|NDT.net - April 2000, Vol. 5 No. 04|
|TABLE OF CONTENTS|
|Fig 1: Flaw position with respect to Probe beam position and overlap|
In a recent report the subject of amplitude sizing was raised, again. Upon closer review of the details of this paper and others that expound this concept as a precision sizing technique, it can be seen that many of the assumptions and conclusions made are incorrect or misleading. This paper will attempt to point these out in an understandable fashion and propose limitations to consider.
Amplitude sizing techniques are commonly used in manual ultrasonic inspection Standards. Amplitude drop methods whereby a signal is compared to distance-amplitude-correction (DAC) curves are more prevalent in North America while amplitude ratio (AVG) methods are more prevalent in Europe.
There is some rationale behind these methods. The DAC system relates echo dynamics of the signal to probe position and relates these back to a known reflector (typically a side drilled hole). The AVG system devised by Krautkramer in 1958 (see ) is a family of distance-amplitude curves. These were originally computed for the case of compressional waves incident upon small, smooth, planar (disc) reflectors, and relating echo height to the size of the disc, its distance from the probe, and the intensity of the back echo. The curves have since been adapted for use with flat-bottomed-hole calibration blocks and shear wave probes.
Gross et al have proposed a variation of the AVG principles to size vertical extent of planar (non-fusion) defects using a linear scanning technique whereby an array of probes is used in fixed positions from the weld. In an earlier paper the writer proposed a similar technique for porosity assessment. However, subsequent experience has indicated that the variability in porosity reflection is far to great to allow an AVG style of treatment of porosity.
In his paper Gross stated, “To measure the height of a flaw with an ultrasonic beam, that beam has to be larger than the flaw height and provide “over-trace” on either side of the flaw.” This seems to derive as an “adaptation” of a statement made in Ultrasonic Testing of Materials (Krautkramer 3rd English edition). On page 91 of this text it states; “The echo wave produced by a circular disc reflector can be analysed most conveniently if we first consider a small circular disc placed on the axis at a great distance from the radiator.” Udo Schlengermann (page 47), states that the substitution of a “reference reflector” for a real reflector is valid if the disc shaped reflector is ”lying on the acoustic axis of the sound beam”. He further states that, “This is the case for all discontinuities which represent small reflectors, i.e. reflectors which do not extend beyond the sound beam in any direction.”
The assumptions made by the AVG system are inappropriate to extrapolate to the application of mechanised UT with probes in fixed positions for two important reasons:
To extrapolate AVG area sizing to a vertical extent sizing ignores the effects of integrated sound pressures from laterally located reflectors as cautioned by Schlengermann. Even in DAC sizing systems it is now commonly recognised that for flaws less than the beam size the dimensions obtained by probe displacement are nothing more than the measurement of the beam size.
The amplitude relationship between a target and a beam is based on the ratio of the target area to the beam area. The AVG (Abstand/Verstarken/Grosse in German) or DGS (in English this is Distance/Gain/Size) was developed to simplify the sizing of a defect, but this is the relative size of the flaw (the S in the DGS system). In the development of the DGS system the flaw is assumed to be detected well into the far zone (Krautkramer 3rd English edition page 93). As well, the flaw size is assumed to be fully encompassed by the beam and lying on the beam axis.
These three items are clearly not met in the mechanised technique using fixed probe positions (as in the zonal discrimination inspection method). E.g.
|Fig 2: Traditional raster scan in a mechanised set-up|
A linear scan moves the probe parallel to the long axis of the weld. Data collection is done on the scan parallel to the weld. The raster step may not be required if multiple probes are used, or if the probes used provide the coverage required (e.g. TOFD and limited pulse-echo coverage).
|Fig 3: Linear scan for increased data collection speed|
Linear scans are used in the zonal discrimination technique discussed earlier.,
Amplitude sizing by an AVG principle using linear scanning would require all flaws be detected well into the far zone on the beam axis by divergent beams, and these flaws would always be smaller than the beam detecting them. Clearly this is not likely to occur.
|Fig 4: Tandem probe arrangement|
Simply considering areas of flaws compared to the beam area is both difficult and not altogether accurate. For the tandem arrangement of probes typically used in linear scanning of narrow gap welds, further considerations must be made. Figure 4 shows a typical configuration for a tandem probe.
Figure 4 shows the centre ray of the tandem configuration for a 14.2mm wall using a 45° transmitter (front) and a 55° receiver (rear). This is appropriate for a 5° bevel face when looking for nonfusion. Again, Krautkramer cautions us (Ultrasonic Testing of Materials, page 99) about the use of tandem probes and the effects of oblique incidence. For example, if we use a 55° transmitter instead of a 45° as illustrated in Figure 3, the incident angle on the planar flaw would be 30° and the reflection coefficient would be reduced to about 60% of that for the 40° incidence provided by the 45° probe.
