Side Drilled Holes

The response from SDHs is measured experimentally and compared to Hybrid simulations. Two set-ups are considered, the rst is a pulse-echo inspection of SDHs with increasing depth and the second considers scattering from a single SDH across an angular range.

4.3.1.1 Response as function of depth

A 2.25 MHz, 0.5", GE MSWQC circular transducer is used to generate normal incident compression waves which reect and scatter from SDHs. The response is measured back along the path of propa-gation for a range of depths between 10 mm and 55 mm. Figure 4.3.1 shows the experimental setup, where a is the transducer diameter, D is the depth of the SDH, and T is the total thickness of the test block.

The range of depths of SDHs is such that a reected compression wave is isolated in time from any transducer ring-down and the response from the back-wall at depth T . The thickness of the block is 60 mm and has compression and shear wave speeds of 5840 ms⁻¹ and 3190 ms⁻¹ respectively. The radius of each SDH is r = 1.5 mm at depths D = 10 mm, 15 mm, 20 mm, 25 mm, 35 mm, 45 mm and 55 mm. When taking the signal amplitude there is some uncertainty over the exact amplitude and position of the response. This is determined by the diculty to accurately know the position of the transducer and the signal to noise amplitude of the responses.

A two-dimensional Hybrid model of this system is shown in Figure 4.3.2. The defect domain imme-diately surrounds the SDH followed by a region of SRM absorbing boundary. The transducer response is estimated to be equivalent to a normal incidence plane wave, illustrated by the excitation line. The response from the SDH is then propagated back towards the centre of the transducer using a domain linking algorithm.

r

D

T a

Figure 4.3.1: Experimental setup for normal incidence compression wave scattering from SDH with radius r, and depth D. The incident wave is generated by a transducer with diameter a, on a test block with thickness T .

r

D Domain

Linking Algorithm

SRM

Excitation Line

Figure 4.3.2: Two-dimensional Hybrid model to calculate the response from SDHs with radius, r, at a range of depths, D.

The response of the transducer can be calculated in a number of ways, reliant upon the hybrid model calculating the scattered eld at discretised points normal to the face of the transducer. Once this has been achieved, the transducer response can be taken as an average of these values, or a weighted average according to the prole of the transducer. A faster method is to only consider the scattered

eld at the centre of the transducer, since this reduces the number of points at which to calculate the scattered eld. In the scenarios considered here, negligible dierence has been observed between either of the approaches, especially when the results are normalised against one-another, therefore, due to the preferred savings in computation time, the response at the centre of the transducer has been taken.

To begin with, the amplitude of the normal incident plane wave remains constant, and is not varied as a function of depth. This does not conform to experimental reality, where the incident amplitude decreases with range from the probe for distances beyond the near-eld of the transducer, which can be approximated by Equation 4.3.1.

N F E = a²

4λinc (4.3.1)

where NF E represents the Near Field Extent, a is the transducer diameter and λinc is the incident wavelength. Later, in Section 4.3.3, the importance of the providing the correct excitation to the FE domain is discussed.

The results from the two-dimensional Hybrid simulation and experimental data are shown in Figure 4.3.3. The respective amplitudes are shown on a dB scale, and are both normalised against the response from the SDH at D = 25 mm. This target has been used to normalise the signals, because it lies suciently beyond the NFE , which in this instance is calculated to be 13.9 mm.

The Hybrid simulations illustrate a general trend, where the amplitude of the reected signal re-turning from a SDH decreases with increasing depth. For defects which lie beyond the NF E, the results from experimental data show the same trend. The amplitudes are consistent with one another, with the greatest dierence in amplitude being 3.1 dB at a depth of 55 mm, however, it is noticed that the reduction in signal amplitude measured experimentally is decreasing at a greater rate than the simulated data. This can be attributed to the amplitude variation of the incident wave not being accounted for as the target has increased range away from the transducer.

Within the NF E there is considerable dierence between simulated and experimental data. The near-eld response is not correctly accounted for and as a result, the simulated data fails to predict the correct trend in signal amplitude. Furthermore, despite a two-dimensional model being a good approximation for calculating the scattering response from a SDH, it is likely that the disagreement observed is due to an incident beam being poorly represented in two-dimensions.

To assess the validity of this nding, the same experimental data can be compared to results from a three-dimensional Hybrid simulation of the same system. Again, the response from both data sets

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Depth (mm)

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Hybrid 2D Experimental SDH

Figure 4.3.3: Comparison between two-dimensional Hybrid simulation and experimental data for the ultrasonic response from SDHs with increasing depth.

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Hybrid 3D Experimental SDH

Figure 4.3.4: Comparison between three-dimensional Hybrid simulation and experimental data for the ultrasonic response from SDHs with increasing depth.

are normalised against a defect that lies suciently beyond the near-eld of the transducer, shown in Figure 4.3.4.

