·Table of Contents ·Methods and Instrumentation | A Study on the Guided Wave Mode Conversion Using Self-calibrating TechniqueCho, YounhoDepartment of Mechanical Engineering, Inje Univ., The Republic of Korea Park, Jung-Chul 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 Contact |
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. |
(1) |
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 |
V_{lr} =P_{l} × S_{l} × T× S_{r}× C_{r} | (2) |
Here,
P_{l} = transfer function to represent the state of transferring from transducer to test piece
S_{l},S_{r}= transfer function including the attenuation & diffraction between transducer and scattering point
T= transmission coefficient
C_{r}= 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,
V_{rr} =P_{r} × S_{r} × R× S_{r} × C_{r} | (3) |
V_{ll} =P_{l} × S_{l} × R× S_{l} × C_{l} | (4) |
V_{rl} =P_{r}× S_{r} ×T × S_{l} × C_{} | (5) |
Now we will say (V_{ll}×V_{rr})/(V_{lr}×V_{rl}),
(6) |
(7) |
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.
Fig 4: The experimental set-up of the self-calibrating technique. | Fig 5: The aluminum specimen with various step discontinuities. |
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) |
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