Damage detection in plate by in-plane waves

In experiment #1, velocity responses were measured in 17 nodes evenly distributed on the left edge of the plate (along line #1 in Fig. 6.4) from x = 0, y = 0 m to x = 0, y = 1 m. As a reference state, the pristine plate was firstly examined. Experimental and numerical veloc-ity signals in the time and spatial domains are given in Fig. 6.9. They consist of particular A-scans, i.e. waveform data plotted as a function of time, registered in consecutive points.

Fronts of the R wave and the S0 mode were registered on the plate edge.

The second example concerned the plate with damage #1 (Fig. 6.10). In both the nu-merical and experimental results, the fronts of the S0 mode reflected from damage were visible. Two fronts of the S0 mode were caused by the 1st and 2nd reflection from damage and they are marked by solid lines in Fig. 6.10. The first reflection in the numerical signal occurred at time t = 0.1149 ms and knowing the plate geometry and the group velocity of the S0 mode (4973.17 m/s) the location of the defect can be identified as 286 mm. In the case of experimental signal, reflection occurred at t = 0.1141 ms and the velocity of the S0

mode was 5009.78 m/s, thus the identified position of damage was 286 mm. Two additional fronts of wave, marked with dashed line in Fig. 6.10, were caused by the S0 mode diffrac-tion from defect ends. This S0 mode arose from a mode conversion upon interaction of the SH0 mode with defect. The fronts of diffracted waves enabled to estimate the defect length.

Moreover, in the experimental signals an additional reflection appeared. It was the R wave reflected by damage (dotted line in Fig. 6.10b). This reflection was identified as coming from imperfect work of the equipment (electromagnetic coupling in the cabling). The am-plifier created additional wave packet (of amplitude about 0.01 of the incident wave) at the moment of arriving the S0 mode reflected from defect. This wave packet induced propaga-tion of new R wave, which provided the addipropaga-tional indicator of damage existence.

6.1. In-plane wave propagation in plate 125

Fig. 6.9. Set of time signals collected at 17 points evenly distributed along the plate edge during propagation of in-plane waves of frequency 250 kHz in the pristine plate: a) spectral element method simulations based on the Kane-Mindlin theory; b) experimental results

Fig. 6.10. Set of time signals collected at 17 points evenly distributed along the plate edge during propagation of in-plane waves of frequency 250 kHz in the plate with damage #1: a) spectral

element method simulations based on the Kane-Mindlin theory; b) experimental results

6.1. In-plane wave propagation in plate 127

Fig. 6.11. Set of time signals collected at 17 points evenly distributed along the plate edge during propagation of in-plane waves of frequency 250 kHz in the plate with damage #2: a) spectral

element method simulations based on the Kane-Mindlin theory; b) experimental results

Figure 6.11 shows propagation of in-plane waves in the plate with damage #2. Both numerical and experimental results revealed the existence of the reflection from the defect.

The front of the S0 mode reflected from damage was partially covered with the R wave, but the identification of damage was still possible. The reflection in the numerical signal oc-curred at time t = 0.2936 ms and the position of the defect was identified as 730 mm. For the experimental signal, the reflection occurred at time t = 0.2902 ms, so the identified position of damage was 727 mm.

In experiment #2, velocity responses were measured in 161 evenly distributed points along each of lines #1 and #2 (see. Fig. 6.4). Lines #1 and #2 were situated on the plate surface and their lengths were insignificantly shorter than the plate length. Moreover, line #1 was shifted from the left edge of the plate at about 2.5 cm thus in the numerical simulations the velocity signals were calculated at the distance of 2.5 cm from the plate edge. The measurements were performed for the plate with damage #1, #2 and #3. Numeri-cal and experimental results are presented in Fig. 6.12 to Fig. 6.18 in the forms of so Numeri-called B-scans, which present data in the form of a time-position scan (a cross-sectional view).

In Fig. 6.12, numerical results for the pristine plate are shown. The horizontal axis rep-resents time while the vertical one gives the distance along the plate width (or length). The amplitudes of waves are displayed as the grey scale values. In the presented B-scans, the S0

and SH0 modes, the R waves, as well as the head waves (a.k.a. PS waves) can be found.

Numerical and experimental B-scans for the plate with damage #1 are presented in Fig. 6.13 and Fig. 6.14, respectively. Observation of the time-position plane enabled to identify both the position and the extent of damage. Fronts of the S0 mode caused by the 1st and 2nd reflection from damage, as well as diffraction from the defect ends are visible in Fig. 6.13a for line #1 based on the numerical data. This scan provided the estimation of the defect length. Figure 6.13b shows the numerical scan data for line #2. In this case, the plot provided information on the distance of damage from the plate edge. Based on the experi-mental data (Fig. 6.14), it was possible to identify both damage position and its size, but the velocity signals did not exactly cover with the numerical ones. This was caused by the presence of the A0 mode in the experiment. The appearance of small amplitude A0 mode caused, that the waves diffracted on the defect ends cannot be clearly observed.

