**I. J. Munns and C. R. A. Schneider**

Presented at conference on 'Review of Progress in Quantitative Nondestructive Evaluation', Montreal, Canada, 26-30 July 1999.

## Introduction

The UK nuclear licensees have recently completed an extensive study to determine the intrinsic capability of radiography for the detection of large planar defects in thick-section welds. This work has concentrated on the experimental detectability of planar manufacturing defects, >15mm in through-wall extent, in butt-welded steel specimens (50-114mm thick). One of the main aims of the study was to quantify the capability of the radiography used during construction of the Magnox reactor pressure vessels (RPVs) in the 1950s/60s. Alongside the experimental work, the performance of the established Pollitt model of radiographic detectability has been assessed and refined to form the basis of a theoretical 'index of detectability'. The index enables the probability of detecting a defect to be predicted, from knowledge of its size, orientation and other relevant parameters. This paper summarizes the work carried out and highlights how the results might be used to improve the safety of existing plant.

## Experimental Approach

The main study concentrated on determining the performance of radiography for those hypothetical manufacturing defects which would be of greatest structural concern in Magnox RPV welds: defined as planar defects >15mm in through-wall extent (TWE). For the investigation, seven butt-welded steel plate specimens were used, containing a total of 19 large planar welding flaws, ranging in through-wall size from 14-52mm. One of these specimens was an existing specimen containing three transverse weld metal hydrogen cracks. The other six specimens were manufactured specifically for this project, and were designed to contain those types of flaw judged most plausible for this large TWE; namely, lack of sidewall fusion, centerline solidification cracking, weld metal hydrogen cracking and hydrogen cracking in the heat-affected zone (HAZ). Great care was taken to ensure that the flaws introduced had a realistic metallurgical morphology. One way of checking this was to compare the flaw-face separation (or gape) of the defect produced with those of similar types of flaw recorded in literature. An example of such a comparison is shown in*Fig.1*. Similar comparisons for the other flaw types showed generally good agreement. A more detailed description of the welding methods used to introduce the majority of flaws is given in a previous paper

^{[1]}.

On completion of welding, the seven specimens were radiographed under a variety of different conditions, using procedures simulating those applied during Magnox RPV construction. The radiography was performed using X-ray (250-400kV) or Cobalt-60 sources. Angled radiography was used in some cases, to vary the angle of misorientation between the flaw and the radiation beam, and additional non-defective plates were used for some exposures to increase the total thickness of steel radiographed. The exposures covered flaw misorientation angles over the range 0° to 60° and penetrated thicknesses from 50 to 125mm. In total, 132 exposures were produced, giving 312 different flaw-radiograph combinations for evaluation. Each radiograph was examined independently by two qualified radiographers.

After radiography, the specimens were sectioned to determine each flaw's size, orientation, gape and roughness. The performance of radiography was then analysed as a function of the different flaw parameters and of experimental parameters, such as source type, unsharpness and film type. The results were also used to assess the accuracy of predictions made using simple Pollitt theory.

## Experimental Results

The experimental results tend to support simple theoretical arguments. For example, flaw detectability deteriorates as both the thickness of steel radiographed increases and as the angle of misorientation between the flaw and the radiographic beam is increased. Conversely, detectability improves with increasing flaw gape (i.e. higher angles of misorientation can be tolerated for more 'open' flaws), as shown in*Fig.2*.

The main study also highlighted the difficulties associated with displaying the raw data in a form that enables a more quantitative comparison with theory. Radiographic detectability depends on a large number of interrelated parameters that vary from one flaw to another and one exposure to another, making it difficult to isolate the effects of any one parameter alone. Simply put, it is not sufficient to plot only two parameters, such as flaw gape and TWE, and expect the radiographic 'detections' and 'non-detections' to fall neatly into two groups. There may, however, be an appropriate way of combining the various flaw and experimental parameters which fully explains radiographic detectability. One simple model of detectability, proposed by Pollitt in 1962 ^{[2]}, offers a good partial explanation, as discussed in the following section.

