Detection of flaws by Lamb waves study

Lamb wave velocity is very sensitive to a change to the stiffness of the material caused by damage. So a reduction of the velocity can be related to the accumulation of damage caused by fatigue.

This reduction can be detected by SHM that is a NDT for detection of damages in large-area structures. A wave is generated by one transducer and received by X sensors. One of the principal objectives in SHM is to maximize efficiency minimizing the number of sensors. So the best locations have to be thought. Usually, these will be implemented in the areas of most damage accumulation called hot spots or on locations likely to have accidental damage.

In this section, is studied how waves propagate in an aluminum plate for later be able to extrapolate the obtained results to a CFRP plate.

The aluminum plate have 600x112x1,4mm dimensions. There is one actuator located at (56,270) mm and six receivers of 8mm diameter in the plate distributed as shown in figure 6.9. The best location has to be determined by the comparison between different waves received by the sensors.

To know much better the influence of damage in the received waves, four cases are studied:

A. Without any damage (reference plate) B. With one hole (6 mm diameter)

C. With three holes (3 x 6 mm diameter) D. With three holes and one crack

Figure 6.9. Different studied cases (own source)

Flaws in the structural material can be detected by comparing the received signals with those from an undamaged reference plate.

A

A

A

A

The actuator emits a five cycle windowed signal of a symmetric mode with a center frequency of 300 kHz. At this frequency, only the S0 and A0 mode are existing and reflected.

With a frequency of 300kHz and a thickness of 1,4mm, a relation f·d of 0,42 MHz·mm is obtained. As can be seen in Figure 6.10, two different modes with different velocities could be generated.

Figure 6.10. Selected modes and their velocities of the study (own source)

However, signals can be quite confusing because when the damage is too small is so complicated to identify. Usually, the defect size should be larger than one half of the wavelength: ! > 1₂!.

Table 6.3. Minimum detectable length of damage for a f=300kHz (own source)

A0 S0 Frequency (kHz) 300 kHz Group velocity (m/ms) 2,8 5,3

Wavelength (mm) 9,3 17,6 Minimum detectable length of

The detectable damage length in this study (f=300kHz) would be minimum 4,6 mm so the holes could be complicate to detect. In Table 6.3 this is calculated for each wave mode.

A representation of Lamb waves emission, propagation and reflection is shown in Figure 6.11. The received waves by the sensors will be a complete signal displayed which is a superposition of different reflected waves and different modes of waves. Concretely, the reflected waves due to the boundaries and the damages.

Figure 6.11. Representation of emission, propagation and reflection of Lamb waves (sfb477.tu- braunschweig.de)

When there is a defect, a conversion into a different wave mode is done and a different behaviour from the wave amplitude can be identified. For example, when only a single S0 mode passes through a flaw, minimum four modes will be generated, including two transmitted A0 and S0 modes, and two reflected A0 and S0 modes.

To compare the different waves, a data of the received waves obtained by simulation is used to display those by MATLAB4 where:

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For more information about the implemented program to plot the waves see the section C.4. +A

sfb4

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sfb4

Change of wave mode

In this study, for each sensor, cases with damages are compared with the undamaged case. This comparison is required to know the damage influence in the sensors for the correct placement selection.

The amplitude peak to peak is the attribute to distinguish the different modes conditions. Principally, it is easy to distinguish a S0 from an A0 mode by the propagation velocity and wavelength.

First of all, the reference waves are compared to observe which modes are appearing and understand how the waves are propagating through the undamaged plate.

These are represented In Figure 6.12.5

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In section C.4. the displayed waves are enlarged to see them in more detail. a1…a6 : received waves by sensors 1…6 in case A.

b1…b6 : received waves by sensors 1…6 in case B. c1…c6 : received waves by sensors 1…6 in case C. f1…f6 : received waves by sensors 1…6 in case D.

Figure 6.12. Received waves for each sensor in the undamaged plate case (own source)

In most of the cases, the first wave is the emitted one and those that follow are some waves attributed to reflected signals returning from the boundaries of the specimen and passing under the sensor.

