CAPÍTULO 3. VALIDACIÓN DEL PROCEDIMIENTO PROPUESTO
3.2 Validación del procedimiento propuesto mediante el juicio de expertos
A pair of EMATs acting respectively as a transmitter and an in-plane receiver are used in a pitch-catch configuration, as explained in Section 3.3. In a preliminary experiment to identify the wave modes present, the transmitter EMAT was fixed at 200 mm from a crack and an in-plane EMAT receiver was scanned with 0.5 mm steps, starting at
50 mm from the crack on the same side of the crack as the transmitter, and scanned to an equal distance on the other side of the crack. At each scan point, the time domain signal detected by the receiver (A-scan) was recorded automatically in a LabVIEW routine. The A-scans were appended into a matrix to form an image representation of the scanned data, known as a B-scan. In a B-scan, the x and y axes show the time and scan distance respectively, while the grayscale represents the signal amplitude: black shows the maximum negative signal value (trough) while white shows the maximum positive signal value (peak).
Figure 4.1 (a) shows a typical B-scan of a surface crack propagating normal to the sample surface of depth 5 mm. The main wave modes indicated in the figure can be identified through their arrival time. The origin of the various reflected, transmitted, and mode-converted wave modes come from the interaction of the Rayleigh wave with the crack. When the Rayleigh wave reaches the crack, some of the low frequency components are transmitted underneath the crack, propagating to the other side of the crack. Some of the low frequency components are also reflected back. The high frequency components, however, can travels down to the crack tip, reflect back to the top of the crack and propagate in opposite direction to the incoming wave. At the crack tip, a number of wave modes are generated; the Rayleigh wave is mode-converted to longitudinal and shear bulk waves. It has been reported that the crack tip acts as a secondary source of ultrasound waves [72].
The arrival time of these various mode can be calculated based on the geometry illustrated in Figure 4.2 as follows:
Incident Rayleigh wave, R (Figure 4.2(b))
tIR = (x1 −x2)/cR (4.1)
Reflected Rayleigh wave, R-R (Figure 4.2(c))
tRR = (x1+x2+ 2kl)/cR (4.2)
Mode converted longitudinal wave, R-L (Figure 4.2(d))
tR−L = (x1+l)/cR+
q
x2
2 +l2/cL (4.3)
(a) 0.24m 0.22 0.20 0.18 0.16
Distance from gen EMAT/m
120µs 100 80 60 40 Time/s R R-L R-SL R-S R-R (b) -40 -20 0 20 40
Dist of detection point to slot/mm
120x10-6 100 80 60 40 Time/s R R-R R-L R-SL R-S
Figure 4.1: (a) In-plane B-scan of a normal (90o)crack, depth = 5 mm from experiment
and (b) 2D FEM model . The main wave modes are the incident Rayleigh (R), reflected Rayleigh (R-R), and mode-converted surface skimming longitudinal wave (R-L).
tR−S = (x1+l)/cR+
q
x2
2 +l2/cS (4.4)
Mode converted surface skimming longitudinal wave, R-SL (Figure 4.2(e))
tR−SL= (x1+l)/cR+ (x2+l)/cL (4.5)
where x1 is the distance from generation point to the crack, x2 is the distance from
the detection point to the crack, k > 0 is the number of reverberations at the crack,
and l is the length of the crack [72]. The Rayleigh wave speed is cR = 2885 ms-1, the
Figure 4.2: (a) Geometry of a normal (90°) crack with generation (Gen.) and detection points (Det.1 and Det. 2). (b)-(e) Travel paths of waves reflected, transmitted and mode converted at the crack. R denotes Rayleigh wave, L denotes longitudinal wave, and S denotes shear wave. L/S indicates that the mode can either be L or S.
(a) 240 220 200 180 160
Distance from gen EMAT/mm
120x10-6 100 80 60 Time/s (b) 240 220 200 180 160
Distance from gen EMAT/mm
120x10-6 100
80 60
Time/s
Figure 4.3: Experimental B-scans of an inclined crack, 22.5°, depth=5 mm, from two directions. (a) The acute angle, 22.5° and (b) The obtuse angle, 157.5° relative to the incident wave direction.
Some of the wave modes indicated by the arrival time lines are not clearly visible in the B-scan from the experiment (Figure 4.3) as there are multiple relfections of surface skimming longitudinal waves and bulk waves (longitudinal and shear) that interfere with the main wave modes. These bulk waves which are generated by the transmitter EMAT, are reflected at the underside of the sample. To see the main surface wave modes more clearly, Figure 4.1 (b) shows the B-scan generated from a two dimensional FEA model for the same size crack. In the model, all the boundaries except the top surface are set to be absorbing. Thus, the bulk wave reflections are removed.
In Figure 4.3, B-scans are shown for scans made on an inclined crack, of angle 22.5° (vertical depth=5 mm) with scanning done in opposite directions. In (a), the EMAT receiver is scanned towards the acute angle (22.5°) of the crack, while in (b) towards the
scanning direction of EMATs are reversed , and hence the angle relative to the incident wave is now 157.5°. The B-scan in (a) contains extra features when compared with the B-scan for normal cracks (Figure 4.1). There is a prominent alternating black and white enhancement pattern which cannot be explained using the wave modes identified earlier, nor by their reflections. Meanwhile, for the obtuse angle (Figure 4.3(b)) the alternating pattern is still observed but is less prominent and occurs when the detector is positioned after the crack. This behaviour is also observed in the 2D model, as shown in Figure 4.4. The difference in the enhancement features between normal and inclined cracks can be used to distinguish the type of crack and classify defects into categories, and this is presented in Section 4.3. The origin of this enhancement pattern will be explained in Section 4.4. A procedure for characterising cracks based on the enhancement features will be explained in details in Chapter 5.