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Invariant Worst-Case Interception of Indications during Nondestructive Testing Scanning

by Kenneth H. Beck*

There is a need during nondestructive testing scanning to be assured that the smallest detectable discontinuity will generate the same response regardless of the initial scan position. In this "Back to Basics" article, the requirements to assure a consistent discontinuity response in terms of beam size, discontinuity size and beam overlap during the scan are presented. The approach is to set the scanning overlap so that the largest possible response from a discontinuity is the same as the smallest possible response. David Kupperman Associate Technical Editor

 

In nondestructive testing, the need is obvious for reliable and repeatable detection of possible locations of discontinuities in a part during scanning. To achieve that goal, the parameters of scanning beam dimensions and scan spacing (index or pitch) must be controlled and related to the minimum allowable indication size. A proper relationship ensures that the amplitude of the response from a minimum size indication does not vary as a result of any random alignment of the scanning pattern starting location with respect to the location of the indication.

Worst-case interception is simply the smallest intersection of a scanning beam with the source of an indication. This occurs for some random alignment of the beam position with respect to the source of the indication. Best-case interception is the full interception of the source by the beam (for beams larger than the target) or the full interception of the beam by a longer source. The goal of the present analysis is to determine the relationship necessary among the parameters noted to ensure that worst-case and best-case interceptions are the same, in spite of random selection of scan start.

Worst-case interception is simply the smallest intersection of
a scanning beam with the source of an indication.

Although much has been written concerning beam profiles (ASNT, 2007), the concept of target interception length is found in very few of them. It has been previously discussed in two papers dealing with ultrasonic discontinuity detection (Beck, 1988; Beck, 2006). These papers include equations that relate the above-named variables but do not present their derivation. They do mention the difference between 100% scanning with overlap of adjacent scan paths, and that with space between scans, sometimes called "barber poll" scanning. In the latter case, the minimum rejectable indication size is usually greater than the length of the scanning beam. This type of scan can miss indications that warrant investigation but are shorter than the reference target, and will not be considered further here. It should also be noted that the reasoning and equations derived therein apply to any form of nondestructive testing, not just ultrasonic testing.

Discussion

An easy application to visualize is that of circumferential angle beam scanning of a cylindrical part with a given beam size when the minimum rejectable discontinuity is represented by a longitudinal target, such as a notch in a reference standard. An equivalent case is normal beam scanning of a flat bottom hole reference target. The relationships derived for these cases are applicable to others, including indexed scanning of a flat plate, for example. Figure 1 defines the symbols used in the derivation to represent the factors of importance. The figure illustrates the condition of scan pitch P being equal to the beam length B. It is obvious that in this case the reference target, of length N, will have the minimum, or worst-case, intersection by the scanning beam when the random alignment of the beam position causes the notch to be detected by one half the beam length on each of two successive scans. In the figure, the beam positions are shown following one another. At some point in the scan the beam and notch lengths might coincide, thus providing maximum, or best-case, interception. Beam and target positions are separated vertically in the figure to provide clarity of the relationships among the variables: beam length B; notch length N; and scan index or pitch P.

Figure 1 — Beam and notch alignment for worst-case interception of notch by beam successive scans with no overlap.

Constant interception by less than the full beam length does not guarantee constant response. Response in this case is a function of beam uniformity. Total interception of a beam of any profile shape by a longer target results in a constant and repeatable response. However, the sensitivity is reduced as compared to the case of a theoretically flat beam profile due to profile variation at the target depth (Beck, 2006).

Figure 2 represents the more typical case of a certain amount of overlap, L, in the positions of two scans. This is always prudent because beam sensitivity is not usually constant over a full assumed length, which is usually defined in terms of a specified number of decibels down from the peak response value. Again, the beam and notch positions have been separated vertically to make clear the relationships of the indicated variables.

Figure 2 — Beam and notch alignment for worst-case interception of notch by overlapping scans.

When, as a result of some random alignment at the beginning of scanning, the center of the overlap occurs in the center of the notch, as shown in Figure 2, the interception of the notch by either beam position is seen to be the shortest possible, or worst-case. This length is identified as I_WC in the figure.

Analysis

From Figure 2:

and

where I_WC can never exceed the beam length or the target length.

This may be expressed as:

The length of the notch or other reference target is specified by the minimum indication size that is to be detected. Therefore, the scan index and the beam size of the scanning device (for example, the transducer in the case of ultrasonic testing) are the variables to be selected to provide reliable detection. It is desirable to provide invariant detection of a reference target in a calibration standard or a discontinuity in a test piece with any random starting alignment with respect to their positions. In other words, worst-case interception should equal best-case interception to produce reliable test results.

Beam Length Selected to be Greater than Target Length

In this case, it is of interest to solve Equation 2 for the percentage of target length N that is intercepted by the beam in the worst case of alignment. From Equation 2, that is found to be:

When the scan pitch equals the beam length, (B - P) / N = 0 and the worst-case interception equals 50% of the target length. Since the best-case interception is 100%, it is seen that at least a 6 dB variation in response can occur with random scan alignment with the target position in this case. Additional increase in the pitch renders the second term negative and reduces the worst-case interception even further.

However, when the pitch is less than the beam length, the value of (B - P) / N becomes equal to 1 at the point where the difference between B and P equals the target length, N. Thus I_WC/N becomes 100% and is the best-case interception.

However, it should be noted that, in this case, the entire beam length will never be intercepted by the minimum discontinuity length, and an additional source of variability of best-case interception occurs due to beam profile peak to valley ratio (Beck, 2006).

Beam Length Selected to be Shorter than Target Length

Assuming uniform response along the entire target length, the percentage of beam length intercepted by the target can be written from Equation 2 as

This says that when the scan pitch equals the target length, (N - P) / B = 0 and the worst-case interception could be taken to be equal to 50% of the beam length. However, upon reflection, it is clear that if the pitch were equal to or greater than the target length, the target might be missed altogether if the beam length were less than the pitch.

This leads to a statement about the conditions under which Equations 2 through 4 are valid. These are expressed as the following conditions:

This may best be expressed as a condition on pitch as:

This says that, for the response to be unchanged by any random alignment of scanning beam and target (that is, worst case = best case), the scan index may not exceed the absolute difference between beam length and notch length, no matter which is greater.

References

ASNT, Nondestructive Testing Handbook, third edition: Vol. 7, Ultrasonic Testing, Columbus, Ohio, American Society for Nondestructive Testing, 2007.

Beck, K.H., "Ultrasonic Transducer Array Configuration for Interlaced Scanning," Materials Evaluation, Vol. 46, 1988, pp. 771-772.

Beck, K.H., "Effect of Ultrasonic Transducer Beam Profile on Accuracy of Discontinuity Detection during Scanning," Materials Evaluation, Vol. 64, 2006, pp. 102-105.

 

* TAC Technical Instrument Corporation, 152 Mercer County Airport, Trenton, NJ 08628-1392; (609) 882-2894; fax (609) 882-3147; e-mail tactictest@aol.com.

 

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