·Table of Contents
·Methods and Instrumentation
A Study on the Guided Wave Mode Conversion Using Self-calibrating Technique
Department of Mechanical Engineering, Inje Univ., The Republic of Korea
NDT Engineering Co., The Republic of Korea
Joseph L. Rose
Engineering Science and Mechanics Dept. Penn State University, USA
Derrick D. Hongerholt
BFGoodrich Aerospace, USA
Guided wave mode conversion phenomena were investigated for NDE of a plate-like structure with thickness variation. The ratios of reflection and transmission (R/T) were measured via the self-calibrating procedure that allows us to obtain experimental guided wave data in a more reliable way, regardless of the coupling uncertainty between the transducer & specimen. The results from R/T could be used to determine the thickness reduction of the structure. It was shown that not only the incident modes but also the converted ones need to be considered in the self-calibrating guided wave inspection to extract a reasonable correlation between experimental data and thickness variation. Through this study, the potential of guided wave inspection as a quantitative NDE technique was explored based on the combined concept of self-calibration and multi-mode conversion in guided wave scattering problems.
The ultrasonic guided wave inspection technique has been recognized as a powerful NDE method that can potentially compensate technical limitations of a conventional bulk wave technique for plate-like structures. The guided waves can be generated as various modes with respect to frequency, thickness, and incident angle and they can propagate a large distance along the geometry of a structure . Predicting mode conversion caused by defects, using dispersion theory and experiments, is one of the important parts in guided wave application studies [4-6]. If these characteristics of guided waves are used in NDT we can get improvement of sensitivity using the various modes and reduce inspection time and cost [2-6]. Guided wave techniques are especially useful in NDT of thin plate-like and tubular structures that are hard to test, resulting in signal overlap from the bulk wave technique. Since the 1980s, guided wave application studies have been carried out by numerous researchers such as Rose and Cawley and it was demonstrated that guided waves can be applied to safety insurance of nuclear power station and aircraft successfully [4-6, 9-10].
In addition to that, in ultrasonic NDE, the self-calibrating technique is suggested to avoid the misinterpretation of test results caused by coupling error. Tittman and Hosten applied this technique to test a welding point and Komsky and Achenbach proved that this is a suitable experimental technique to give stable test results in defect detection of plate-like structures using guided waves [7-8]. However, these studies were carried out without the detailed presence of mode conversion. In this study, we propose the feature extracting technique of reflector classification with mode conversion theory in the case of thickness variation.
2. MODE CONVERSION AND SELF CALIBRATING TECHNIQUE
2.1 Mode conversion phenomena of Guided waves
A Lamb type guided wave is generated with multi-reflection and interference in thin thickness structures when the bulk wave is induced in the structure with a particular incident angle, as shown in Fig.1. This wave has dispersive characteristics, i.e. the velocity and propagating pattern vary with frequency, thickness, and incident angle (Fig.2).
Fig 1: The oblique incidence method for the generation of guided waves.
Fig 2: The horizontal mode shifting in the phase velocity dispersion curves due to plate thickness variation.
The phase velocity of the Lamb modes generated at each of the fd values on the dispersion curve can be controlled with variation of angle, and we can calculate the suitable angle with Snell's Law as follows.
Guided wave scattering has different mode conversion phenomena with respect to frequency, thickness, and reflector shape. This means that the variation of plate shape could cause unique scattering at a certain frequency. If plate thickness is fixed, mode conversion occurs only in the vertical direction at the unique fd value as indicated in Fig. 2. At this time, the transmitting and receiving of each mode is available by control of the wedge angle.
Thickness of plate-like structures can be varied by partial coating, corrosion, and joints in the plate. This variation controls not only the vertical direction mode conversion but also horizontal direction mode conversion on the dispersion curve. The complex mode conversion phenomena are the reason that guided wave scattering analysis for reflector classification is difficult. Komsky and Achenbach were concerned with the scattering characteristics of incident mode but in this study the scattering characteristics of different modes after multi-mode conversion is also proposed.
2.2 Self-calibrating technique
In general, defect classification and sizing in ultrasonic NDT is determined using reflection coefficient (R) and transmission coefficient (T) but it is so difficult to obtain stable test results because of coupling state, transducer aging, etc. The self-calibrating technique overcomes the difficulties. [7, 8]
Fig 3: A schematic for the self-calibration concept|
As in Fig.3, with two variable angle beam transducers the defect, or scattering source, in a plate could be detected. Here pulse-echo and through transmission techniques are used simultaneously to separate echo signals from two transducers located at different distances.