In receiver 1 and 3 an asymmetric mode is not apparently shown. That would happen because the propagation speed of S0 mode is higher than that of A0 mode and it would be expected that in a specified time domain, no A0 mode would be collected due

RECEIVER 1 RECEIVER 2

RECEIVER 3 RECEIVER 4

to its slow velocity. Also can be seen that in this two receivers the waves are similar. That is due to the symmetric position of them in relation to vertical axis.

On the other hand, for all other sensors a change in the asymmetric mode is observed. Those waves can be identified because have less energy when pass through the sensor so the amplitude is lower.

At first, seems that there is symmetry between sensor 4 and 5 but the received waves are very different. After watching more carefully, the distances from the vertical axis are a little different and the sensor 5 is 5mm further. Therefore, the result has to be different between these. Also, in both cases, after an interval of time there is a wave with higher amplitude. That could be caused because different reflected waves are overlapped.

After observing the reference wave, the comparison between received waves in the damage cases with the undamaged one can be done. These waves are showed in Figure 6.13 to 6.15. All the graphics represent time domain in x-axis (µs) and the amplitude in y-axis (mV).

The maximum and mean of amplitude variance due to damage reflection in comparison with the reference wave will be the criteria to choose the best location for the sensor. So this will be the aspect that will be focused at the following figures and tables.

Figure 6.13. Comparison between one hole case and undamaged case waves for sensor 1 to 6 (own source)

R1 R2 R3 R4 R5 R6

Maximum 5,981E-9 1,041E-8 6,062E-9 6,637E-9 9,225E-9 9,492E-9 Mean 1,485E-9 1,962E-9 1,497E-9 1,521E-9 2,202E-9 2,139E-9

Table 6.4. Comparison of the amplitude difference between receivers in cases A-B (own source)

In this A-B case, receiver 2 has the maximum amplitude difference and receiver 5 has the most variation of amplitude during all the interval of time. These are the most affected by the presence of a hole.

Figure 6.14. Comparison between three holes case and undamaged case waves for sensor 1 to 6 (own source)

R1 R2 R3 R4 R5 R6

Maximum 1,106E-8 1,511E-8 1,113E-8 1,178E-8 1,280E-8 1,458E-8 Mean 2,679E-9 4,011E-9 2,674E-9 1,138E.9 2,551E-9 3,514E-9

Table 6.5. Comparison of the amplitude difference between receivers in cases A-C (own source)

In this A-C case, receiver 2 is the most afefected by the presence of three holes. This has the maximum amplitude difference most variation of amplitude during all the interval of time.

Figure 6.15. Comparison between three holes with crack case and undamaged case waves for sensor 1 to 6 (own source)

Table 6.6. Comparison of the amplitude difference between receivers in cases A-D (own source)

R1 R2 R3 R4 R5 R6

Maximum 1,155E-8 1,742E-8 2,063E-8 1,963E-8 1,737E-8 1,795E-8 Mean 2,416E-9 4,192E-9 2,890E-9 3,834E-9 2,665E-9 3,961E-9

In this final A-D case, receiver 3 has the maximum amplitude difference and receiver 2 has the most variation during all the interval of time. These are the most affected by the presence of three holes and a crack.

Based on the numerical simulations above, it can be seen that the interaction between different signal modes and reflection from the boundaries waves is very complex. With the previous graphics, is not easy to see what is happening exactly and due to it, choosing a concrete placement of the sensor is not so accurate. Even so, once the arrival time of a reflected wave from the delamination is determined, the difference between the arrival times of the incident and reflected waves can be used to detect the damage position if the distance between the emitter and the sensor is known.

If there would be damage close to the boundaries it gets complicated because the reflected signal of the damage can be completely overlapped with the reflections from the boundaries.

Overall, can be determined that sensor 2 has the higher influence by the presence of damage and therefore, this would be the selected receiver to make an SHM inspection in this case of study.