## Modelling Work

### The Pollitt Model

Pollitt considers planar flaws as smooth, parallel-sided slots of a particular size, orientation and gape. This information is then combined with additional parameters from the radiographic inspection procedure, such as source-size and source-to-film distance, and the achieved radiographic image quality, to predict whether or not the flaw is detectable.

Fundamentally, Pollitt theory works by converting both the flaw and the Image Quality Indicator (IQI) reading to equivalent step-changes in thickness Δ*x,* which can then be compared directly with one another. This is achieved by means of the following equation:

where δ*v* is the volume of the flaw/IQI, δ*A* is the projected area of the flaw/IQI on the radiographic film and F is the so-called form factor. The underlying principle of this approach is that each calculated Δ*x* value theoretically produces the same level of blackening on the radiograph as the flaw/IQI respectively.

The form factor in Equation (1) is the reciprocal of the ratio of (i) the peak of the density distribution over the image to (ii) the density of a rectangular density distribution curve giving the same amount of total blackening over the given image width δ*A* (note: a unit flaw length is assumed). A uniform density distribution across the image gives a form factor of 1. Other density distributions, in general, give form factors less than 1. An example, showing the calculation of Δ*x* for a planar flaw, is presented in *Fig.3*.

^{Δx}flaw = equivalent step height of flaw

δ^{v} = volume of flaw *F*= form factor

δ^{A} = area of film blackened by flaw *U _{T}* = total unsharpness

**Fig.3 Equivalent step-change in thickness for a planar flaw, as derived by Pollitt theory.**

Having calculated a theoretical step-change in thickness for the flaw (^{Δx}flaw) and converted the measured IQI value (usually the diameter of the last visible IQI wire on the radiograph) to an equivalent step-change in thickness (^{Δx}IQI) these two theoretical values can be compared to determine flaw detectability. If ^{Δx}flaw is greater than or equal to ^{Δx}IQI, then Pollitt theory predicts that the flaw is detectable. If, however, ^{Δx}flaw is less than ^{Δx}IQI then, according to Pollitt theory, the flaw will be missed by radiography.

During the development of the model in the 1960s, some experimental work was carried out to validate the theoretical approach used ^{[3]}. This work involved radiographing a steel test block containing parallel-sided, planar slots of different depths and orientations. The agreement observed between Pollitt theory and the practical results was sufficiently close to enable the limits of detectability of these artificial 'defects' to be predicted with considerable confidence. This is not surprising since Pollitt theory itself considers flaws to be of relatively simple shape. For example, a crack or lack of sidewall fusion flaw is modelled as a smooth parallel-sided slot, identical in character to those flaws examined experimentally. What is not so clear is whether Pollitt predictions are valid for the more complex morphologies of real welding flaws, which may be rough and of variable gape.

A full comparison between Pollitt theory and the experimental detectability of real welding flaws was performed as part of this current study. The results show a strong correlation between experiment and theory. In over 89% of the cases considered, basic Pollitt theory correctly predicted the response of one or both of the radiographers. In the few cases where predictions made by Pollitt disagreed with experiment, there was a tendency for Pollitt theory to behave conservatively - predicting that flaws should not have been detected where in fact they were. The conservatism inherent in basic Pollitt theory is not entirely unexpected and, is likely to be due to the roughness, waviness and variation in gape of real welding flaws - all characteristics which may enhance radiographic detectability but which are not fully considered by simple Pollitt theory.

As part of the study reported here, TWI made a number of incremental refinements to basic Pollitt theory, drawing on ideas from Halmshaw ^{[4-6]}. The refinements included the consideration of geometrical image enlargement in the calculation of δ*A* (due to beam divergence and shot angle), and a more rigorous treatment of radiographic image unsharpness (also used in the calculation of δ*A*. Each of these refinements has been shown to improve the correlation between theory and experiment.