After many years of development it has been shown that focused probes have provided a higher signal-to-noise ratio for flaw detection and are less subject to false calls associated with reflections from surface geometries. In spite of this proven history, there are still some systems using standard flat element divergent probes. This might be rationalised by cost of the probes and the concept that these are needed for AVG sizing.
Figure 5 shows a view of the ideal beam for a flat element 5Mhz 9mm diameter on the same tandem set-up in Figure 4. The upper half of the image shows the view from an end-on position with the beam conic section projected onto the notch. The lower half of the image shows the proportion of the through wall dimension occupied by the divergent beam.
|Fig 5: Standard Divergent Beam for a 5MHz 9mm diameter probe|
Using a standard divergent beam calculation for the 6dB drop
When focused probe modelling is done using RayTracing a misconception results that a small beam with a spot size smaller than 2mm diameter is achievable as shown in Figure 6.
|Fig 6: RayTracing of a focused beam||Fig 7: Wavelet model representation of the focused transmitted beam in Figure 6|
A more realistic representation is seen using a Huygen wavelet modelling as in Figure 7 where a 12.5mm diameter 5MHz probe is focused with a radius of curvature of 80mm. This indicates that the minimum –6dB beam size possible is on the order of 3.5mm diameter, which when projected at 40° shows a vertical extent of about 4.6mm. This is only a slightly better spot size than the unfocused 9mm probe. However, lobes that exist when using an unfocused element are more wide spread compared to the focused probe, thereby focusing improves the signal-to-noise ratio.
This beam sizing background can now be used to consider amplitude sizing.
A drop in amplitude from a target in a beam can be caused by several variables:
If the premise is made that the flaw detected is a simple nonfusion on the weld bevel, then items 5 and 6 can reasonably assumed to be known. For a nonfusion type defect the texture of the target interface is always assumed to be smooth but fracture images clearly show this is not entirely true. The actual vertical position of the flaw may vary due to its actual position in the test piece or it may vary “virtually” as a result of small changes in the probe position with respect to the centre reference line of the weld if the probes are not exactly where they are calibrated to be.
Since position and area of the defect with respect to the beam axis have identical effects on the signal amplitude, no definitive judgement can be made regarding these parameters separately when using a mechanised set up with a linear scan.
|where D is the length of the major axis and d the length of the minor axis.|
For an ideal spot using the 3.5mm minor axis proposed as the best lateral extent of the spot, and 5mm as the major axis the spot area is 13.7mm2. For the more likely 8mm vertical extent of the major axis, the area of the unfocused spot is 22 mm2.
For an ideal spot using the 2mm diameter proposed for a well focused beam, 2.0mm would be the minor axis for the best lateral extent of the spot and 3.5mm the projected major axis, giving an area of 5.5mm2.
We can then compare notch and flat bottom hole areas as they would appear in the beam.
For on-axis assessments, a reasonable linear correlation between area and amplitude is seen (as verified by Gross et al). However, when the same reflector is positioned off axis, amplitude also drops. Movement of a point reflector in the beam is in fact the most commonly used method of characterising beam shape (e.g. ASTM E-1065, BS 4331, AS-2083 and ASME Section V). In these codes and standards the target used is a side drilled hole for contact testing probes. The probe movement related to the amplitude drop indicates the beam dimension. Military Standards and ASTM (MIL STD 2154 and ASTM E-127) have used the area amplitude relationships for area estimates, but these are for on axis targets and compression mode only.
Since moving a target position relative to the beam axis can have the same effect as changing the target area for an on-axis target, i.e. alter the amplitude, separating the effects becomes a troublesome issue when making assumptions of defect size based on amplitude. Efforts to apportion amplitudes from adjacent zones using divergent beams encounter a problem when a flaw changes dimensions along its lateral extent as well as changing its vertical position in the weld.
Each time a calibration is run in a linear scan using the zonal discrimination technique an assessment of beam size is made. These calibration blocks use FBHs located at equally spaced intervals on a weld bevel profile to indicate the zones. By knowing the vertical separation of the targets and by observing the relative amplitudes one can get an estimate of beam size.
