# Assessment of the Length and Depth of Delamination-Type Defects Using Ultrasonic Guided Waves
## 3 Estimation of Reference Dependencies
### Numerical and Experimental Verification of Reference Dependencies
#### 3.2.2 Experimental Verification  
In addition to numerical calculations, experiments on a custom-made aluminum alloy plate with the dimensions of 1250 mm \(\times\) 600 mm \(\times\) 5 mm were carried out as well. The aluminum plate was selected for the verification of the method due to a few reasons. At first, the properties of aluminum and the dispersion relations of guided waves in it are well known. The second reason is that it was the most reliable way to create thin delamination with a strictly defined length. Afterwards, the method can be applied on any other types of materials with known properties. In the experiments, a special aluminum sample with a machined groove was produced in order to obtain the response adequate to that obtained with the delamination-type defect. In the course of the production of the sample, two aluminum sheets with thicknesses of 2 mm and 3 mm were bonded adhesively to produce a total thickness of 5 mm. Prior to bonding, the 3 mm sheet was machined to produce a wedge-shaped groove with a depth of 500 \(\upmu\)m. The lateral dimensions of the groove ranged from 35 to 335 mm, which enabled the delamination-type defect of a variable size to be simulated. The sketch of the experimental setup used for validation purposes is presented in Figure 10a.  
The experimental investigation was conducted by using custom-made low frequency ultrasonic transducers (130 kHz) operating in a thickness mode with an active diameter of 10 mm. The transducers possess the bandwidth of 100 kHz at \(-6\) dB level and were driven by a 50 V tone-burst with a Gaussian envelope of 3 periods and a central frequency of 130 kHz. The number of cycles were selected to maintain a good balance between the amplitude measurements for depth estimation which requires narrowband excitation and ToF measurements for defect length assessment where a wideband excitation is preferred for better resolution. The best compromise between the propagation distance, the number of cycles, the wavelength and the resolution was selected according to the concept of the minimum resolvable distance (MRD), which was described by [PERSON] et al. (2018) In the experiment, the transducers were arranged in a pitch-catch configuration and attached perpendicularly to the surface of the sample to introduce A\({}_{0}\) mode. The transmitter and the receiver were linked together and scanned along the short edge of the artificial defect as it is shown in Figure 10a. To achieve a reliable and uniform acoustic contact between the transducer and the specimen, custom-made spring type adjusters were used (Figure 10b). As a result of the experiment, a set of waveforms at different defect lengths were collected. The peak-to-peak amplitude of each time trace was compared to the reference time history captured at the same basis on the defect-free region.  
The comparison between mathematical predictions and experimental measurements can be seen in Figure 11. The results demonstrate a fairly good agreement between the experimental values  
Figure 10: Illustration of experimental setup used to validate the predictions (**a**), spring type adjusters used in the experiment to ensure reliable acoustic contact (**b**).  
and the mathematical predictions, especially below the defect lengths of 200 mm. The mismatch in the amplitude ratio between the mathematical and experimental estimations may appear due to the mismatch of dispersion curves, ignored transmission and reflection coefficients in Equations (9) and (10), and by diffraction losses. The discrepancies between magnitude variations and length of defect that are visible in Figures 9 and 11 have a minor impact for damage depth estimation. The actual size of the defect is obtained from ToF measurement, using the damage depth information from magnitude variation of forward scattered direct A\({}_{0}\) mode.