The far-eld amplitude response from the SDHs now shows good agreement between experimental and three-dimensional Hybrid simulated data, however, it is important to remember that the variation in the incident signal amplitude as a function of depth is not considered. The greatest disagreement observed in the far-eld response is 0.5 dB and both responses are following the same trend in signal attenuation. Disagreement still exists within the NF E, suggesting that a plane wave excitation is invalid within this region. This result provides a level of condence in the ability of Hybrid simulations to accurately predict the response from scatterers beyond the NF E, but the uncertainty in the nature of the incident signal must be called into question.

4.3.1.2 Response as function of scattering angle

The response from a SDH is measured experimentally as a function of scattering angle θsc. In this example a normal incidence 2 MHz compression wave is transmitted from the rst element from within a 128 element array. The remaining elements detect the scattered signal, allowing for the response as a function of scattering angle to be measured as shown in Figure 4.3.5.

r

D

θsc T

Figure 4.3.5: Experimental setup for normal incidence compression wave scattering at angle θsc, from a SDH with radius r, depth D. The incident wave is generated from the rst element of a 128 element array, on a test block with thickness T .

r

D θsc

SRM Excitation Line

Domain Linking Algorithm

Figure 4.3.6: Three-dimensional Hybrid model to calculate the response from SDH with radius r, and depth D, at scattering angle θsc.

A three-dimensional Hybrid simulation is compared to the experimental data, as shown in Figure 4.3.6. The defect domain immediately surrounds the SDH followed by a region of SRM absorbing boundary. The transducer response is estimated to be equivalent to a normal incidence plane wave, illustrated by the excitation line. The response from the SDH is then propagated back towards elements within the array using the domain linking algorithm.

In this case, the range of the target from the transmitting element within the array remains xed, thereby making the plane wave excitation a good approximation to the incident wave. The reception of scattered response on the receiving elements is calculated using the same method as described in Section 4.3.1.1; the directivity of the elements has not been considered as this is thought to have little inuence with this array at this inspection frequency.

The SDH has radius r = 1.5 mm at depth D = 50 mm and is isolated from any other scatterers. The array consists of 128 elements with a width of 0.55 mm, each separated by 0.20 mm. An in-house, data acquisition software package, is used to control the array and capture the ultrasonic eld scattered from the SDH. Figure 4.3.7a) shows the data captured from the array.

From Figure 4.3.7a) three signals can be identied. The rst occurs early in time and corresponds to the ring down of the ring element and the propagation of a surface wave along the length of the array.

The second is a reected compression wave from the SDH, which occurs at approximately 18 µs for θ_sc = 0^o. The third is a mode converted shear wave reecting from the SDH. The experimental scan data has isolated the reected compression and shear wave modes, apart from a point at a scattering

a) .

b)

c) ^{0 10 20 30 40 50 60}

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Surface Wave ↓

Dead Element →

Amplitude (dB)

Scattering Angle (degrees) Experimental SDH p wave Hybrid 3D p wave

. ^{0 10 20 30 40 50 60}

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← Dead Element

Amplitude (dB)

Scattering Angle (degrees) Experimental SDH s wave Hybrid 3D s wave

Figure 4.3.7: Absolute amplitude of the scattered eld from a SDH as a function of the scattering angle for a) experimental measurement, b) reected compression wave and c) a mode converted

angle of 50^o where the surface wave propagating along the array, coincides with the arrival of the reected compression wave. This is not included in the Hybrid model.

Figure 4.3.7b) and Figure 4.3.7c) show the amplitude of the reected compression and shear wave modes respectively from the SDH as a function of scattering angle. The results are normalised against the reected compression wave at θsc = 0^o and Hybrid and experimental data sets are directly com-pared.

Figure 4.3.7b) and Figure 4.3.7c) both show good agreement. The three-dimensional Hybrid simula-tion is capable of accurately predicting the amplitude of the scattered signal across the angular range considered. There are two areas of disagreement in Figure 4.3.7b) and Figure 4.3.7c) which can easily be explained.

The experiential data shows a signicantly reduced amplitude at θsc = 30^o and an uncharacteristic increase in amplitude between 45^o− 55^o. The rst corresponds to a dead element within the array that is incapable of collecting the ultrasonic data. The latter is due to a surface wave propagating along the array that interacts with the scattered compression wave at this particular angle. Disagreement is observed between the mode converted shear wave at scattering angles beyond 55^o, with the Hybrid model over estimating the amplitude of the scattered signal, however this is of the order 2.5 dB, which is an acceptable variation. This dierence could be attributed to the element directivity of the receiving elements not being considered.