### Theoretical Index of Detectability

Recently, TWI has extended the Pollitt model to include the concept of an 'index of detectability', which quantifies the theoretical detectability of a particular flaw under specified radiographic conditions. In other words, it is now possible to estimate the margin of flaw detectability rather than simply stating whether the flaw is detectable or not. The index ( *I*) is defined as:

where, as before:

^{Δx}flaw is the equivalent step-change in thickness for the flaw, calculated using improved Pollitt theory, and ^{Δx}IQI is the achieved step-edge thickness sensitivity, measured directly from the radiograph using an IQI (usually a set of wires of decreasing diameter) and converted to a step-change in thickness using improved Pollitt theory.

Having defined the index in this way, it follows that flaws which produce positive indices are detectable according to improved Pollitt theory, and flaws with negative indices are undetectable according to improved Pollitt theory. The introduction of an index of detectability enables the conservatism inherent in Pollitt theory to be displayed visually. Thus, *Fig.4* shows a scatter plot of the experimental data against the index of detectability for both radiographers. During the original interpretation, each radiographer was asked to classify any flaw they detected as being either 'easily visible' (EV) or 'barely visible' (BV). This distinction is shown in *Fig.4* (those flaws not detected are denoted by 'ND'). As anticipated, the majority of 'easily visible' flaws have a relatively high positive index and, conversely, all non-detections have a negative detection index. The conservatism inherent in Pollitt theory is best demonstrated by the considerable number of 'barely visible' flaws (and a lesser number of 'easily visible' flaws) which have negative detection indices, yet were still seen by one or both radiographers.

The trends evident in *Fig.4* lead naturally to the derivation of Probability of Detection (POD) curves. For the data considered in this study, there is an approximate relationship between the probability of flaw detection *p* and the theoretical index of detectability *I*, given by:

where the constants *A* and *B* of this relationship are estimated from the experimental data, using a type of regression theory known as 'logistic' regression ^{[7]}.

*Figure 5* shows the experimental results, together with the relationship fitted using Equation 3. In this figure, the experimental probability of detection is estimated by grouping the data displayed in *Fig.4* according to bands of detection indices, and plotting the proportion of detections within each group. The results in *Fig.5* clearly demonstrate the high reliability of detection ( *p* >96%) for all cases where the improved Pollitt model predicts detection (i.e. *I* >0). Thus, the index is shown to be a valuable derived parameter that can be used to give a far more accurate prediction of detectability than any of the other parameters (such as flaw gape, misorientation angle, TWE, etc) studied in isolation.

### Additional Factors Influencing Detectability

A detailed statistical analysis has shown that the conservatism inherent in the Pollitt model is largely attributable to the effects of flaw roughness. Experimental evidence indicates that rougher flaws are easier to detect than improved Pollitt theory suggests. As already mentioned, roughness is not explicitly considered by the Pollitt model - planar flaws are modeled as smooth slots of uniform gape. A useful parameter in quantifying the effect of roughness (and hence the conservatism of Pollitt theory) is the root mean square (RMS) angle of tilt of the flaw in the through-wall direction. This RMS angle was determined from adjacent pairs of sectioning measurements, and is a measure of the variation in defect tilt from one region of the defect to another. Extrapolation of the experimental data to a RMS tilt angle of zero suggests that the Pollitt model would cease to be conservative for perfectly smooth flaws, as initially suspected.

Another factor that appears to have an important effect on detectability, over and above that already built into the theoretical index, is flaw TWE. However, further work is needed to be confident of the functional relationship between flaw POD and TWE.

After the index, RMS angle and flaw TWE, the next most important factor influencing radiographic detectability appears to be human performance (the interpreter), but its statistical significance is marginal. A separate study of human performance confirmed that there was little variability between different interpreters in the detectability of large planar flaws.

## Application

A greater understanding of the factors affecting radiographic detectability and the ability to derive POD data for specific flaws examined under specific radiographic conditions, provides the engineer with a powerful tool which can be used to improve plant safety in a number of different ways. For example:

- If an Engineering Critical Assessment (ECA) is used to define the critical size of flaw which can be tolerated by plant operating under known loading conditions, then the index can be used to determine how reliably flaws of thissize can be detected by a standard radiographic procedure.
- Alternatively, prior knowledge of the likely types, sizes and orientations of flaw which might occur in a particular structure can be used, in conjunction with the index, to define the minimum performance which must be achieved byradiography if a radiographic inspection regime is to be effective.

