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Detection of Defects in a Thin Steel Plate Using Ultrasonic Guided wave Hee Don Jeong, Mechanical and Electrical Engineering Research Team, Research Institute of Industrial Science and Technology(RIST), Hyoja-dong San32, Pohang 790-330, Korea Hyeon Jae Shin, School of Mechanical Engineering and Safety and Structural Integrity Research Center, Sungkyunkwan University, 300 Chunchun-dong, Suwon, 440-746, South Korea Joseph L. Rose, Ultrasonic Laboratory, Pennsylvania State University, 114 Hollowell Building, University Park PA 16802 USA Contact

Abstract

In order to establish a technical concept for the detection of defects in thin steel plates, an experimental investigation was carried out for the artificial defects in 2.4mm thick steel plates by using guided wave technique. The goal was to find the most efficient testing parameters paying attention to the relationship between the excitation frequency by tone burst system and various incident angles. It was found that the test conditions that worked best was for a frequency of 840kHz and an incident angle of 30 or 80 degrees, most of the defects, such as various sizes of through wall holes and elliptically defects, were detected. For the case of S₀ mode impingement, amplitudes of reflected signals were proportional to sizes of defects. A₀ mode was also sensitive to the same defects but proportional relation was not observed.

Key words; Steel Plate, Ultrasonic, Guided Wave, Frequency, Incident Angle, Symmetric Mode, Antisymmetric Mode, Defect.

Introduction

Guided waves in plates that are known as Lamb waves have great attention for the large area nondestructive inspection. Fundamental concepts on theoretical aspect could be found many publications [1,2]. Frequency and phase velocity tuning is used for the experimental selection of guided wave modes for the best results in the given inspection purposes [3]. Also mode selection concepts and optimization of guided wave inspection are studied [4, 5]. The use of guided waves in tubular structures are introduced [6-11]. The extensive summary of the guided wave theory and experimental applications introduced by J. L. Rose [12]. Through those previous studies it was known that there are infinite number of guided wave modes that have different propagation characteristics and sensitivity to defects, so that the proper mode selection is recommend for the successful application of guided waves in nondestructive testing.
In this study, guided wave modes are found for the best results in the detection of defects in a thin steel plate by using frequency and phase velocity tuning. Artificial defects are made in 2.4 mm thick steel plates. Tone burst signals are used to control the excited frequency and a variable angle shoe is used for the continuous change of the incident angle. Optimum guided wave modes are found for the detection of defects and the results are discussed.

Specimens and Experimental Set up

Various shapes of defects were machined in steel plates that were 2.4 mm thick. Machined defects were 42% flat bottomed hole with 3 mm diameter, 100% through wall holes having various diameters of 0.8, 1.28, 1.58, 3.2, and 4 mm and elliptical bottomed defects shown in Figure 1. Tone burst signals were used to control the center frequency and frequency bandwidth of excited signals. To generate high power tone burst signals, Matec Explorer-2 system was used with the test conditions shown in Table 1.


Fig 1: Artificial defect specimen used in this study

Table 1: Test conditions and wedge configuration

Ultrasonic pulse-echo technique was used with the variable angle beam shoe shown in Figure 2. With the shoe, it was possible to change the angle continuously. Center frequencies of the transducers for the preliminary tests 500kHz, 800kHz, 1MHz, 1.5MHz, and 2.5MHz. After the preliminary tests, the transducer having the center frequency of 800kHz selected for the tests in this study. By using the tone burst signal and the angled shoe, frequency and angle tuning was used for the generation of a nice packet of guided waves.

Dispersion Curves

The dispersion curves of Lamb wave modes could be obtained by solving wave equation with boundary conditions. For the traction free boundary conditions at the surface of plate, the frequency equations [1] are

where q²= (w /C_T)² - c ² , p²= (w /C_L)² - c ²
C_L= longitudinal wave velocity (5670 m/s), C_T= shear wave velocity (3136m/s),
h= half of the plate thickness, w =2p f, c = 2p /l
Eq. 1 and Eq. 2 could calculate antisymmetric and symmetric modes, respectively. The modes can be represented in velocity versus frequency times thickness of the plate that are dispersion curves shown in Figure 2. Phase velocity could be controlled by the angle of incident so that the phased velocity dispersion curves could be used to find the excitation conditions, such as frequency and angle of incident, of a desired mode. Group velocity indicate the wave propagation velocity so that it is possible to predict the wave propagation velocity of an excited mode under certain excitation conditions obtained from phased velocity dispersion curves.


(a)	(b)
Fig 2: (a) Phased velocity dispersion curves and (b) group velocity dispersion curves for a steel plate

Mode selection

Since there are infinite Lamb wave modes in a steel plate, it is necessary to select a proper mode for the experimental purpose. Mode selection could be performed by two-dimensional tuning that is frequency and phase velocity tuning. In this case, the phase velocity is continuously controlled by variable angle shoe so that the phased velocity tuning could be performed by incident angle tuning.
Figure 3 shows the frequency tuning results for the fixed incident angle of 30 degrees. The pulse-echo signals indicated by arrows were reflected from 380mm away free edge of the steel plate. Frequency was swept from 650 kHz to 1000 kHz. In case of 840 kHz shown in Figure 3 (c), the most strong signal was received and the wave form was compact.


