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“light”, “moderate” and “heavy”, respectively, by Network Rail (see Figure 2.7) have been modelled to investigate the influences of crack dimensions on the relationship between Bz trough-peak ratios and the crack vertical angles. Each crack has been studied with the maximum and minimum elliptical ratios reported for RCF cracks of 1 and 1.75.

The Bz trough-peak ratio is a reflection of the asymmetrical distribution of the Bz magnetic field caused by the vertical angle, as discussed above. Cracks with the same surface length but different ellipse values show the same Bz trough-peak ratio when the vertical angle is between 30° to 90°, as shown in Figure 4.8. As the cracks become shallower, at vertical angles less than 30°, the Bz trough-peak ratios are no longer the same for the same surface length. The Bz trough-peak ratio values for the small elliptical ratio, i.e. the longer pocket length, are lower than for the higher elliptical ratio. The variations are caused by the different pocket lengths of the cracks, as cracks with a longer pocket length give a shorter distance from the negative area

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of the magnetic field to the measurement line, leading to the difference between the highest and lowest values along the measurement line becoming much greater. However, this effect becomes less obvious with an increase of surface length, as for the results for the 21 mm surface length cracks. The longer surface length causes a large shift in the Bz magnetic field along the surface length when compared to the displacement perpendicular to the surface length with changing vertical angle. Therefore, the distance from the measurement line to the Bz maximum and minimum value is greater, which decreases the difference caused by the variations of the pocket length between the highest and lowest values along the measurement line.

Figure 4.8 Bz trough-peak ratios against crack vertical angle along the 45° measurement line for semi-elliptical cracks from light to heavy category with elliptical ratios 1:1 and 1:1.75 (S denotes the surface length, P denotes the pocket length and R denotes the elliptical ratio).

4.4.3 Angle of measurement line to the crack surface-breaking component

The Bz trough-peak ratio along the 45° measurement line has been shown to record differences caused by variations in vertical angle, through modelling and experimental validation in section 4.4.1. However from the contour plot of the Bz magnetic field (Figure 4.5), it would be expected that the Bz trough-peak ratio is

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rather sensitive to the angle of the measurement line, i.e. the angle at which the sensor is scanned across the crack opening component. To investigate the sensitivity, the ACFM sensor was moved by hand at 0 mm lift-off through the centre of the crack surface-breaking component at different measurement angles with the sensor orientated such that current flows perpendicular to the crack surface-breaking component. The measurement angle in the model was varied between 0° to 85° with respect to the crack surface length and experimental measurements were carried out at angles of 15°, 25°, 45°, 75° to compare with the modelling results.

Figure 4.9 shows the Bz trough-peak ratios against measurement angle for cracks with surface lengths of 8 and 15 mm (elliptical ratio of 1.25). For the crack at an angle of 90°, the distances from the measurement line to the negative and positive valued areas of Bz at any measurement angle are similar, therefore the Bz trough- peak ratio values remain at -1. As the measurement angle increases, the negative and positive valued areas of the Bz magnetic field move away from the measurement line. The distance to the positive valued area is greater than to the negative valued area, leading to the difference between the minimum and maximum values along the measurement line becoming larger. This explains why the Bz trough-peak ratios decrease with an increase in the measurement angle, as shown in Figure 4.9.

Experimental results, with error bars, for the calibration cracks with vertical angles of 21° and 12° (cracks 5 and 6, respectively) are also shown in Figure 4.9a. The figure indicates that it is difficult to distinguish the crack vertical angle using the Bz trough-peak ratio for measurement lines at low angles with respect to the crack surface-breaking component. The Bz trough-peak ratio starts to saturate at larger measurement angle, e.g. 75° and 65° for the crack with surface lengths of 8 and 15 mm, respectively. Results at greater measurement angles will make it easier to distinguish the crack vertical angle in the model results, however in experimental inspection with the ACFM sensor, the Bz trough-peak ratio measured via a measurement line at greater angles is more influenced by noise, as the magnitude of the maximum and minimum values along the measurement line are rather small. An optimization study to determine the best measurement line angle for the Bz trough- peak ratio could be carried out with regard to different crack surface lengths,

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however, in this study 45° was selected as giving a sufficiently large signal-to-noise ratio and Bz trough-peak ratio to allow the crack vertical angle to be determined.

Figure 4.9 Bz trough-peak ratio against the measurement angle ranging from 0° to 85° for cracks with surface length of (a) 8 and (b) 15 mm (with elliptical ratio of 1.25); experimental results for calibration cracks with surface length of 8 mm and vertical angle of 10° and 20° are also shown (S denotes the surface length and VA denotes the vertical angle).