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While eddy-current NDE is a reliable method for crack detection, its use for crack depth measurement has been limited by an incomplete understanding of the interaction between the electromagnetic fields and flaws in conducting materials. Current methods for practical crack sizing using eddy-current NDE are based either on the use of calibration cracks or on the estimation of crack depth from measurements of the surface crack length assuming that the crack has a known aspect ratio. The limited nature of these methods restricts the potential value of eddy-current NDE because accurate knowledge of crack size and shape, combined with structural loads information, is essential if the significance of the crack is to be assessed using the principles of fracture mechanics. In this presentation, methods for crack depth measurement are briefly reviewed, the results of research to develop techniques for eddy-current measurement of crack depth based on first principles are described and the prospects for practical implementation are discussed.
Keywords: Eddy-current testing, Crack sizing, Fatigue cracks, EDM slots, Mathematical Modelling.
To be fully effective, an inspection must not only detect defects reliably but also provide accurate information on the defect size and shape. This information is required so that the defect severity can be assessed and the appropriate maintenance action can be taken. Of the major inspection techniques, eddy-current NDE is the most poorly exploited for crack sizing. This situation has arisen not because of any intrinsic limitations in the technique itself, but from a lack of accurate mathematical models for the eddy-current field-flaw interaction. In the absence of such quantitative understanding, the capability for eddy-current crack sizing has been severely limited and, in many cases, strategies have had to be developed to work around the lack of crack depth information.
Over the past decade there has been significant progress in the development of mathematical models for eddy-current NDE, opening the way to an eddy-current crack sizing capability based on theoretical first principles. In this paper, the mainstream methods for determination of fatigue crack depth are briefly reviewed, the major limitations of conventional methods for eddy-current crack sizing are described and the results of research to develop new techniques for eddy-current crack sizing based on first principles are presented.
Crack depth measurement using ultrasonics
Ultrasonics arguably provides the most mature and reliable route to crack depth measurement. In ultrasonic testing, crack depth is determined through an analysis of the waves reflected, transmitted or diffracted by the crack (Silk, 1991). One of the more common techniques relies on measurement of the distance that the transducer must be moved in order for the signal intensity reflected from the crack to reduced by a given amount, typically 6dB or 20dB. This distance, together with knowledge of the probe characteristics, can then be used to determine the crack depth. More reliable crack depth measurements can be made using the waves diffracted from the crack tips and crack mouth through the "time-of-flight diffraction" techniques (see for example, Ditchburn, Burke and Scala (1996) and references therein). With increasing research in ultrasonic testing other more specialized techniques for crack sizing continue to be developed. For example, in an innovative approach, Scala and Bowles (1996) describe a method for estimating the depth of sub-millimeter cracks in Al alloys through measurement of the frequency spectrum of near-field Rayleigh waves transmitted by a crack.
Potential drop techniques
Both DC and AC potential drop techniques can be used to determine fatigue crack depth (Donald and Ruschau, 1991). The two techniques require electrical contact with the metal surface to inject the current and to measure the potential difference across the crack. By virtue of the skin effect, AC potential drop (ACPD) has the advantage of lower current requirements and greater sensitivity to surface breaking cracks than its DC counterpart. In the case of uniform field ACPD measurements, it is possible to deduce crack depths and crack shapes without the use of calibration blocks and there is a well-developed theoretical base for this variant. Calibration blocks are required if smaller hand-held ACPD units are used because the incident field is highly non-uniform. The major application for ACPD has been in sizing surface-breaking cracks in ferritic welds and for cracks in threaded components.
Crack depth measurement using ACFM
AC field measurement (ACFM) is a recently developed electromagnetic technique which offers the capability of detection and sizing of surface-breaking cracks without the need for calibration or cleaning to bare metal (see for example Zhou, Lugg and Collins 1999). ACFM is in effect a natural extension of ACPD with the uniform injected current replaced by a uniform field induced by a driver coil and the contact electrodes replaced by a set of orthogonal pick-up coils. The measurements are performed by scanning the probe along the crack, using a sophisticated mathematical model to deduce the crack depth and length from the field perturbations via a PC. Like ACPD, ACFM is well suited to the sizing of surface cracks in magnetic steels and has been adapted for underwater use in the offshore industry.
Eddy-current crack depth measurement
Current methods for practical crack-sizing using eddy-current NDE are based either on the use of calibration cracks or on the estimation of crack depth from measurements of the surface crack length assuming that the crack has a known aspect ratio. In contrast to the techniques described above, both approaches have serious limitations.