Figure 8 represents the beams from an ideal unfocused probe (left) and an ideal focused probe (right) as they would appear when projected onto the plane of the flat bottom holes for the set-up shown in Figure 4. The circles represent the flat bottom hole targets. The main target is centred in the beam (grey shaded area indicates ideal –6dB boundary) and the “adjacent zone” target is located 2.8mm up from the main target (as would be for the configuration in Figure 4).
|Fig 8: Calculated beam shapes as per modelling|
When we combine the ideal model with actual scan results from calibrations an even greater area is projected as indicated in Figure 9. This is established from the –6dB envelope amplitude and length of the travel in the lateral direction for the width of the beam and the amplitude of the adjacent zone target.
|Fig 9: Most probable beam shapes as per echo response from known 2mm diameter reflectors (unfocused 9mm diameter probe on left and focused probe on right)|
Again, using the 2mm diameter FBH images separated by the 2.8mm vertical displacement, area representations of actual beams can be represented based on measured lateral beam widths from the two types of beam. The typical standard probe (flat) has a lateral beam extent of 6 to 7mm as measured off typical calibration charts (based on 6dB drop from peak of the 2mm diameter FBH). Similarly measured, a typical focused probe provides a 4 to 5mm beam width. It is interesting to note that using the –20dB envelope, the adjacent FBH centred 2.8mm above the on-axis target would be just about totally encompassed by the –20dB envelope for the focused beam. These modelled results compare well with scan results. Gross et al reported that the unfocused probe used in their experiment reported a 50% “over-trace” with the adjacent zone target and the focused probe they used had a 20% over-trace. This would indicate that the 2mm diameter FBH used in this calibration was a reasonable approximation of a point reflector.
Had the beam been smaller and/or the target larger, the amplitude differences may not have been as easy to relate to calculated beam sizes. This follows as the area ratio (beam to target) more closely approximates unity.
Fig 10a: Unfocused beam at 190mm waterpath (3.8mm spot size using infinite reflector principle.
Fig 10b: Standard 6dB drop from the reflection off a rod indicates 4.6mm at 190mm
||Fig 10: Beam size comparisons using delta 3dB from midpoint
In Figure 10 two illustrations are made. Signal amplitude is in the vertical scale and probe position with respect to a target is indicated on the horizontal scale. The experiment was done using an immersion probe 12.7mm diameter and 5Mhz nominal frequency. The left image shows the signals from an aluminium plate set to near full screen height and then the probe is moved horizontally until the beam no longer interacts with the plate (zero amplitude). An FFT on the unfocused probe indicated an actual frequency of 6.5MHz putting the near zone at about 180mm waterpath. Modelling indicated that the spot size would be about 3.4mm at this point. The measured displacement using the 3dB difference from the midpoint gives this a 3.8mm 6dB spot size. For comparison of techniques the unfocused probe was evaluated using a steel rod 1.8mm diameter. Using the 6dB drop at the same waterpath, a 6dB beam width of 4.6mm was established.
If a beam is relatively small with respect to the target, the centre of the beam can be located in the target most of the time. As the target dimension changes such that the beam “edges” miss the target, the amplitude drops from its maximum. If the target is long and the height reduces, then the drop in amplitude can be attributed to a height reduction or a shift of the probe with respect to the flaw centre as shown in Figure 11.
The ellipse in Figure 11 represents a beam 7mm wide with a 2.5mm 6dB vertical projection. When compared against a 3mm high notch, the beam is seen to be totally covering the notch. When the notch is made smaller (1.5mm high in top right of Figure 11) the beam interaction with the target is reduced. The same effect occurs for the offset of the target or beam with respect to one another as in the lower example in Figure 11.
|Fig 11: Amplitude reduction due to change in height or probe position for small spot size|
7mm x 2.5mm focused beam on notch-type targets. Change in target size upper right and change in probe or notch position lower right, result in reduction in signal amplitude.
|Fig 12: Phased Array amplitude responses using “sub-zones” (courtesy RD Tech)|
Production of good quality spot sizes (small vertical extent) is possible using standard single element probes, but use of phased arrays for this purpose is even more effective. In a recent experiment a 15mm thick weld section was divided into 29 different zones using a phased array system (see Figure 12). When using a standard calibration configuration this provided a very small (-14dB to –20dB) overlap between the 2mm diameter FBHs centred in the traditional locations. Each of the 4 fill zones was sampled at 5-6 different vertical positions. With sub-zones less than the weld pass height, it is possible to see variations in both flaw vertical position due to wandering of the weld puddle and total vertical extent.
In Figure 12 the left side shows a C-scan presentation of the root notch and 4 Fill targets (Root notch on the Top Right and the 2mm diameter FBH Fill 4, on the bottom left). Late arrivals in the Fill 1 gate show over-trace with the Root Notch and similarly the Root channels show over-trace on Fill 1. However, when the first arrivals in the gate are plotted against a weld profile (on the right side of the image), the overlaid target positions show how no areas are missed and the targets are correctly positioned. This presentation makes it is easy to see how flaw position and extent would be more readily discerned using “sub-zones”. Any movement of a flaw “between” the main calibration target centres is seen as a shift in the affected “sub-zones”.
