Problem 1(10 marks) Problem 2 (10 marks)
Problem 1 (10 marks) Copper has a density of 8940 kg/m3, a Young's modulus of 117 GN/m2, and a Poisson's ratio of 0.34. Calculate: a) The shear modulus; b) The bulk modulus; c) The longitudinal wave velocity; d) The shear wave velocity.
Problem 2 (10 marks) Bakclite has a density of 1400 kg/m3 and an acoustic impedance of3630 x 103 kg/sm2• a) What is the velocity of a longitudinal wave in Bakelite? b) What is the wavelength of a longitudinal ultrasonic wave in Bakelite if the frequency is 10 MHz? c) If Bakelite is placed between a probe and a piece of steel, which has an acoustic impedance of 46488 x 103 kg/sm2, how much of the longitudinal wave will penetrate the steel when the beam is transmitted vertically?
Problem 3 (10 marks) A circular probe with a diameter of 16 mm uses a 4 MHz transverse wave in steel. Use Ermolov's equations to calculate the following, assuming that the velocity in steel is 3.235 mm/fls, and the attenuation coefficient is 0.04 nepers/mm: (a) the amplitude ofthe back wall echo as a fraction of the transmitted pulse when the back wall is a distance of 40 mm from the transmitter; (b) the height ofthe pulse be that is reflected from a circular reflector with a diameter of I mm at a depth of 15 mm.
Problem 4 (10 marks) Three common flaws found in welds are slag inclusions, gas pores and cracks. Describe the way in which each of these may occur, and sketch the waveforms that would be found during an ultrasonic test using an A-scan with the probe at position A, Band C as shown below.
"""L u [J A
B
C
SLAG
o
PORE
CRACK
14J
Figure I A scans of samples with slag, a gas pore and a crack
Problem 5 (10 marks) The attenuation coefficient of steel is known to be 0.26 dB/mm for longitudinal waves at 2 MHz. If a block of steel, 50 mm thick is tested, the required amplification of the back wall echo is 37.6 dB. Now a block of cast iron, 50 mm thick, is tested using the same probes and couplant and the required amplification of the back wall echo is found to be 72.4 dB. What is the attenuation coefficient of cast iron?
Problem 6 (10 marks) A set of 3 mm side-drilled-hole reference blocks are used to generate the Distance Amplitude Curve (DAC) shown in Figure 2. A flaw is detected at a depth of25 mm in a 50 mm sample which produces an echo which has an amplitude of 20% FSH for a flaw length of 12 mm. For this particular application, the acceptance levels are as shown in Table I. Would this flaw be recorded, accepted or rejected and why?
90 80 :I: Ul
"-
70
'.""
60
Q.
40
';;
~
50
E m
30 20 10 0 0
10
20
30
40
50
60
depth/mm
Figure 2 DAC for Question 6 Amplitude, x Thresholds x>Ref Unacceptable DAC Reference level - 6 dB Ref> x > Rec Record (50% DAC) Evaluation level Reference level -10 dB x>Eval Evaluate (33% DAC) flaw length Snecimen thickness t 8-15mm >20mm Flaw lemrth I I>t I>O.5t Unacceptable
Reference level Recording level
Table 1 Acceptance levels for the material in Question 6
Problem 7 (10 marks) A 12 mm diameter transducer at 2 MHz is used to detect a disc-shaped reflector at a depth of20 mm. The amplitude of the echo is -30 dB. [fwe assume the velocity in the block is 5.96 mm/fls, use the normalized DGS diagram to estimate the area of the reflector.
o 10
20 V(d8)
•
30
1.1
-
--
tlORMALI
--
--
-
--
50
D G S
~
-- -- -
40
. . .
10
--
... 100'
o
ZED
-
D
r A G R A K
10
( disc reflect or )
20 30
40
~ q,.. 'C
60
q
., .,>
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•
50
eo
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0
e,/
70
.;a, 70
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,,
80
0.1
10
80
100
Figure 3 DGS for Question 7
Problem 8 (10 marks) Briefly describe the following two techniques, and list some of their advantages and disadvantages compared to conventional ultrasonic probes: (a) Phased-array; (b) EMAT.
Problem 9 (10 marks) A TOFD method is used to find a vertical crack in steel. The steel is 15 mm thick, and a 45 degree shear wave probe is used to generate the beam, with a probe diameter of 12 mm and a frequency of2 MHz. The transmitter and receiver probes are placed 40 mm apart, and the times of the signals received from the top of the crack and the bottom of the crack are 13.2 /lS and 14.4 /lS respectively. What is the size of the crack?