A major drawback in using the surface crack length (whether determined from the eddy-current probe response or directly from in-situ metallography) to infer crack depth is that the assumed length-to-depth ratio may be incorrect for the particular crack under investigation. For example, the crack depth will be overestimated if the crack has grown through coalescence of shallow cracks having multiple origins rather than through the growth of a single crack, or may be underestimated if the crack has initiated from an unexpected sub-surface defect. A further question is what length-to-depth ratio should be assumed in the absence of any fractographic or detailed fracture mechanics information. Such problems are less severe in the case of quadrant or corner cracks, where the crack intersects two surfaces and abnormal crack geometry can be more easily ruled out.
In principle it is possible to estimate crack depth by comparing the eddy-current signal from an unknown crack against data from a calibration crack of the same surface length in the same component, presuming the depth of the calibration crack is already known and that materials factors such as crack closure, crack branching and crack-face contact are equivalent. In practice, such a library of calibration cracks is rarely available, leading to considerable uncertainty in depth estimation because the influence of factors other than depth cannot be isolated from the signal (Bishop and Goldsmith, 1984). It is tempting therefore to substitute a set of electro-discharge machined (EDM) slots for actual fatigue cracks and to attempt to determine crack depth by comparing the signal from an unknown crack against that of an EDM slot of known depth. Although convenient, this approach is wrong.
Among others, Rummel, Moulder and Nakagawa (1991), have shown that the response from an EDM slot can be either larger or smaller than a fatigue crack of the same size depending on the measurement frequency, probe geometry, crack size and material. The mechanisms leading to the difference in response between slots and cracks of the same shape, length and depth are now largely understood (Beissner, 1994). First, electrical contact between the crack faces of a tight crack will effectively short circuit the eddy-current flow generally leading to a smaller response from a crack compared to a slot. The second, and more predictable effect, is due to the finite width of the slot. It can be shown theoretically that the magnitude and phase of the response from a slot in a nonmagnetic material is significantly different to that of a crack, even in the absence of crack-face contact, due to the larger width of EDM slots compared with typical fatigue cracks.
Fig 1: Cracks vs. EDM slots. (a) Normalized inductance change and (b) normalized resistance change as a function of frequency for a small air-cored coil centred on a fatigue crack and an EDM slot. The crack and EDM slot are the same nominal depth (9 mm) but the slot has an opening width of 0.41 mm. The impedance change is normalized to the free-space coil reactance in the usual way.
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The difference in the response from a crack and an EDM slot with nominally the same shape and depth is shown in Figure 1. Here, the normalized probe reactance and resistance change are plotted as a function of frequency for
Over the past decade, there have been great advances in the development of mathematical models for eddy-current NDE. These models have for the first time allowed accurate predictions of the probe response to be made and have opened up the possibility of crack sizing techniques based on first principles rather than the empirical methods used at present.
Swept frequency methods
DSTO is developing a first-principles approach to eddy-current crack sizing in which the crack size is inferred from measurements of the probe response using mathematical models that are valid in the limit of small skin depth.
Fig 2: Eddy-current determination of crack depth for a semi-elliptical EDM slot in a plate (schematic). The air-cored coil is scanned along the axis of the crack and the probe response is measured as a function of frequency at higher frequencies.
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In this crack sizing method, the absolute values of the change in coil impedance DZ due to the crack are measured as a function of frequency and coil position (Figure 2) using a low-frequency impedance analyser (HP4192a) interfaced to a PC. The measurements are made over a frequency range corresponding to "small" skin depth in the metal (for Al alloys typically 50 kHz to 500 kHz) and an approximate solution to Maxwell's equations is used to determine the crack depth. Custom-made air-cored coils are used so that the coil geometry is known precisely and the electrical conductivity of the metal must also be known. The method is described in more detail elsewhere (Burke 1994) but can be paraphrased as swept-frequency eddy-current technique where the crack depth is determined "using the skin depth as a ruler."
Cracks in plates
The swept-frequency crack-sizing method was first tested for the simple geometry of a long wire-cut EDM slot in a flat plate (Burke, 1994). For this simple geometry the slot depth could be determined within 10% or better, with the more accurate results in the case where the coil radius is larger than the crack depth. The crack-sizing algorithm was then generalized to slots with finite length and more general shape (Figure 2). Typical results are given for range of rectangular and semi-elliptical EDM slots in Al alloy plates in Figure 3, and show that the depth could be determined to within about 15% or better using the swept frequency method.
Fig 3: Crack depth determined by swept-frequency eddy-current NDE for a series of rectangular and semi-elliptical EDM slots in Al alloy plates. The slot depth determined using eddy-current NDE agrees with the actual slot depth to within 15% or better.
