timation of off-axis flaws
Section 4.6.2 has presented the curve fitting method. This method has shown a very important result: it is possible to measure the transverse position of a defect when performing an ultrasonic D-scan by studying how the arcs of a defect indication vary with scan position. This information would normally be obtained only from a B-scan image. This method suffers from one limitation: it does not indicate whether the defect is off-axis to the right or to the left of the weld (direction of the displacement). In other words, the value of X is determined
To overcome this limitation, a novel solution is proposed here by exploiting the information in the mode-converted region of the D-scan. This region is generally overlooked or discarded when sizing defects, and does not feature in most TOFD standards [3, 63, 67]. Upon close inspection, however, mode-converted returns are highly indicative, as shear waves are twice as sensitive as longitudinal waves, having shorter wavelength and a lower velocity. Recall that the mode-converted waves are generated due to the change of the ultrasonic wave propagation upon reflection or refraction at acute angles at an interface.
It is therefore possible to exploit the fact that mode-converted returns are inher- ently asymmetric in that the inward (longitudinal) pulse travels faster than the outward (shear wave) pulse. This allows the direction of the lateral offset to be determined by reversing the direction of the beams and comparing the resulting echo times. Figure 6.1 shows two symmetrical flaws and their indications in the compression and the mode-converted waves regions. The two flaws have the same indication in the compression waves region in contrast with the mode-converted region where two distinct indications are present. By checking the time of the two mode-converted indications, the flaws can be concluded to be either closer to the transmitter or the receiver of the scan equipment.
Most commercial equipment used for TOFD scanning can provide the feature of operating multichannel probes concurrently (called software channels). Using this feature (and referring to Figure 6.2), two channels are defined as follows:
Figure 6.1: Time difference between defects in the mode-converted indication
a) Channel 1: Probe 1 is transmitting while probe 2 is receiving.
b) Channel 2: Probe 2 is transmitting while probe 1 is receiving.
As it can be seen from Figure 6.2, the indication in the compression (upper) region shows almost the same position for both transmitter-receiver setups. The differ- ence is found in the mode-converted (lower) region, where there are two different times (t1 and t2). As the inward (compression wave) propagation is always faster
than the outward (shear wave) propagation, the defect will consistently appear to the shallower (closer to the surface) when the probe closest to it is receiving.
Figure 6.2: The flaw is actually closer toR1 inT1−R1 setup (shortest time)
6.6
Mode-converted waves and flaw sizing esti-
mation of off-axis flaws
The previous section shows a possible use of the mode-converted waves to help in accurate positioning of flaws. This section proposes some further concepts, methods and techniques that utilise the shear times of the mode-converted waves
for the task of accurate sizing and positioning of flaws when the conventional methods fail due to data issues, complexity or the presence of shallow defects.
Consider a flaw of height (or length) L and oriented vertically at a depth d from the scanning surface in a component of thicknessD(see Figure 6.3). It is required to express the diffracted echo of the top and bottom tips of the flaw in terms of shear times instead of the longitudinal ones. When the the flaw tip is located exactly in the centre line between the probes, then the time-of-flight is straight forward and will be shown in the following steps.
Figure 6.3: Typical TOFD representation of a defect lying on the centre line
between the probes
The time-of-flight of the longitudinal backwall echo (tBW) can be shown to be:
tBW = 2
vL
√
s2+D2 (6.1)
where all the parameters have their ordinary definition. The times of the longitudinal- diffracted echoes from the defect top and bottom tips ttl and tbl are given by:
ttl = 2
vL
√
On the other hand, the times for the shear-diffracted (transverse) echoes from the defect top and bottom tips tts and tbs can be expressed as:
tts = 1 vL + 1 vS √ s2+d2 (6.4) and tbs = 1 vL + 1 vS p s2+ (d+L)2 (6.5)
where vS is the shear velocity in the material. Now, relating the two sets of equations for longitudinal- and shear-diffracted echoes, it can be shown that
tts = n+ 1 2 ttl (6.6) and tbs = n+ 1 2 tbl (6.7)
where n =vL/vS. In physical terms, this can be seen as in line with the concept of Poisson’s effect in materials. Recall that the Poisson’s ratio for a certain object is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force [93]. For the above case, Poisson’s ratio is positive and is equal to (n+ 1)/2.
