip distance
51.1 [s2]
81.5 [t2]
Material thickness
34.8 [d]
Based on the above-mentioned measurement values, the transverse sound velocity in aluminium is cT =
3135 m/s.
Crack depth determination in accordance with the echo amplitude method
During the fracture-mechanical evaluation of components, material flaws are considered as planar separations (cracks). For the assessment of components, certain test specifications are defined, which may
not be exceeded. This requires precise information concerning the flaw geometry, such as crack depth,
crack length, and crack depth location. Surface cracks can be precisely proven with ultrasonic angle
beam probes. The method that is applied makes use of the so-called corner effect, which is an echo that
is generated in a corner between the crack and the surface. This echo is greater, the deeper the crack is
located in the material.
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TOFD (time of flight diffraction)
Table 2: Maximum corner echo amplitude and the depth that was measured with the vernier calliper
Nominal depth [mm]
Measured crack depth [mm]
Corner echo amplitude [V]
1
0.8
0.118
2
1.9
0.347
4
3.8
0.502
6
5.7
0.613
8
7.9
0.672
10
10.0
0.675
14
14.2
0.675
Flaw depth Measurement
using
Crack depth measurement
in accordance
withEcho
the Amplitude
echo amplitude methode
0,7
0,6
0,5
0,4
0,3
0,2
Angle beam echo amplitude in V
Angle Beam echo Amplitude in V
0,8
0,1
0
0
2
4
6
8
10
12
14
16
Flaw depth
depth in
inmm
mm
Crack
Fig. 11: Characteristic groove curve for the aluminium test block in accordance with the echo amplitudes of the corner echoes as a function of the crack depth
This, however, only applies to those cracks that are smaller than half the probe diameter. Deeper cracks
cannot be distinguished.
The crack depth determination based on the corner echo amplitude is the method with the highest detection sensitivity for small depths, since for these cases the TOFD method does not provide any results.
The crack depth of the test specimen can be estimated based on the determination of the echo amplitude with the aid of reference objects (characteristic groove curve). In the case of crack depths in the range of half of the probe diameter (probe diameter: 16 mm), the echo amplitude becomes saturated so that
the crack depth cannot be estimated. It is still possible, however, to locate the cracks and to scan the
crack length.
The saturation limit results from geometrical considerations. Since the ultrasound beam has a limited la-
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TOFD (time of flight diffraction)
teral expansion, only part of the beam will be reflected in the case of small cracks. As of a certain crack
size, however, the entire beam will be reflected so that the corner echo amplitude remains unchanged
even if the crack expands still further.
Crack depth determination in accordance with the TOFD method
Deep cracks can be analysed particularly precisely with the TOFD method (time of flight diffraction),
which makes use of the diffraction of the sound waves at the tip of the crack. The sound wave that is generated at the tip of the crack produces a corner echo and also a time-shifted diffraction echo. The position of the two echoes can be used to determine the crack depth.
Based on a test block with the know material thickness d and the material sound velocity cT , the crack
depth T results from the following considerations:
Fig. 12: Reflection of an ultrasound beam at a small crack (left) and at a deep crack (right)
Fig. 13: Geometrical conditions for the crack depth determination in accordance with the TOFD method
With the measured projection distances (distance between the front edge of the angle beam probe and
the edge of the workpiece) s2 at the maximum of the corner echo and s1 at the maximum of the diffraction echo and with the corresponding times of flight t1 and t2, the following is true for the movement of
the probe:
Probe movement:
s = s2-s1
And for the path difference of the two echoes:
Path difference:
a = cT (t2-t1)/2
In accordance with the Pythagorean theorem, the crack depth results from the following equation:
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TOFD (time of flight diffraction)
T
(a)  (s)
2
2
 2 (  )2 
2
  cT t 2 t1   s2  s1 


4


The measurements provide the following results:
Table 3: Measurement results of the TOFD method
Nominal crack depth [mm] Time of flight t1 [µs]
Distance s1 [mm]
Time of flight t2 [µs]
Distance s2 [mm]
1
2
4
46.3
124
50.3
129
6
44.6
159.5
50.2
166
8
42.6
195.5
50.2
204.5
10
41.1
231
49.9
240.5
14
37.5
39
50.3
54.5
Material thickness d [mm]
34.8
The above-mentioned measurement results and the consideration of a transverse sound velocity in aluminium cT = 3135 m/s lead to the following values for the crack depths in accordance with the TOFD method.
Table 4: Crack depth determination in accordance with the TOFD method
Nominal crack depth [mm] Mechanically measured crack depth [mm]
TOFD-measured crack depth [mm]
1
0.8
2
1.9
4
3.8
3.8
6
5.7
5.9
8
7.9
7.8
10
10.0
10.0
14
14.2
13.9
The two smallest cracks (crack depth 1 mm and 2 mm) cannot be resolved since the diffraction echo is
superimposed by the corner echo. When the crack depth increases, the diffraction signal can be distinguished more clearly from the corner echo. The distance between the corner echo and the diffraction
echo provides the crack depth. The TOFD method can also be applied for very deep cracks.
The material, however, can only be tested in its entirety with a combination of both test methods.
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TOFD (time of flight diffraction)
Flaw depth Measurement
using with
TOFDthe
Method
Crack depth measurement
in accordance
TOFD method
16,0
Flaw depth TOFD Method in mm
Crack depth (TOFD) in mm
14,0
12,0
10,0
8,0
6,0
4,0
2,0
0,0
0
2
4
6
8
10
12
14
16
Crack
depthininmm
mm
Flaw depth
Fig. 14: Crack depth determination in accordance with the TOFD method
TOFD scanning method
During a TOFD scan, two combined angle beam probes are moved over the test object surface with a
Fig. 15
Angle beam probe arrangement for the TOFD scanning method
constant distance. The measuring system is operated in the transmission mode. Depending on the probe
geometry and the material and quality of the test object, various different echoes may be generated.
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On the surface, a Rayleigh wave forms and then travels to the receiver at Rayleigh wave velocity. The
probe combination should have a corresponding distance so that the Rayleigh wave appears after the
bottom echo. The amplitude and the time of flight of the bottom echo result from the angle of incidence,
bottom echo
Fig. 16: Crack representation in the TOFD scan
the distance between the probes, and the thickness of the test object. The diffraction waves of the cracks
will then appear prior to the bottom echo as a function of their depth.
The TOFD scan shows six of seven cracks. The 2 mm crack is just visible above the bottom echo. In the
A-mode, when the times of the flight of the echoes were measured, this crack was not visible. This
shows that the TOFD scanning method is perfectly suitable for detecting material inhomogeneities.
After the calibration of the measuring equipment in view of the test object material, the crack depths can
be estimated directly based on the TOFD scan. The value of the sound velocity can be used for the
calibration though, however, it is not possible to simply use the calculated value of the sound velocity in
the material. Instead, the transverse sound velocity must be multiplied with the cosine of the angle of incidence ( = 44.5°). The result (cT*cos   2400 m/s) must be entered into the program in place of the
sound velocity and the system must be switched to the depth display. Now, a measurement cursor can
be activated in the B-scan by simultaneously clicking the right and left mouse button. If you then click the
left mouse button on the B-scan and then with the right mouse button on another point of the B-scan, the
resulting distances will be displayed in the upper right-hand corner of the screen. As a result, the crack
depths can be estimated directly based on the scan image, although a relatively large error must be
reckoned with since only a mean angle was taken into consideration for the individual echoes.
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TOFD (time of flight diffraction)
Fig. 17: TOFD scan with the measurement cursor for determining the crack depth
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