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The performance of the method was also tested for a range of fatigue cracks grown in compact tension specimens using a range of R-values to give different degrees of crack closure. Good agreement was obtained for larger cracks but there was a tendency for the depth of the smaller cracks to be underestimated. In this first-principles method, the difference in opening width between a crack and an EDM slot is taken into account but the effect of crack face contact and crack closure is not. The undersizing of the smaller cracks is considered to be the result of crack-face contact effects.
Cracks in boreholes/thick tubes
In the next stage of complexity, the swept-frequency method was applied to geometry shown in Figure 4, where a bobbin coil is located coaxially in a borehole (or thick tube) containing a long wire-cut EDM slot. The results are also shown in Figure 4, where the slot depth obtained from the swept-frequency method is compared with the actual depth for a series of slots in reamed holes in 2024 Al alloy. Four coils were used. In this case, by extending the theory to include higher-order approximations, agreement of typically 5-10% or better could be obtained. A similar degree of accuracy was obtained for a more realistic defect shape when the sizing algorithm was applied to a semi-elliptical EDM slot within the borehole.
Fig 4: Crack depth measurement in boreholes. The slot depth determined using swept-frequency eddy-current NDE agrees with the actual slot depth to within 10% or better. Results are shown for four coils (10 mm and 8 mm diameter bores).
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Cracks in the root of "fir-tree" slots
In a further extension, the application of swept frequency method to sizing cracks in the base of an aircraft engine turbine blade retaining slot was investigated. For the purposes of eddy-current crack sizing, only the local features of the geometry near the base of the slot are important and are shown schematically in Figure 5 together with a coaxial air-cored probe coil used for the measurements. Even with this simplified geometry, the fields produced by the eddy-current probe were sufficiently complicated that the calculations of the incident fields had to be performed using electromagnetic finite element (FE) modelling (Hart and Burke 1997). The finite element results were incorporated to produce a hybrid swept-frequency crack-sizing algorithm.
Fig 5: Crack depth measurement for a crack at the base of an aircraft engine turbine blade retaining slot. The geometry of the coaxial eddy-current coil at the base of the slot is shown schematically (a) side view (b) top view.
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The hybrid crack-sizing algorithm was successful in determining the depth of a 1 mm deep wire-cut EDM slot in the fir-tree root of a Ni-based superalloy to within an accuracy of 20%. The results of the crack sizing algorithm are shown in Figure 6, where the measured coil response is compared with the computed response as a function of skin depth. From a practical point-of-view, a significant probe redesign would be required to reduce the probe size and improve the probe signal to noise ratio before attempting to size realistic cracks in this geometry.
Fig 6: Determination of the depth of a wire-cut EDM slot at the base of a turbine retaining slot from measurements of coil response. The slot is 1 mm deep. The shaded regions indicate the scatter in the experimental data and the open circles represent the average experimental values. The results of a nonlinear least-squares fit to the experimental data with the slot depth and slot width as the fitted parameters are shown by the solid line.
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Cracks in boltholes
Rotating probe eddy-current NDE has proved very effective in detecting cracks in fastener holes - one of the most common sites for fatigue cracking in aircraft. DSTO is investigating the application of the swept-frequency crack sizing method to determine the depth of fatigue cracks in boltholes. For an eddy-current bolthole probe, the coil axis is perpendicular to the axis of the hole, so that the incident probe fields must again be computed using electromagnetic FE methods.
Determination of crack shape
There are a number of different first-principles methods for eddy-current crack sizing also under development. These are generally based on more computationally intensive mathematical models than those used in the swept-frequency work described above. In one implementation, Bowler, Norton and Harrison (1994) demonstrated that measurements of DZ can be used not only determine the defect size but also to reconstruct the defect shape for a range of EDM slots in a plate.
With the advent of sophisticated mathematical models for eddy-current NDE, it has been possible to develop new approaches to crack depth measurement. One of these approaches, based on swept-frequency measurements, has been used successfully to determine the depth of fatigue cracks and EDM slots in plates and boreholes. Despite this progress, more work is required before eddy-current crack sizing can be a day-to-day practical reality.
The highest priority is to gain more experience in sizing a wide range of fatigue cracks so that the effect of interfacial contacts, crack branching and multiple cracking can be assessed. As discussed above, more work is also required to extend the eddy-current crack sizing capability to the rotating bolthole probe geometry. The practical implementation of the crack sizing algorithms under field rather than laboratory environments will also need careful consideration. In particular,
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