In a fixed thickness plate if the transmitted mode and received mode are the same, the voltage of the signal transmitted from the left hand side transducer and received at the right hand side transducer could be expressed by the following equation.
Vlr =Pl ×
Sl × T× Sr× Cr
Pl = transfer function to represent the state of transferring from transducer to test piece
Sl,Sr= transfer function including the attenuation & diffraction between transducer and scattering point
T= transmission coefficient
Cr= transfer function to represent the state of transferring from test piece to transducer
where l and r denote the left and right hand sides, respectively. Similarly,
Vrr =Pr ×
Sr × R× Sr × Cr
Vll =Pl ×
Sl × R× Sl × Cl
Sr ×T × Sl × C
Now we will say (Vll×Vrr)/(Vlr×Vrl),
If transducer (l) and transducer (r) transmit the different modes A and B and receive converted modes C and D, Eq.6 could be modified as follow.
In Eqs. 6 and 7, according to the R/T expressed by the measured voltage of the signal itself, the error factors such as coupling state and internal attenuation were reduced automatically and then R/T values are self-calibrated experimentally.
3. MEASUREMENT OF R/T USING THE SELF-CALIBRATING TECHNIQUE
As in Fig.4, a tone burst signal with controlled number of cycles, frequency, and amplitude is loaded to a 2 MHz variable angle beam transducer located at both sides of the plate. The longitudinal waves from both transducers are induced into the plate at the optimum angle determined from the dispersion curve. The incident longitudinal wave is converted to a Lamb wave and received by both transducers. The received signal is observed with a digital oscilloscope. At this time, received modes are the same as the incident modes. To receive the converted modes receiving angle tuning is needed
Fig 4: The experimental set-up of the self-calibrating technique.
Fig 5: The aluminum specimen with various step discontinuities.
The 2 mm thickness aluminum plate specimen has artificially manufactured 0.5 mm steps that create 3 thickness variation cases. Two transducers are located at different positions, 40 mm and 120 mm from both sides of the thickness varied position (Fig.5).
4. RESULTS AND DISCUSSION
4.1 Guided wave mode conversion caused by plate thickness variation
The angle has to be adjusted to compensate for the different fd values on the dispersion curve resulting from the thickness variation. For example, in the case that the left hand side thickness is 1 mm and right hand side thickness is 2 mm, both transducer's transmitting and receiving angles were adjusted to obtain the three separated signals as shown in Fig. 6. But we cannot regard those signals as the same modes. Actually, the left hand side generated mode is S0 at fd = 2 (MHzmm) and right hand side generated mode is A1 at fd = 4 (MHzmm). To generate the same modes (A1) at both sides, the angle of the left hand side transducer has to be adjusted to 18 degrees (Fig.7). Fig. 6 and Fig. 7 are different from each other. Together they determine that even though the scattering source is the same, different scattering results are available with respect to the incident mode variation. The first of the three time arrived signals in Fig.7 is the reflected signal (Vll) received at the left hand side transducer. The last signal is the reflected signal (Vrr) received at right hand side transducer. The middle signal is the combined transmitted signals (Vlr; from left to right, Vrl; from right to left). The converted modes that do not appear in Fig.7 were measured by tuning receiving angle and are displayed all in Fig. 8. It is shown that the voltage of converted modes can be even higher than that of incident modes and this tells us if guided wave measurements are carried out without concern for the converted modes, experimental error could exist. Here, Vlr(A1S0) is the S0 mode signal converted from A1 mode excited at left side transducer and received at right side transducer. Vlr(A1A1), Vlr(A1S1), Vlr(A1S2), Vrl(A1S0), Vrl(A1A1) are subsequently determined in the same way.
Fig 6: RF wave signal in a plate with thickness variation (dr-dl)/dr=0.5 (incident modes: left-S0, right-A1).|
Fig 7: RF wave signal in a plate with thickness variation (dr-dl)/dr=0.5 (incident modes: left-A1, right A1).
Fig 8: RF wave signals showing multi-mode conversion in a plate with thickness variation for (dr-dl)/dr=0.5 (incident modes : left-A1, right-A1)
4.2 Determination of thickness variation using the mode conversion and self-calibrating technique
In three cases the plate thickness variation ratio ((dr-dl)/dr) is 0.25 (1.5mm-2mm), 0.5 (1mm-2mm), and 0.75 (0.5mm-2mm). The cases are graphically depicted in Fig. 9.