In both of the above cases, the quality of the POD data generated depends critically on how accurately flaw parameters, such as TWE, orientation and gape, can be defined. In many instances it is possible to define a 'worst-case' flaw orientation angle based on knowledge of the weld prep, and an upper limit to flaw through-wall size based on ECA data or knowledge of the weld bead size. This leaves flaw gape, which is usually the most difficult parameter to define.

Extensive gape measurements on sectioned flaws have shown that it is virtually impossible to describe a single flaw using a single gape value. In *Fig.6*, for example, the two flaws presented are each characterised by a range of measured gapes. If these results are supplemented with data from other similar sized flaws, then it is possible to assign flaws of a particular type and size a characteristic gape distribution. These gape distributions can then be used to calculate a range of detection indices associated with that particular type and size of flaw.

Figure 7 is an illustrative example, showing how this knowledge might be used to define the minimum performance which must be achieved by radiography for it to be an effective inspection tool. This figure shows a series of POD curves associated with different quality radiographic procedures. The quality of the procedure is indicated by the number of IQI wires visible on the radiograph. As already mentioned, a wire IQI comprises a series of seven wires of decreasing diameter. Image quality is measured by recording the number of wires that can be seen on the radiograph. The more wires visible, the higher the sensitivity of the technique and, theoretically, the better the radiographic detection performance. In practice, it is envisaged that design engineers and metallurgists will be able to define the likely types, sizes and orientations of flaw which might occur in a particular structure, in order to enable a range of equivalent thickness sensitivities ^{Δx}flaw to be calculated and located on the POD curves. This is illustrated by the shaded region in *Fig.7*. Knowing this, it is now possible to estimate the performance of any new radiographic technique, directly from the IQI sensitivity achieved. For example, if a particular technique produces radiographs where only 3 wires are visible, then the majority of flaws defined by the shaded area in *Fig.7* will be missed. However, if the technique is improved (by using a better quality film, a smaller source size, etc.), so that 5 wires are now visible, then detectability also improves and the vast majority of the same flaws will be detected.

## Conclusions

Overall, this extensive program of work has shown that radiography is capable of detecting a wide range of planar flaws, particularly if they are extensive in both length and height. However, in some cases flaws can exhibit unfavorable combinations of gape and orientation, which may make even sizeable flaws undetectable. Nevertheless this work has shown that the capability of radiography to detect large planar flaws is surprisingly high and better than simple predictive modeling would suggest. The introduction of an 'index' of detectability enables, for the first time, POD to be predicted for different radiographic techniques.

## Acknowledgements

This paper is published by permission of the Industry Management Committee (IMC) of the UK nuclear licensees, who also funded the work. The IMC comprises members of British Nuclear Fuels Ltd and British Energy plc. The authors are grateful to acknowledge the contributions of Dr R K Chapman, Mr A B Wooldridge, Mr G S Woodcock and Dr G A Georgiou throughout this program of work.

## References

1 | A. B. Wooldridge, R. K. Chapman, G. S. Woodcock, I. Munns and G. Georgiou, | 'Reliability of radiography for detection of planar manufacturing defects in thick-section welds', INSIGHT, Vol. 39, No. 3, pp139-147, March 1997. |

2 | C. G. Pollitt, | 'Radiographic sensitivity', Brit. J. NDT, Vol. 4, No. 3, pp 71-80, September 1962. |

3 | Anon, | 'Limitations of radiography in detecting crack-like defects in thick sections', Brit. J. NDT, Vol. 4, No. 4, pp 103-119, 1962. |

4 | R. Halmshaw, | 'Industrial radiography - theory and practice', Applied Science, London and New Jersey, 1982. |

5 | R. Halmshaw, | 'Industrial radiology', 1966 (earlier edition of reference 4). |

6 | R. Halmshaw, | 'The factors involved in an assessment of radiographic definition', J. Photographic Science, Vol. 3, pp 161-168, 1955. |

7 | D.W. Hosmer and S. Lemeshow, | 'Applied logistic regression', John Wiley & Sons, New York, 1989. |