Flat Bottomed Holes

The response from FBHs tilted at 45^o with depths ranging between 2.7 mm and 27.0 mm is measured.

A comparison is made at two dierent inspection frequencies in order to assess the performance of the Hybrid simulation for dierent congurations, one at 2.25 MHz and the other at 3.50 MHz.

In both cases a 0.25", GE MSWQC circular transducer is used to generate 45^o shear waves which reect and scatter from the front face of the FBH. The transducer is coupled to the test block using a Perspex wedge. The response is measured back along the path of propagation. Figure 4.3.8 shows the experimental setup, where a is the transducer diameter, D is the depth of the FBH, and T is the total thickness of the test block.

The range of depths of FBHs is such that a reected shear wave is isolated in time from any transducer ring-down. The thickness of the block is 35 mm and has compression and shear wave speeds of 5840 ms⁻¹ and 3190 ms⁻¹ respectively. The radius of each FBH is r = 1.5 mm at depths D = 2.7 mm, 5.4 mm, 8.1 mm, 10.8 mm, 13.5 mm, 16.2 mm, 18.9 mm, 21.6 mm, 24.3 mm and 27.0 mm.

A two-dimensional Hybrid model of this system is shown in Figure 4.3.9. The defect domain imme-diately surrounds the FBH followed by a region of SRM absorbing boundaries. Because the scatterer must lie within the defect domain the back-wall is not considered. Therefore, in two-dimensions the

r

D T a

θinc

45^o

Figure 4.3.8: Experimental setup for 45^o shear waves scattering from a FBH with radius r, depth D.

The incident wave is generated by a transducer with diameter a, on a test block with thickness T .

r a

θinc

SRM

Excitation Line

Domain Linking Algorithm

D

Figure 4.3.9: Two-dimensional Hybrid model to calculate the response from FBHs with radius r, at a range of depths D.

FBH is consistent with an innite rectangular slot and in three-dimensions becomes an embedded penny shaped reector.

As in Section 4.3.1.1, the transducer response is approximated to be equivalent to a normal incidence plane wave, illustrated by the excitation line. To generate a shear wave excitation the displacement of the excitation line is perpendicular to the path of propagation. The response from the FBH is then propagated back towards the centre of the transducer using the domain linking algorithm.

4.3.2.1 Response at 2.25 MHz inspection

The results from the 2.25 MHz frequency inspection are shown in Figure 4.3.10 and Figure 4.3.11 for the two and three-dimensional cases respectively. The respective amplitudes are shown on a dB scale and are both normalised against the response from the FBH at D = 10.8 mm, which lies suciently beyond the near-eld of the transducer.

0 5 10 15 20 25 30

−10

−5 0 5 10

Depth (mm)

Normalised Amplitude (dB)

Hybrid 2D Experimental FBH

Figure 4.3.10: Comparison between two-dimensional Hybrid simulation and experimental data for a 45^o, 2.25 MHz, incident and reected shear wave from tilted FBHs with increasing depth.

Both the two-dimensional Hybrid and experimental data show that increasing the depth of the FBH results in a reduction in the reected signal amplitude. There is disagreement in the rate of attenuation between the two data sets. The biggest disagreement is observed at a depth of 27.0 mm, where the two-dimensional Hybrid simulation is over estimating the reected shear wave signal by 4.5 dB. This suggests that the two-dimensional approximation is not correctly considering the full attenuation of the scatterer as a function of depth, which is as expected since the variation in the incident signal amplitude has not been accounted for.

0 5 10 15 20 25 30

−10

−5 0 5 10

Depth (mm)

Normalised Amplitude (dB)

Hybrid 3D Experimental FBH

Figure 4.3.11: Comparison between three-dimensional Hybrid simulation and experimental data for a 45^o, 2.25 MHz, incident and reected shear wave from tilted FBHs with increasing depth.

A three-dimensional Hybrid simulation, has also been compared to the same experimental data, shown in Figure 4.3.11.

In this instance there is now better agreement between the simulated and experimental data, although consideration must be given to the xed nature of the incident wave as a function of depth. Both are correctly predicting the same rates of attenuation. The near-eld eects of the transducer are not as apparent in this comparison, this can be attributed to the fact that the transducer diameter is smaller and an incident shear wave is used. The biggest dierence observed in this comparison is 2.5 dB for the 2.7 mm deep FBH. This level of disagreement is within an acceptable level of tolerance and occurs at a depth that is within the NF E, where the exact form of the incident ultrasonic wave is not considered.

When comparing two-dimensional and dimensional simulations, it is apparent that a three-dimensional model shows better agreement with experimental data. Generally speaking, two-three-dimensional approximations will over estimate defect response. The level of disagreement will increase with an in-crease in the range of the target. This is attributed to the nature of attenuation as a function of depth between two-dimensional and three-dimensional models.

4.3.2.2 Response at 3.50 MHz inspection

The variation in ultrasonic response from FBHs is measured against increasing depth using a 3.50 MHz inspection frequency. The results from the two and three-dimensional simulations are shown in Figure 4.3.12 and Figure 4.3.13 respectively. The respective amplitudes are shown on a dB scale, and are

0 5 10 15 20 25 30

Figure 4.3.12: Comparison between two-dimensional Hybrid simulation and experimental data for a 45^o, 3.50 MHz, incident and reected shear wave from tilted FBHs with increasing depth.

Figure 4.3.13: Comparison between three-dimensional Hybrid simulation and experimental data for a 45^o, 3.50 MHz, incident and reected shear wave from tilted FBHs with increasing depth.

both normalised against the response from the FBH at D = 8.1 mm, where the target lies suciently beyond the near-eld of the transducer.

The variation in ultrasonic response at 3.50 MHz remains consistent with that which is observed at

2.25 MHz. Increasing the depth of the FBH results in a reduction in the reected signal amplitude.

For the two-dimensional simulation, there is disagreement in the rate of attenuation between the two data sets. The biggest disagreement is observed at a depth of 27.0 mm, where the two-dimensional Hybrid simulation is over estimating the reected shear wave signal by 6.4 dB. This suggests that the two-dimensional approximation is not correctly considering the full attenuation of the scatterer as a function of depth. This can be improved by using a three-dimensional Hybrid simulation, which has been compared to the same experimental data, shown in Figure 4.3.13.

The three-dimensional simulation shows better agreement with the experimental data. The rate of attenuation with increasing depth is consistent across experimental and simulated data. The biggest disagreement is observed in the NF E of the transducer at D = 2.7 mm, with the Hybrid simulation overestimating the response by 2.3 dB. This can be attributed to the plane wave excitation used in the Hybrid simulation, which does not correctly represent the transducer response.