Fig 9: Graphical depiction of the three plate thickness ratios.|
The correlation of R/T based on the measurement of left incident mode S0 and right incident mode A1 and also left incident mode S0 and right incident mode S2 along with thickness variation is presented in Fig. 10. The results in Fig. 10 represent the case where the left side incident mode is S0, the right side incident mode is A1, and at both sides the same modes are measured, [Rll(S0S0)×Rrr(AlAl)]/[Tlr(S0Al)×Trl(AlS0)] (symbol: solid diamond). The values are useful to determine the variation of thickness because of their proportional pattern. In addition [Rll(S0S0)×Rrr(AlAl)] / [Tlr(S0S1)×Trl(AlS0)] (symbol: solid square) can also be chosen to monitor the thickness variation. If the two results are used simultaneously, more reliable determination of thickness variation can be obtained.
Fig 10: Variation of R/T for the incidence of S0(left) and A1(right)|
Fig 11: Variation of R/T for the incidence of S0(left) and S2(right)
Fig. 11 contains the results of left side incident mode S0 and right side incident mode S2. In this case, [Rll(S0S0)×Rrr(S2S2)] / [Tlr(S0S2)×Trl(S2S0)] (symbol: solid circle) cannot be used in thickness variation determination because it does not provide any monotonic trend in variation. However, rather [Rll(S0S0)×Rrr(S2S2)] / [Tlr(S0S0)×Trl(S2S0)] (symbol: solid triangle) is proportional to the thickness variation and determination of that is available with this value. From the results, it is shown that optimum test requirements for quantitative guided wave NDE can be suggested considering the guided wave mode conversion phenomena.
From the study on the dispersion theory and self-calibrating technique to analyze the guided wave mode conversion phenomena in thickness variation condition, the following results are obtained.
- The guided wave mode conversion phenomena caused by thickness variation is experimentally explored by the combination of self-calibrating and angle tuning techniques.
- It is shown that optimum test requirements for quantitative guided wave NDE can be suggested considering the guided wave mode conversion phenomena.
The authors wish to acknowledge the partial financial support of the Korean Ministry of Science and Technology as a part of the 1999 Nuclear Basic Research program and the BFGoodrich Aerospace Co., US.
- H. Lamb, "The Flexure of an Elastic Plate", Proceedings of London Mathematical Society, pp. 85-90, (1989)
- D. N. Alleyne and P. Cawley, "The interaction of Lamb waves with defects," IEEE Trans. Ultrasonic., Ferro. Freq. Cont., vol. 39, no. 3, pp. 381-397, (1992)
- J. L. Rose and J. J. Ditri, "Waves in solid media: A focus on ultrasound," Penn. State Univ., (1996)
- J. J. Ditri, J. L. Rose, and G. Chen, "Mode selection criteria for defect detection optimization using Lamb waves," Review of Progress in Quantitative Non-Destructive Evaluation, vol. 11, pp. 2109-2115, (1992)
- Y. Cho, D. D. Hongerholt and J. L. Rose, "The Lamb Wave Scattering Analysis for Reflector Characterization," The IEEE Transaction on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 44, No. 1, pp. 44-52, January (1997)
- Y. Cho, J. L. Rose, D. D. Hongerholt, "Defect characterization and sizing potential with guided waves: theory," presented at Review of Progress in Quantitative Nondestructive Evaluation, Seattle, WA, (1995)
- B. R. Tittmann, B. H. Hosten, "A Self-Calibrating Technique for the Ultrasonic Discrimination of Solid-State Welds," Journal of NDE, Vol. 7, Nos. 3/4, (1988)
- J. D. Achenbach, I. N. Komsky, Y. C. Lee, and Y. C. Angel, "Self-Calibrating Ultrasonic Technique for Crack Depth Measurement," Journal of NDE, Vol. 11,
No. 2, (1992)
- Cho, Younho, Park, Jung-Chul, "The Study on the NDE using the wedge for the excitation of Lamb wave in tubular structures," KSNT 1998 Spring Conference, pp. 48-56, (1998)
- Cho, Younho, Park, Jung-Chul, "Modal Characteristics of Lamb wave with respect to plate thickness variation," KSNT 1999 Fall Conference