When a –14dB beam overlap between two zones is seen on a calibration run some have expressed concerns for “missing coverage” between zones when using well focused probes. However, this concern is not well founded when a system is calibrated on a FBH. Gross et al reported that a difference of 6dB existed between the response from a 2mm FBH and a 2mm high flat notch. It was not explained if they used a focused or unfocused probe for this determination but 4 to 8dB would be typical, depending on the probe quality and beam size. Therefore, if a system is calibrated on a FBH, there is a built in over-sensitivity to longer flaws with the same vertical extent. For example, using a 12.7mm diameter 7MHz probe focused with a 60mm radius of curvature, the –6dB spot size is about 2.2mm diameter at the focal point. But if scanning is done so that a 2mm diameter FBH is brought to 80% screen height then sensitivity to longer reflectors (e.g. a notch) results in a signal about 6dB greater. Using the standard 40% evaluation threshold, this is equivalent to examining for the longer flaws down to the –12dB level. For a 12.7mm diameter 7MHz focused probe the –12dB envelope at the focal point increases to 3.0mm (a 36% increase in vertical extent compared to the –6dB coverage).
In practice, a small diameter spot size calibrated on a 2mm FBH would be operated in the region around the +3dB from the probe centre response as indicated in Figure 10. This follows from the fact that the ratio of areas for the FBH and spot size of a well-focused probe is greater than 50%. Such a probe, when encountering an infinite reflector (like the “backwall in an AVG diagram) would reflect nearly all of the available pressure back to the receiver. If the flaw is longer than the beam width then the 6dB extra sensitivity that exists between the FBH response and the long notch response for the focused probe, would place the amplitude response from the flaw at a point comparable to nearly 3dB under the maximum possible response for a 100% return of sound pressure. This implies that over-sizing by 12dB is not possible for small focal spots, but might easily occur for unfocused probes. Attempts to compensate for this oversizing when using unfocused probes by using logarithmic amplifiers and signal characteristics from adjacent zones is of limited value considering the relatively large areas integrated in the beams.
Use of a small spot size beam for vertical extent estimations is also subject to off axis and area effects on signal amplitude. However, providing the spot size can stay small compared to the flaw height, the effects of off axis variations can be better monitored by the presence of signals in the adjacent zones. When the vertical zones are closely matched to spot sizes (and both are small), signals with amplitudes over an agreed level and confined to a single zone, may reasonably be assumed to have variations in amplitude due to variations in flaw area restricted to the zone height of that probe. When a small flaw moves between two zones such that it is off axis for both probes detecting it, the apportioning of amplitudes minus the overlap seen on calibrations may provide a means of preventing excessive over-sizing. However, this option must also be used with caution as the effects of flaw vertical position need not vary amplitude in exactly the same way that variation in probe stand-off would. This is especially true when using tandem probe techniques where the stand-offs of both the transmitter and the receiver vary with the vertical position being covered.
Compared to large beams from unfocused probes, the use of more and smaller beams is a more effective method of estimating flaw extent and position in the vertical plane when using mechanised linear scanning.
Since these prerequisite parameters do not exist for the mechanised UT used in the zonal discrimination method, all efforts to “accurately” size flaws in the vertical extent using amplitude are prone to errors. These errors can be minimised by using focal spots very closely matching the zone height. Assessment of vertical extent can be improved by observing zonal interaction of signals from zones with smaller height using beams with similarly small spot sizes. Vertical assessments are further improved using sub-zones feasible when using phased arrays.
Concerns for “missed coverage” between zones when using small focal spots can be reduced when calibration is performed on FBHs instead of notches. This follows because increased sensitivity results to long. off-axis reflectors (more typical of nonfusion) as compared to the point reflector sensitivity provided by the FBH calibration target .
For the purposes of fracture mechanics fitness-for-purpose, sizing estimates are made using the information ascertained from the zone amplitudes. However, even with the observance of interaction of signals between zones, amplitude sizing will always require that reasonable tolerances be used due to the variety of sources of amplitude differences. In a paper by Kopp et al , sectioned results showed that amplitude based evaluations were often close to sectioned flaw sizes but variations of 0.5 to 1.5mm could occur. In the more recent efforts reported by Gross et al, their results indicated an average error in amplitude sizing using unfocused probes to be around 0.5mm also but even so, some items in the report showed over-sizing by 3.3mm and 2.6mm (Appendix C & F2 of the report) and they often used a range of 3mm (3.0-6.0mm) to allow for possible variations. Low repair rates claimed by the technique expounded by Gross et al are therefore not a result of improved sizing but in fact a result of reducing the evaluation level by 12 dB as compared to previous projects.
Suggestions by some, that present sizing “accuracies” exist that are small percentages of a millimetre, are unrealistic. This would make the putative “accuracy” 10 to 50 times greater than the tolerances established by statistics.
When designing an acceptance criteria this statistical deviation must be allowed for as reported by Fרrli . Comparing the reports by Kopp et al and Gross et al, the tolerances for unfocused probes are greater than for focused probes. Projects conforming to DNV requirements will probably need a statistical analysis involving both PoD and tolerance determinations . This will put the results of unfocused probes at a distinct disadvantage.
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