Figures 6.15 and 6.16 give the B-scans for the plate with damage #2 for numerical and experimental data, respectively. Both the extent and position of the defect can be detected from the numerical, as well as the experimental signals. In the experimental results, the influence of the A0 mode was insignificant in comparison with the test on the plate with damage #1. This was caused by slightly different mounting of the actuator. Therefore it is visible, that the excitation of pure S0 mode depends on the quality of actuator mounting.

Numerical and experimental B-scans for the plate with defect #3 are illustrated in Fig. 6.17 and Fig. 6.18, respectively. The defect #3 was situated perpendicularly to the plate left edge. Detection of such defect was more difficult than of the defects parallel to left plate edge (defect #1 and defect #2). The extent of the defect can be superficially assessed from the B-scan along line #2 and its position can be calculated from the B-scan along line #1, knowing the time of the reflection and the group velocity. Moreover, the B-scan along line #1 showed, that the defect occurs on the upper half of the plate.

Finally, C-scans were analysed based on the numerical velocity signals. The C-scan provides a two-dimensional xy plane view at selected time instants. Velocity components parallel to the x axis are illustrated in Fig. 6.19 to 6.22. Results for the pristine plate are given inFig.6.19 at the time instants t = 0.12;0.2;0.25;0.4ms.Theforceappliednormalto

6.1. In-plane wave propagation in plate 129

Fig. 6.12. B-scans of numerical in-plane waves in the pristine plate: a) line #1; b) line #2

Fig. 6.13. B-scans of numerical in-plane waves in the plate with damage #1: a) line #1; b) line #2

6.1. In-plane wave propagation in plate 131

Fig. 6.14. B-scans of experimental in-plane waves in the plate with damage #1: a) line #1; b) line #2

Fig. 6.15. B-scans of numerical in-plane waves in the plate with damage #2: a) line #1; b) line #2

6.1. In-plane wave propagation in plate 133

Fig. 6.16. B-scans of experimental in-plane waves in the plate with damage #2: a) line #1; b) line #2

Fig. 6.17. B-scans of numerical in-plane waves in the plate with damage #3: a) line #1; b) line #2

6.1. In-plane wave propagation in plate 135

Fig. 6.18. B-scans of experimental in-plane waves in the plate with damage #3: a) line #1; b) line #2

Fig. 6.19. C-scans of numerical in-plane waves in the pristine plate registered at selected time instants: a) t = 0.12 ms; b) t = 0.2 ms; c) t = 0.25 ms; d) t = 0.4 ms

Fig. 6.20. C-scans of numerical in-plane waves in the plate with damage #1 registered at selected time instants: a) t = 0.12 ms; b) t = 0.2 ms

6.1. In-plane wave propagation in plate 137

Fig. 6.21. C-scans of numerical in-plane waves in the plate with damage #2 registered at selected time instants: a) t = 0.17 ms; b) t = 0.2 ms

Fig. 6.22. C-scans of numerical in-plane waves in the plate with damage #3 registered at selected time instants: a) t = 0.11 ms; b) t = 0.16 ms

theplateedgeresultsinpropagationofcylindricalfrontedS0 andSH0 modes, as indicated in Fig. 6.19. The straight-crested PS wave is the von Schmidt head wave, arising from the reflection of a grazing incidence P wave (Graff 1975). Moreover, the Rayleigh wave is visible. The R wave is not separated clearly from the SH wave due to the early stage of the wave development (Fig. 6.19a). Lamb wave interaction with defect #1 is shown in Fig. 6.20. The defect is indicated at position corresponding to its actual location. At time t = 0.12 ms (Fig. 6.20a) the S0 mode 1st reflection from damage approaches the plate left edge. It is also visible, that the SH0 mode after interaction with damage is converted into the S0 mode, which is then diffracted by the defect ends. The second reflection of the S0

mode from damage is visible at t = 0.2 ms (Fig. 6.20b). The C-scans for the plate with damage #2 are presented in Fig. 6.21. Based on the C-scan at t = 0.17 ms both position and extent of damage can be identified. Figure 6.22 shows the numerical results for the plate with damage #3. The C-scan at t = 0.11 ms shows interaction of the S0 mode with damage.

At the time instant t = 0.16 ms interaction of the S0 and SH0 mode with the defect is visible.

Diffraction of waves on the defect ends indicates the defect length.

6.2. Flexural wave propagation in plate