Fig 3: Effects of tuning ultrasonic tone burst frequency on wave reflection

Fig 4: Effects of tuning incident angle on the generation of Lamb waves

Figure 4 shows the effect of incident angle for the fixed frequency of 840 kHz. For the incident angle of 25 degrees, a tiny amount of energy was received as shown in Figure 4 (a). The result was same for the angle between 0 and 25 degrees. For the angle between 30 and 37 degrees, the results were very close to Figure 4 (b) that was the result for the incident angle of 35 degrees. There was no signal received for the angle between 40 and 70 degrees. For 85 degrees, there was a signal received as shown in Figure 4 (c).

Phase velocity for the incident angle,q _I , could found by Snell's law;

V_Lwedge / sin q _I = V_phase -------------------------------------(3)

The incident angles of 30 and 85degrees are correspond to 5420 and 2700 m/sec, respectively. Comparing these phase velocities with in the frequency bandwidth, it is possible to find the Lamb wave modes that could be excited. Table 2 shows the group velocity predicted by dispersion curves and measured by experiments. The identified modes for incident angle of 30 and 85 degrees are S₀ and A₀ modes, respectively.


Mode	Angle	Frequency	Phase Velocity (theorical)	Group Velocity (theorical)	Group Velocity (experimental)
So	30	840 kHz	5420 m/s	3500 m/s	4100 m/s
Ao	85	840 kHz	2700 m/s	3100 m/s	3200 m/s
Table 2: Selected Lamb wave modes

Experimental results and discussion

Figure 5 shows the Lamb wave test results for the elliptical defects with the S₀ mode. In this case, depths of the defects are Figure 5 (a) 0.5, (b) 1.0, and (c) 2.4 mm (through wall) when the widths of the defects are constant as 30 mm. The signals from the defects are indicated by F and the signals from the plate edge are indicated by BWE. It is observed that the amplitudes of the reflected signals from the defects are proportional to the depth of the defects. For the through wall defect shown in Figure 5 (c), the BWE is not observed since most of the Lamb wave energy is reflected from the defect.
Figure 6 shows the test results by using A₀ mode for the same specimens that were used in Figure 5. In this case the amplitudes of the defect signals are not proportional to the depth of the defects. And Lamb wave mode conversion is observed for the through wall defect as shown in Figure 6 (c).


Fig 5: Lamb wave test results for the elliptical defects with S0 mode

Fig 6: Lamb wave test results for the elliptical defects with A0 mode

For the case of through wall holes, both S₀ and A₀ mode could detect all sizes of hole diameters from 0.8 to 4.0 mm. Figure 7 shows the relation between amplitude of the reflected signals and the diameters of the holes. Again the amplitude of S₀ mode is proportional to the diameters of the holes but the amplitude of A₀ mode is not.


Fig 7: Relation between amplitude of reflected signals and hole diameters

Concluding remarks

From the phase velocity and frequency tuning experiments, it was found that A₀ and S₀ modes around the 840kHz could be used for the detection of defects in 2.4 mm thick steel plates. For the case of S₀ mode impingement, amplitudes of reflected signals were proportional to the diameters of through holes and the depths of elliptical defects. A₀ mode was also sensitive to the same defects but proportional relation was not observed.

References

1. Graff, K. F., "Wave motion in elastic solids," Dover Publications, Inc., 1973.
2. Auld, B. A.,"Acoustic field and waves in solids", 2^nd edition, Krieger Publishing Co., 1994.
3. Shin, H.J. and Rose, J.L., "Guided Wave Tuning Principles for Defect Detection in Tubing", Journal of Nondestructive Evaluation, Vol. 17, No. 1, pp. 27-36, 1998
4. Ditri, J. J., Rose, J. L, and Chen, G., "Mode selection criteria for defect detection optimization using Lamb waves," in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 11, D. O. Thompson and D. E. Chimenti, eds. (Plenum press, New York), pp. 2109-2115, 1992.
5. David N. Alleyne and Peter Cawley, "Optimization of Lamb wave inspection techniques," NDT&E international Vol. 25, No. 1, pp. 11-22, 1992.
6. Rose, J. L., Ditri, J. J., Pilarski, A., Rajana, K. M. and Carr, F. "A guided wave Inspection Technique for Nuclear Steam Generator Tubing," NDT&E International, Vol. 27, No6, pp. 307-310, 1994.
7. Ditri, J. J., "Utilization of guided elastic waves for the characterization of circumferential cracks in hollow cylinders," J. Acoust. Soc. Am., Vol. 96, 3769-3775 1994.
8. Shin, H.J., Yi, R., and Rose, J.L., "Defect detection and characterization in power plant tubing using ultrasonic guided waves," 14^th WCNDT, New Delhi, India, December 8-13, 1996.
9. Alleyne, D. N., Lowe, M., and Cawley, P., "The excitation of Lamb waves in pipes using dry-coupled piezoelectric transducers," Journal of Nondestructive Evaluation, 15 (1), pp. 11-20, 1996.
10. Ditri, J. J. and Rose, J. L., "Excitation of guided wave modes in hollow cylinders by applied surface tractions," J. App. Phys., Vol 72(7), 2589-2597, 1992.
11. Shin, H. J. and Rose, J.L., "Guided waves by axisymmetric and non-axisymmetric surface loading on hollow cylinders", Ultrasonics, 37, Issue 5, pp. 355-363, June 1999.
12. J.L. Rose, "Waves in solid media" ,1999, The Press Syndicate of the University of Cambridge

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