Problem 10 (10 marks) Describe the methods of scanning in ultrasonics using an A-Scan, B-Scan and C-Scan. Illustrate your solution with an example of a test piece with a small crack at its centre.
Problem 2 (10 marks) Bakclite has a density of 1400 kg/m3 and an acoustic impedance of3630 x 103 kg/sm2• a) What is the velocity of a longitudinal wave in Bakelite? b) What is the wavelength of a longitudinal ultrasonic wave in Bakelite if the frequency is 10 MHz? c) If Bakelite is placed between a probe and a piece of steel, which has an acoustic impedance of 46488 x 103 kg/sm2, how much of the longitudinal wave will penetrate the steel when the beam is transmitted vertically?
Problem 3 (10 marks) A circular probe with a diameter of 16 mm uses a 4 MHz transverse wave in steel. Use Ermolov's equations to calculate the following, assuming that the velocity in steel is 3.235 mm/fls, and the attenuation coefficient is 0.04 nepers/mm: (a) the amplitude ofthe back wall echo as a fraction of the transmitted pulse when the back wall is a distance of 40 mm from the transmitter; (b) the height ofthe pulse be that is reflected from a circular reflector with a diameter of I mm at a depth of 15 mm.
Problem 4 (10 marks) Three common flaws found in welds are slag inclusions, gas pores and cracks. Describe the way in which each of these may occur, and sketch the waveforms that would be found during an ultrasonic test using an A-scan with the probe at position A, Band C as shown below.
"""L u [J A
B
C
SLAG
o
PORE
CRACK
14J
Figure I A scans of samples with slag, a gas pore and a crack
Problem 5 (10 marks) The attenuation coefficient of steel is known to be 0.26 dB/mm for longitudinal waves at 2 MHz. If a block of steel, 50 mm thick is tested, the required amplification of the back wall echo is 37.6 dB. Now a block of cast iron, 50 mm thick, is tested using the same probes and couplant and the required amplification of the back wall echo is found to be 72.4 dB. What is the attenuation coefficient of cast iron?
Problem 6 (10 marks) A set of 3 mm side-drilled-hole reference blocks are used to generate the Distance Amplitude Curve (DAC) shown in Figure 2. A flaw is detected at a depth of25 mm in a 50 mm sample which produces an echo which has an amplitude of 20% FSH for a flaw length of 12 mm. For this particular application, the acceptance levels are as shown in Table I. Would this flaw be recorded, accepted or rejected and why?
90 80 :I: Ul
"-
70
'.""
60
Q.
40
';;
~
50
E m
30 20 10 0 0
10
20
30
40
50
60
depth/mm
Figure 2 DAC for Question 6 Amplitude, x Thresholds x>Ref Unacceptable DAC Reference level - 6 dB Ref> x > Rec Record (50% DAC) Evaluation level Reference level -10 dB x>Eval Evaluate (33% DAC) flaw length Snecimen thickness t 8-15mm >20mm Flaw lemrth I I>t I>O.5t Unacceptable
Reference level Recording level
Table 1 Acceptance levels for the material in Question 6
Problem 7 (10 marks) A 12 mm diameter transducer at 2 MHz is used to detect a disc-shaped reflector at a depth of20 mm. The amplitude of the echo is -30 dB. [fwe assume the velocity in the block is 5.96 mm/fls, use the normalized DGS diagram to estimate the area of the reflector.
o 10
20 V(d8)
•
30
1.1
-
--
tlORMALI
--
--
-
--
50
D G S
~
-- -- -
40
. . .
10
--
... 100'
o
ZED
-
D
r A G R A K
10
( disc reflect or )
20 30
40
~ q,.. 'C
60
q
., .,>
• •
•
50
eo
~H-'k-l'
0
e,/
70
.;a, 70
~ N
~
,,
80
0.1
10
80
100
Figure 3 DGS for Question 7
Problem 8 (10 marks) Briefly describe the following two techniques, and list some of their advantages and disadvantages compared to conventional ultrasonic probes: (a) Phased-array; (b) EMAT.
Problem 9 (10 marks) A TOFD method is used to find a vertical crack in steel. The steel is 15 mm thick, and a 45 degree shear wave probe is used to generate the beam, with a probe diameter of 12 mm and a frequency of2 MHz. The transmitter and receiver probes are placed 40 mm apart, and the times of the signals received from the top of the crack and the bottom of the crack are 13.2 /lS and 14.4 /lS respectively. What is the size of the crack?
Problem 10 (10 marks) Describe the methods of scanning in ultrasonics using an A-Scan, B-Scan and C-Scan. Illustrate your solution with an example of a test piece with a small crack at its centre.