Logically, the shear-diffracted echo must appear after the longitudinal echo so that the longitudinal and transverse waves will not overlap (a situation that happens when the probes are too close together for example). As a result, the shear- diffracted echo from the defect top tip must appear after the longitudinal backwall echo. In mathematical terms:
tts > tBW (6.8) and using the equations above for both terms, then:
s > r D2−Rd2 R−1 (6.9) where R = 1 4(1 +n) 2 (6.10)
For simplification, it can be assumed that vL≈ 2vS, then Equation (6.9) reduces to:
s >
r
4D2−9d2
5 (6.11)
Equation (6.11) leads to the definition of the minimum PCS required for shear- diffracted echo to appear after longitudinal echo. Based on this equation, it can be concluded easily that the following relation must be met:
d < 2
3D (6.12)
bottom-reflected signaltBW. For a given PCS, the general form of this relation is:
d <
r
D2−s2(R−1)
R (6.13)
As a numerical example, for a sample plate of 25 mm thickness, in order to be able to detect a flaw of 3 mm depth, the selected PCS should be taken to be less than 44 mm. This, of course, should be done in conjunction with other system parameters to assure the sensitivity and resolution required to detect that defect.
Returning back to Equations (6.4) and (6.5) and rearranging, the depth of the defect d and length (height) L can be shown to be:
d= s v2 Lt2ts (n+ 1)2 −s 2 (6.14) L= s v2 Lt2bs (n+ 1)2 −s 2−d (6.15)
As a quick verification, n = 1 for the longitudinal incidence and longitudinal diffraction, and Equations (6.14) and (6.15) reduce to the essential time-of-flight equations with longitudinal times:
d = r v2 Lt2tl 4 −s 2 (6.16)
and L= r v2 Lt2bl 4 −s 2−d (6.17)
Consider now the situation when the crack is off-axis. In this case, there are two possibilities (a flaw that is either off-axis to the right or to the left). Recall that the previous section has discussed and addressed the problem to distinguish between the two possibilities. For that reason, only one case (right off-axis) will be discussed. In this case, the time-of-flight of the diffracted signal from the top tip of the crack due to the shear wave can be expressed as:
tts = 1 vL p d2+ (s+X)2+ 1 vS p d2+ (s−X)2 (6.18)
and that of the bottom tip is:
tbs = 1 vL p (d+L)2+ (s+X)2+ 1 vS p (d+L)2+ (s−X)2 (6.19)
Equation (6.18) can be solved (numerically) for d to get the depth of an off-axis crack derived from shear wave time-of-flight. Similarly, Equation (6.19) can be solved for Lto get the crack length. Symbolic expressions ford and Lin this case are much more complicated than the ones in Equations (6.14) and (6.15), and only numerical solution can be found after substituting the values of the other variables. It is worth mentioning that this requires accurate knowledge of the value of X (Section 4.6.2) in order to end up with accurate determination of d
and L.
estimating the values ofd and L.
6.7
Sizing of shallow and near-surface defects
Surface-breaking and near-surface cracks are always overlooked or incorrectly sized in TOFD systems due to the fact that the lateral wave masks most of flaw indica- tion. In most of the cases, there is a clear sign of such flaws in the mode-converted waves region indicating that there is a flaw for consideration. Even though a defect can be detected and sized based on the compression regions indications (longitudinal times), there is no guaranty that the obtained sizing measurements are accurate. It has been found that shear times can be very useful in such cases. Hence, in order to measure accurately the size and position of such flaws, a similar procedure to that mentioned in the previous section can be followed.